Prompt:
Misconception:
Mistakes lines as parallel

Question:
Which of the following are corresponding angles on this diagram? ![Three almost horizontal lines, two marked with arrows. One almost vertical line crossing them. The twelve angles created are marked a-l. ]()

Options:
A. \( c \) and \( g \)
B. \( c \) and \( k \)
C. \( d \) and \( j \)
D. \( b \) and \( f \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Mixes up the value of two terms when substituting

Question:
This is a table of values for \( 3 x+2 y=6 \)
What should replace the star? \begin{tabular}{|l|c|c|c|c|c|}
\hline\( x \) & \( 0 \) & \( 1 \) & \( 2 \) & \( 3 \) & \( 4 \) \\
\hline\( y \) & \( \color{gold}\bigstar \) &   \\
\hline
\end{tabular}

Options:
A. \( 3 \)
B. \( 2 \)
C. \( 1.5 \)
D. \( 12 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Believes 0 multiplied by a number gives the number

Question:
This is a table of values for \( 3 x+2 y=6 \)
What should replace the star? \begin{tabular}{|l|c|c|c|c|c|}
\hline\( x \) & \( 0 \) & \( 1 \) & \( 2 \) & \( 3 \) & \( 4 \) \\
\hline\( y \) & \( \color{gold}\bigstar \) &   \\
\hline
\end{tabular}

Options:
A. \( 3 \)
B. \( 2 \)
C. \( 1.5 \)
D. \( 12 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
When solving an equation, uses the same operation rather than the inverse.

Question:
This is a table of values for \( 3 x+2 y=6 \)
What should replace the star? \begin{tabular}{|l|c|c|c|c|c|}
\hline\( x \) & \( 0 \) & \( 1 \) & \( 2 \) & \( 3 \) & \( 4 \) \\
\hline\( y \) & \( \color{gold}\bigstar \) &   \\
\hline
\end{tabular}

Options:
A. \( 3 \)
B. \( 2 \)
C. \( 1.5 \)
D. \( 12 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
When asked to find data points above a certain value, gives the number of data points below this value

Question:
How many months have an average temperature above 23⁰C ? ![A line graph with title "Monthly Average temperatures for Zakynthos, Greece. (⁰C)".
The x-axis is labelled with the first letter of every month of the year and is titled "Months".
The y-axis is titled "Average temperature (⁰C)" and the scale is labelled from 18 to 34 in steps of 2. The following points are plotted and joined together: (J, 18), (F, 20), (M, 21), (A, 22), (M, 23), (J, 25), (J, 29), (A, 32), (S, 27), (O, 22), (N, 20), (D, 18).]()

Options:
A. \( 7 \)
B. \( 4 \)
C. \( 5 \)
D. \( 8 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Includes a data point with the value, when asked to find the number of data points above a value

Question:
How many months have an average temperature above 23⁰C ? ![A line graph with title "Monthly Average temperatures for Zakynthos, Greece. (⁰C)".
The x-axis is labelled with the first letter of every month of the year and is titled "Months".
The y-axis is titled "Average temperature (⁰C)" and the scale is labelled from 18 to 34 in steps of 2. The following points are plotted and joined together: (J, 18), (F, 20), (M, 21), (A, 22), (M, 23), (J, 25), (J, 29), (A, 32), (S, 27), (O, 22), (N, 20), (D, 18).]()

Options:
A. \( 7 \)
B. \( 4 \)
C. \( 5 \)
D. \( 8 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
When asked to find data points above a certain value, gives the number of data points below this value

Question:
How many months have an average temperature above 23⁰C ? ![A line graph with title "Monthly Average temperatures for Zakynthos, Greece. (⁰C)".
The x-axis is labelled with the first letter of every month of the year and is titled "Months".
The y-axis is titled "Average temperature (⁰C)" and the scale is labelled from 18 to 34 in steps of 2. The following points are plotted and joined together: (J, 18), (F, 20), (M, 21), (A, 22), (M, 23), (J, 25), (J, 29), (A, 32), (S, 27), (O, 22), (N, 20), (D, 18).]()

Options:
A. \( 7 \)
B. \( 4 \)
C. \( 5 \)
D. \( 8 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Does not think a number can be a factor of itself

Question:
Which of these is not a factor of \( 18 \) ?

Options:
A. Thirty-six
B. Six
C. Nine
D. Eighteen

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Rounds to the wrong degree of accuracy (rounds too much)

Question:
What is \( \mathbf{3 . 1 5 3} \) rounded to the nearest \( \mathbf{0 . 0 2} \) ?

Options:
A. \( 3.2 \)
B. \( 3.12 \)
C. \( 3.16 \)
D. \( 3.15 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Rounds to the wrong degree of accuracy (rounds too little)

Question:
What is \( \mathbf{3 . 1 5 3} \) rounded to the nearest \( \mathbf{0 . 0 2} \) ?

Options:
A. \( 3.2 \)
B. \( 3.12 \)
C. \( 3.16 \)
D. \( 3.15 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Calculates circumference when asked for area

Question:
What is the area of the face marked \( F \) ![A cylinder with height 9cm and radius 5cm. An arrow points to the circular face at the bottom of the cylinder.]()

Options:
A. \( 10 \pi\ \mathrm{cm}^{2} \)
B. \( 25 \pi\ \mathrm{cm}^{2} \)
C. \( 45 \pi\ \mathrm{cm}^{2} \)
D. \( 100 \pi\ \mathrm{cm}^{2} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Confuses diameter and radius

Question:
What is the area of the face marked \( F \) ![A cylinder with height 9cm and radius 5cm. An arrow points to the circular face at the bottom of the cylinder.]()

Options:
A. \( 10 \pi\ \mathrm{cm}^{2} \)
B. \( 25 \pi\ \mathrm{cm}^{2} \)
C. \( 45 \pi\ \mathrm{cm}^{2} \)
D. \( 100 \pi\ \mathrm{cm}^{2} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Thinks the shape of the graph does not affect the area calculation

Question:
The velocity-time graph shows the velocity of a car during a journey ![A velocity-time graph. Section A goes from (0,0) to (10,20). With the 10 being 10 seconds and the 20 being 20 m/s.]() What was the distance travelled during section
A?

Options:
A. \( 200 \mathrm{~m} \)
B. \( 2 \mathrm{~m} \)
C. \( 100 \mathrm{~m} \)
D. \( 22.36 \mathrm{~m} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Believes distance = speed/time

Question:
The velocity-time graph shows the velocity of a car during a journey ![A velocity-time graph. Section A goes from (0,0) to (10,20). With the 10 being 10 seconds and the 20 being 20 m/s.]() What was the distance travelled during section
A?

Options:
A. \( 200 \mathrm{~m} \)
B. \( 2 \mathrm{~m} \)
C. \( 100 \mathrm{~m} \)
D. \( 22.36 \mathrm{~m} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Believes the length of the line in a velocity time graph gives the distance (rather than the area underneath that line).

Question:
The velocity-time graph shows the velocity of a car during a journey ![A velocity-time graph. Section A goes from (0,0) to (10,20). With the 10 being 10 seconds and the 20 being 20 m/s.]() What was the distance travelled during section
A?

Options:
A. \( 200 \mathrm{~m} \)
B. \( 2 \mathrm{~m} \)
C. \( 100 \mathrm{~m} \)
D. \( 22.36 \mathrm{~m} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Solves for y=0 instead of given y-value when reading from a quadratic graph

Question:
According to the graph, what is the approximate solution to
\(x^{2}-3 x-6=2\) ![A set of axes with the quadratic graph y=x^2-3x-6 drawn on.]()

Options:
A. \( x=-1.4, \quad x=4.3 \)
B. \( y=-6 \)
C. \( x=-1.75, \quad x=4.75 \)
D. \( x=1.4, \quad x=-4.3 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Finds the y intercept when asked to read the solution to a quadratic equation from a graph

Question:
According to the graph, what is the approximate solution to
\(x^{2}-3 x-6=2\) ![A set of axes with the quadratic graph y=x^2-3x-6 drawn on.]()

Options:
A. \( x=-1.4, \quad x=4.3 \)
B. \( y=-6 \)
C. \( x=-1.75, \quad x=4.75 \)
D. \( x=1.4, \quad x=-4.3 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Does not know how to identify common factors from algebraic terms

Question:
Tom and Katie are discussing factors
Tom says \( 3 \) is a common factor of \( 12 x \) and \( 15 y^{2} \)
Katie says \( x \) is a common factor of \( 12 x \) and \( 15 y^{2} \)
Who is correct?

Options:
A. Only
Tom
B. Only
Katie
C. Both Tom and Katie
D. Neither is correct

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Rounds down instead of up

Question:
What is \( 356,958 \) rounded to the nearest \( 100 \) ?

Options:
A. \( 356,900 \)
B. \( 356,960 \)
C. \( 400,000 \)
D. \( 357,000 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Rounds to the wrong degree of accuracy (rounds too little)

Question:
What is \( 356,958 \) rounded to the nearest \( 100 \) ?

