Prompt:
Misconception:
Believes the solution of a quadratic inequality is always the interval between the roots

Question:
Using the graph of
\(
y=x^{2}-x-6
\)

What is the correct way to write the solution to
\(
y=x^{2}-x-6 \geq 0 ?
\) ![The is a parabolic graph that crosses the x axis at the points (-2,0) and (3,0) and crosses the y axis at (0, -6).]()

Options:
A. \( \{x \leq-2\} \cup\{x \geq 3\} \)
B. \( \{-2 \leq x \leq 3\} \)
C. \( \{-2 \geq x \geq 3\} \)
D. \( \{x \geq-2\} \cup\{x \leq 3\} \)

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:
Believes any two inequalities can be combined into a double inequality

Question:
Using the graph of
\(
y=x^{2}-x-6
\)

What is the correct way to write the solution to
\(
y=x^{2}-x-6 \geq 0 ?
\) ![The is a parabolic graph that crosses the x axis at the points (-2,0) and (3,0) and crosses the y axis at (0, -6).]()

Options:
A. \( \{x \leq-2\} \cup\{x \geq 3\} \)
B. \( \{-2 \leq x \leq 3\} \)
C. \( \{-2 \geq x \geq 3\} \)
D. \( \{x \geq-2\} \cup\{x \leq 3\} \)

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:
Mixes up greater than and less than symbols

Question:
Using the graph of
\(
y=x^{2}-x-6
\)

What is the correct way to write the solution to
\(
y=x^{2}-x-6 \geq 0 ?
\) ![The is a parabolic graph that crosses the x axis at the points (-2,0) and (3,0) and crosses the y axis at (0, -6).]()

Options:
A. \( \{x \leq-2\} \cup\{x \geq 3\} \)
B. \( \{-2 \leq x \leq 3\} \)
C. \( \{-2 \geq x \geq 3\} \)
D. \( \{x \geq-2\} \cup\{x \leq 3\} \)

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 what a square number is

Question:
In which region would \( \mathbf{1 5} \) belong? ![A Venn diagram with two sets, one labelled Square number and one labelled Odd number. Square Number without the intersection is labelled A, Odd Number without the intersection is labelled C, the intersection of the two sets is labelled B, and outside the circles is labelled D.]()

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:
Does not know what a square number is

Question:
In which region would \( \mathbf{1 5} \) belong? ![A Venn diagram with two sets, one labelled Square number and one labelled Odd number. Square Number without the intersection is labelled A, Odd Number without the intersection is labelled C, the intersection of the two sets is labelled B, and outside the circles is labelled D.]()

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:
Mixes up odd and even numbers

Question:
In which region would \( \mathbf{1 5} \) belong? ![A Venn diagram with two sets, one labelled Square number and one labelled Odd number. Square Number without the intersection is labelled A, Odd Number without the intersection is labelled C, the intersection of the two sets is labelled B, and outside the circles is labelled D.]()

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:
Orders integers based on first digits without taking into account place value

Question:
Which of these options show the numbers
650,312
3,506,212
3,652
605,321
in order from smallest to largest?

Options:
A. \( \begin{array}{l}3,506,212 \\ 3,652 \\ 605,321 \\ 650,312\end{array} \)
B. \( \begin{array}{l}3,652 \\ 605,321 \\ 650,312 \\ 3,506,212\end{array} \)
C. \( \begin{array}{l}605,321 \\ 3,506,212 \\ 650,312 \\ 3,652\end{array} \)
D. \( \begin{array}{l}3,506,212 \\ 650,312 \\ 605,321 \\ 3,652\end{array} \)

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:
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
650,312
3,506,212
3,652
605,321
in order from smallest to largest?

Options:
A. \( \begin{array}{l}3,506,212 \\ 3,652 \\ 605,321 \\ 650,312\end{array} \)
B. \( \begin{array}{l}3,652 \\ 605,321 \\ 650,312 \\ 3,506,212\end{array} \)
C. \( \begin{array}{l}605,321 \\ 3,506,212 \\ 650,312 \\ 3,652\end{array} \)
D. \( \begin{array}{l}3,506,212 \\ 650,312 \\ 605,321 \\ 3,652\end{array} \)

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:
Mixes up greater than and less than symbols

Question:
Which of the following shows " \( x \) is greater than \( 9 \) "?

Options:
A. \( x<9 \)
B. \( x \leq 9 \)
C. \( x>9 \)
D. \( x \geq 9 \)

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:
When using inequality notation, thinks "greater than/less than or equal to" symbols are instead the "greater than/less than" symbols and vice versa

Question:
Which of the following shows " \( x \) is greater than \( 9 \) "?

Options:
A. \( x<9 \)
B. \( x \leq 9 \)
C. \( x>9 \)
D. \( x \geq 9 \)

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:
Rounds up instead of down

Question:
Round this number to \( 1 \) significant figure:
\( 400099 \)

Options:
A. \( 400000 \)
B. \( 500000 \)
C. \( 400100 \)
D. \( 400099 \)

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:
Rounded to nearest 100 instead of 1sf

Question:
Round this number to \( 1 \) significant figure:
\( 400099 \)

Options:
A. \( 400000 \)
B. \( 500000 \)
C. \( 400100 \)
D. \( 400099 \)

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 the x variable when giving the equation of a horizontal line

Question:
What is the equation of this line? ![A graph of a horizontal line going through 3 on the y axis. ]()

Options:
A. \( y=3 x \)
B. \( y=3 \)
C. \( x=3 \)
D. \( x=3 y \)

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 x = ? is a horizontal line through ?

Question:
What is the equation of this line? ![A graph of a horizontal line going through 3 on the y axis. ]()

Options:
A. \( y=3 x \)
B. \( y=3 \)
C. \( x=3 \)
D. \( x=3 y \)

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 equation of a horizontal line is in the form x = ay, where a is the y intercept

Question:
What is the equation of this line? ![A graph of a horizontal line going through 3 on the y axis. ]()

Options:
A. \( y=3 x \)
B. \( y=3 \)
C. \( x=3 \)
D. \( x=3 y \)

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 first term of a sequence must be 1

Question:
What is the first term of the sequence given by this rule:
\[
2-7 n
\]

Options:
A. \( 1 \)
B. \( -7 \)
C. \( -5 \)
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:
When finding the nth term of a linear sequence, thinks the the first term is the coefficient in front of n.

Question:
What is the first term of the sequence given by this rule:
\[
2-7 n
\]

Options:
A. \( 1 \)
B. \( -7 \)
C. \( -5 \)
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:
When adding fractions, adds the numerators and denominators

Question:
Work out:
\(
\frac{4}{11}+\frac{7}{11}
\)
Write your answer in its simplest form.

Options:
A. \( \frac{11}{22} \)
B. \( \frac{1}{2} \)
C. \( \frac{11}{11} \)
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 adding fractions, adds the numerators and denominators

Question:
Work out:
\(
\frac{4}{11}+\frac{7}{11}
\)
Write your answer in its simplest form.

Options:
A. \( \frac{11}{22} \)
B. \( \frac{1}{2} \)
C. \( \frac{11}{11} \)
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:
Forgot to simplify the fraction

Question:
Work out:
\(
\frac{4}{11}+\frac{7}{11}
\)
Write your answer in its simplest form.

Options:
A. \( \frac{11}{22} \)
B. \( \frac{1}{2} \)
C. \( \frac{11}{11} \)
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:
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
\(x^{2}+4 x-1=-6\) ![A set of axes with the quadratic graph y=x^2+4x-1 drawn on.]()

Options:
A. \( x=4.25, \quad x=-0.25 \)
B. No real solutions
C. \( x=-4.25, \quad x=0.25 \)
D. \( x=-1 \)

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:
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
\(x^{2}+4 x-1=-6\) ![A set of axes with the quadratic graph y=x^2+4x-1 drawn on.]()

Options:
A. \( x=4.25, \quad x=-0.25 \)
B. No real solutions
C. \( x=-4.25, \quad x=0.25 \)
D. \( x=-1 \)

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:
Thinks depth always goes front to back in a diagram of a 3D shape

Question:
![A triangular based prism]() Tom likes to remember:

Volume of a prism = Area of cross section \( X \) depth

In this shape, what length is the "depth"?

