Prompt:
Misconception:
Describes term to term rules using position to term rules

Question:
![Square and then subtract \( 4 \)]() The first three terms of which sequence below is produced by this term-to-term rule?

Options:
A. \( -3,9,5 \)
B. \( -3,-13,-173 \)
C. \( -3,5,21 \)
D. \( -3,0,5 \)

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


Prompt:
Misconception:
Does not work out all possibilites when given an 'at least' question in probability

Question:
There are \( 5 \) red balls and \( 4 \) yellow balls in a cup ![A cup with 5 red and 4 yellow balls in it. All of the balls are the same size.]() Kate picks out two balls at the same time.

What is the probability at least one ball is red?

Options:
A. \( \frac{67}{72} \)
B. \( \frac{20}{72} \)
C. \( \frac{60}{72} \)
D. \( \frac{40}{72} \)

Solve the problem as a student with the misconception above.
You 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 can just give the probability of the first event for a combined probability

Question:
There are \( 5 \) red balls and \( 4 \) yellow balls in a cup ![A cup with 5 red and 4 yellow balls in it. All of the balls are the same size.]() Kate picks out two balls at the same time.

What is the probability at least one ball is red?

Options:
A. \( \frac{67}{72} \)
B. \( \frac{20}{72} \)
C. \( \frac{60}{72} \)
D. \( \frac{40}{72} \)

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


Prompt:
Misconception:
Calculates perimeter when asked for area

Question:
What is the area of the parallelogram? ![A parallelogram with length 7cm, perpendicular height (marked by a right angle) 3cm, and slanted height 4cm. Not to scale]()

Options:
A. \( 21 \mathrm{~cm}^{2} \)
B. \( 22 \mathrm{~cm}^{2} \)
C. \( 28 \mathrm{~cm}^{2} \)
D. \( 84 \mathrm{~cm}^{2} \)

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 length 7cm, perpendicular height (marked by a right angle) 3cm, and slanted height 4cm. Not to scale]()

Options:
A. \( 21 \mathrm{~cm}^{2} \)
B. \( 22 \mathrm{~cm}^{2} \)
C. \( 28 \mathrm{~cm}^{2} \)
D. \( 84 \mathrm{~cm}^{2} \)

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:
Multiplies all given dimensions when calculating an area

Question:
What is the area of the parallelogram? ![A parallelogram with length 7cm, perpendicular height (marked by a right angle) 3cm, and slanted height 4cm. Not to scale]()

Options:
A. \( 21 \mathrm{~cm}^{2} \)
B. \( 22 \mathrm{~cm}^{2} \)
C. \( 28 \mathrm{~cm}^{2} \)
D. \( 84 \mathrm{~cm}^{2} \)

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 division is commutative

Question:
Jacob makes a conjecture: If you have two different numbers, \( P \) and \( Q \), the order you divide does not matter. \( P \div Q=Q \div P \) Is Jacob's conjecture...

Options:
A. Always true
B. Sometimes true
C. Never true
D. I don't
know

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


Prompt:
Misconception:
Believes division is sometimes commutative

Question:
Jacob makes a conjecture: If you have two different numbers, \( P \) and \( Q \), the order you divide does not matter. \( P \div Q=Q \div P \) Is Jacob's conjecture...

Options:
A. Always true
B. Sometimes true
C. Never true
D. I don't
know

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


Prompt:
Misconception:
Believes that when eliminating a variable, if the signs of the terms with matching coefficients are different, we subtract the equations.

Question:
What do you need to do to eliminate the \( q s \) in each of these pairs of simultaneous equations? Pair \( 1 \)
\(
\begin{array}{l}
-5 p+2 q=12 \\
3 p-2 q=8
\end{array}
\) Pair \( 2 \)
\(
\begin{array}{l}
-5 p-2 q=12 \\
3 p+2 q=8
\end{array}
\)

Options:
A. Add Pair \( 1 \)
Subtract Pair \( 2 \)
B. Add Pair \( 1 \)
Add Pair \( 2 \)
C. Subtract Pair \( 1 \)
Add Pair \( 2 \)
D. Subtract Pair \( 1 \)
Subtract Pair \( 2 \)

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 include units in answer.

Question:
This graph shows how much a block of ice melted over time. ![Chart of water depth (cm) against time (minutes)]() What was the difference between the second minute and fourth minute?

Options:
A. \( 6 \mathrm{~cm} \)
B. \( 6 \)
C. \( 9 \mathrm{~cm} \)
D. \( 2 \mathrm{~cm} \)

Solve the problem as a student with the misconception above.
You 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 command word 'difference'

Question:
This graph shows how much a block of ice melted over time. ![Chart of water depth (cm) against time (minutes)]() What was the difference between the second minute and fourth minute?

Options:
A. \( 6 \mathrm{~cm} \)
B. \( 6 \)
C. \( 9 \mathrm{~cm} \)
D. \( 2 \mathrm{~cm} \)

Solve the problem as a student with the misconception above.
You 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 wrong data point on the graph

Question:
This graph shows how much a block of ice melted over time. ![Chart of water depth (cm) against time (minutes)]() What was the difference between the second minute and fourth minute?

Options:
A. \( 6 \mathrm{~cm} \)
B. \( 6 \)
C. \( 9 \mathrm{~cm} \)
D. \( 2 \mathrm{~cm} \)

Solve the problem as a student with the misconception above.
You 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:
James is expanding these two brackets.

What should he get when he multiplies the two terms indicated by the arrows? ![The brackets shown are (x-8)(x-2). The arrows are pointing at the -8 in the first bracket and the -2 in the second bracket.]()

Options:
A. \( -10 \)
B. \( +16 \)
C. \( -6 \)
D. \( -16 \)

Solve the problem as a student with the misconception above.
You 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:
James is expanding these two brackets.

What should he get when he multiplies the two terms indicated by the arrows? ![The brackets shown are (x-8)(x-2). The arrows are pointing at the -8 in the first bracket and the -2 in the second bracket.]()

Options:
A. \( -10 \)
B. \( +16 \)
C. \( -6 \)
D. \( -16 \)

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


Prompt:
Misconception:
Rounds down instead of up

Question:
\( 154.1762 \) to \( 1 \) decimal place is.

Options:
A. \( 154.1 \)
B. \( 154.2 \)
C. \( 155.2 \)
D. \( 155.1 \)

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 incorrectly by changing multiple place values

Question:
\( 154.1762 \) to \( 1 \) decimal place is.

Options:
A. \( 154.1 \)
B. \( 154.2 \)
C. \( 155.2 \)
D. \( 155.1 \)

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 incorrectly by changing multiple place values

Question:
\( 154.1762 \) to \( 1 \) decimal place is.

Options:
A. \( 154.1 \)
B. \( 154.2 \)
C. \( 155.2 \)
D. \( 155.1 \)

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 there are 10m in a km

Question:
\( 4000 m \) is the same as ____ \(km\)

Options:
A. \( 400 \)
B. \( 400000 \)
C. \( 4 \)
D. \( 40 \)

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:
Multiplies rather than divides

Question:
\( 4000 m \) is the same as ____ \(km\)

Options:
A. \( 400 \)
B. \( 400000 \)
C. \( 4 \)
D. \( 40 \)

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:
Thinks there are 100m and a km

Question:
\( 4000 m \) is the same as ____ \(km\)

Options:
A. \( 400 \)
B. \( 400000 \)
C. \( 4 \)
D. \( 40 \)

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:
When describing a translation, miscounts when crossing an axis

Question:
![A coordinate grid with point V marked at (2,2) and point W marked at (-3,-1)]() Describe the movements to get from point \( \mathrm{V} \) to point \( \mathrm{W} \).