Options:
A. \( 356,900 \)
B. \( 356,960 \)
C. \( 400,000 \)
D. \( 357,000 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Rounds to the wrong degree of accuracy (rounds too much)

Question:
What is \( 356,958 \) rounded to the nearest \( 100 \) ?

Options:
A. \( 356,900 \)
B. \( 356,960 \)
C. \( 400,000 \)
D. \( 357,000 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Believes a curve can show a constant rate

Question:
Tom and Katie are discussing graphs that show the volume of water
(V) flowing from a kitchen tap over time (t). Tom says this graph shows water flowing at a constant rate ![A sketch of a graph showing V on the y axis and t on the x axis. A line starts at the origin and slopes upwards getting gradually steeper. ]() Katie says this graph shows water flowing at a constant rate ![A sketch of a graph showing V on the y axis and t on the x axis. A horizontal straight line goes from halfway up the y axis straight across the graph. ]() Who is correct?

Options:
A. Only Tom
B. Only Katie
C. Both Tom and Katie
D. Neither is correct

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Believes a curve can show a constant rate

Question:
Tom and Katie are discussing graphs that show the volume of water
(V) flowing from a kitchen tap over time (t). Tom says this graph shows water flowing at a constant rate ![A sketch of a graph showing V on the y axis and t on the x axis. A line starts at the origin and slopes upwards getting gradually steeper. ]() Katie says this graph shows water flowing at a constant rate ![A sketch of a graph showing V on the y axis and t on the x axis. A horizontal straight line goes from halfway up the y axis straight across the graph. ]() Who is correct?

Options:
A. Only Tom
B. Only Katie
C. Both Tom and Katie
D. Neither is correct

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Adds instead of multiplies

Question:
Simplify, if possible:
\[
6 a \times 4 b
\]

Options:
A. \( 10 a b \)
B. \( 24+a b \)
C. \( 24 a b \)
D. Does not simplify

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Multiplies coefficients and letters separately and writes as an addition

Question:
Simplify, if possible:
\[
6 a \times 4 b
\]

Options:
A. \( 10 a b \)
B. \( 24+a b \)
C. \( 24 a b \)
D. Does not simplify

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Does not understand how to multiply algebraic terms

Question:
Simplify, if possible:
\[
6 a \times 4 b
\]

Options:
A. \( 10 a b \)
B. \( 24+a b \)
C. \( 24 a b \)
D. Does not simplify

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Believes you can subtract from inside brackets without expanding when solving an equation

Question:
Jo and Paul are arguing about a first step to solve this equation:
\(
6(m+4)=24
\)
Jo says you can write: \( m+4=4 \)
Paul says you can write: \( 6 m=20 \)
Who is correct?

Options:
A. Only
Jo
B. Only
Paul
C. Both Jo and Paul
D. Neither is correct

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Believes they must expand brackets before solving an equation

Question:
Jo and Paul are arguing about a first step to solve this equation:
\(
6(m+4)=24
\)
Jo says you can write: \( m+4=4 \)
Paul says you can write: \( 6 m=20 \)
Who is correct?

Options:
A. Only
Jo
B. Only
Paul
C. Both Jo and Paul
D. Neither is correct

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Rounds to wrong degree of accuracy (decimal places rather than significant figures)

Question:
Round \( 0.0735 \) to \( 1 \) significant figure

Options:
A. \( 0.07 \)
B. \( 0.1 \)
C. \( 0.7 \)
D. \( 1.0 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Changes wrong place value column when rounding

Question:
Round \( 0.0735 \) to \( 1 \) significant figure

Options:
A. \( 0.07 \)
B. \( 0.1 \)
C. \( 0.7 \)
D. \( 1.0 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Rounds to the wrong degree of accuracy (rounds too much)

Question:
Round \( 0.0735 \) to \( 1 \) significant figure

Options:
A. \( 0.07 \)
B. \( 0.1 \)
C. \( 0.7 \)
D. \( 1.0 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Does not know the meaning of the word identity

Question:
Tom and Katie are discussing identities
Tom says an identity sign should replace the star here: \( 5 y+7 \underset{\star}{2} 7+5 y \) Katie says an identity sign should replace the star here: \( 5 y-7 \underset{\star} 7-5 y \) Who is correct?

Options:
A. Only Tom
B. Only Katie
C. Both Tom and Katie
D. Neither is correct

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Ignores the negative sign when thinking about the value of a term

Question:
Tom and Katie are discussing identities
Tom says an identity sign should replace the star here: \( 5 y+7 \underset{\star}{2} 7+5 y \) Katie says an identity sign should replace the star here: \( 5 y-7 \underset{\star} 7-5 y \) Who is correct?

Options:
A. Only Tom
B. Only Katie
C. Both Tom and Katie
D. Neither is correct

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Does not realise addition is commutative

Question:
Tom and Katie are discussing identities
Tom says an identity sign should replace the star here: \( 5 y+7 \underset{\star}{2} 7+5 y \) Katie says an identity sign should replace the star here: \( 5 y-7 \underset{\star} 7-5 y \) Who is correct?

Options:
A. Only Tom
B. Only Katie
C. Both Tom and Katie
D. Neither is correct

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Believes the sides of a square must be horizontal and vertical, not diagonal

Question:
Tom and Katie are discussing what coordinates would complete a square.
Tom says \( (1,8) \) and \( (5,8) \)
Katie says \( (3,6) \) and \( (3,2) \)
Who is correct? ![A pair of axes with no labels, 1st quadrant only. 2 points are marked with red dots and are labelled with co-ordinates: (1, 4) and (5, 4).]()

Options:
A. Only Tom
B. Only Katie
C. Both Tom and Katie
D. Neither is correct

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Does not know how to find the length of a line segment from coordinates

Question:
Tom and Katie are discussing what coordinates would complete a square.
Tom says \( (1,8) \) and \( (5,8) \)
Katie says \( (3,6) \) and \( (3,2) \)
Who is correct? ![A pair of axes with no labels, 1st quadrant only. 2 points are marked with red dots and are labelled with co-ordinates: (1, 4) and (5, 4).]()

Options:
A. Only Tom
B. Only Katie
C. Both Tom and Katie
D. Neither is correct

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Believes subtracting a positive number from a negative number makes the answer less negative

Question:
What is the solution to the following inequality?
\(-3<2 x+1<7\)

Options:
A. \( -2<x<3 \)
B. \( -1<x<3 \)
C. \( -0.5<x<2.5 \)
D. \( -5<x<15 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Does not reverse the order of operations when solving an equation

Question:
What is the solution to the following inequality?
\(-3<2 x+1<7\)

Options:
A. \( -2<x<3 \)
B. \( -1<x<3 \)
C. \( -0.5<x<2.5 \)
D. \( -5<x<15 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
When solving an equation, uses the same operation rather than the inverse.

Question:
What is the solution to the following inequality?
\(-3<2 x+1<7\)

Options:
A. \( -2<x<3 \)
B. \( -1<x<3 \)
C. \( -0.5<x<2.5 \)
D. \( -5<x<15 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Only multiplies the numerical terms when expanding a bracket

Question:
\(
3(4 x+6)-2(x-9) \equiv A x+B
\)

What is the value of \( A \) ?

Options:
A. \( 3 \)
B. \( 5 \)
C. \( 14 \)
D. \( 10 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Subtracts instead of adds when answering worded problems

Question:
Colm wins \( £ 55750 \) on the lottery and gives \( £ 25250 \) to charity.
How much money does Colm keep?

Options:
A. \( £ 81000 \)
B. \( £ 30500 \)
C. \( £ 35500 \)
D. \( £ 80000 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Adds rather than subtracts when answering worded problems

Question:
Colm wins \( £ 55750 \) on the lottery and gives \( £ 25250 \) to charity.
How much money does Colm keep?