Options:
A. \( 5 \mathrm{~mm} \)
B. \( 7 \mathrm{~mm} \)
C. \( 10 \mathrm{~mm} \)
D. \( 15 \mathrm{~mm} \)

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 first term of a sequence must be 1

Question:
What is the first term of the sequence given by this rule:
\[
1-5 n
\]

Options:
A. \( 1 \)
B. \( -5 \)
C. \( 6 \)
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 finding the nth term of a linear sequence, thinks the the first term is the coefficient in front of n.

Question:
What is the first term of the sequence given by this rule:
\[
1-5 n
\]

Options:
A. \( 1 \)
B. \( -5 \)
C. \( 6 \)
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:
Assumes that opposite angles are equal in a quadrilateral

Question:
What is the size of angle \( p \) in this quadrilateral? ![Not drawn to scale]()

Options:
A. \( 120^{\circ} \)
B. \( 50^{\circ} \)
C. \( 70^{\circ} \)
D. Not enough information to work it out

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 what dashes on the sides of shapes mean

Question:
What is the size of angle \( p \) in this quadrilateral? ![Not drawn to scale]()

Options:
A. \( 120^{\circ} \)
B. \( 50^{\circ} \)
C. \( 70^{\circ} \)
D. Not enough information to work it out

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 what dashes on the sides of shapes mean

Question:
What is the size of angle \( p \) in this quadrilateral? ![Not drawn to scale]()

Options:
A. \( 120^{\circ} \)
B. \( 50^{\circ} \)
C. \( 70^{\circ} \)
D. Not enough information to work it out

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 a quadratic must be in the form ax^2+bx+c=0 to be factorised

Question:
What would be the most useful first step if we wanted to solve the following quadratic equation? \( x^{2}+7 x=8 \)

Options:
A. Divide by \( x \)
B. Square root both sides of the equation
C. Subtract \( 7 x \) from both sides of the equation
D. Subtract \( 8 \) from both sides of the equation

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 a quadratic must be in the form ax^2+bx+c=0 to be factorised

Question:
What would be the most useful first step if we wanted to solve the following quadratic equation? \( x^{2}+7 x=8 \)

Options:
A. Divide by \( x \)
B. Square root both sides of the equation
C. Subtract \( 7 x \) from both sides of the equation
D. Subtract \( 8 \) from both sides of the equation

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 a quadratic must be in the form ax^2+bx+c=0 to be factorised

Question:
What would be the most useful first step if we wanted to solve the following quadratic equation? \( x^{2}+7 x=8 \)

Options:
A. Divide by \( x \)
B. Square root both sides of the equation
C. Subtract \( 7 x \) from both sides of the equation
D. Subtract \( 8 \) from both sides of the equation

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 fully simplify ratio

Question:
Write the following ratio in its simplest form so both sides of the ratio are integers:
\(
\frac{1}{4}: \frac{1}{2}
\)

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

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:
Forgets to swap the sign of roots when placing into brackets

Question:
What is the equation of this curve? ![A quadratic curve with minimum point (1,0).]()

Options:
A. \( y=(x-1)^{2} \)
B. \( y=(x+1)^{2} \)
C. \( y=x^{2}-1 \)
D. \( y=x^{2}+1 \)

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 the graph of x squared + c has the turning point of (-c, 0)

Question:
What is the equation of this curve? ![A quadratic curve with minimum point (1,0).]()

Options:
A. \( y=(x-1)^{2} \)
B. \( y=(x+1)^{2} \)
C. \( y=x^{2}-1 \)
D. \( y=x^{2}+1 \)

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 the graph of x squared + c has the turning point of (c, 0)

Question:
What is the equation of this curve? ![A quadratic curve with minimum point (1,0).]()

Options:
A. \( y=(x-1)^{2} \)
B. \( y=(x+1)^{2} \)
C. \( y=x^{2}-1 \)
D. \( y=x^{2}+1 \)

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:
Does not understand the term quadratic

Question:
Tom and Katie are discussing quadratic sequences.

Tom says this is a quadratic sequence: \( 24,15,8,3,0 \ldots \)

Katie says this is a quadratic sequence: \( 124,63,26,7,3,0, \ldots \)

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 term quadratic

Question:
Tom and Katie are discussing quadratic sequences.

Tom says this is a quadratic sequence: \( 24,15,8,3,0 \ldots \)

Katie says this is a quadratic sequence: \( 124,63,26,7,3,0, \ldots \)

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:
Thinks a decreasing sequence cannot be quadratic

Question:
Tom and Katie are discussing quadratic sequences.

Tom says this is a quadratic sequence: \( 24,15,8,3,0 \ldots \)

Katie says this is a quadratic sequence: \( 124,63,26,7,3,0, \ldots \)

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:
In ratio question where the difference between the sides is given, uses that as the total for one side instead

Question:
Percy, Quentin and Robbie share gold coins in the ratio of
\[
3: 7: 8
\]
Percy gets \( 36 \) fewer coins than Quentin.
How many gold coins did Robbie get?

Options:
A. \( 96 \)
B. \( 72 \)
C. \( 12 \)
D. \( 63 \)

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:
In ratio question where the difference between the sides is given, uses that as the total

Question:
Percy, Quentin and Robbie share gold coins in the ratio of
\[
3: 7: 8
\]
Percy gets \( 36 \) fewer coins than Quentin.
How many gold coins did Robbie get?

Options:
A. \( 96 \)
B. \( 72 \)
C. \( 12 \)
D. \( 63 \)

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 sides of a ratio

Question:
Percy, Quentin and Robbie share gold coins in the ratio of
\[
3: 7: 8
\]
Percy gets \( 36 \) fewer coins than Quentin.
How many gold coins did Robbie get?

Options:
A. \( 96 \)
B. \( 72 \)
C. \( 12 \)
D. \( 63 \)

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 the smallest digit from the largest digit

Question:
Tom and Katie are arguing about a first step to solve this equation:
\(4 v+1=9 v-3\)

Tom says you can write: \( 5 v+1=-3 \)

Katie says you can write: \( 4 v+4=9 v \)

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:
Subtracts the smallest digit from the largest digit

Question:
Tom and Katie are arguing about a first step to solve this equation:
\(4 v+1=9 v-3\)

Tom says you can write: \( 5 v+1=-3 \)

Katie says you can write: \( 4 v+4=9 v \)

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:
Confuses alternate and opposite angles

Question:
Which of the following correctly describes the relationship between the two marked angles? ![A diagram showing 3 lines crossing at a point to form 6 angles. Two angles are marked in orange, there are two unmarked angles between them on either side.]()

Options:
A. Alternate angles
B. Corresponding angles
C. Vertically opposite angles
D. Angles on a straight line

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 corresponding and vertically opposite angles

Question:
Which of the following correctly describes the relationship between the two marked angles? ![A diagram showing 3 lines crossing at a point to form 6 angles. Two angles are marked in orange, there are two unmarked angles between them on either side.]()

Options:
A. Alternate angles
B. Corresponding angles
C. Vertically opposite angles
D. Angles on a straight line

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 with angles on a straight line

Question:
Which of the following correctly describes the relationship between the two marked angles? ![A diagram showing 3 lines crossing at a point to form 6 angles. Two angles are marked in orange, there are two unmarked angles between them on either side.]()

Options:
A. Alternate angles
B. Corresponding angles
C. Vertically opposite angles
D. Angles on a straight line

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 graph of
\(y=0.4 x-3\) ![A set of axes with the graph y=0.4x-3 drawn on.]() Use the graph to solve
\(0.4 x-3=-1\)

Options:
A. \( x=-3.3 \)
B. \( x=7.5 \)
C. \( x=-1 \)
D. \( x=5 \)

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 solution to mx + c = a is the x intercept of y = mx +c

Question:
This is a graph of
\(y=0.4 x-3\) ![A set of axes with the graph y=0.4x-3 drawn on.]() Use the graph to solve
\(0.4 x-3=-1\)

Options:
A. \( x=-3.3 \)
B. \( x=7.5 \)
C. \( x=-1 \)
D. \( x=5 \)

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 solution of mx + c = a is x =a

Question:
This is a graph of
\(y=0.4 x-3\) ![A set of axes with the graph y=0.4x-3 drawn on.]() Use the graph to solve
\(0.4 x-3=-1\)

Options:
A. \( x=-3.3 \)
B. \( x=7.5 \)
C. \( x=-1 \)
D. \( x=5 \)

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:
When given the perimeter of a regular polygon, multiplies instead of divides to find each side length

Question:
A regular pentagon has a total perimeter of \( 17 \mathrm{~cm} \).
What is the length of each of its sides?