Options:
A. Left \( 4 \) squares, down \( 3 \) squares
B. Left \( 5 \) squares, down \( 3 \) squares
C. Right \( 5 \) squares, up \( 3 \) squares
D. Left \( 5 \) squares, up \( 3 \) squares

Solve the problem as a student with the misconception above.
You 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 describing a translation, goes from the image to the original

Question:
![A coordinate grid with point V marked at (2,2) and point W marked at (-3,-1)]() Describe the movements to get from point \( \mathrm{V} \) to point \( \mathrm{W} \).

Options:
A. Left \( 4 \) squares, down \( 3 \) squares
B. Left \( 5 \) squares, down \( 3 \) squares
C. Right \( 5 \) squares, up \( 3 \) squares
D. Left \( 5 \) squares, up \( 3 \) squares

Solve the problem as a student with the misconception above.
You 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 describing a translation, identifies the correct number of jumps but mixes up the directions .

Question:
![A coordinate grid with point V marked at (2,2) and point W marked at (-3,-1)]() Describe the movements to get from point \( \mathrm{V} \) to point \( \mathrm{W} \).

Options:
A. Left \( 4 \) squares, down \( 3 \) squares
B. Left \( 5 \) squares, down \( 3 \) squares
C. Right \( 5 \) squares, up \( 3 \) squares
D. Left \( 5 \) squares, up \( 3 \) squares

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


Prompt:
Misconception:
Multiplies rather than adds when given the command word 'more'

Question:
What number is \( 100 \) more than \( 28902 ? \)

Options:
A. \( 2,890,200 \)
B. \( 29,902 \)
C. \( 28,002 \)
D. \( 29,002 \)

Solve the problem as a student with the misconception above.
You 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 powers of 10 adds onto the wrong column

Question:
What number is \( 100 \) more than \( 28902 ? \)

Options:
A. \( 2,890,200 \)
B. \( 29,902 \)
C. \( 28,002 \)
D. \( 29,002 \)

Solve the problem as a student with the misconception above.
You 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 two digits sum to 10 or more during an addition problem, does not add one to the preceding digit

Question:
What number is \( 100 \) more than \( 28902 ? \)

Options:
A. \( 2,890,200 \)
B. \( 29,902 \)
C. \( 28,002 \)
D. \( 29,002 \)

Solve the problem as a student with the misconception above.
You 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 that the square root of an expression square roots each term in the expression, rather than square rooting the whole expression

Question:
A right-angled tringle has sides a, b, and \( c \) as shown.

Choose the formula for finding side a. ![Right-angled triangle with height a, base b and hypotenuse c.]()

Options:
A. \( a=c-b \)
B. \( a^{2}=b^{2}+c^{2} \)
C. \( a^{2}=b^{2}-c^{2} \)
D. \( a^{2}=c^{2}-b^{2} \)

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


Prompt:
Misconception:
When converting from an improper fraction to a mixed number, adds on the part left to make the whole, rather than subtracting it

Question:
Write \( \textbf{nineteen fifths} \) as a mixed number fraction.

Options:
A. \( 4 \frac{1}{5} \)
B. \( 19 \frac{1}{5} \)
C. \( \frac{19}{5} \)
D. \( 3 \frac{4}{5} \)

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:
Writes the numerator of an improper fraction as the number of wholes when converting to a mixed number

Question:
Write \( \textbf{nineteen fifths} \) as a mixed number fraction.

Options:
A. \( 4 \frac{1}{5} \)
B. \( 19 \frac{1}{5} \)
C. \( \frac{19}{5} \)
D. \( 3 \frac{4}{5} \)

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:
Confused mixed numbers with improper fractions

Question:
Write \( \textbf{nineteen fifths} \) as a mixed number fraction.

Options:
A. \( 4 \frac{1}{5} \)
B. \( 19 \frac{1}{5} \)
C. \( \frac{19}{5} \)
D. \( 3 \frac{4}{5} \)

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:
Converts a fraction to a decimal by using the denominator after the decimal point

Question:
What is \( \frac{4}{5} \) as a decimal?

Options:
A. \( 0.5 \)
B. \( 0.8 \)
C. \( 0.4 \)
D. \( 0.45 \)

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


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

Question:
What is \( \frac{4}{5} \) as a decimal?

Options:
A. \( 0.5 \)
B. \( 0.8 \)
C. \( 0.4 \)
D. \( 0.45 \)

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


Prompt:
Misconception:
Converts a fraction to a decimal by placing all values of the fraction after the decimal point

Question:
What is \( \frac{4}{5} \) as a decimal?

Options:
A. \( 0.5 \)
B. \( 0.8 \)
C. \( 0.4 \)
D. \( 0.45 \)

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


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

Question:
Which of these statements show that \( \mathrm{t} \) is greater than \( 9 \) ?

Options:
A. \( t<9 \)
B. \( t=9 \)
C. \( \mathrm{t} \leq 9 \)
D. \( t>9 \)

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:
Confuses inequality symbols with equality

Question:
Which of these statements show that \( \mathrm{t} \) is greater than \( 9 \) ?

Options:
A. \( t<9 \)
B. \( t=9 \)
C. \( \mathrm{t} \leq 9 \)
D. \( t>9 \)

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:
Does not know that you can have a decimal percentage

Question:
What percentage is represented by:
\(
\frac{3}{10}+ \frac{7}{1000}
\)

Options:
A. \( 307 \% \)
B. \( 3.7 \% \)
C. \( 37 \% \)
D. \( 30.7 \% \)

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:
Thinks you just add a % sign to the numerator to make a fraction into a percentage

Question:
What percentage is represented by:
\(
\frac{3}{10}+ \frac{7}{1000}
\)

Options:
A. \( 307 \% \)
B. \( 3.7 \% \)
C. \( 37 \% \)
D. \( 30.7 \% \)

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

Question:
Hannah's journey to camp is \( 3 \) hours and \( 26 \) minutes.
Tori's journey to camp is \( 204 \) minutes.
What is the difference in their journeys in minutes?

Options:
A. \( 206 \) minutes
B. \( 122 \) minutes
C. \( 2 \) minutes
D. \( 410 \) minutes

Solve the problem as a student with the misconception above.
You 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:
Hannah's journey to camp is \( 3 \) hours and \( 26 \) minutes.
Tori's journey to camp is \( 204 \) minutes.
What is the difference in their journeys in minutes?

Options:
A. \( 206 \) minutes
B. \( 122 \) minutes
C. \( 2 \) minutes
D. \( 410 \) minutes

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


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

Question:
![A rectangle drawn on a coordinate grid. Three of the vertices are labelled (3,12) (10,12) and (10,7). There is a red arrow between (3,12) and (10,12) indicating the width.]() What is the width of this rectangle as indicated by the arrow?

Options:
A. \( 12 \)
B. \( 7 \)
C. \( 5 \)
D. \( 13 \)

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:
Mixes up width and height of a rectangle

Question:
![A rectangle drawn on a coordinate grid. Three of the vertices are labelled (3,12) (10,12) and (10,7). There is a red arrow between (3,12) and (10,12) indicating the width.]() What is the width of this rectangle as indicated by the arrow?

Options:
A. \( 12 \)
B. \( 7 \)
C. \( 5 \)
D. \( 13 \)

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

Question:
![A rectangle drawn on a coordinate grid. Three of the vertices are labelled (3,12) (10,12) and (10,7). There is a red arrow between (3,12) and (10,12) indicating the width.]() What is the width of this rectangle as indicated by the arrow?

Options:
A. \( 12 \)
B. \( 7 \)
C. \( 5 \)
D. \( 13 \)

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:
When solving an equation forgets to eliminate the coefficient in front of the variable in the last step

Question:
\begin{tabular}{|l|l|l|c|c|c|}
\hline\( x \) & \( 0 \) & \( 1 \) & \( 2 \) & \( 3 \) & \( 4 \) \\
\hline\( y \) & \( 4 \) &  \( \ \) & \(\color{gold}\bigstar\)
\end{tabular}

This is a table of values for \( x+2 y=8 \) What should replace the star?