Options:
A. \( £ 81000 \)
B. \( £ 30500 \)
C. \( £ 35500 \)
D. \( £ 80000 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
When multiplying a fraction by an integer, multiplies both numerator and denominator by the integer

Question:
\( \frac{1}{6} \times 6=? \)

Options:
A. \( 1 \)
B. \( \frac{6}{36} \)
C. \( \frac{1}{36} \)
D. \( 6 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
When multiplying a fraction by an integer, multiplies the denominator instead of the numerator

Question:
\( \frac{1}{6} \times 6=? \)

Options:
A. \( 1 \)
B. \( \frac{6}{36} \)
C. \( \frac{1}{36} \)
D. \( 6 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Thinks converting an integer to a fraction means both the numerator and denominator are equal

Question:
\( \frac{1}{6} \times 6=? \)

Options:
A. \( 1 \)
B. \( \frac{6}{36} \)
C. \( \frac{1}{36} \)
D. \( 6 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Believes extreme values can affect the median

Question:
Which of the following would not be representative of this data?
\[
5,6,7,8,8,9,11,12,320
\]

Options:
A. Mean
B. Median
C. Mode
D. All are representative

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Believes extreme values can affect the mode

Question:
Which of the following would not be representative of this data?
\[
5,6,7,8,8,9,11,12,320
\]

Options:
A. Mean
B. Median
C. Mode
D. All are representative

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Believes the mean is always representative

Question:
Which of the following would not be representative of this data?
\[
5,6,7,8,8,9,11,12,320
\]

Options:
A. Mean
B. Median
C. Mode
D. All are representative

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Mixes up greater than and less than symbols

Question:
Which symbol makes the following statement correct?
\(
725,912 \quad \square \quad 2,705,291
\)

Options:
A. \( < \)
B. \( > \)
C. None of these
D. \( = \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Does not understand inequality notation

Question:
Which symbol makes the following statement correct?
\(
725,912 \quad \square \quad 2,705,291
\)

Options:
A. \( < \)
B. \( > \)
C. None of these
D. \( = \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Does not understand inequality notation

Question:
Which symbol makes the following statement correct?
\(
725,912 \quad \square \quad 2,705,291
\)

Options:
A. \( < \)
B. \( > \)
C. None of these
D. \( = \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Believes a line segment can be opposite an axis

Question:
![A set of axes: x-axis from -4 to 4, y-axis from -4 to 4. A red line is drawn from (-2,2) to (2,2).]() The red line is _________ to the y axis.

Options:
A. Parallel
B. Opposite
C. Perpendicular
D. Equidistant

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Does not know the meaning of perpendicular

Question:
![A set of axes: x-axis from -4 to 4, y-axis from -4 to 4. A red line is drawn from (-2,2) to (2,2).]() The red line is _________ to the y axis.

Options:
A. Parallel
B. Opposite
C. Perpendicular
D. Equidistant

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Does not understand that in the ratio 1:n the total number of parts would be 1+n

Question:
What is the ratio of \( x \) to \( y \) ? ![A triangle. The bottom width is marked '15cm'. One side is split into two parts, one part is called 'x', the other is marked 'y'. A second line goes across the triangle from where the side is split into two parts. It is marked '5cm'. ]()

Options:
A. \( 1: 2 \)
B. \( 1: 3 \)
C. \( 1: 4 \)
D. \( 1: 5 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Does not understand that in the ratio 1:n the total number of parts would be 1+n

Question:
What is the ratio of \( x \) to \( y \) ? ![A triangle. The bottom width is marked '15cm'. One side is split into two parts, one part is called 'x', the other is marked 'y'. A second line goes across the triangle from where the side is split into two parts. It is marked '5cm'. ]()

Options:
A. \( 1: 2 \)
B. \( 1: 3 \)
C. \( 1: 4 \)
D. \( 1: 5 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Does not understand that in the ratio 1:n the total number of parts would be 1+n

Question:
What is the ratio of \( x \) to \( y \) ? ![A triangle. The bottom width is marked '15cm'. One side is split into two parts, one part is called 'x', the other is marked 'y'. A second line goes across the triangle from where the side is split into two parts. It is marked '5cm'. ]()

Options:
A. \( 1: 2 \)
B. \( 1: 3 \)
C. \( 1: 4 \)
D. \( 1: 5 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Believes the inverse of square rooting is halving

Question:
Solve this equation, giving all solutions:
\(
3 p^{2}+9=39
\)

Options:
A. \[
n=5
\]
or
\[
n=-5
\]
B. \(
p=\sqrt{10}
\)
or
\(
p=-\sqrt{10}
\)
C. \[
p=2
\]
or
\[
p=-2
\]
D. \[
p=4
\]
or
\[
p=-4
\]

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Does not reverse the order of operations when solving an equation

Question:
Solve this equation, giving all solutions:
\(
3 p^{2}+9=39
\)

Options:
A. \[
n=5
\]
or
\[
n=-5
\]
B. \(
p=\sqrt{10}
\)
or
\(
p=-\sqrt{10}
\)
C. \[
p=2
\]
or
\[
p=-2
\]
D. \[
p=4
\]
or
\[
p=-4
\]

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
When solving an equation, uses the same operation rather than the inverse.

Question:
Solve this equation, giving all solutions:
\(
3 p^{2}+9=39
\)

Options:
A. \[
n=5
\]
or
\[
n=-5
\]
B. \(
p=\sqrt{10}
\)
or
\(
p=-\sqrt{10}
\)
C. \[
p=2
\]
or
\[
p=-2
\]
D. \[
p=4
\]
or
\[
p=-4
\]

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Ignores numerical terms when setting up an equation from a question

Question:
Which of the following statements can you prove from this diagram? ![Angles around a point split into three parts with the parts labelled: m+50, 2m+n and 220-2m]()

Options:
A. \( m=n \)
B. \( m+n=90 \)
C. \( m+n=270 \)
D. \( m+n=360 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Does not use angle facts when setting up an equation from an angle diagram

Question:
Which of the following statements can you prove from this diagram? ![Angles around a point split into three parts with the parts labelled: m+50, 2m+n and 220-2m]()

Options:
A. \( m=n \)
B. \( m+n=90 \)
C. \( m+n=270 \)
D. \( m+n=360 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Ignores numerical terms when setting up an equation from a question

Question:
Which of the following statements can you prove from this diagram? ![Angles around a point split into three parts with the parts labelled: m+50, 2m+n and 220-2m]()

Options:
A. \( m=n \)
B. \( m+n=90 \)
C. \( m+n=270 \)
D. \( m+n=360 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Thinks two letters next to each other is a division

Question:
Which of the following is the correct way of writing: \( p \) divided by \( q \), then add \( 3 \) using algebraic convention?

Options:
A. \( p q+3 \)
B. \( \frac{p}{q}+3 \)
C. \( \frac{p}{q+3} \)
D. \( p-q+3 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Does not account for grammar when writing algebra e.g. ,then making a group

Question:
Which of the following is the correct way of writing: \( p \) divided by \( q \), then add \( 3 \) using algebraic convention?

Options:
A. \( p q+3 \)
B. \( \frac{p}{q}+3 \)
C. \( \frac{p}{q+3} \)
D. \( p-q+3 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Has used a subtraction sign to represent division

Question:
Which of the following is the correct way of writing: \( p \) divided by \( q \), then add \( 3 \) using algebraic convention?

Options:
A. \( p q+3 \)
B. \( \frac{p}{q}+3 \)
C. \( \frac{p}{q+3} \)
D. \( p-q+3 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
When calculating the range does not reorder the data to find the largest number minus the smallest number

Question:
What is the range of the following numbers?
\[
0.2, \quad 0.22, \quad 0.212
\]

Options:
A. \( 0.02 \)
B. \( 0.012 \)
C. \( 0.21 \)
D. \( 0.2 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
When calculating the range does not reorder the data to find the largest number minus the smallest number

Question:
What is the range of the following numbers?
\[
0.2, \quad 0.22, \quad 0.212
\]

Options:
A. \( 0.02 \)
B. \( 0.012 \)
C. \( 0.21 \)
D. \( 0.2 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
When subtracting decimals with a different number of decimal places, lines up the digits incorrectly

Question:
What is the range of the following numbers?
\[
0.2, \quad 0.22, \quad 0.212
\]

Options:
A. \( 0.02 \)
B. \( 0.012 \)
C. \( 0.21 \)
D. \( 0.2 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Confuses powers and multiples

Question:
Which of the following is a power of \( 5 \) ?

Options:
A. \( 55 \)
B. \( 100 \)
C. \( 500 \)
D. \( 125 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Confuses powers and multiples

Question:
Which of the following is a power of \( 5 \) ?

Options:
A. \( 55 \)
B. \( 100 \)
C. \( 500 \)
D. \( 125 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Confuses powers and multiples

Question:
Which of the following is a power of \( 5 \) ?

Options:
A. \( 55 \)
B. \( 100 \)
C. \( 500 \)
D. \( 125 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Finds 10% of an amount rather than the percentage being asked

Question:
\( 20 \% \) of \( 35= \)

Options:
A. \( 4 \)
B. \( 7 \)
C. \( 3.5 \)
D. \( 70 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
When finding a percentage of an amount, assumes they divide the percentage by 10, but not the amount, before multiplying

Question:
\( 20 \% \) of \( 35= \)

Options:
A. \( 4 \)
B. \( 7 \)
C. \( 3.5 \)
D. \( 70 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Does not know a rectangle is a type of parallelogram

Question:
Tom and Katie are arguing about parallelograms. Tom says this shape is a parallelogram ![A four sided shape. All sides are equal, opposite angles are equal. There are no right angles.]() Katie says this shape is a parallelogram ![A four sided shape. Opposite sides are equal, all angles are right angles.]() Who is correct?