Options:
A. \( 85 \mathrm{~cm} \)
B. \( 12 \mathrm{~cm} \)
C. \( 3.4 \mathrm{~cm} \)
D. Not enough information

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 given the perimeter of a regular polygon, subtracts instead of divides to find each side length

Question:
A regular pentagon has a total perimeter of \( 17 \mathrm{~cm} \).
What is the length of each of its sides?

Options:
A. \( 85 \mathrm{~cm} \)
B. \( 12 \mathrm{~cm} \)
C. \( 3.4 \mathrm{~cm} \)
D. Not enough information

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 regular

Question:
A regular pentagon has a total perimeter of \( 17 \mathrm{~cm} \).
What is the length of each of its sides?

Options:
A. \( 85 \mathrm{~cm} \)
B. \( 12 \mathrm{~cm} \)
C. \( 3.4 \mathrm{~cm} \)
D. Not enough information

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:
Reads the complement of what is required from a pie chart

Question:
This pie chart shows the colour of hats that Tom owns. ![Pie chart showing the colour of Tom's hats. Blue is 90 degrees. Yellow is approximately 195 degrees. Red is approximately 40 degrees and green approximately 35 degrees.]() What fraction of Tom's hats are not blue?

Options:
A. \( \frac{1}{4} \)
B. \( 75 \)
C. \( \frac{3}{4} \)
D. Impossible to say

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 percentage when asked for a fraction

Question:
This pie chart shows the colour of hats that Tom owns. ![Pie chart showing the colour of Tom's hats. Blue is 90 degrees. Yellow is approximately 195 degrees. Red is approximately 40 degrees and green approximately 35 degrees.]() What fraction of Tom's hats are not blue?

Options:
A. \( \frac{1}{4} \)
B. \( 75 \)
C. \( \frac{3}{4} \)
D. Impossible to say

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 square sign for right angle

Question:
This pie chart shows the colour of hats that Tom owns. ![Pie chart showing the colour of Tom's hats. Blue is 90 degrees. Yellow is approximately 195 degrees. Red is approximately 40 degrees and green approximately 35 degrees.]() What fraction of Tom's hats are not blue?

Options:
A. \( \frac{1}{4} \)
B. \( 75 \)
C. \( \frac{3}{4} \)
D. Impossible to say

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 percentage by writing the numerator followed by the denominator

Question:
What is \( 8 \) out of \( 40 \) as a percentage?

Options:
A. \( 8.4 \% \)
B. \( 20 \% \)
C. \( 16 \% \)
D. \( 24 \% \)

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:
Thinks they double the numerator to turn a fraction into a percentage

Question:
What is \( 8 \) out of \( 40 \) as a percentage?

Options:
A. \( 8.4 \% \)
B. \( 20 \% \)
C. \( 16 \% \)
D. \( 24 \% \)

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:
Makes an assumption about line segments being equal within a shape

Question:
What is value of \( p \) in this compound shape made with rectangles? ![Compound shape made of two rectangles with the sides labelled p (in red) cm, 15 cm, 12 cm, 7 cm and 7 cm. One side is unlabelled]()

Options:
A. \( 5 \mathrm{~cm} \)
B. \( 6 \mathrm{~cm} \)
C. \( 7 \mathrm{~cm} \)
D. Not enough information

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 line segments being equal within a shape

Question:
What is value of \( p \) in this compound shape made with rectangles? ![Compound shape made of two rectangles with the sides labelled p (in red) cm, 15 cm, 12 cm, 7 cm and 7 cm. One side is unlabelled]()

Options:
A. \( 5 \mathrm{~cm} \)
B. \( 6 \mathrm{~cm} \)
C. \( 7 \mathrm{~cm} \)
D. Not enough information

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 that we can use the conservation of perimeter to find missing lengths

Question:
What is value of \( p \) in this compound shape made with rectangles? ![Compound shape made of two rectangles with the sides labelled p (in red) cm, 15 cm, 12 cm, 7 cm and 7 cm. One side is unlabelled]()

Options:
A. \( 5 \mathrm{~cm} \)
B. \( 6 \mathrm{~cm} \)
C. \( 7 \mathrm{~cm} \)
D. Not enough information

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 the area of a parallelogram does not understand which lengths to use

Question:
What is the area of the parallelogram? ![A parallelogram with the length labelled 10cm, the slanted height labelled 4cm, and the perpendicular height (marked with a right angle) labelled 3cm]()

Options:
A. \( 120 \mathrm{~cm}^{2} \)
B. \( 40 \mathrm{~cm}^{2} \)
C. \( 30 \mathrm{~cm}^{2} \)
D. \( 15 \mathrm{~cm}^{2} \)

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:
Has used slant height and base to find area of a parallelogram rather than perpendicular height and base

Question:
What is the area of the parallelogram? ![A parallelogram with the length labelled 10cm, the slanted height labelled 4cm, and the perpendicular height (marked with a right angle) labelled 3cm]()

Options:
A. \( 120 \mathrm{~cm}^{2} \)
B. \( 40 \mathrm{~cm}^{2} \)
C. \( 30 \mathrm{~cm}^{2} \)
D. \( 15 \mathrm{~cm}^{2} \)

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:
Has found the area of a triangle rather than an area of a parallelogram

Question:
What is the area of the parallelogram? ![A parallelogram with the length labelled 10cm, the slanted height labelled 4cm, and the perpendicular height (marked with a right angle) labelled 3cm]()

Options:
A. \( 120 \mathrm{~cm}^{2} \)
B. \( 40 \mathrm{~cm}^{2} \)
C. \( 30 \mathrm{~cm}^{2} \)
D. \( 15 \mathrm{~cm}^{2} \)

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

Question:
A student wishes to solve the equation below.

Which of the following is a correct next step?
\(
(d-6)^{2}-16=0
\)

Step \( 1 \)
\(
(d-6)^{2}=16
\)

Options:
A. \( d^{2}=22 \)
B. \( d-6= \pm 4 \)
C. \( d-6=4 \)
D. \( d-3=8 \)

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:
Only considers the positive solution when calculating a square root

Question:
A student wishes to solve the equation below.

Which of the following is a correct next step?
\(
(d-6)^{2}-16=0
\)

Step \( 1 \)
\(
(d-6)^{2}=16
\)

Options:
A. \( d^{2}=22 \)
B. \( d-6= \pm 4 \)
C. \( d-6=4 \)
D. \( d-3=8 \)

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:
Mistakes lines as parallel

Question:
What is the size of angle \( p \) ? ![3 intersecting lines. Towards the top of the image two of the lines intersect and at this point there are two marked angles, 138 degrees and 42 degrees. The angle opposite the 42 degree angle is marked p]()

Options:
A. \( 53^{\circ} \)
B. \( 42^{\circ} \)
C. \( 138^{\circ} \)
D. Not enough information

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 any two angles along a straight line are equal

Question:
What is the size of angle \( p \) ? ![3 intersecting lines. Towards the top of the image two of the lines intersect and at this point there are two marked angles, 138 degrees and 42 degrees. The angle opposite the 42 degree angle is marked p]()

Options:
A. \( 53^{\circ} \)
B. \( 42^{\circ} \)
C. \( 138^{\circ} \)
D. Not enough information

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 that vertically opposite angles are equal

Question:
What is the size of angle \( p \) ? ![3 intersecting lines. Towards the top of the image two of the lines intersect and at this point there are two marked angles, 138 degrees and 42 degrees. The angle opposite the 42 degree angle is marked p]()

Options:
A. \( 53^{\circ} \)
B. \( 42^{\circ} \)
C. \( 138^{\circ} \)
D. Not enough information

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 angle on a pie chart is the frequency multiplied by 10

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  & \( 7 \) & \(  \) \\
\hline 1  & \(  \) & \( 144 \degree \) \\
\hline 2  & \(  \) & \(  \) \\
\hline 3  & \( 4 \) & \( \bigstar \) \\
\hline 4 or more  & \(  \) & \(  \) \\
\hline  TOTAL  & 30  & \(  \) \\
\end{tabular} Jenny wants to draw a pie chart of the information.
What should replace the star?