Options:
A. \( 16 \)
B. \( 3 \)
C. \( 2 \)
D. \( 6 \)

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


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

Question:
Factorise this expression, if possible:
\(
p^{2}+5 p+4
\)

Options:
A. \( (p+2)(p+3) \)
B. \( (p+1)(p+5) \)
C. \( (p+1)(p+4) \)
D. Does not factorise

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


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

Question:
Factorise this expression, if possible:
\(
p^{2}+5 p+4
\)

Options:
A. \( (p+2)(p+3) \)
B. \( (p+1)(p+5) \)
C. \( (p+1)(p+4) \)
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 a coordinate cannot be placed beyond the bounds of the grid shown

Question:
![A coordinate grid with a line segment from (0,2) to (3,1)]() The line segment is one side of a square.

Tom says a vertex of the square could be \( (2,-2) \).

Katie says a vertex of the square could be \( (1,5) \).
Who is correct?

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

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


Prompt:
Misconception:
Does not realise that if the horizontal and vertical measurements of a diagonal line segment switch it remains the same size

Question:
![A coordinate grid with a line segment from (0,2) to (3,1)]() The line segment is one side of a square.

Tom says a vertex of the square could be \( (2,-2) \).

Katie says a vertex of the square could be \( (1,5) \).
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 difference between a value on a graph and the gradient of a graph

Question:
The graph shows information about the velocity, \( v \mathrm{~m} / \mathrm{s} \), of a parachutist \( t \) seconds after leaving a plane.

Which of the following is the best estimate for the gradient of the curve when \[t=8\]? ![A graph showing time in seconds on the x axis and velocity in metres per second on the y axis. A curve is shown with a tangent to the curve drawn in at (8,51). The tangent also passes through the point (0,40)]()

Options:
A. \( 51 \)
B. \( 0.72... \)
C. \( 1.375 \)
D. \( 6.375 \)

Solve the problem as a student with the misconception above.
You 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 gradient = change in x/change in y

Question:
The graph shows information about the velocity, \( v \mathrm{~m} / \mathrm{s} \), of a parachutist \( t \) seconds after leaving a plane.

Which of the following is the best estimate for the gradient of the curve when \[t=8\]? ![A graph showing time in seconds on the x axis and velocity in metres per second on the y axis. A curve is shown with a tangent to the curve drawn in at (8,51). The tangent also passes through the point (0,40)]()

Options:
A. \( 51 \)
B. \( 0.72... \)
C. \( 1.375 \)
D. \( 6.375 \)

Solve the problem as a student with the misconception above.
You 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 difference between two points on a time series graph, only uses one of the points.

Question:
The graph shows information about the velocity, \( v \mathrm{~m} / \mathrm{s} \), of a parachutist \( t \) seconds after leaving a plane.

Which of the following is the best estimate for the gradient of the curve when \[t=8\]? ![A graph showing time in seconds on the x axis and velocity in metres per second on the y axis. A curve is shown with a tangent to the curve drawn in at (8,51). The tangent also passes through the point (0,40)]()

Options:
A. \( 51 \)
B. \( 0.72... \)
C. \( 1.375 \)
D. \( 6.375 \)

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


Prompt:
Misconception:
Struggles to visualise nets of 3D shapes

Question:
Which is the correct net for this shape? ![Net of a cuboid]()

Options:
A. ![Correct net of a cuboid]()
B. ![Net of a triangular prism]()
C. ![Net of a cube]()
D. ![None of the above]()

Solve the problem as a student with the misconception above.
You 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 cubes and cuboids

Question:
Which is the correct net for this shape? ![Net of a cuboid]()

Options:
A. ![Correct net of a cuboid]()
B. ![Net of a triangular prism]()
C. ![Net of a cube]()
D. ![None of the above]()

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


Prompt:
Misconception:
Struggles to visualise nets of 3D shapes

Question:
Which is the correct net for this shape? ![Net of a cuboid]()

Options:
A. ![Correct net of a cuboid]()
B. ![Net of a triangular prism]()
C. ![Net of a cube]()
D. ![None of the above]()

Solve the problem as a student with the misconception above.
You 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 subtraction button writes a fraction

Question:
Which of the following would give you the correct value of \( \frac{1}{7} \) on your calculator? ![A scientific calculator]()

Options:
A. ![The number 1, then a calculator button labelled \(-\), then the number 7]()
B. ![The number 7, then a calculator button labelled \(x^{-1} \)]()
C. ![The number 1, then a calculator button labelled \(x^{\square} \), then the number 7]()
D. None of these

Solve the problem as a student with the misconception above.
You 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 power button writes a fraction

Question:
Which of the following would give you the correct value of \( \frac{1}{7} \) on your calculator? ![A scientific calculator]()

Options:
A. ![The number 1, then a calculator button labelled \(-\), then the number 7]()
B. ![The number 7, then a calculator button labelled \(x^{-1} \)]()
C. ![The number 1, then a calculator button labelled \(x^{\square} \), then the number 7]()
D. None of these

Solve the problem as a student with the misconception above.
You 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:
\( 5 \times(-4)= \)

Options:
A. \( -9 \)
B. \( 9 \)
C. \( 20 \)
D. \( -20 \)

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


Prompt:
Misconception:
Believes division is commutative

Question:
![Six groups of three dots]() Jo says the diagram above represents
\[
3 \div 18=6
\]
Paul says the diagram represents \( 6 \times 3=18 \)
Who is correct?

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

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


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

Question:
\(y= x^{2}+8x+2 \)

Write in the form
\( (x+a)^{2}+b \)

Options:
A. \( (x+4)^{2}-14 \)
B. \( (x+4)^{2}+2 \)
C. \( (x+8)^{2}+2 \)
D. \( (x+4)^{2}-16 \)

Solve the problem as a student with the misconception above.
You 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:
\(y= x^{2}+8x+2 \)

Write in the form
\( (x+a)^{2}+b \)

Options:
A. \( (x+4)^{2}-14 \)
B. \( (x+4)^{2}+2 \)
C. \( (x+8)^{2}+2 \)
D. \( (x+4)^{2}-16 \)

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


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

Question:
\(y= x^{2}+8x+2 \)

Write in the form
\( (x+a)^{2}+b \)

Options:
A. \( (x+4)^{2}-14 \)
B. \( (x+4)^{2}+2 \)
C. \( (x+8)^{2}+2 \)
D. \( (x+4)^{2}-16 \)

Solve the problem as a student with the misconception above.
You 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 placing all values of the fraction after the decimal point

Question:
\( \frac{6}{25}=? \)

Options:
A. \( 0.625 \)
B. \( 0.6 \)
C. \( 6.25 \)
D. \( 0.24 \)

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

Question:
\( \frac{6}{25}=? \)

Options:
A. \( 0.625 \)
B. \( 0.6 \)
C. \( 6.25 \)
D. \( 0.24 \)

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:
Converts a fraction to a decimal by placing a decimal point between the numerator and denominator

Question:
\( \frac{6}{25}=? \)

Options:
A. \( 0.625 \)
B. \( 0.6 \)
C. \( 6.25 \)
D. \( 0.24 \)

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

Question:
Which number is the greatest?

Options:
A. \( 6 \)
B. \( 6.2 \)
C. \( 6.079 \)
D. \( 6.0001 \)

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


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

Question:
\(x_{n+1}=\sqrt{\frac{1}{x_{n}+1}}\)

Using a starting value of \( x_{1}=0.5 \), what is the value of \( x_{2} \) ?