Options:
A. Only
Tom
B. Only
Katie
C. Both Tom and Katie
D. Neither is correct

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Does not know a rhombus is a type of parallelogram

Question:
Tom and Katie are arguing about parallelograms. Tom says this shape is a parallelogram ![A four sided shape. All sides are equal, opposite angles are equal. There are no right angles.]() Katie says this shape is a parallelogram ![A four sided shape. Opposite sides are equal, all angles are right angles.]() Who is correct?

Options:
A. Only
Tom
B. Only
Katie
C. Both Tom and Katie
D. Neither is correct

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Does not believe a shape can have two correct names e.g. rectangle and parallelogram

Question:
Tom and Katie are arguing about parallelograms. Tom says this shape is a parallelogram ![A four sided shape. All sides are equal, opposite angles are equal. There are no right angles.]() Katie says this shape is a parallelogram ![A four sided shape. Opposite sides are equal, all angles are right angles.]() Who is correct?

Options:
A. Only
Tom
B. Only
Katie
C. Both Tom and Katie
D. Neither is correct

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
When completing the square in the form (x - a)^2 + b, believes b = a^2 + the original constant

Question:
When Sarah completes the square, what should replace the triangle?
\[
p^{2}-10 p-1 \equiv(p-5)^{2}  \Delta
\]

Options:
A. \( \Delta=-26 \)
B. \( \Delta=+24 \)
C. \( \Delta =-11 \)
D. \( \Delta=-24 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Mixes up squaring and multiplying by 2 or doubling

Question:
When Sarah completes the square, what should replace the triangle?
\[
p^{2}-10 p-1 \equiv(p-5)^{2}  \Delta
\]

Options:
A. \( \Delta=-26 \)
B. \( \Delta=+24 \)
C. \( \Delta =-11 \)
D. \( \Delta=-24 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Reflects instead of rotates

Question:
![A pair of axes: x-axis is from -2 to 4; y-axis is from -2 to 4. A 6-sided polygon, labelled "P", is made by joining the following points, in order, with straight lines: (1, 2), (2, 2), (2, 3), (4, 3), (4, 4), (1, 4) and back to (1, 2).
The point (2, 2) is marked with a red dot.
Also, the following points are plotted and labelled with the following letters: A (-2, -2); B (2, -2); C (-1, -2); D (-2, -1).]() Shape \( \mathrm{P} \) is rotated \( 180^{\circ} \) through the origin.

Where will the red point be on the rotated shape?

Options:
A. A
B. B
C. C
D. D

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Forgets that a number divided by itself is 1

Question:
This is a part of the table of values for the equation \( y=\frac{3}{x} \) \begin{tabular}{|c|c|}
\hline\( x \) & \( 3 \) \\
\hline\( y \) & \( \bigstar \) \\
\hline
\end{tabular} What should replace the star?

Options:
A. \( 1 \)
B. \( 3 \)
C. \( \frac{1}{3} \)
D. \( 0 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Believes that a fraction with equal numerator and denominator cancels to 0

Question:
This is a part of the table of values for the equation \( y=\frac{3}{x} \) \begin{tabular}{|c|c|}
\hline\( x \) & \( 3 \) \\
\hline\( y \) & \( \bigstar \) \\
\hline
\end{tabular} What should replace the star?

Options:
A. \( 1 \)
B. \( 3 \)
C. \( \frac{1}{3} \)
D. \( 0 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Divides by the order of the root

Question:
\( \sqrt[3]{216}= \)

Options:
A. \( 72 \)
B. \( 6 \)
C. \( 108 \)
D. \( 9 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Halves when asked to find the cube root

Question:
\( \sqrt[3]{216}= \)

Options:
A. \( 72 \)
B. \( 6 \)
C. \( 108 \)
D. \( 9 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Believes that to find an angle for a pie chart sector you divide the total frequency by 360 and multiply by its frequency

Question:
A class of students were surveyed about how many siblings they have.

A selection of results are shown in the table. \begin{tabular}{|c|c|c|}
\hline Number of siblings & Frequency & Angle on a pie chart \\
\hline  0  & \( 7 \) & \( \bigstar \) \\
\hline 1  & \( \) & \( 144 \degree \) \\
\hline 2  & \(  \) & \(  \) \\
\hline 3  & \( 4 \) & \(  \) \\
\hline 4 or more  & \(  \) & \(  \) \\
\hline  TOTAL  & 30  & \(  \) \\
\end{tabular} Jenny wants to draw a pie chart of the information.

Which of the following calculations would work out what replaces the star?

Options:
A. \( \frac{30}{360} \times 7 \)
B. \( \frac{7}{30} \times 360 \)
C. \( \frac{30}{7} \times 360 \)
D. \( 7 \times 30 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Believes that a fraction means dividing the denominator by the numerator

Question:
A class of students were surveyed about how many siblings they have.

A selection of results are shown in the table. \begin{tabular}{|c|c|c|}
\hline Number of siblings & Frequency & Angle on a pie chart \\
\hline  0  & \( 7 \) & \( \bigstar \) \\
\hline 1  & \( \) & \( 144 \degree \) \\
\hline 2  & \(  \) & \(  \) \\
\hline 3  & \( 4 \) & \(  \) \\
\hline 4 or more  & \(  \) & \(  \) \\
\hline  TOTAL  & 30  & \(  \) \\
\end{tabular} Jenny wants to draw a pie chart of the information.

Which of the following calculations would work out what replaces the star?

Options:
A. \( \frac{30}{360} \times 7 \)
B. \( \frac{7}{30} \times 360 \)
C. \( \frac{30}{7} \times 360 \)
D. \( 7 \times 30 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Believes you find the angle for a pie chart sector by doing its frequency multiplied by total frequency

Question:
A class of students were surveyed about how many siblings they have.

A selection of results are shown in the table. \begin{tabular}{|c|c|c|}
\hline Number of siblings & Frequency & Angle on a pie chart \\
\hline  0  & \( 7 \) & \( \bigstar \) \\
\hline 1  & \( \) & \( 144 \degree \) \\
\hline 2  & \(  \) & \(  \) \\
\hline 3  & \( 4 \) & \(  \) \\
\hline 4 or more  & \(  \) & \(  \) \\
\hline  TOTAL  & 30  & \(  \) \\
\end{tabular} Jenny wants to draw a pie chart of the information.

Which of the following calculations would work out what replaces the star?

Options:
A. \( \frac{30}{360} \times 7 \)
B. \( \frac{7}{30} \times 360 \)
C. \( \frac{30}{7} \times 360 \)
D. \( 7 \times 30 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Multiplied by 1000 instead of 100

Question:
What is \( 0.03 \) written as a percentage?

Options:
A. \( 3 \% \)
B. \( 30 \% \)
C. \( 0.03 \% \)
D. \( 0.3 \% \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Thinks you need to just add a % sign to a decimal to convert to a percentage

Question:
What is \( 0.03 \) written as a percentage?

Options:
A. \( 3 \% \)
B. \( 30 \% \)
C. \( 0.03 \% \)
D. \( 0.3 \% \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Multiplied by 10 rather than 100

Question:
What is \( 0.03 \) written as a percentage?

Options:
A. \( 3 \% \)
B. \( 30 \% \)
C. \( 0.03 \% \)
D. \( 0.3 \% \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Confuses reciprocal and quadratic graphs

Question:
Which of the following graphs show that \( \mathrm{x} \) is inversely proportional to \( y \) ?

Options:
A. ![A graph with a straight line going from bottom left to top right. The graph starts from above the  origin on the y axis. ]()
B. ![A graph that starts in the top left, drops steeply down as you move right, briefly levels off, then steeply up back to the same level as the starting point, forming a symmetrical U shape]()
C. ![A graph with a straight line going from bottom left to top right. The graph starts from 0 on the y axis. ]()
D. ![A graph starting at the top left and rapidly decreasing as it moves right before slowing down and starting to level off ]()

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Confuses the graphs of  direct and inverse proportion

Question:
Which of the following graphs show that \( \mathrm{x} \) is inversely proportional to \( y \) ?

Options:
A. ![A graph with a straight line going from bottom left to top right. The graph starts from above the  origin on the y axis. ]()
B. ![A graph that starts in the top left, drops steeply down as you move right, briefly levels off, then steeply up back to the same level as the starting point, forming a symmetrical U shape]()
C. ![A graph with a straight line going from bottom left to top right. The graph starts from 0 on the y axis. ]()
D. ![A graph starting at the top left and rapidly decreasing as it moves right before slowing down and starting to level off ]()

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Believes division is commutative

Question:
\( 4 \div 2 \frac{4}{5} \) Which of the following is a correct way to write the answer to this calculation?

Options:
A. \( 1 \frac{3}{7} \)
B. \( 2 \frac{1}{5} \)
C. \( 1 \frac{2}{5} \)
D. \( \frac{7}{10} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Thinks you add all the bricks in a row in an addition pyramid.