Options:
A. \( 40^{\circ} \)
B. \( 48^{\circ} \)
C. \( 120^{\circ} \)
D. Not enough information

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  & \( 7 \) & \(  \) \\
\hline 1  & \(  \) & \( 144 \degree \) \\
\hline 2  & \(  \) & \(  \) \\
\hline 3  & \( 4 \) & \( \bigstar \) \\
\hline 4 or more  & \(  \) & \(  \) \\
\hline  TOTAL  & 30  & \(  \) \\
\end{tabular} Jenny wants to draw a pie chart of the information.
What should replace the star?

Options:
A. \( 40^{\circ} \)
B. \( 48^{\circ} \)
C. \( 120^{\circ} \)
D. Not enough information

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 dividing an integer by a fraction, thinks they multiply numerator and denominator by the integer

Question:
How many times does \( \frac{3}{5} \) go into \( 15 \) ?

Options:
A. \( \frac{45}{75} \)
B. \( 75 \)
C. \( 9 \)
D. \( 25 \)

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 dividing by a non unit fraction, thinks you multiply by the reciprocal of the corresponding unit fraction rather than the fraction given.

Question:
How many times does \( \frac{3}{5} \) go into \( 15 \) ?

Options:
A. \( \frac{45}{75} \)
B. \( 75 \)
C. \( 9 \)
D. \( 25 \)

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 dividing a fraction by an integer, multiplies the numerator by the integer

Question:
How many times does \( \frac{3}{5} \) go into \( 15 \) ?

Options:
A. \( \frac{45}{75} \)
B. \( 75 \)
C. \( 9 \)
D. \( 25 \)

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 multiplying when expanding bracket

Question:
John is expanding these two brackets.

What should he get when he multiplies the two terms indicated by the arrows? ![The two brackets are (x+5)(x-3). The arrows are pointing at the +5 in the first bracket and the -3 in the second bracket.]()

Options:
A. \( +2 \)
B. \( -15 \)
C. \( -8 \)
D. \( +15 \)

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:
Ignores negative sign when expanding bracket

Question:
John is expanding these two brackets.

What should he get when he multiplies the two terms indicated by the arrows? ![The two brackets are (x+5)(x-3). The arrows are pointing at the +5 in the first bracket and the -3 in the second bracket.]()

Options:
A. \( +2 \)
B. \( -15 \)
C. \( -8 \)
D. \( +15 \)

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 simultaneous equations graphically, they think the solutions are the x-intercepts

Question:
Tom and Katie are discussing quadratic graphs.

Tom says a quadratic expression that cannot be factorised will not intercept the \( x \) axis.

Katie says a graph of a quadratic that does not intercept the \( x \) axis cannot be factorised.
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 solving simultaneous equations graphically, they think the solutions are the x-intercepts

Question:
Tom and Katie are discussing quadratic graphs.

Tom says a quadratic expression that cannot be factorised will not intercept the \( x \) axis.

Katie says a graph of a quadratic that does not intercept the \( x \) axis cannot be factorised.
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 reading value from graph, reads from the wrong axes.

Question:
This is a conversion graph between kilograms and pounds.

Which of the following is the best estimate for the number of kilograms equivalent to \( 20 \) pounds? ![A graph on gridded paper with pounds (lb) on the y axis from 0 to 80 and kilograms (kg) on the x axis from 0 to 80. Both axis are labelled in increments of 20, with each increment split by gridlines into another 4 squares. A straight line goes from the origin and sloped upwards going through (25, 55) (not labelled - just a coordinate that it goes through) ]()

Options:
A. \( 9 \) kilograms
B. \( 19 \) kilograms
C. \( 44 \) kilograms
D. \( 50 \) kilograms

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 regular

Question:
Which quadrilateral below is a regular polygon?

Options:
A. ![Trapezium]()
B. ![Rhombus]()
C. ![Rectangle]()
D. ![Square]()

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 regular

Question:
Which quadrilateral below is a regular polygon?

Options:
A. ![Trapezium]()
B. ![Rhombus]()
C. ![Rectangle]()
D. ![Square]()

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 regular

Question:
Which quadrilateral below is a regular polygon?

Options:
A. ![Trapezium]()
B. ![Rhombus]()
C. ![Rectangle]()
D. ![Square]()

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 bar means subtract rather than divide

Question:
Which calculation is equivalent to the fraction \( \frac{3}{4} \) ?

Options:
A. \( 3-4 \)
B. \( 3 \div 4 \)
C. \( 4-3 \)
D. \( 4 \div 3 \)

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 the fraction bar means subtract rather than divide

Question:
Which calculation is equivalent to the fraction \( \frac{3}{4} \) ?

Options:
A. \( 3-4 \)
B. \( 3 \div 4 \)
C. \( 4-3 \)
D. \( 4 \div 3 \)

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

Question:
Which calculation is equivalent to the fraction \( \frac{3}{4} \) ?

Options:
A. \( 3-4 \)
B. \( 3 \div 4 \)
C. \( 4-3 \)
D. \( 4 \div 3 \)

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 realise that subtracting a negative is the same as adding it's additive inverse

Question:
Expand and simplify:
\[
4(2 x+1)-(5 x-9)
\]

Options:
A. \( 3 x-5 \)
B. \( 3 x+13 \)
C. \( 13 x-5 \)
D. \( 13 x+13 \)

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:
Expand and simplify:
\[
4(2 x+1)-(5 x-9)
\]

Options:
A. \( 3 x-5 \)
B. \( 3 x+13 \)
C. \( 13 x-5 \)
D. \( 13 x+13 \)

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 multiplying a positive by a negative gives a positive answer

Question:
When you multiply out the brackets and simplify, what replaces the triangle?
\(
m(m+5)(m-5) \equiv m^{3} \bigstar \ m^{2} \triangle \ m \bigcirc
\)

Options:
A. \( \triangle=-25 \)
B. \( \triangle=+25 \)
C. \( \triangle=+5 \)
D. \(
\triangle=+0
\)
(no \( m \) term)

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 out 2 or more brackets, does not multiply all the combinations of terms

Question:
When you multiply out the brackets and simplify, what replaces the triangle?
\(
m(m+5)(m-5) \equiv m^{3} \bigstar \ m^{2} \triangle \ m \bigcirc
\)

Options:
A. \( \triangle=-25 \)
B. \( \triangle=+25 \)
C. \( \triangle=+5 \)
D. \(
\triangle=+0
\)
(no \( m \) term)

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 constant in an expanded quadratic comes from adding the two numbers in the brackets

Question:
When you multiply out the brackets and simplify, what replaces the triangle?
\(
m(m+5)(m-5) \equiv m^{3} \bigstar \ m^{2} \triangle \ m \bigcirc
\)

Options:
A. \( \triangle=-25 \)
B. \( \triangle=+25 \)
C. \( \triangle=+5 \)
D. \(
\triangle=+0
\)
(no \( m \) term)

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 a negative x value in a column vector means to move right rather than left

Question:
Three left and five down in vector notation is... \( \left(\begin{array}{c}\triangle \\ \bigcirc\end{array}\right) \) What should replace the \( \triangle \) ?

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

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:
Thinks the movement of the top number in a column vector is vertical, and the bottom number is horizontal rather than the other way round

Question:
Three left and five down in vector notation is... \( \left(\begin{array}{c}\triangle \\ \bigcirc\end{array}\right) \) What should replace the \( \triangle \) ?