Options:
A. \( 0.8164 \ldots \)
B. \( 0.6666 \ldots \)
C. \( 0.7419 \ldots \)
D. Another answer

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


Prompt:
Misconception:
Estimated when not appropriate

Question:
Find the value of \( \mathrm{M} \). ![Horizontal blue bar divided into 5 equal sections. Every section is labelled with M. A curly bracket shows that 4 of the sections sum to 420.]()

Options:
A. \( 105 \)
B. \( 84 \)
C. \( 100 \)
D. \( 1680 \)

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


Prompt:
Misconception:
Confusion over whether multiplication or division is the correct way to solve the problem.

Question:
Find the value of \( \mathrm{M} \). ![Horizontal blue bar divided into 5 equal sections. Every section is labelled with M. A curly bracket shows that 4 of the sections sum to 420.]()

Options:
A. \( 105 \)
B. \( 84 \)
C. \( 100 \)
D. \( 1680 \)

Solve the problem as a student with the misconception above.
You 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:
\(
-5=p+10
\)

Options:
A. \( p=5 \)
B. \( p=-5 \)
C. \( p=-15 \)
D. \( p=15 \)

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:
Believes that a number divided by itself equals 0

Question:
Solve the equation:
\(20 t-5=5 t+10\)

Options:
A. \( t=0 \)
B. \( t=1 \)
C. \( t=-1 \)
D. \( t=\frac{1}{5} \)

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


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

Question:
Solve the equation:
\(20 t-5=5 t+10\)

Options:
A. \( t=0 \)
B. \( t=1 \)
C. \( t=-1 \)
D. \( t=\frac{1}{5} \)

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


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

Question:
Solve the equation:
\(20 t-5=5 t+10\)

Options:
A. \( t=0 \)
B. \( t=1 \)
C. \( t=-1 \)
D. \( t=\frac{1}{5} \)

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


Prompt:
Misconception:
Gets order of ratio wrong

Question:
James and Cameron are watching a film. They pause it with one sixth left to watch.

What is the ratio for how much they have watched to how much they have yet to see? ![An image of a television]()

Options:
A. 5:1
B. 1:5
C. \( 6: 1 \)
D. 1:6

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:
Uses the denominator when converting from fractions to ratio, rather than numerator.

Question:
James and Cameron are watching a film. They pause it with one sixth left to watch.

What is the ratio for how much they have watched to how much they have yet to see? ![An image of a television]()

Options:
A. 5:1
B. 1:5
C. \( 6: 1 \)
D. 1:6

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 angles on a straight line add to 100 degrees

Question:
The sum of angle \( a \) and \( b \) would be... ![A straight line split in to two angles, a and b.]()

Options:
A. \( 180^{\circ} \)
B. \( 100^{\circ} \)
C. \( 360^{\circ} \)
D. \( 90^{\circ} \)

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:
Believes angles on a straight line add to 360 degrees

Question:
The sum of angle \( a \) and \( b \) would be... ![A straight line split in to two angles, a and b.]()

Options:
A. \( 180^{\circ} \)
B. \( 100^{\circ} \)
C. \( 360^{\circ} \)
D. \( 90^{\circ} \)

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:
Believes angles on a straight line add to 90 degrees

Question:
The sum of angle \( a \) and \( b \) would be... ![A straight line split in to two angles, a and b.]()

Options:
A. \( 180^{\circ} \)
B. \( 100^{\circ} \)
C. \( 360^{\circ} \)
D. \( 90^{\circ} \)

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:
Given a line segment with a midpoint that is not the origin, assumes that the two end points will still have the same absolute value

Question:
Here are two points and their midpoint.
What should replace the star? ![A set of axis including all four quadrants. Lilac circle marked and labelled by coordinates (-6, 3). Red circle marked and labelled coordinates (-1,1). Another lilac circle in the fourth quadrant marked and labelled with a set of brackets, x coordinate covered by a yellow star and y coordinate covered by a green triangle. ]()

Options:
A. \(\color{gold}\bigstar\) = -2.5
B. \(\color{gold}\bigstar\) = 4
C. \(\color{gold}\bigstar\) = 6
D. \(\color{gold}\bigstar\) = -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:
Mixes up squaring and multiplying by 2 or doubling

Question:
\( 2 \times 3^{2}= \)

Options:
A. \( 18 \)
B. \( 12 \)
C. \( 36 \)
D. \( 11 \)

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


Prompt:
Misconception:
Carries out operations from left to right regardless of priority order

Question:
\( 2 \times 3^{2}= \)

Options:
A. \( 18 \)
B. \( 12 \)
C. \( 36 \)
D. \( 11 \)

Solve the problem as a student with the misconception above.
You 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:
\( 2 \times 3^{2}= \)

Options:
A. \( 18 \)
B. \( 12 \)
C. \( 36 \)
D. \( 11 \)

Solve the problem as a student with the misconception above.
You 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 find the values for the quadratic formula

Question:
Before Zain uses the quadratic formula to solve this equation, what must he do?
\(
p^{2}-16=p
\)

Options:
A. Square root everything
B. Add \( 16 \) to both sides
C. Divide everything by \( p \)
D. Subtract \( p \) from both sides

Solve the problem as a student with the misconception above.
You 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 find the values for the quadratic formula

Question:
Before Zain uses the quadratic formula to solve this equation, what must he do?
\(
p^{2}-16=p
\)

Options:
A. Square root everything
B. Add \( 16 \) to both sides
C. Divide everything by \( p \)
D. Subtract \( p \) from both sides

Solve the problem as a student with the misconception above.
You 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 find the values for the quadratic formula

Question:
Before Zain uses the quadratic formula to solve this equation, what must he do?
\(
p^{2}-16=p
\)

Options:
A. Square root everything
B. Add \( 16 \) to both sides
C. Divide everything by \( p \)
D. Subtract \( p \) from both sides

Solve the problem as a student with the misconception above.
You 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 include brackets when required

Question:
When calculating the mean of the following numbers which calculation will give the correct answer?
\[
0,0,2,6,9
\]

Options:
A. \( 0+0+2+6+9 \div 5 \)
B. \( \frac{2+6+9}{5} \)
C. \( \frac{2+6+9}{3} \)
D. None of them

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


Prompt:
Misconception:
When asked for the mean of a list of data, does not count any zeros in the data when working out what to divide by

Question:
When calculating the mean of the following numbers which calculation will give the correct answer?
\[
0,0,2,6,9
\]

Options:
A. \( 0+0+2+6+9 \div 5 \)
B. \( \frac{2+6+9}{5} \)
C. \( \frac{2+6+9}{3} \)
D. None of them

Solve the problem as a student with the misconception above.
You 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 calculate the mean

Question:
When calculating the mean of the following numbers which calculation will give the correct answer?
\[
0,0,2,6,9
\]

Options:
A. \( 0+0+2+6+9 \div 5 \)
B. \( \frac{2+6+9}{5} \)
C. \( \frac{2+6+9}{3} \)
D. None of them

Solve the problem as a student with the misconception above.
You 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 cube number is

Question:
Which of these is a cube number?

Options:
A. \( 3 \)
B. \( 36 \)
C. \( 64 \)
D. \( 21 \)

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:
Mixes up square numbers and cube numbers

Question:
Which of these is a cube number?

Options:
A. \( 3 \)
B. \( 36 \)
C. \( 64 \)
D. \( 21 \)

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 what a cube number is

Question:
Which of these is a cube number?

Options:
A. \( 3 \)
B. \( 36 \)
C. \( 64 \)
D. \( 21 \)

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:
Forgets to multiply up for the correct time frame in a worded question

Question:
Which one of the following calculations would work out the number of hours in \( 5 \) weeks?