Question:
Which expression should replace the star in the addition pyramid? ![A pyramid showing the expressions 2a, -b and 2a-2b across the base from left to right. Above the 2a and -b is a star. Above the -b and the 2a-2b is written 2a-3b]()

Options:
A. \( 4 a-3 b \)
B. \( -2 a b \)
C. \( 4 a-4 b \)
D. \( 2 a-b \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Multiplies rather than adds

Question:
Which expression should replace the star in the addition pyramid? ![A pyramid showing the expressions 2a, -b and 2a-2b across the base from left to right. Above the 2a and -b is a star. Above the -b and the 2a-2b is written 2a-3b]()

Options:
A. \( 4 a-3 b \)
B. \( -2 a b \)
C. \( 4 a-4 b \)
D. \( 2 a-b \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Has added the powers rather than multiplying them

Question:
\( \left(4^{6}\right)^{2}= \)

Options:
A. \( 4^{8} \)
B. \( 16^{12} \)
C. \( 4^{12} \)
D. None of these options

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Selects y>a solutions instead of y<a solutions for a quadratic inequality

Question:
Use the graph to approximate the solution to \( x^{2}-x-6<-4 \) ![A set of axes with the quadratic graph y=x^2-x-6 drawn on.]()

Options:
A. \( x<-1, x>2 \)
B. \( -1<x<2 \)
C. \( -2<x<3 \)
D. \( x=2 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Solves for y=0 instead of given y-value when reading from a quadratic graph

Question:
Use the graph to approximate the solution to \( x^{2}-x-6<-4 \) ![A set of axes with the quadratic graph y=x^2-x-6 drawn on.]()

Options:
A. \( x<-1, x>2 \)
B. \( -1<x<2 \)
C. \( -2<x<3 \)
D. \( x=2 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
When reading value from graph, reads from the wrong axes.

Question:
This graph shows the relationship between journey time and the speed of a car.
How long will the journey take if the car travels at \( 30 \mathrm{mph} \) ? ![A graph showing speed in miles per hour on the x axis and journey time in hours on the y axis. A curve is shown that has a steep negative gradient to start with, that gradually becomes less steep until it is nearly horizontal. The curve passes through the points (8,30) and (30,7)]()

Options:
A. \( 7 \) hours
B. \( 8 \) hours
C. \( 30 \) hours
D. \( 15 \) hours

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
When asked to read a value from a graph, thinks they give the corresponding value on the other axis, rather than reading from the graph

Question:
This graph shows the relationship between journey time and the speed of a car.
How long will the journey take if the car travels at \( 30 \mathrm{mph} \) ? ![A graph showing speed in miles per hour on the x axis and journey time in hours on the y axis. A curve is shown that has a steep negative gradient to start with, that gradually becomes less steep until it is nearly horizontal. The curve passes through the points (8,30) and (30,7)]()

Options:
A. \( 7 \) hours
B. \( 8 \) hours
C. \( 30 \) hours
D. \( 15 \) hours

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Makes an assumption about the squares on a scale representing either 1 or 10

Question:
This graph shows the relationship between journey time and the speed of a car.
How long will the journey take if the car travels at \( 30 \mathrm{mph} \) ? ![A graph showing speed in miles per hour on the x axis and journey time in hours on the y axis. A curve is shown that has a steep negative gradient to start with, that gradually becomes less steep until it is nearly horizontal. The curve passes through the points (8,30) and (30,7)]()

Options:
A. \( 7 \) hours
B. \( 8 \) hours
C. \( 30 \) hours
D. \( 15 \) hours

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
When simplifying surds, does not multiply the number in front of the surd with the square root of the largest square number that has been removed from the surd

Question:
\(
2 \sqrt{5}+2 \sqrt{45} \equiv d \sqrt{5}
\)

What is the value of \( d \) ?

Options:
A. \( 7 \)
B. \( 20 \)
C. \( 8 \)
D. \( 4 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
When simplifying surds, does not square root the largest square number that goes into the number under the surd before putting it in front of the surd

Question:
\(
2 \sqrt{5}+2 \sqrt{45} \equiv d \sqrt{5}
\)

What is the value of \( d \) ?

Options:
A. \( 7 \)
B. \( 20 \)
C. \( 8 \)
D. \( 4 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
When adding or subtracting surds, does not simplify the surd before adding the numbers in front of the surd

Question:
\(
2 \sqrt{5}+2 \sqrt{45} \equiv d \sqrt{5}
\)

What is the value of \( d \) ?

Options:
A. \( 7 \)
B. \( 20 \)
C. \( 8 \)
D. \( 4 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Adds or subtracts from numerator first when solving an equation with a fraction

Question:
Tom and Katie are discussing how to solve:
\(\frac{5 x-1}{3}=2\)

Tom says a correct next line of working could be: \( 5 x-1=6 \)

Katie says a correct next line of working could be: \( \frac{5 x}{3}=3 \)

Who is correct?

Options:
A. Only Tom
B. Only
Katie
C. Both Tom and Katie
D. Neither is correct

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Adds or subtracts from numerator first when solving an equation with a fraction

Question:
Tom and Katie are discussing how to solve:
\(\frac{5 x-1}{3}=2\)

Tom says a correct next line of working could be: \( 5 x-1=6 \)

Katie says a correct next line of working could be: \( \frac{5 x}{3}=3 \)

Who is correct?

Options:
A. Only Tom
B. Only
Katie
C. Both Tom and Katie
D. Neither is correct

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Does not understand the concept of inverse operations in algebra

Question:
Tom and Katie are discussing how to solve:
\(\frac{5 x-1}{3}=2\)

Tom says a correct next line of working could be: \( 5 x-1=6 \)

Katie says a correct next line of working could be: \( \frac{5 x}{3}=3 \)

Who is correct?

Options:
A. Only Tom
B. Only
Katie
C. Both Tom and Katie
D. Neither is correct

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Uses only the first two terms of a sequence to work out a term-to-term rule

Question:
![The triangle numbers represented using purple circles with the first term having 3 purple circles. The second and third terms are also shown.]() How many circles will the next term in this sequence have?

Options:
A. \( 20 \)
B. \( 14 \)
C. \( 15 \)
D. \( 18 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Only looks at the difference between one pair of terms when discerning the pattern

Question:
![The triangle numbers represented using purple circles with the first term having 3 purple circles. The second and third terms are also shown.]() How many circles will the next term in this sequence have?

Options:
A. \( 20 \)
B. \( 14 \)
C. \( 15 \)
D. \( 18 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Believes angles around a point sum to 180

Question:
What is the size of angle \( z \) ? ![Angles around a point made up of two angles labelled 162 degrees and z]()

Options:
A. \( 18^{\circ} \)
B. \( 162^{\circ} \)
C. \( 208^{\circ} \)
D. \( 198^{\circ} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Confuses vertically opposite angles and angles around a point

Question:
What is the size of angle \( z \) ? ![Angles around a point made up of two angles labelled 162 degrees and z]()

Options:
A. \( 18^{\circ} \)
B. \( 162^{\circ} \)
C. \( 208^{\circ} \)
D. \( 198^{\circ} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
When “borrowing” during a subtraction problem, does not subtract one from the preceding digit

Question:
What is the size of angle \( z \) ? ![Angles around a point made up of two angles labelled 162 degrees and z]()

Options:
A. \( 18^{\circ} \)
B. \( 162^{\circ} \)
C. \( 208^{\circ} \)
D. \( 198^{\circ} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Does not understand set notation for complement (eg. A')

Question:
Which element(s) is/are in \( P^{\prime} \) ? ![A diagram showing a Venn diagram of 2 circles. The left cicle is for Set P and contains cat in its left part, horse in the intersection. The right circle is for set Q and contains goat in its right part, horse in the intersection. Outside of the circles it says toad.]()

Options:
A. cat
B. cat & horse
C. \( \begin{array}{c}\text { goat \& } \\ \text { toad }\end{array} \)
D. horse, goat
& toad

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Believes that the complement of a set includes any elements which are also in another set.

Question:
Which element(s) is/are in \( P^{\prime} \) ? ![A diagram showing a Venn diagram of 2 circles. The left cicle is for Set P and contains cat in its left part, horse in the intersection. The right circle is for set Q and contains goat in its right part, horse in the intersection. Outside of the circles it says toad.]()

Options:
A. cat
B. cat & horse
C. \( \begin{array}{c}\text { goat \& } \\ \text { toad }\end{array} \)
D. horse, goat
& toad

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
When ordering integers, orders from the digits at the end of the number instead of the digits at the start

Question:
Which of these options show the numbers
\[
8,605,527 \quad 8,605,572 \quad 8,650,527 \quad 8,605,752
\]
in order from smallest to largest?