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

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:
When solving a problem that requires an inverse operation (e.g. missing number problems), does the original operation

Question:
\( \frac{3}{5} \times ?=\frac{1}{2} \)

Options:
A. \( \frac{2}{3} \)
B. \( \frac{5}{6} \)
C. \( \frac{3}{10} \)
D. There are no values that make this calculation work

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 that division can be used to find the missing value in a multiplication problem

Question:
\( \frac{3}{5} \times ?=\frac{1}{2} \)

Options:
A. \( \frac{2}{3} \)
B. \( \frac{5}{6} \)
C. \( \frac{3}{10} \)
D. There are no values that make this calculation work

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 a difference of one part in a ratio means the quantities will differ by one unit

Question:
To make pink paint, you mix red paint with white paint in the ratio \( 3: 4 \).
What should replace the star? ![Red, White, Total | 1200 ml, Star, Blank]()

Options:
A. \( 1201 \ \mathrm{ml} \)
B. \( 900 \ \mathrm{ml} \)
C. \( 4800 \ \mathrm{ml} \)
D. \( 1600 \ \mathrm{ml} \)

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 sides of a ratio

Question:
To make pink paint, you mix red paint with white paint in the ratio \( 3: 4 \).
What should replace the star? ![Red, White, Total | 1200 ml, Star, Blank]()

Options:
A. \( 1201 \ \mathrm{ml} \)
B. \( 900 \ \mathrm{ml} \)
C. \( 4800 \ \mathrm{ml} \)
D. \( 1600 \ \mathrm{ml} \)

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:
In ratio question where one side of ratio is given, uses that as one part in ratio without dividing

Question:
To make pink paint, you mix red paint with white paint in the ratio \( 3: 4 \).
What should replace the star? ![Red, White, Total | 1200 ml, Star, Blank]()

Options:
A. \( 1201 \ \mathrm{ml} \)
B. \( 900 \ \mathrm{ml} \)
C. \( 4800 \ \mathrm{ml} \)
D. \( 1600 \ \mathrm{ml} \)

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 convert measurements to have the same units before calculating area or volume

Question:
What should replace the star to calculate the area of this trapezium?
 Area \( =\frac{90+40}{2} \times \) \(\color{gold}\bigstar\)
 ![Trapezium with parallel sides of lengths 90mm and 40mm. The length of one slanted side is 6cm and the perpendicular height is 5cm.]()

Options:
A. \( 5 \)
B. \( 50 \)
C. \( 6 \)
D. \( 60 \)

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 slant height instead of perpendicular height to find area of a trapezium

Question:
What should replace the star to calculate the area of this trapezium?
 Area \( =\frac{90+40}{2} \times \) \(\color{gold}\bigstar\)
 ![Trapezium with parallel sides of lengths 90mm and 40mm. The length of one slanted side is 6cm and the perpendicular height is 5cm.]()

Options:
A. \( 5 \)
B. \( 50 \)
C. \( 6 \)
D. \( 60 \)

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 slant height instead of perpendicular height to find area of a trapezium

Question:
What should replace the star to calculate the area of this trapezium?
 Area \( =\frac{90+40}{2} \times \) \(\color{gold}\bigstar\)
 ![Trapezium with parallel sides of lengths 90mm and 40mm. The length of one slanted side is 6cm and the perpendicular height is 5cm.]()

Options:
A. \( 5 \)
B. \( 50 \)
C. \( 6 \)
D. \( 60 \)

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 multiplying two negatives gives a negative answer

Question:
Tom and Katie are trying to write different calculations for the diagram on the left.
Tom writes: \( -3 \times(-8)=-24 \)
Katie writes: \( \frac{(-24)}{-3}=-8 \)
Who is correct? ![A diagram showing an arrow to the left, marked with a value of -24. Underneath this arrow there is a smaller arrow, still pointing to the left, that is a third of the length of the larger arrow]()

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 dividing a negative by a negative gives a negative answer

Question:
Tom and Katie are trying to write different calculations for the diagram on the left.
Tom writes: \( -3 \times(-8)=-24 \)
Katie writes: \( \frac{(-24)}{-3}=-8 \)
Who is correct? ![A diagram showing an arrow to the left, marked with a value of -24. Underneath this arrow there is a smaller arrow, still pointing to the left, that is a third of the length of the larger arrow]()

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 convert measurements to have the same units before calculating area or volume

Question:
Square \( \mathrm{P} \) has an area of \( 4 \mathrm{~cm}^{2} \)
Square \( Q \) has an area of \( 4 \mathrm{~mm}^{2} \)
What is the total area of squares \( P \) and \( Q \) in \( \mathrm{mm}^{2} \) ?

Options:
A. \( 8 \mathrm{~mm}^{2} \)
B. \( 44 \mathrm{~mm}^{2} \)
C. \( 404 \mathrm{~mm}^{2} \)
D. \( 40004 \mathrm{~mm}^{2} \)

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 square the conversion factor when converting squared units

Question:
Square \( \mathrm{P} \) has an area of \( 4 \mathrm{~cm}^{2} \)
Square \( Q \) has an area of \( 4 \mathrm{~mm}^{2} \)
What is the total area of squares \( P \) and \( Q \) in \( \mathrm{mm}^{2} \) ?

Options:
A. \( 8 \mathrm{~mm}^{2} \)
B. \( 44 \mathrm{~mm}^{2} \)
C. \( 404 \mathrm{~mm}^{2} \)
D. \( 40004 \mathrm{~mm}^{2} \)

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 there are 100mm in a centimetre

Question:
Square \( \mathrm{P} \) has an area of \( 4 \mathrm{~cm}^{2} \)
Square \( Q \) has an area of \( 4 \mathrm{~mm}^{2} \)
What is the total area of squares \( P \) and \( Q \) in \( \mathrm{mm}^{2} \) ?

Options:
A. \( 8 \mathrm{~mm}^{2} \)
B. \( 44 \mathrm{~mm}^{2} \)
C. \( 404 \mathrm{~mm}^{2} \)
D. \( 40004 \mathrm{~mm}^{2} \)

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:
Believes that the coefficient of x represents the gradient even when a line is not in the form y = mx+c

Question:
What is the gradient of this line?
\(5 x+3 y=15\)

Options:
A. \( 5 \)
B. \( -5 \)
C. \( \frac{5}{3} \)
D. \( -\frac{5}{3} \)

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 solving an equation, believes that when they get to ax = b, b is the solution

Question:
What is the gradient of this line?
\(5 x+3 y=15\)

Options:
A. \( 5 \)
B. \( -5 \)
C. \( \frac{5}{3} \)
D. \( -\frac{5}{3} \)

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 solving an equation, uses the same operation rather than the inverse.

Question:
What is the gradient of this line?
\(5 x+3 y=15\)

Options:
A. \( 5 \)
B. \( -5 \)
C. \( \frac{5}{3} \)
D. \( -\frac{5}{3} \)

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 a lower average means the data is more consistent

Question:
The table shows the summary statistics from some girls and boys who took a test.
Who performed the most consistently? ![\begin{tabular}{|c|c|c|}
\hline Gender & Mean & Range \\
\hline Girls & \( 75 \) & \( 20 \) \\
\hline Boys & \( 60 \) & \( 40 \) \\
\hline
\end{tabular}]()

Options:
A. The girls because their range is lower
B. The boys because their mean is lower
C. The boys because their range is higher
D. The girls because their mean is higher

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 a greater range means more consistent data

Question:
The table shows the summary statistics from some girls and boys who took a test.
Who performed the most consistently? ![\begin{tabular}{|c|c|c|}
\hline Gender & Mean & Range \\
\hline Girls & \( 75 \) & \( 20 \) \\
\hline Boys & \( 60 \) & \( 40 \) \\
\hline
\end{tabular}]()

Options:
A. The girls because their range is lower
B. The boys because their mean is lower
C. The boys because their range is higher
D. The girls because their mean is higher

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 a higher average means more consistent data

Question:
The table shows the summary statistics from some girls and boys who took a test.
Who performed the most consistently? ![\begin{tabular}{|c|c|c|}
\hline Gender & Mean & Range \\
\hline Girls & \( 75 \) & \( 20 \) \\
\hline Boys & \( 60 \) & \( 40 \) \\
\hline
\end{tabular}]()

Options:
A. The girls because their range is lower
B. The boys because their mean is lower
C. The boys because their range is higher
D. The girls because their mean is higher

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 two lines of the same length are parallel

Question:
Tom and Katie are discussing parallel lines. Tom says these two lines are parallel ![Image of a grid of squares with 2 lines on it. One line goes two squares to the right and one square up. The second line goes four squares to the right and two squares up.]() Katie says these two lines are parallel ![Image of a grid of squares with 2 lines on it. One line goes two squares to the right and one square up. The second line goes two squares to the right and one square down.]() 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 subtracting a negative thinks the answer must be negative

Question:
What number belongs in the box?
\(
(-8)-(-5)=
\square\)

Options:
A. \( -13 \)
B. \( 13 \)
C. \( 3 \)
D. \( -3 \)

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 subtracting from a negative thinks the answer must be positive

Question:
What number belongs in the box?
\(
(-8)-(-5)=
\square\)

Options:
A. \( -13 \)
B. \( 13 \)
C. \( 3 \)
D. \( -3 \)

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 subtracting from a negative thinks the answer must be positive

Question:
What number belongs in the box?
\(
(-8)-(-5)=
\square\)