Options:
A. \( 5 \times 24 \)
B. \( 5 \times 7 \times 12 \)
C. \( 5 \times 5 \times 24 \)
D. \( 5 \times 7 \times 24 \)

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 there are 12 hours in 1 day

Question:
Which one of the following calculations would work out the number of hours in \( 5 \) weeks?

Options:
A. \( 5 \times 24 \)
B. \( 5 \times 7 \times 12 \)
C. \( 5 \times 5 \times 24 \)
D. \( 5 \times 7 \times 24 \)

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 there are 5 days in a week

Question:
Which one of the following calculations would work out the number of hours in \( 5 \) weeks?

Options:
A. \( 5 \times 24 \)
B. \( 5 \times 7 \times 12 \)
C. \( 5 \times 5 \times 24 \)
D. \( 5 \times 7 \times 24 \)

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:
Adds rather than multiplies for combined probabilities

Question:
There are \( 5 \) red balls and \( 4 \) yellow balls in a cup ![A cup with 5 red and 4 yellow balls in it. All of the balls are the same size.]() Kate picks out three balls at the same time.

She wants to work out the probability all the balls are red.

What is the denominator of the final unsimplified answer?

Options:
A. \( 24 \)
B. \( 9 \)
C. \( 504 \)
D. \( 729 \)

Solve the problem as a student with the misconception above.
You 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 denominator in a combined probablity will be the same as the denominator in the probability of the first event.

Question:
There are \( 5 \) red balls and \( 4 \) yellow balls in a cup ![A cup with 5 red and 4 yellow balls in it. All of the balls are the same size.]() Kate picks out three balls at the same time.

She wants to work out the probability all the balls are red.

What is the denominator of the final unsimplified answer?

Options:
A. \( 24 \)
B. \( 9 \)
C. \( 504 \)
D. \( 729 \)

Solve the problem as a student with the misconception above.
You 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 reduce the denominator when an item is not replaced in a probability question

Question:
There are \( 5 \) red balls and \( 4 \) yellow balls in a cup ![A cup with 5 red and 4 yellow balls in it. All of the balls are the same size.]() Kate picks out three balls at the same time.

She wants to work out the probability all the balls are red.

What is the denominator of the final unsimplified answer?

Options:
A. \( 24 \)
B. \( 9 \)
C. \( 504 \)
D. \( 729 \)

Solve the problem as a student with the misconception above.
You 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 a right angle is 90 degrees

Question:
What is the size of angle \( a \) ? ![Angles on a straight line split into 3 unequal parts labelled with a, 4a and a right angle marker]()

Options:
A. \( 18^{\degree} \)
B. \( 36^{\degree} \)
C. \( 22.5^{\degree} \)
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 solving an equation where there is a negative sign in front of the variable at the final stage, believes they can ignore it and treat it as if it's positive

Question:
Nick has almost solved a pair of simultaneous equations.
He just needs to find the value of \( y \).
He writes down:
\[
3-y=5
\]

What is the correct value of \( y \) ?

Options:
A. \( y=2 \)
B. \( y=-2 \)
C. \( y=8 \)
D. \( y=-8 \)

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


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

Question:
Nick has almost solved a pair of simultaneous equations.
He just needs to find the value of \( y \).
He writes down:
\[
3-y=5
\]

What is the correct value of \( y \) ?

Options:
A. \( y=2 \)
B. \( y=-2 \)
C. \( y=8 \)
D. \( y=-8 \)

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:
Fails to reflect across mirror line

Question:
If you reflect the rectangle in the horizontal line, where does the marked corner end up? ![Square paper with a red rectangle drawn, a mirror line and then the labels A, B C and D. A is above B which is above C and D is two spaces to the right of C. The red rectangle has its top left vertex highlighted with a blue circle.]()

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:
Fails to reflect across mirror line

Question:
If you reflect the rectangle in the horizontal line, where does the marked corner end up? ![Square paper with a red rectangle drawn, a mirror line and then the labels A, B C and D. A is above B which is above C and D is two spaces to the right of C. The red rectangle has its top left vertex highlighted with a blue circle.]()

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:
Fails to reflect across mirror line

Question:
If you reflect the rectangle in the horizontal line, where does the marked corner end up? ![A grid of 9 squares across and 7 squares up. A red horizontal line goes across the whole grid, it is 3 squares up from the bottom of the grid. An orange rectangle (3 squares width and 2 squares height) is drawn below the red line.  Horizontally, the rectangle is exactly in the middle of the grid. Vertically, the rectangle is 1 square down from the red line. The bottom left corner of the rectangle is marked with a tiny blue circle.
A letter "A" is marking a point directly above the tiny blue circle, 3 squares above the red line. A letter "B" is marking a point directly above the tiny blue circle, 2 squares above the red line. A letter "C" is marking a point directly above the tiny blue circle, 1 square above the red line. A letter "D" is marking a point 6 squares along from the tiny blue circle and 3 squares above the red line. ]()

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:
Rotates instead of reflects

Question:
If you reflect the rectangle in the horizontal line, where does the marked corner end up? ![A grid of 9 squares across and 7 squares up. A red horizontal line goes across the whole grid, it is 3 squares up from the bottom of the grid. An orange rectangle (3 squares width and 2 squares height) is drawn below the red line.  Horizontally, the rectangle is exactly in the middle of the grid. Vertically, the rectangle is 1 square down from the red line. The bottom left corner of the rectangle is marked with a tiny blue circle.
A letter "A" is marking a point directly above the tiny blue circle, 3 squares above the red line. A letter "B" is marking a point directly above the tiny blue circle, 2 squares above the red line. A letter "C" is marking a point directly above the tiny blue circle, 1 square above the red line. A letter "D" is marking a point 6 squares along from the tiny blue circle and 3 squares above the red line. ]()

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:
Cannot identify mutually exclusive events

Question:
Percy is playing a game where all \( 26 \) letters of the alphabet at placed into a bag and Percy has to pick one out at random.
Picking a \( \mathrm{P} \) and a vowel are known as...

Options:
A. Independent events
B. Mutually exclusive events
C. Probability events
D. Dependant events

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


Prompt:
Misconception:
Cannot identify mutually exclusive events

Question:
Percy is playing a game where all \( 26 \) letters of the alphabet at placed into a bag and Percy has to pick one out at random.
Picking a \( \mathrm{P} \) and a vowel are known as...

Options:
A. Independent events
B. Mutually exclusive events
C. Probability events
D. Dependant events

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


Prompt:
Misconception:
Cannot identify mutually exclusive events

Question:
Percy is playing a game where all \( 26 \) letters of the alphabet at placed into a bag and Percy has to pick one out at random.
Picking a \( \mathrm{P} \) and a vowel are known as...

Options:
A. Independent events
B. Mutually exclusive events
C. Probability events
D. Dependant events

Solve the problem as a student with the misconception above.
You 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 multiplied the base number and the power

Question:
\(
P=4^{k}
\)

What is the value of \( P \) when \( k=-3 \) ?

Options:
A. \( -12 \)
B. \( -64 \)
C. \( \frac{1}{64} \)
D. \( -\frac{1}{64} \)

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


Prompt:
Misconception:
Believes a negative power results in a negative answer

Question:
\(
P=4^{k}
\)

What is the value of \( P \) when \( k=-3 \) ?

Options:
A. \( -12 \)
B. \( -64 \)
C. \( \frac{1}{64} \)
D. \( -\frac{1}{64} \)

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


Prompt:
Misconception:
Believes a negative power results in a negative answer

Question:
\(
P=4^{k}
\)

What is the value of \( P \) when \( k=-3 \) ?