Options:
A. \( \begin{array}{l}8,650,527 \\ 8,605,752 \\ 8,605,572 \\ 8,605,527\end{array} \)
B. \( \begin{array}{l}8,605,752 \\ 8,605,572 \\ 8,650,527 \\ 8,605,527\end{array} \)
C. \( \begin{array}{l}8,605,527 \\ 8,605,752 \\ 8,605,572 \\ 8,650,527\end{array} \)
D. \( \begin{array}{l}8,605,527 \\ 8,605,572 \\ 8,605,752 \\ 8,650,527\end{array} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Think cross section of a prism is the biggest face

Question:
Amy wants to calculate the volume of this shape.

Which face should she work out the area of to help her? ![The diagram shows a right angled triangular prism with arrows pointing to one of the right angled triangle faces and the three rectangular faces.]()

Options:
A. ![A points to 'the slope' which is the rectangular face coming off the hypotenuse of the right angled triangle]()
B. ![B points to 'the front' which is the right angled triangle face]()
C. ![C points to 'the back' which is the rectangular face coming off the short vertical side of the right angled triangle]()
D. ![D points to 'the base' which is the rectangular face coming off the long horizontal side of the right angled triangle]()

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Thinks cross section of a prism can be any face

Question:
Amy wants to calculate the volume of this shape.

Which face should she work out the area of to help her? ![The diagram shows a right angled triangular prism with arrows pointing to one of the right angled triangle faces and the three rectangular faces.]()

Options:
A. ![A points to 'the slope' which is the rectangular face coming off the hypotenuse of the right angled triangle]()
B. ![B points to 'the front' which is the right angled triangle face]()
C. ![C points to 'the back' which is the rectangular face coming off the short vertical side of the right angled triangle]()
D. ![D points to 'the base' which is the rectangular face coming off the long horizontal side of the right angled triangle]()

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Thinks cross section of a prism can be any face

Question:
Amy wants to calculate the volume of this shape.

Which face should she work out the area of to help her? ![The diagram shows a right angled triangular prism with arrows pointing to one of the right angled triangle faces and the three rectangular faces.]()

Options:
A. ![A points to 'the slope' which is the rectangular face coming off the hypotenuse of the right angled triangle]()
B. ![B points to 'the front' which is the right angled triangle face]()
C. ![C points to 'the back' which is the rectangular face coming off the short vertical side of the right angled triangle]()
D. ![D points to 'the base' which is the rectangular face coming off the long horizontal side of the right angled triangle]()

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Confuses factors and multiples

Question:
A hot tap drips every \( 12 \) seconds
A cold tap drips every \( 8 \) seconds
They both drip at exactly the same time
After how many seconds will they next drip at the same time?
To solve this problem you need to work out the  \( _____ \) of \( 12 \) and \( 8 \)

Options:
A. Lowest Common Multiple
B. Highest Common Factor
C. Product
D. Sum

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Finds a common multiple but not the lowest common multiple

Question:
A hot tap drips every \( 12 \) seconds
A cold tap drips every \( 8 \) seconds
They both drip at exactly the same time
After how many seconds will they next drip at the same time?
To solve this problem you need to work out the  \( _____ \) of \( 12 \) and \( 8 \)

Options:
A. Lowest Common Multiple
B. Highest Common Factor
C. Product
D. Sum

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Believes adding two numbers finds their lowest common multiple

Question:
A hot tap drips every \( 12 \) seconds
A cold tap drips every \( 8 \) seconds
They both drip at exactly the same time
After how many seconds will they next drip at the same time?
To solve this problem you need to work out the  \( _____ \) of \( 12 \) and \( 8 \)

Options:
A. Lowest Common Multiple
B. Highest Common Factor
C. Product
D. Sum

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Rounds down instead of up

Question:
What is \( \mathbf{1 1 . 4 7 8 1} \) rounded to \( 2 \) decimal places?

Options:
A. \( 11.47 \)
B. \( 11.48 \)
C. \( 11.58 \)
D. \( 11.59 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Rounds incorrectly by changing multiple place values

Question:
What is \( \mathbf{1 1 . 4 7 8 1} \) rounded to \( 2 \) decimal places?

Options:
A. \( 11.47 \)
B. \( 11.48 \)
C. \( 11.58 \)
D. \( 11.59 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Rounds incorrectly by changing multiple place values

Question:
What is \( \mathbf{1 1 . 4 7 8 1} \) rounded to \( 2 \) decimal places?

Options:
A. \( 11.47 \)
B. \( 11.48 \)
C. \( 11.58 \)
D. \( 11.59 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Believes all possible outcomes must have equal probability

Question:
This five-sided spinner is fair.
What is the probability of spinning a \( \mathbf{3} \) ?
Give your answer as a percentage ![A five sided spinner labelled with 1, 1, 2, 3 and 4]()

Options:
A. \( 30 \% \)
B. \( 25 \% \)
C. \( \frac{1}{5} \)
D. \( 20 \% \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Believes a mixed number can contain an improper fraction

Question:
\(
2 \frac{1}{3}+\frac{3}{4}=3 \frac{\bigstar}{12}
\)
What should replace the star?

Options:
A. \( 1 \)
B. \( 13 \)
C. \( 4 \)
D. \( 37 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Finds an equivalent improper fraction when asked for a mixed number

Question:
\(
2 \frac{1}{3}+\frac{3}{4}=3 \frac{\bigstar}{12}
\)
What should replace the star?

Options:
A. \( 1 \)
B. \( 13 \)
C. \( 4 \)
D. \( 37 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Forgets you need a ruler to measure lengths

Question:
Which combination of mathematical instruments has been used to construct this triangle? ![Constructed triangle with two sides and an angle labelled]()

Options:
A. Protractor
Compass
B. Ruler
Compass
C. Ruler
Protractor
Compass
D. Ruler
Protractor

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Forgets you need a protractor to measure angles

Question:
Which combination of mathematical instruments has been used to construct this triangle? ![Constructed triangle with two sides and an angle labelled]()

Options:
A. Protractor
Compass
B. Ruler
Compass
C. Ruler
Protractor
Compass
D. Ruler
Protractor

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Believes constructing a triangle with given SAS requires a compass

Question:
Which combination of mathematical instruments has been used to construct this triangle? ![Constructed triangle with two sides and an angle labelled]()

Options:
A. Protractor
Compass
B. Ruler
Compass
C. Ruler
Protractor
Compass
D. Ruler
Protractor

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Divides when converting to a smaller unit

Question:
3 litres =  \( \color{gold}\bigstar \) millilitres What should replace the star?

Options:
A. \( 0.3 \)
B. \( 30 \)
C. \( 300 \)
D. \( 3000 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Thinks there are 10ml in a litre

Question:
3 litres =  \( \color{gold}\bigstar \) millilitres What should replace the star?

Options:
A. \( 0.3 \)
B. \( 30 \)
C. \( 300 \)
D. \( 3000 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Thinks there are 100 ml in a litre

Question:
3 litres =  \( \color{gold}\bigstar \) millilitres What should replace the star?

Options:
A. \( 0.3 \)
B. \( 30 \)
C. \( 300 \)
D. \( 3000 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Believes that when factorising a quadratic, they can choose any two numbers that multiply to give the constant

Question:
Factorise \( x^{2}+20 x+64 \)

Options:
A. \( (x+4)(x+16) \)
B. \( (x+8)(x+8) \)
C. \( (x+12)(x+8) \)
D. \( (x+14)(x+6) \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Believes that when factorising a quadratic, they can choose any two numbers that add to give the coefficient of x

Question:
Factorise \( x^{2}+20 x+64 \)

Options:
A. \( (x+4)(x+16) \)
B. \( (x+8)(x+8) \)
C. \( (x+12)(x+8) \)
D. \( (x+14)(x+6) \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Believes that when factorising a quadratic, they can choose any two numbers that add to give the coefficient of x

Question:
Factorise \( x^{2}+20 x+64 \)

Options:
A. \( (x+4)(x+16) \)
B. \( (x+8)(x+8) \)
C. \( (x+12)(x+8) \)
D. \( (x+14)(x+6) \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Believes speed is distance multiplied by time

Question:
Work out the speed \( v \) if the distance travelled is \( 50 \) miles. ![A speed-time graph. The vertical axis is labelled Speed (mph) and has no scale marked except for the letter v four squares up.
The horizontal axis is labelled Time (seconds) and the scale is 0, 1, 2, 3, 4 in even steps.
The graph consists of two sloped lines. The first is from (0,0) to (2, v) and the second is from (2, v) to (4, 0).]()

Options:
A. \( 100 \mathrm{mph} \)
B. \( 50 \mathrm{mph} \)
C. \( 25 \mathrm{mph} \)
D. \( 12.5 \mathrm{mph} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Thinks the shape of the graph does not affect the area calculation

Question:
Work out the speed \( v \) if the distance travelled is \( 50 \) miles. ![A speed-time graph. The vertical axis is labelled Speed (mph) and has no scale marked except for the letter v four squares up.
The horizontal axis is labelled Time (seconds) and the scale is 0, 1, 2, 3, 4 in even steps.
The graph consists of two sloped lines. The first is from (0,0) to (2, v) and the second is from (2, v) to (4, 0).]()

Options:
A. \( 100 \mathrm{mph} \)
B. \( 50 \mathrm{mph} \)
C. \( 25 \mathrm{mph} \)
D. \( 12.5 \mathrm{mph} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Does not understand bar modelling in algebra

Question:
Jodie was \( y \) years old on her birthday \( 3 \) years ago.
Her father was \( 43 \) years old. This year Jodie is half her father's age.
Which answer does not correctly represent this scenario?