Options:
A. \( -13 \)
B. \( 13 \)
C. \( 3 \)
D. \( -3 \)

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:
Ignores negative sign when expanding bracket

Question:
On what line is the first mistake when proving \( (n+1)^{2}-(n-1)^{2} \) is divisible by \( 4 \) ? \( n^{2}+2 n+1-\left(n^{2}-2 n+1\right) \quad \) Line \( 1 \) \( n^{2}+2 n+1-n^{2}-2 n+1 \quad \) Line \( 2 \) \[
2
\]

Line \( 3 \)

Options:
A. Line \( 1 \)
B. Line \( 2 \)
C. Line \( 3 \)
D. Everything 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 an incorrect side length when splitting a composite shape into parts

Question:
What is the area of the shaded section of this composite shape made from rectangles? ![A composite shape made from two rectangles that form an "L" shape.  The base of the shape is horizontal and is 13cm long. The vertical height of the whole shape is 14cm. The horizontal width of the top part of the shape is 6cm. The vertical height of the top rectangle is 8cm. The right handed rectangle is shaded blue]()

Options:
A. \( 48 \mathrm{~cm}^{2} \)
B. \( 104 \mathrm{~cm}^{2} \)
C. \( 42 \mathrm{~cm}^{2} \)
D. \( 56 \mathrm{~cm}^{2} \)

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:
Uses an incorrect side length when splitting a composite shape into parts

Question:
What is the area of the shaded section of this composite shape made from rectangles? ![A composite shape made from two rectangles that form an "L" shape.  The base of the shape is horizontal and is 13cm long. The vertical height of the whole shape is 14cm. The horizontal width of the top part of the shape is 6cm. The vertical height of the top rectangle is 8cm. The right handed rectangle is shaded blue]()

Options:
A. \( 48 \mathrm{~cm}^{2} \)
B. \( 104 \mathrm{~cm}^{2} \)
C. \( 42 \mathrm{~cm}^{2} \)
D. \( 56 \mathrm{~cm}^{2} \)

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:
Uses an incorrect side length when splitting a composite shape into parts

Question:
What is the area of the shaded section of this composite shape made from rectangles? ![A composite shape made from two rectangles that form an "L" shape.  The base of the shape is horizontal and is 13cm long. The vertical height of the whole shape is 14cm. The horizontal width of the top part of the shape is 6cm. The vertical height of the top rectangle is 8cm. The right handed rectangle is shaded blue]()

Options:
A. \( 48 \mathrm{~cm}^{2} \)
B. \( 104 \mathrm{~cm}^{2} \)
C. \( 42 \mathrm{~cm}^{2} \)
D. \( 56 \mathrm{~cm}^{2} \)

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:
Believes that the coefficient of x represents the gradient even when a line is not in the form y = mx+c

Question:
In which region would \( x+y=1 \) belong? ![A Venn diagram with two intersecting sets. The set on the right is 'Crosses the y-axis at (0,1)' and the set of the right is 'Has a positive gradient'. A is in the 'Crosses the y-axis at (0,1)' set only, B is in the intersection, C is in the 'Has a positive gradient' only and D is outside both sets.]()

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:
Does not follow the arrows through a function machine, changes the order of the operations asked.

Question:
Jo and Paul are arguing about the result of this Function Machine:
Jo says the output is: \( \frac{n}{5}+3 \)
Paul says the output is: \( \frac{n+3}{5} \)
Who is correct? ![A function machine showing an input of n and operations divide by 5 and add 3]()

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:
Does not follow the arrows through a function machine, changes the order of the operations asked.

Question:
Jo and Paul are arguing about the result of this Function Machine:
Jo says the output is: \( \frac{n}{5}+3 \)
Paul says the output is: \( \frac{n+3}{5} \)
Who is correct? ![A function machine showing an input of n and operations divide by 5 and add 3]()

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:
Thinks the fraction bar means subtract rather than divide

Question:
When \( h=10 \)
\(
\frac{h}{2}=
\)

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

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 dividing two positives will give a negative answer

Question:
When \( h=10 \)
\(
\frac{h}{2}=
\)

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

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:
When finding the differences between terms in a sequence, believes they can do so from right to left

Question:
\(
6,14,28,48,74, \ldots
\)

When calculating the nth-term rule of this sequence, what should replace the triangle?

nth-term rule: \( 3 n^{2} \)\( \color{red}\triangle \)  \(n\) \( \color{purple}\square \)

Options:
A. \[
+1
\]
(or just a + sign)
B. \( -1 \)
(or just a - sign)
C. \( +3 \)
D. \( -3 \)

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 finding the nth term rule for a quadratic sequence, believes they only need to use the first term to calculate the coefficient of n

Question:
\(
6,14,28,48,74, \ldots
\)

When calculating the nth-term rule of this sequence, what should replace the triangle?

nth-term rule: \( 3 n^{2} \)\( \color{red}\triangle \)  \(n\) \( \color{purple}\square \)

Options:
A. \[
+1
\]
(or just a + sign)
B. \( -1 \)
(or just a - sign)
C. \( +3 \)
D. \( -3 \)

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 adding an integer to a fraction, thinks you add the integer to the numerator

Question:
Solve the equation:
\(
p-5=\frac{1}{10}
\)

Options:
A. \( p=\frac{6}{15} \)
B. \( p=\frac{6}{10} \)
C. \( p=\frac{51}{10} \)
D. \( p=\frac{5}{50} \)

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, multiplies instead of adding

Question:
Solve the equation:
\(
p-5=\frac{1}{10}
\)

Options:
A. \( p=\frac{6}{15} \)
B. \( p=\frac{6}{10} \)
C. \( p=\frac{51}{10} \)
D. \( p=\frac{5}{50} \)

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 can multiply/divide through by a negative number without changing the direction of the inequality

Question:
Tom and Katie are arguing about solving inequalities.
Tom says \( -2 m>12 \) gives \( m>-6 \)
Katie says \( -2+m>12 \) gives \( m>14 \)
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 recognise that interior and exterior angles are supplementary

Question:
Tom and Katie are discussing how to calculate the size of each interior angle in a regular \( 20 \) sided shape

Tom says you can do \( \frac{18 \times 180}{20} \)

Katie says you can do \( 180-\frac{360}{20} \)

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 only way to find the interior angle of a regular polygon is to subtract the exterior angle from 180.

Question:
Tom and Katie are discussing how to calculate the size of each interior angle in a regular \( 20 \) sided shape

Tom says you can do \( \frac{18 \times 180}{20} \)

Katie says you can do \( 180-\frac{360}{20} \)

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:
Counts leading zero as a significant figure

Question:
\(
0.095643
\)

What is this number rounded to \( 1 \) significant figure?

Options:
A. \( 0 \)
B. \( 0.09 \)
C. \( 0.01 \)
D. \( 0.1 \)

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:
Rounds down instead of up when next digit is 5

Question:
\(
0.095643
\)

What is this number rounded to \( 1 \) significant figure?

Options:
A. \( 0 \)
B. \( 0.09 \)
C. \( 0.01 \)
D. \( 0.1 \)

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 rounding up from a 9, does not add one on to the digit to the left

Question:
\(
0.095643
\)

What is this number rounded to \( 1 \) significant figure?

Options:
A. \( 0 \)
B. \( 0.09 \)
C. \( 0.01 \)
D. \( 0.1 \)

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:
Identifies the wrong part of a fraction model as the whole

Question:
Complete the missing value. ![A circle with two other circles below it, connected to the top circle by lines. The top circle has 60% in, one of the bottom circles has 2/5, and the other is blank.]()

Options:
A. \( 100 \% \)
B. \( 60 \% \)
C. \( \frac{2}{10} \)
D. \( 0.4 \)

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:
Believes to complete a part whole model you select a value already given in the model

Question:
Complete the missing value. ![A circle with two other circles below it, connected to the top circle by lines. The top circle has 60% in, one of the bottom circles has 2/5, and the other is blank.]()

Options:
A. \( 100 \% \)
B. \( 60 \% \)
C. \( \frac{2}{10} \)
D. \( 0.4 \)

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:
Believes to complete a part whole model you select a value already given in the model

Question:
Complete the missing value. ![A circle with two other circles below it, connected to the top circle by lines. The top circle has 60% in, one of the bottom circles has 2/5, and the other is blank.]()

Options:
A. \( 100 \% \)
B. \( 60 \% \)
C. \( \frac{2}{10} \)
D. \( 0.4 \)

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:
Believes multiplying two negatives gives a negative answer

Question:
The product of two numbers is \( -24 \).
What could the two numbers be?