Options:
A. \( -12 \)
B. \( -64 \)
C. \( \frac{1}{64} \)
D. \( -\frac{1}{64} \)

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


Prompt:
Misconception:
Believes division is commutative

Question:
Tom and Katie are discussing expressions
Tom says \( \frac{p}{q} \) is equivalent to \( \frac{q}{p} \)
Katie says \( p q \) is equivalent to \( q p \)
Who do you agree with?

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

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


Prompt:
Misconception:
Believes division is commutative

Question:
Tom and Katie are discussing expressions
Tom says \( \frac{p}{q} \) is equivalent to \( \frac{q}{p} \)
Katie says \( p q \) is equivalent to \( q p \)
Who do you agree with?

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

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


Prompt:
Misconception:
Believes multiplication is not commutative

Question:
Tom and Katie are discussing expressions
Tom says \( \frac{p}{q} \) is equivalent to \( \frac{q}{p} \)
Katie says \( p q \) is equivalent to \( q p \)
Who do you agree with?

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

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


Prompt:
Misconception:
Believes the gradient of a distance-time graph is the acceleration

Question:
This graph shows how far Jodie is from home whilst she is out on a walk.
What might the positive sloping section represent? ![A distance time graph formed by three line segments in the shape of a trapezium. The first line segment is upward sloping and starts at 0. The end of this line segment is connected to a horizontal line that is extending to the right. The third line connects this line to the x axis and has a relatively steep negative gradient.]()

Options:
A. Jodie is accelerating
B. Jodie is walking away from home
C. Jodie is walking towards home
D. Jodie has stopped walking

Solve the problem as a student with the misconception above.
You 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 an upward slope on a distance-time graph means travelling back towards the starting point.

Question:
This graph shows how far Jodie is from home whilst she is out on a walk.
What might the positive sloping section represent? ![A distance time graph formed by three line segments in the shape of a trapezium. The first line segment is upward sloping and starts at 0. The end of this line segment is connected to a horizontal line that is extending to the right. The third line connects this line to the x axis and has a relatively steep negative gradient.]()

Options:
A. Jodie is accelerating
B. Jodie is walking away from home
C. Jodie is walking towards home
D. Jodie has stopped walking

Solve the problem as a student with the misconception above.
You 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 an upward slope on a distance-time graph means the movement has stopped

Question:
This graph shows how far Jodie is from home whilst she is out on a walk.
What might the positive sloping section represent? ![A distance time graph formed by three line segments in the shape of a trapezium. The first line segment is upward sloping and starts at 0. The end of this line segment is connected to a horizontal line that is extending to the right. The third line connects this line to the x axis and has a relatively steep negative gradient.]()

Options:
A. Jodie is accelerating
B. Jodie is walking away from home
C. Jodie is walking towards home
D. Jodie has stopped walking

Solve the problem as a student with the misconception above.
You 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 square numbers are triangle numbers

Question:
\( 1,3,6,10,15,21,28 \ldots \) What is the name commonly given to this sequence of numbers?

Options:
A. The square numbers
B. The triangle numbers
C. The cube numbers
D. The Fibonacci numbers

Solve the problem as a student with the misconception above.
You 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 cube numbers are triangular numbers

Question:
\( 1,3,6,10,15,21,28 \ldots \) What is the name commonly given to this sequence of numbers?

Options:
A. The square numbers
B. The triangle numbers
C. The cube numbers
D. The Fibonacci numbers

Solve the problem as a student with the misconception above.
You 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 Fibonacci numbers are triangle numbers

Question:
\( 1,3,6,10,15,21,28 \ldots \) What is the name commonly given to this sequence of numbers?

Options:
A. The square numbers
B. The triangle numbers
C. The cube numbers
D. The Fibonacci numbers

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


Prompt:
Misconception:
Estimates the length of diagonal lines rather than working out based on horizontal and vertical measurements

Question:
![A coordinate grid with a line segment labelled K from (-1,2) to (4,3) and a line segment marked L from (-3,-4) to (-2,0)]() What can you say about line segments \( \mathrm{K} \) and \( \mathrm{L} \) ?

Options:
A. \( \mathrm{K} \) is longer than \( \mathrm{L} \)
B. \( \mathrm{K} \) is shorter than \( \mathrm{L} \)
C. \( \mathrm{K} \) and \( \mathrm{L} \) are the same length
D. We don't have enough information without measuring them

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


Prompt:
Misconception:
Does not believe the length of a diagonal line can be worked out based on horizontal and vertical measurements

Question:
![A coordinate grid with a line segment labelled K from (-1,2) to (4,3) and a line segment marked L from (-3,-4) to (-2,0)]() What can you say about line segments \( \mathrm{K} \) and \( \mathrm{L} \) ?

Options:
A. \( \mathrm{K} \) is longer than \( \mathrm{L} \)
B. \( \mathrm{K} \) is shorter than \( \mathrm{L} \)
C. \( \mathrm{K} \) and \( \mathrm{L} \) are the same length
D. We don't have enough information without measuring them

Solve the problem as a student with the misconception above.
You 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 volume when asked for surface area

Question:
Which calculation would give you the area of the face of this cuboid labelled \( \boldsymbol{Q} \) ('the base')? ![An image of a cuboid, with the height marked as 7cm, the width as 4cm and the depth as 2cm. The bottom face is shaded red and marked Q. ]()

Options:
A. \( 2 \mathrm{~cm} \times 4 \mathrm{~cm} \times 7 \mathrm{~cm} \)
B. \( 4 \mathrm{~cm} \times 7 \mathrm{~cm} \)
C. \( 4 \mathrm{~cm} \times 2 \mathrm{~cm} \)
D. \( 2 \mathrm{~cm} \times 7 \mathrm{~cm} \)

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


Prompt:
Misconception:
Cannot identify the correct side lengths to use when asked to find the area of a face

Question:
Which calculation would give you the area of the face of this cuboid labelled \( \boldsymbol{Q} \) ('the base')? ![An image of a cuboid, with the height marked as 7cm, the width as 4cm and the depth as 2cm. The bottom face is shaded red and marked Q. ]()

Options:
A. \( 2 \mathrm{~cm} \times 4 \mathrm{~cm} \times 7 \mathrm{~cm} \)
B. \( 4 \mathrm{~cm} \times 7 \mathrm{~cm} \)
C. \( 4 \mathrm{~cm} \times 2 \mathrm{~cm} \)
D. \( 2 \mathrm{~cm} \times 7 \mathrm{~cm} \)

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


Prompt:
Misconception:
Cannot identify the correct side lengths to use when asked to find the area of a face

Question:
Which calculation would give you the area of the face of this cuboid labelled \( \boldsymbol{Q} \) ('the base')? ![An image of a cuboid, with the height marked as 7cm, the width as 4cm and the depth as 2cm. The bottom face is shaded red and marked Q. ]()

Options:
A. \( 2 \mathrm{~cm} \times 4 \mathrm{~cm} \times 7 \mathrm{~cm} \)
B. \( 4 \mathrm{~cm} \times 7 \mathrm{~cm} \)
C. \( 4 \mathrm{~cm} \times 2 \mathrm{~cm} \)
D. \( 2 \mathrm{~cm} \times 7 \mathrm{~cm} \)

Solve the problem as a student with the misconception above.
You 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 a parallelogram

Question:
Tom and Katie are discussing this shape
Tom says it is a rectangle
Katie says it is a parallelogram
Who do you agree with? ![Purple parallelogram with parallel sides labelled]()

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

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


Prompt:
Misconception:
Does not know the properties of a rectangle

Question:
Tom and Katie are discussing this shape
Tom says it is a rectangle
Katie says it is a parallelogram
Who do you agree with? ![Purple parallelogram with parallel sides labelled]()

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 a parallelogram

Question:
Tom and Katie are discussing this shape
Tom says it is a rectangle
Katie says it is a parallelogram
Who do you agree with? ![Purple parallelogram with parallel sides labelled]()

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

Question:
Calculate
\(
\frac{2}{5} \div 3
\)

Options:
A. \( \frac{6}{5} \)
B. \( \frac{15}{2} \)
C. \( \frac{2}{15} \)
D. \( \frac{6}{15} \)

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 dividing fractions, does the reciprocal of the first fraction instead of the second

Question:
Calculate
\(
\frac{2}{5} \div 3
\)

Options:
A. \( \frac{6}{5} \)
B. \( \frac{15}{2} \)
C. \( \frac{2}{15} \)
D. \( \frac{6}{15} \)

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 dividing a fraction by an integer, multiplies both the numerator and denominator by the integer

Question:
Calculate
\(
\frac{2}{5} \div 3
\)

Options:
A. \( \frac{6}{5} \)
B. \( \frac{15}{2} \)
C. \( \frac{2}{15} \)
D. \( \frac{6}{15} \)

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


Prompt:
Misconception:
Does not 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?