Options:
A. \( 2(y+3)=43 \)
B. \( y+3=\frac{43+3}{2} \)
C. ![A bar model showing a bar for Jodie's age as y + 3 which is half the width of her father's bar.  Her father's bar is shown as 2 lots of y + 3, where the first y + 3 + y total to 43.]()
D. ![A bar model showing a bar for Jodie's age as y + 3 which is half the width of her father's bar.  Her father's bar is shown as 46 in total, split into 2 lots of 23.]()

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Does not understand bar modelling in algebra

Question:
Jodie was \( y \) years old on her birthday \( 3 \) years ago.
Her father was \( 43 \) years old. This year Jodie is half her father's age.
Which answer does not correctly represent this scenario?

Options:
A. \( 2(y+3)=43 \)
B. \( y+3=\frac{43+3}{2} \)
C. ![A bar model showing a bar for Jodie's age as y + 3 which is half the width of her father's bar.  Her father's bar is shown as 2 lots of y + 3, where the first y + 3 + y total to 43.]()
D. ![A bar model showing a bar for Jodie's age as y + 3 which is half the width of her father's bar.  Her father's bar is shown as 46 in total, split into 2 lots of 23.]()

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Mixes up greater than and less than symbols

Question:
In which of the following inequalities could \( \boldsymbol{d}=\mathbf{5} \) ? \begin{tabular}{ll}
Inequality \( 1 \) & Inequality 2 \\
\( 2 d>11 \) & \( 11>d+2 \)
\end{tabular}

Options:
A. Only Inequality \( 1 \)
B. Only Inequality \( 2 \)
C. Both Inequalities \( 1 \) and \( 2 \)
D. Neither Inequality \( 1 \) nor \( 2 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Rounds up instead of down

Question:
Jane measures the length and width of her rectangular classroom as \( 8.3 \mathrm{~m} \) and \( 12.9 \mathrm{~m} \).
Which calculation will give the best estimate of the area?

Options:
A. \( 9 \times 13 \)
B. \( 8 \times 13 \)
C. \( 8 \times 12 \)
D. \( 9 \times 12 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Rounds down instead of up

Question:
Jane measures the length and width of her rectangular classroom as \( 8.3 \mathrm{~m} \) and \( 12.9 \mathrm{~m} \).
Which calculation will give the best estimate of the area?

Options:
A. \( 9 \times 13 \)
B. \( 8 \times 13 \)
C. \( 8 \times 12 \)
D. \( 9 \times 12 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Rounds up rather than to one significant figure

Question:
Jane measures the length and width of her rectangular classroom as \( 8.3 \mathrm{~m} \) and \( 12.9 \mathrm{~m} \).
Which calculation will give the best estimate of the area?

Options:
A. \( 9 \times 13 \)
B. \( 8 \times 13 \)
C. \( 8 \times 12 \)
D. \( 9 \times 12 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Writes times in the afternoon as if they are morning on a 24 hour clock

Question:
A coach takes \( 2 \) hours \( 40 \) minutes to complete a journey from Manchester to Milton Keynes.

If the coach leaves Manchester at 10:45, what time does it arrive in Milton Keynes?

Options:
A. \( 13: 25 \)
B. 01:25
C. \( 12: 85 \)
D. \( 13: 15 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Answers as if there are 100 minutes in an hour when changing from hours to minutes

Question:
A coach takes \( 2 \) hours \( 40 \) minutes to complete a journey from Manchester to Milton Keynes.

If the coach leaves Manchester at 10:45, what time does it arrive in Milton Keynes?

Options:
A. \( 13: 25 \)
B. 01:25
C. \( 12: 85 \)
D. \( 13: 15 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
When solving an equation where there is a negative sign in front of the variable and its equivalent value, assumes the variable has a negative value

Question:
This is a part of the table of values for the equation
\[
y=3-x
\] ![\begin{tabular}{|l|l|}
\hline\( x \) & \(\bigstar\)  \\
\hline\( y \) & \( -9 \) \\
\hline
\end{tabular}

]() What should replace the star?

Options:
A. \( 6 \)
B. \( -6 \)
C. \( -12 \)
D. \( 12 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Hasn't lined up the place value columns when writing out the calculation

Question:
\( 5.39-2.1= \)

Options:
A. \( 3.38 \)
B. \( 7.49 \)
C. \( 5.18 \)
D. \( 3.29 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Adds instead of subtracts

Question:
\( 5.39-2.1= \)

Options:
A. \( 3.38 \)
B. \( 7.49 \)
C. \( 5.18 \)
D. \( 3.29 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Hasn't lined up the place value columns when writing out the calculation

Question:
\( 5.39-2.1= \)

Options:
A. \( 3.38 \)
B. \( 7.49 \)
C. \( 5.18 \)
D. \( 3.29 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Mixes up the numerator and denominator when writing a division as a fraction

Question:
Samia has \( 12 \) cakes to share between \( 5 \) people.
What fraction of a cake does each person get?

Options:
A. \( \frac{12}{5} \)
B. \( \frac{5}{12} \)
C. \( \frac{1}{5} \)
D. \( \frac{1}{12} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Thinks the fraction 1/n can express sharing any number of items between n people

Question:
Samia has \( 12 \) cakes to share between \( 5 \) people.
What fraction of a cake does each person get?

Options:
A. \( \frac{12}{5} \)
B. \( \frac{5}{12} \)
C. \( \frac{1}{5} \)
D. \( \frac{1}{12} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Does not know how to interpret a fraction worded problem

Question:
Samia has \( 12 \) cakes to share between \( 5 \) people.
What fraction of a cake does each person get?

Options:
A. \( \frac{12}{5} \)
B. \( \frac{5}{12} \)
C. \( \frac{1}{5} \)
D. \( \frac{1}{12} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Does not know the units column is before the decimal point

Question:
How should you line up the digits to calculate \( 7-0.612 \) ?

Options:
A. ![A column subtraction written as 7.000 - 0.612 with the decimal points lined up.]()
B. ![A column subtraction written as 0.007 - 0.612 with the decimal points lined up.]()
C. ![A column subtraction written as 0.700 - 0.612 with the decimal points lined up.]()
D. ![A column subtraction written as 7.0 - 0.612 The 7 is above the 6, the decimal point in 7.0 is above the 1 and the 0 of 7.0 is above the 2.]()

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Does not know the units column is before the decimal point

Question:
How should you line up the digits to calculate \( 7-0.612 \) ?

Options:
A. ![A column subtraction written as 7.000 - 0.612 with the decimal points lined up.]()
B. ![A column subtraction written as 0.007 - 0.612 with the decimal points lined up.]()
C. ![A column subtraction written as 0.700 - 0.612 with the decimal points lined up.]()
D. ![A column subtraction written as 7.0 - 0.612 The 7 is above the 6, the decimal point in 7.0 is above the 1 and the 0 of 7.0 is above the 2.]()

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Lines up the digits incorrectly when doing a subtraction involving two numbers with a different amount of digits

Question:
How should you line up the digits to calculate \( 7-0.612 \) ?

Options:
A. ![A column subtraction written as 7.000 - 0.612 with the decimal points lined up.]()
B. ![A column subtraction written as 0.007 - 0.612 with the decimal points lined up.]()
C. ![A column subtraction written as 0.700 - 0.612 with the decimal points lined up.]()
D. ![A column subtraction written as 7.0 - 0.612 The 7 is above the 6, the decimal point in 7.0 is above the 1 and the 0 of 7.0 is above the 2.]()

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Student thinks that negative decimals behave the same as positive decimals when positioning a decimal between two consecutive negative integers, placing the decimal with a greater absolute value to the right.

Question:
What is the value of A? ![A horizontal number-line with 11 vertical, equally spaced, dashes representing the position of numbers. "-6" below the 2nd dash and "3" below the last dash are the only numbers marked on the line. An arrow, labelled "A" is pointing halfway between the 4th and 5th dashes. ]()

Options:
A. \( -4.5 \)
B. \( -3.5 \)
C. \( -8.5 \)
D. \( -1 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
When placing a negative number on a number line student assumes numbers with a greater absolute value are placed to the right.