Options:
A. \( -3 \) and \( -8 \)
B. \( -4 \) and \( 6 \)
C. \( -10 \) and \( -14 \)
D. \( -3 \) and \( 9 \)

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 product means add rather than multiply

Question:
The product of two numbers is \( -24 \).
What could the two numbers be?

Options:
A. \( -3 \) and \( -8 \)
B. \( -4 \) and \( 6 \)
C. \( -10 \) and \( -14 \)
D. \( -3 \) and \( 9 \)

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

Question:
Tom is has correctly drawn the graph of the following function:
\(
y=\left\{\begin{array}{c}
3 \text { for } 0 \leq x<Q \\
P \text { for } 1.5 \leq x<4 \\
2.5 \text { for } 4 \leq x<7
\end{array}\right.
\)

What are the values of \( P \) and \( Q \) ? ![The graph is three separate horizontal lines. It goes from (0,3) to (1.5, 3), then (1.5, 2) to (4, 2) and the last section is from (4, 2.5) to (7, 2.5)]()

Options:
A. \( \begin{array}{c}P=1.5 \\ Q=2\end{array} \)
B. \( \begin{array}{c}P=2 \\ Q=1.5\end{array} \)
C. \( \begin{array}{l}P=2 \\ Q=1\end{array} \)
D. \( \begin{array}{l}P=1 \\ Q=2\end{array} \)

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:
When reading graph, chooses nearest marked value on axis instead of reading accurately

Question:
Tom is has correctly drawn the graph of the following function:
\(
y=\left\{\begin{array}{c}
3 \text { for } 0 \leq x<Q \\
P \text { for } 1.5 \leq x<4 \\
2.5 \text { for } 4 \leq x<7
\end{array}\right.
\)

What are the values of \( P \) and \( Q \) ? ![The graph is three separate horizontal lines. It goes from (0,3) to (1.5, 3), then (1.5, 2) to (4, 2) and the last section is from (4, 2.5) to (7, 2.5)]()

Options:
A. \( \begin{array}{c}P=1.5 \\ Q=2\end{array} \)
B. \( \begin{array}{c}P=2 \\ Q=1.5\end{array} \)
C. \( \begin{array}{l}P=2 \\ Q=1\end{array} \)
D. \( \begin{array}{l}P=1 \\ Q=2\end{array} \)

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:
Names one of the faces of a 3D shape rather than the 3D shape name

Question:
This is the net of a... ![An image with an equilateral triangle in the centre. Connected to each of the three sides of the equilateral triangle are 3 more identical, equilateral triangles forming a larger triangle shape.]()

Options:
A. Triangle
B. Triangular prism
C. Triangularbased pyramid
D. Icosahedron

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 pyramid with prism

Question:
This is the net of a... ![An image with an equilateral triangle in the centre. Connected to each of the three sides of the equilateral triangle are 3 more identical, equilateral triangles forming a larger triangle shape.]()

Options:
A. Triangle
B. Triangular prism
C. Triangularbased pyramid
D. Icosahedron

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 multiplying two negatives gives a negative answer

Question:
Alison is expanding these two brackets.
What should she get when she multiplies the two terms indicated by the arrows? ![The two brackets are (5p-4)(2p-3). The arrows are pointing at the -4 in the first bracket and the -3 in the second bracket.]()

Options:
A. \( +7 \)
B. \( -12 \)
C. \( +12 \)
D. \( -7 \)

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:
Alison is expanding these two brackets.
What should she get when she multiplies the two terms indicated by the arrows? ![The two brackets are (5p-4)(2p-3). The arrows are pointing at the -4 in the first bracket and the -3 in the second bracket.]()

Options:
A. \( +7 \)
B. \( -12 \)
C. \( +12 \)
D. \( -7 \)

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 factorising a quadratic without a non variable term, tries to double bracket factorise

Question:
Factorise this expression, if possible:
\(
p^{2}-99p
\)

Options:
A. \( (p+9)(p-9) \)
B. \( (p+3 \sqrt{11})(p-3 \sqrt{11}) \)
C. \( p(p-99) \)
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:
When factorising a quadratic without a non variable term, tries to double bracket factorise

Question:
Factorise this expression, if possible:
\(
p^{2}-99p
\)

Options:
A. \( (p+9)(p-9) \)
B. \( (p+3 \sqrt{11})(p-3 \sqrt{11}) \)
C. \( p(p-99) \)
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 square of a negative will also be negative

Question:
Tom and Katie are discussing the table of values for \( y=x^{2}-1 \) \begin{tabular}{|l|l|}
\hline\( x \) & \( \bigstar \) \\
\hline\( y \) & \( 15 \) \\
\hline
\end{tabular} Tom says the star could be \( 4 \)

Katie says the star could be \( -4 \)

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:
Correct scale but wrong value on protractor reading.

Question:
What is the size of the marked angle? ![A 360 degree protractor with 2 red lines and a pink sector marking out a reflex angle being measured by the protractor. The inner scale goes from 0 to 360 in an anti-clockwise direction. The angle is between one red line that is at 0 (inner scale) and 180 (outer scale) on the protractor and goes anti-clockwise to the other red line that is half way between 330 and 340 (inner scale) and halfway between 210 and 200 (outer scale).
]()

Options:
A. \( 345^{\circ} \)
B. \( 215^{\circ} \)
C. \( 335^{\circ} \)
D. \( 205^{\circ} \)

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:
Reads the wrong scale on the protractor when measuring reflex angles

Question:
What is the size of the marked angle? ![A 360 degree protractor with 2 red lines and a pink sector marking out a reflex angle being measured by the protractor. The inner scale goes from 0 to 360 in an anti-clockwise direction. The angle is between one red line that is at 0 (inner scale) and 180 (outer scale) on the protractor and goes anti-clockwise to the other red line that is half way between 330 and 340 (inner scale) and halfway between 210 and 200 (outer scale).
]()

Options:
A. \( 345^{\circ} \)
B. \( 215^{\circ} \)
C. \( 335^{\circ} \)
D. \( 205^{\circ} \)

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:
Reads the wrong scale on the protractor when measuring reflex angles

Question:
What is the size of the marked angle? ![A 360 degree protractor with 2 red lines and a pink sector marking out a reflex angle being measured by the protractor. The inner scale goes from 0 to 360 in an anti-clockwise direction. The angle is between one red line that is at 0 (inner scale) and 180 (outer scale) on the protractor and goes anti-clockwise to the other red line that is half way between 330 and 340 (inner scale) and halfway between 210 and 200 (outer scale).
]()

Options:
A. \( 345^{\circ} \)
B. \( 215^{\circ} \)
C. \( 335^{\circ} \)
D. \( 205^{\circ} \)

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 completing the square, believes the constant in the bracket is the coefficient of x

Question:
When Sarah completes the square, what should replace the star? \( 2 g^{2}-6 g-5 \equiv 2(g  \bigstar)^{2} \triangle \)

Options:
A. \( \bigstar=-6 \)
B. \( \bigstar=-3 \)
C. \( \bigstar=-1.5 \)
D. \( \bigstar=-\sqrt{6} \)

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 completing the square, believes that a is always half the x-coefficient.

Question:
When Sarah completes the square, what should replace the star? \( 2 g^{2}-6 g-5 \equiv 2(g  \bigstar)^{2} \triangle \)

Options:
A. \( \bigstar=-6 \)
B. \( \bigstar=-3 \)
C. \( \bigstar=-1.5 \)
D. \( \bigstar=-\sqrt{6} \)

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 completing the square, believes the constant in the bracket is the square root of the coefficient of x

Question:
When Sarah completes the square, what should replace the star? \( 2 g^{2}-6 g-5 \equiv 2(g  \bigstar)^{2} \triangle \)

Options:
A. \( \bigstar=-6 \)
B. \( \bigstar=-3 \)
C. \( \bigstar=-1.5 \)
D. \( \bigstar=-\sqrt{6} \)

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 triangle numbers are formed differently to the correct way

Question:
If you add together consecutive triangle numbers you get...