\(
x^{2}-5 x=6
\)

Options:
A. Add \( 5 x \) to both sides of the equation
B. Subtract \( 6 \) from both sides of the equation
C. Divide by \( x \)
D. Square root 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?

\(
x^{2}-5 x=6
\)

Options:
A. Add \( 5 x \) to both sides of the equation
B. Subtract \( 6 \) from both sides of the equation
C. Divide by \( x \)
D. Square root 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?

\(
x^{2}-5 x=6
\)

Options:
A. Add \( 5 x \) to both sides of the equation
B. Subtract \( 6 \) from both sides of the equation
C. Divide by \( x \)
D. Square root 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:
Divided by 100 rather than 1000

Question:
\( 609 \div 1000= \)

Options:
A. \( 0.609 \)
B. \( 0.69 \)
C. \( 6.09 \)
D. \( 609.000 \)

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


Prompt:
Misconception:
Adds 3 decimal places rather than moving 3 places

Question:
\( 609 \div 1000= \)

Options:
A. \( 0.609 \)
B. \( 0.69 \)
C. \( 6.09 \)
D. \( 609.000 \)

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


Prompt:
Misconception:
Only multiplies the first term in the expansion of a bracket

Question:
\(
x(2 x-1)+3(4 x-2) \equiv P x^{2}+Q x+R
\)

What is the value of \( R \) ?

Options:
A. \( -2 \)
B. \( -3 \)
C. \( -7 \)
D. \( -6 \)

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


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

Question:
\(
x(2 x-1)+3(4 x-2) \equiv P x^{2}+Q x+R
\)

What is the value of \( R \) ?

Options:
A. \( -2 \)
B. \( -3 \)
C. \( -7 \)
D. \( -6 \)

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


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

Question:
\(
x(2 x-1)+3(4 x-2) \equiv P x^{2}+Q x+R
\)

What is the value of \( R \) ?

Options:
A. \( -2 \)
B. \( -3 \)
C. \( -7 \)
D. \( -6 \)

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


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

Question:
\(
\frac{7}{10}-\frac{2}{5}=\frac{\bigstar}{10}
\)
What should replace the star?

Options:
A. \( 11 \)
B. \( 5 \)
C. \( 3 \)
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:
Does not find a common denominator when adding/subtracting fractions

Question:
\(
\frac{7}{10}-\frac{2}{5}=\frac{\bigstar}{10}
\)
What should replace the star?

Options:
A. \( 11 \)
B. \( 5 \)
C. \( 3 \)
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:
Does not know the properties of a cylinder

Question:
Name the polyhedron that can be made from this net ![Net showing four rectangles and two squares]()

Options:
A. Rectangular prism
B. Cylinder
C. Rectangular pyramid
D. Cube

Solve the problem as a student with the misconception above.
You 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:
Name the polyhedron that can be made from this net ![Net showing four rectangles and two squares]()

Options:
A. Rectangular prism
B. Cylinder
C. Rectangular pyramid
D. Cube

Solve the problem as a student with the misconception above.
You 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 cubes and cuboids

Question:
Name the polyhedron that can be made from this net ![Net showing four rectangles and two squares]()

Options:
A. Rectangular prism
B. Cylinder
C. Rectangular pyramid
D. Cube

Solve the problem as a student with the misconception above.
You 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 subtraction is commutative

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

Options:
A. \( 6 \)
B. \( -6 \)
C. \( -9 \)
D. \( 12 \)

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


Prompt:
Misconception:
Believes the y intercept is given by the difference between the x and y coordinates of any point on the line, not just the point (0, c)

Question:
A line has a gradient of \( 4 \) and passes through the point \( (1,9) \). What is it's equation?

Options:
A. \( y=4 x+8 \)
B. \( y=4 x+5 \)
C. \( y=4 x+9 \)
D. \( y=9 x+4 \)

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  c, in y=mx+c, will be the y value of the coordinate given despite the x coordinate not being 0.

Question:
A line has a gradient of \( 4 \) and passes through the point \( (1,9) \). What is it's equation?

Options:
A. \( y=4 x+8 \)
B. \( y=4 x+5 \)
C. \( y=4 x+9 \)
D. \( y=9 x+4 \)

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:
Mixes up odd and even numbers

Question:
\[
27,64,125, \ldots
\]

This is the \( 3^{\text {rd }}, 4^{\text {th }} \) and \( 5^{\text {th }} \) term from what sequence of numbers?

Options:
A. The odd numbers
B. The square numbers
C. The triangular numbers
D. The cube numbers

Solve the problem as a student with the misconception above.
You 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:
\[
27,64,125, \ldots
\]

This is the \( 3^{\text {rd }}, 4^{\text {th }} \) and \( 5^{\text {th }} \) term from what sequence of numbers?

Options:
A. The odd numbers
B. The square numbers
C. The triangular numbers
D. The cube numbers

Solve the problem as a student with the misconception above.
You 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 cube numbers are triangular numbers

Question:
\[
27,64,125, \ldots
\]

This is the \( 3^{\text {rd }}, 4^{\text {th }} \) and \( 5^{\text {th }} \) term from what sequence of numbers?

Options:
A. The odd numbers
B. The square numbers
C. The triangular numbers
D. The cube numbers

Solve the problem as a student with the misconception above.
You 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 decimals, does not realize that the order and position of the digits (relative to each other) has to remain constant.

Question:
\( 70.04 \div 0.1= \)

Options:
A. \( 70.004 \)
B. \( 700.04 \)
C. \( 700.4 \)
D. \( 7.004 \)

Solve the problem as a student with the misconception above.
You 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 decimals, does not realize that the order and position of the digits (relative to each other) has to remain constant.

Question:
\( 70.04 \div 0.1= \)

Options:
A. \( 70.004 \)
B. \( 700.04 \)
C. \( 700.4 \)
D. \( 7.004 \)

Solve the problem as a student with the misconception above.
You 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 decimals, divides rather than multiplies when reinserting the decimal.