Question:
What is the value of A? ![A horizontal number-line with 11 vertical, equally spaced, dashes representing the position of numbers. "-6" below the 2nd dash and "3" below the last dash are the only numbers marked on the line. An arrow, labelled "A" is pointing halfway between the 4th and 5th dashes. ]()

Options:
A. \( -4.5 \)
B. \( -3.5 \)
C. \( -8.5 \)
D. \( -1 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
When reading integers on a number line, assumes each dash is 2

Question:
What is the value of A? ![A horizontal number-line with 11 vertical, equally spaced, dashes representing the position of numbers. "-6" below the 2nd dash and "3" below the last dash are the only numbers marked on the line. An arrow, labelled "A" is pointing halfway between the 4th and 5th dashes. ]()

Options:
A. \( -4.5 \)
B. \( -3.5 \)
C. \( -8.5 \)
D. \( -1 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Believes there is a multiplicative relationship between values of terms in a linear sequence e.g. 10th term is double 5th term

Question:
The \( 1^{\text {st }} \) term in a linear sequence is \( 8 \). The \( 4^{\text {th }} \) term of the sequence is \( 41 \). What is the \( 8^{\text {th }} \) term of the sequence?

Options:
A. \( 82 \)
B. \( 85 \)
C. \( 74 \)
D. \( 88 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Believes you multiply the constant difference by the term number to get the term value

Question:
The \( 1^{\text {st }} \) term in a linear sequence is \( 8 \). The \( 4^{\text {th }} \) term of the sequence is \( 41 \). What is the \( 8^{\text {th }} \) term of the sequence?

Options:
A. \( 82 \)
B. \( 85 \)
C. \( 74 \)
D. \( 88 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Confused mixed numbers with improper fractions

Question:
\( 2 \frac{4}{5}-1 \frac{2}{5}= \) Leave your answer as a mixed number

Options:
A. \( 1 \frac{2}{5} \)
B. \( \frac{7}{5} \)
C. \( \frac{7}{0} \)
D. \( 1 \frac{2}{0} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
When subtracting fractions, subtracts the numerators and denominators

Question:
\( 2 \frac{4}{5}-1 \frac{2}{5}= \) Leave your answer as a mixed number

Options:
A. \( 1 \frac{2}{5} \)
B. \( \frac{7}{5} \)
C. \( \frac{7}{0} \)
D. \( 1 \frac{2}{0} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Thinks the fraction 1/n can express sharing any number of items between n people

Question:
A group of \( 8 \) friends share \(  £6 \) equally.
What fraction of the money do they each get?

Options:
A. \( \frac{1}{8} \)
B. \( \frac{3}{4} \)
C. \( \frac{1}{6} \)
D. \( \frac{8}{6} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Thinks the fraction 1/n can express sharing n items between any number of people

Question:
A group of \( 8 \) friends share \(  £6 \) equally.
What fraction of the money do they each get?

Options:
A. \( \frac{1}{8} \)
B. \( \frac{3}{4} \)
C. \( \frac{1}{6} \)
D. \( \frac{8}{6} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Believes that a fraction means dividing the denominator by the numerator

Question:
A group of \( 8 \) friends share \(  £6 \) equally.
What fraction of the money do they each get?

Options:
A. \( \frac{1}{8} \)
B. \( \frac{3}{4} \)
C. \( \frac{1}{6} \)
D. \( \frac{8}{6} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Adds instead of subtracts

Question:
Work out: \( \frac{5}{8}-\frac{1}{5} \) Give your answer in the simplest form.

Options:
A. \( \frac{33}{40} \)
B. \( \frac{17}{40} \)
C. \( \frac{4}{3} \)
D. \( \frac{1}{10} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
When subtracting fractions, subtracts the numerators and denominators

Question:
Work out: \( \frac{5}{8}-\frac{1}{5} \) Give your answer in the simplest form.

Options:
A. \( \frac{33}{40} \)
B. \( \frac{17}{40} \)
C. \( \frac{4}{3} \)
D. \( \frac{1}{10} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
When adding fractions, changes to common denominator but leaves numerators the same

Question:
Work out: \( \frac{5}{8}-\frac{1}{5} \) Give your answer in the simplest form.

Options:
A. \( \frac{33}{40} \)
B. \( \frac{17}{40} \)
C. \( \frac{4}{3} \)
D. \( \frac{1}{10} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Believes that when factorising a quadratic, they can choose any two numbers that multiply to give the constant

Question:
Factorise this expression, if possible:
\(
p^{2}+25 p+100
\)

Options:
A. \( (p+25)(p+4) \)
B. \( (p+5)(p+5) \)
C. \( (p+5)(p+20) \)
D. Does not factorise

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Believes the coefficent of x in an expanded quadratic comes from multiplying the two numbers in the brackets

Question:
Factorise this expression, if possible:
\(
p^{2}+25 p+100
\)

Options:
A. \( (p+25)(p+4) \)
B. \( (p+5)(p+5) \)
C. \( (p+5)(p+20) \)
D. Does not factorise

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Converts a fraction to a decimal by using only the numerator after the decimal point

Question:
\( \frac{5}{15}= \)

Options:
A. \( \frac{1}{5} \)
B. \( 0.5 \)
C. \( 33 \frac{1}{3} \% \)
D. A and B

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Thinks there are 100 ml in a litre

Question:
A can of pop is \( 330 \mathrm{ml} \).

What is this in litres?

Options:
A. \( 3.3 \) litres
B. \( 0.3 \) litres
C. \( 0.303 \) litres
D. \( 0.33 \) litres

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Cannot reflect shape when line of symmetry is diagonal

Question:
Tom and Katie are discussing reflections ![Tom says this reflection will create a rectangle. There is a diagonal dashed line with a square sitting on the line.]() ![Katie says this reflection will create a square. There is a diagonal dashed line with a rectangle sitting on the line.]() Who do you agree with?

Options:
A. Only Tom
B. Only Katie
C. Both Tom and Katie
D. Neither is correct

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Does not know how many days are in a leap year

Question:
\( 1 \) leap year \( =\square \) days

Options:
A. \( 730 \)
B. \( 366 \)
C. \( 364 \)
D. \( 365 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Does not know how many days are in a leap year

Question:
\( 1 \) leap year \( =\square \) days

Options:
A. \( 730 \)
B. \( 366 \)
C. \( 364 \)
D. \( 365 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Thinks you subtract rather than add when finding the previous term in a descending linear sequence

Question:
![An image of 5 boxes, each box representing a number in a sequence. The first box contains a star, the second is empty, the third contains the number 488 and the fourth and fifth boxes are also empty.]() A descending linear sequence has a constant difference of \( 17 \) and the \( 3^{\text {rd }} \) term is \( 488 \).
What should replace the star?

Options:
A. \( 471 \)
B. \( 454 \)
C. \( 505 \)
D. \( 522 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Thinks you subtract rather than add when finding the previous term in a descending linear sequence

Question:
![An image of 5 boxes, each box representing a number in a sequence. The first box contains a star, the second is empty, the third contains the number 488 and the fourth and fifth boxes are also empty.]() A descending linear sequence has a constant difference of \( 17 \) and the \( 3^{\text {rd }} \) term is \( 488 \).
What should replace the star?

Options:
A. \( 471 \)
B. \( 454 \)
C. \( 505 \)
D. \( 522 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
When asked for a specific term in a sequence just gives the next term

Question:
If the first term of a sequence is \( 100 \) and the term-to-term rule is \( -5 \), what is the \( 10^{\text {th }} \) term in this sequence?

Options:
A. \( 95 \)
B. \( 55 \)
C. \( 50 \)
D. \( 45 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
When asked for a specific term in a sequence gives the term after

Question:
If the first term of a sequence is \( 100 \) and the term-to-term rule is \( -5 \), what is the \( 10^{\text {th }} \) term in this sequence?

Options:
A. \( 95 \)
B. \( 55 \)
C. \( 50 \)
D. \( 45 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Identifies how much repeated use of the term-to-term rule changes a number but does not apply to the sequence

Question:
If the first term of a sequence is \( 100 \) and the term-to-term rule is \( -5 \), what is the \( 10^{\text {th }} \) term in this sequence?

Options:
A. \( 95 \)
B. \( 55 \)
C. \( 50 \)
D. \( 45 \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Mixes up squaring and multiplying by 2 or doubling

Question:
Which of the following is the correct solution to the inequality?
\(
x^{2}<64
\)

Options:
A. \( \{-32<x<32\} \)
B. \( \{x<8\} \)
C. \( \{-8<x<8\} \)
D. \( \{x<-8\} \cup\{x>8\} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.


Prompt:
Misconception:
Does not think a square root can be negative

Question:
Which of the following is the correct solution to the inequality?
\(
x^{2}<64
\)

Options:
A. \( \{-32<x<32\} \)
B. \( \{x<8\} \)
C. \( \{-8<x<8\} \)
D. \( \{x<-8\} \cup\{x>8\} \)

Solve the problem as a student with the misconception above.
You may think step-by-step.
Put the option letter you choose in a box: \boxed{A} / \boxed{B} / \boxed{C} / \boxed{D}.