Options:
A. a square number
B. another triangle number
C. a cube number
D. a Fibonacci number

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 mixed numbers, forgets to multiply the fraction

Question:
\( 1 \frac{1}{2} \times 3 \frac{2}{3}=\bigstar\frac{3}{6} \) What should replace the star?

Options:
A. \( 3 \)
B. \( 7 \)
C. \( 4 \)
D. \( 5 \)

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:
When multiplying mixed numbers thinks they add the integers

Question:
\( 1 \frac{1}{2} \times 3 \frac{2}{3}=\bigstar\frac{3}{6} \) What should replace the star?

Options:
A. \( 3 \)
B. \( 7 \)
C. \( 4 \)
D. \( 5 \)

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:
Has used the decimal point to separate numerator and denominator

Question:
How do you say this fraction?
\(
\frac{3}{5}
\)

Options:
A. Three point five
B. Three fives
C. Three fifths
D. Third fifths

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 say a fraction

Question:
How do you say this fraction?
\(
\frac{3}{5}
\)

Options:
A. Three point five
B. Three fives
C. Three fifths
D. Third fifths

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 say a fraction

Question:
How do you say this fraction?
\(
\frac{3}{5}
\)

Options:
A. Three point five
B. Three fives
C. Three fifths
D. Third fifths

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 signs belong in the boxes to make the statement correct?

\( 0.705 \)\[ {\color{blue}\square} \]\( 0.750 \)\[ {\color{orange}\square} \]\( 0.570 \)

Options:
A. ![A blue box containing a "greater than" symbol  and an orange box containing a "less than" symbol]()
B. ![A blue box containing a "less than" symbol  and an orange box containing a "less than" symbol]()
C. ![A blue box containing a "greater than" symbol  and an orange box containing a "greater than" symbol]()
D. ![A blue box containing a "less than" symbol  and an orange box containing a "greater than" symbol]()

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 the denominator after the decimal point

Question:
Convert this to a fraction:
\( 1.4 \)

Options:
A. \( \frac{1}{4} \)
B. \( 1 \frac{4}{5} \)
C. \( \frac{7}{5} \)
D. Not possible as it is greater than \( 1 \)

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:
Thinks numbers greater than 1 cannot be converted into fractions

Question:
Convert this to a fraction:
\( 1.4 \)

Options:
A. \( \frac{1}{4} \)
B. \( 1 \frac{4}{5} \)
C. \( \frac{7}{5} \)
D. Not possible as it is greater than \( 1 \)

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 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?
\[
0.31,0.30,0.331
\]

Options:
A. \( 0.021 \)
B. \( 0.301 \)
C. \( 0.031 \)
D. \( 0.21 \)

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?
\[
0.31,0.30,0.331
\]

Options:
A. \( 0.021 \)
B. \( 0.301 \)
C. \( 0.031 \)
D. \( 0.21 \)

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?
\[
0.31,0.30,0.331
\]

Options:
A. \( 0.021 \)
B. \( 0.301 \)
C. \( 0.031 \)
D. \( 0.21 \)

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 that cubic means the same as cubed in units

Question:
Which of the following is not a measure of volume?

Options:
A. Cubic metres
B. Centimetres cubed
C. Litres
D. Metres

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 that units of volume are usually cubed

Question:
Which of the following is not a measure of volume?

Options:
A. Cubic metres
B. Centimetres cubed
C. Litres
D. Metres

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 recognise litres as a unit of volume

Question:
Which of the following is not a measure of volume?

Options:
A. Cubic metres
B. Centimetres cubed
C. Litres
D. Metres

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:
Which of the following term-to-term rule describes this sequence? \( 4, \quad 10, \quad 14, \quad 24, \quad \ldots \)

Options:
A. To get the next term you add \( 6 \) to the previous term
B. To get the next term you add the previous two terms together
C. To get the next term you double the previous term and add \( 2 \)
D. To get the next term you multiply the previous term by \( 3 \) and subtract \( 2 \)

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

Question:
Which of the following term-to-term rule describes this sequence? \( 4, \quad 10, \quad 14, \quad 24, \quad \ldots \)

Options:
A. To get the next term you add \( 6 \) to the previous term
B. To get the next term you add the previous two terms together
C. To get the next term you double the previous term and add \( 2 \)
D. To get the next term you multiply the previous term by \( 3 \) and subtract \( 2 \)

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

Question:
Which of the following term-to-term rule describes this sequence? \( 4, \quad 10, \quad 14, \quad 24, \quad \ldots \)

Options:
A. To get the next term you add \( 6 \) to the previous term
B. To get the next term you add the previous two terms together
C. To get the next term you double the previous term and add \( 2 \)
D. To get the next term you multiply the previous term by \( 3 \) and subtract \( 2 \)

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 to the wrong degree of accuracy (rounds too much)

Question:
What is \( 5050 \) rounded to the nearest \( 10 \) ?

Options:
A. \( 5050 \)
B. \( 5100 \)
C. \( 5000 \)
D. \( 5010 \)

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 \( 5050 \) rounded to the nearest \( 10 \) ?

Options:
A. \( 5050 \)
B. \( 5100 \)
C. \( 5000 \)
D. \( 5010 \)

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 rounding must change the number

Question:
What is \( 5050 \) rounded to the nearest \( 10 \) ?

Options:
A. \( 5050 \)
B. \( 5100 \)
C. \( 5000 \)
D. \( 5010 \)

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 the equation:
\(12 d-3=0\)

Options:
A. \( d=-\frac{1}{4} \)
B. \( d=4 \)
C. \( d=-4 \)
D. \( d=\frac{1}{4} \)

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:
Swaps the dividend and divisor in order to get an integer answer

Question:
Solve the equation:
\(12 d-3=0\)

Options:
A. \( d=-\frac{1}{4} \)
B. \( d=4 \)
C. \( d=-4 \)
D. \( d=\frac{1}{4} \)

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

Question:
This displacement-time graph shows the start of Mo's journey home.

During that time he travelled at a speed of \( 4 \mathrm{~m} / \mathrm{s} \).
What are the coordinates of the marked point? ![The vertical axis of the graph is labelled Distance (m) and has a scale marked from 0 to 60 in even steps. The horizontal axis is labelled Time (secs) and has no scale marked on it. The graph is a straight line that goes from point (0,60) and touches the Time axis three squares from the origin (0,0).
The marked point is one square in on the Time axis and at 40 on the Distance axis.]()

Options:
A. \( (1,40) \)
B. \( (5,40) \)
C. \( (10,40) \)
D. \( (20,40) \)

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 displacement-time graph shows the start of Mo's journey home.

During that time he travelled at a speed of \( 4 \mathrm{~m} / \mathrm{s} \).
What are the coordinates of the marked point? ![The vertical axis of the graph is labelled Distance (m) and has a scale marked from 0 to 60 in even steps. The horizontal axis is labelled Time (secs) and has no scale marked on it. The graph is a straight line that goes from point (0,60) and touches the Time axis three squares from the origin (0,0).
The marked point is one square in on the Time axis and at 40 on the Distance axis.]()

Options:
A. \( (1,40) \)
B. \( (5,40) \)
C. \( (10,40) \)
D. \( (20,40) \)

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 scales on graphs must match on both axes

Question:
This displacement-time graph shows the start of Mo's journey home.

During that time he travelled at a speed of \( 4 \mathrm{~m} / \mathrm{s} \).
What are the coordinates of the marked point? ![The vertical axis of the graph is labelled Distance (m) and has a scale marked from 0 to 60 in even steps. The horizontal axis is labelled Time (secs) and has no scale marked on it. The graph is a straight line that goes from point (0,60) and touches the Time axis three squares from the origin (0,0).
The marked point is one square in on the Time axis and at 40 on the Distance axis.]()

Options:
A. \( (1,40) \)
B. \( (5,40) \)
C. \( (10,40) \)
D. \( (20,40) \)

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 slant heights instead of parallel sides to find area of a trapezium

Question:
When calculating the area of this trapezium, what are the values of \( a \) and \( b \) in the formula? ![Diagram of a trapezium with its 2 parallel sides horizontal. The parallel sides are labelled as 9cm and 10cm. The lengths of the 2 non-parallel sides are labelled as 7cm and 7.5cm. The perpendicular height is labelled as 6cm.]() Area \( =\left(\frac{a+b}{2}\right) h \)

Options:
A. \( 7+7.5 \)
B. \( 9+10 \)
C. \( 7+6 \)
D. \( 6+7.5 \)

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}.