Question:
\( 70.04 \div 0.1= \)

Options:
A. \( 70.004 \)
B. \( 700.04 \)
C. \( 700.4 \)
D. \( 7.004 \)

Solve the problem as a student with the misconception above.
You 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 a term with an equation

Question:
Which of the following is the most appropriate word to describe \( y^{2} \) in this: \( y^{2}-9 \)

Options:
A. Equation
B. Term
C. Variable
D. Expression

Solve the problem as a student with the misconception above.
You 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 a term with a variable

Question:
Which of the following is the most appropriate word to describe \( y^{2} \) in this: \( y^{2}-9 \)

Options:
A. Equation
B. Term
C. Variable
D. Expression

Solve the problem as a student with the misconception above.
You 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 an expression with a term

Question:
Which of the following is the most appropriate word to describe \( y^{2} \) in this: \( y^{2}-9 \)

Options:
A. Equation
B. Term
C. Variable
D. Expression

Solve the problem as a student with the misconception above.
You 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 co-interior angles are equal

Question:
Tom and Katie are arguing about angle relationships on parallel lines.
Tom says allied (co-interior) angles are equal.
Katie says corresponding angles are equal.
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 co-interior angles are equal

Question:
Tom and Katie are arguing about angle relationships on parallel lines.
Tom says allied (co-interior) angles are equal.
Katie says corresponding angles are equal.
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 corresponding angles sum to 180 degrees

Question:
Tom and Katie are arguing about angle relationships on parallel lines.
Tom says allied (co-interior) angles are equal.
Katie says corresponding angles are equal.
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:
Writes a variable to the power of n as nx

Question:
If we want to write
"\( \boldsymbol{m} \) multiplied by \( \boldsymbol{m} \)"
using algebra, this would be:

Options:
A. \( 2 m \)
B. \( \mathrm{mm} \)
C. \( m^{m} \)
D. \( m^{2} \)

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 realize we can simplify a term that involves powers

Question:
If we want to write
"\( \boldsymbol{m} \) multiplied by \( \boldsymbol{m} \)"
using algebra, this would be:

Options:
A. \( 2 m \)
B. \( \mathrm{mm} \)
C. \( m^{m} \)
D. \( m^{2} \)

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:
Multiplies by the index

Question:
If we want to write
"\( \boldsymbol{m} \) multiplied by \( \boldsymbol{m} \)"
using algebra, this would be:

Options:
A. \( 2 m \)
B. \( \mathrm{mm} \)
C. \( m^{m} \)
D. \( m^{2} \)

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


Prompt:
Misconception:
Does not know how to find order of rotational symmetry

Question:
Which shape has the highest order of rotational symmetry?

Options:
A. ![Equilateral triangle]()
B. ![Circle]()
C. ![Square]()
D. ![Hexagon]()

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


Prompt:
Misconception:
Does not know how to find order of rotational symmetry

Question:
Which shape has the highest order of rotational symmetry?

Options:
A. ![Equilateral triangle]()
B. ![Circle]()
C. ![Square]()
D. ![Hexagon]()

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


Prompt:
Misconception:
Does not know how to find order of rotational symmetry

Question:
Which shape has the highest order of rotational symmetry?

Options:
A. ![Equilateral triangle]()
B. ![Circle]()
C. ![Square]()
D. ![Hexagon]()

Solve the problem as a student with the misconception above.
You 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 with a non-unit coefficient of x squared, believes that coefficient will be in front of both x terms in the factorised form

Question:
Step 1: Factorise the following expression
\(
2 x^{2}+7 x+3
\)

Options:
A. \( (2 x+1)(x+3) \)
B. \( (2 x+3)(x+1) \)
C. \( (2 x+1)(2 x+3) \)
D. Cannot be factorised

Solve the problem as a student with the misconception above.
You 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 number from a positive number, uses a method which assumes one of the negative signs can be ignored

Question:
This is a part of the table of values for the equation
\[y=x^{2}-x\] \begin{tabular}{|c|c|}
\hline\( x \) & \( -7 \) \\
\hline\( y \) & \(\bigstar\) \\
\hline
\end{tabular} What should replace the star?

Options:
A. \( 42 \)
B. \( -56 \)
C. \( -42 \)
D. \( 56 \)

Solve the problem as a student with the misconception above.
You 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:
This is a part of the table of values for the equation
\[y=x^{2}-x\] \begin{tabular}{|c|c|}
\hline\( x \) & \( -7 \) \\
\hline\( y \) & \(\bigstar\) \\
\hline
\end{tabular} What should replace the star?

Options:
A. \( 42 \)
B. \( -56 \)
C. \( -42 \)
D. \( 56 \)

Solve the problem as a student with the misconception above.
You 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 multiplied the base number and the power

Question:
What answer would your calculator give if you typed in
\(
-6^{2}
\) ![A scientific calculator]()

Options:
A. \( 12 \)
B. \( -12 \)
C. \( 36 \)
D. \( -36 \)

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


Prompt:
Misconception:
Multiplies by the index

Question:
What answer would your calculator give if you typed in
\(
-6^{2}
\) ![A scientific calculator]()

Options:
A. \( 12 \)
B. \( -12 \)
C. \( 36 \)
D. \( -36 \)

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


Prompt:
Misconception:
Carries out operations from left to right regardless of priority order

Question:
What answer would your calculator give if you typed in
\(
-6^{2}
\) ![A scientific calculator]()

Options:
A. \( 12 \)
B. \( -12 \)
C. \( 36 \)
D. \( -36 \)

Solve the problem as a student with the misconception above.
You 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 cm, 10 cm, 7 cm, 3 cm and 4 cm. One side is unlabelled.]()

Options:
A. \( 4 \mathrm{~cm} \)
B. \( 3 \mathrm{~cm} \)
C. \( 3.5 \mathrm{~cm} \)
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 cm, 10 cm, 7 cm, 3 cm and 4 cm. One side is unlabelled.]()

Options:
A. \( 4 \mathrm{~cm} \)
B. \( 3 \mathrm{~cm} \)
C. \( 3.5 \mathrm{~cm} \)
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 cm, 10 cm, 7 cm, 3 cm and 4 cm. One side is unlabelled.]()

Options:
A. \( 4 \mathrm{~cm} \)
B. \( 3 \mathrm{~cm} \)
C. \( 3.5 \mathrm{~cm} \)
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:
Believes the frequency represented by a pie chart sector can be judged visually, without considering the total it represents

Question:
These pie charts show how people travel to work in two towns. The populations of the towns are given. In which town do more people travel to work by train? ![A diagram showing two pie charts and a key. The key consists of car, bike, walk and train. The pie chart for town A (population 2000) has 1/2 a pie chart for bike, 1/4 for car and two smaller sections for walk and train. The pie chart for town B (population 10 000) has a proportion just under 1/2 for bike, a section just over 1/4 for walk, and just under a 1/4 for train. The section for car is very small.]()

Options:
A. Town A
B. Town B
C. Both the same
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:
Counts leading zero as a significant figure

Question:
\( 0.009753 \)

What is this number rounded to \( 2 \) significant figures?

Options:
A. \( 0.0 \)
B. \( 0.0098 \)
C. \( 0.01 \)
D. \( 0.0097 \)

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


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

Question:
\( 0.009753 \)

What is this number rounded to \( 2 \) significant figures?

Options:
A. \( 0.0 \)
B. \( 0.0098 \)
C. \( 0.01 \)
D. \( 0.0097 \)

Solve the problem as a student with the misconception above.
You 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:
\( 0.009753 \)

What is this number rounded to \( 2 \) significant figures?

Options:
A. \( 0.0 \)
B. \( 0.0098 \)
C. \( 0.01 \)
D. \( 0.0097 \)

Solve the problem as a student with the misconception above.
You 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 in the wrong direction on a number line

Question:
What number belongs in the box?
\(
(-8)+3=
\square\)

Options:
A. \( -5 \)
B. \( -11 \)
C. \( 11 \)
D. \( -6 \)

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


Prompt:
Misconception:
Counts the starting number when counting on

Question:
What number belongs in the box?
\(
(-8)+3=
\square\)

Options:
A. \( -5 \)
B. \( -11 \)
C. \( 11 \)
D. \( -6 \)

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


Prompt:
Misconception:
When asked to rotate by 180 degrees rotates by 90 degrees

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

Where will the red point be on the rotated shape?

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

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


Prompt:
Misconception:
Rotates by the wrong center of rotation (not including the origin)

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

Where will the red point be on the rotated shape?

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

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


Prompt:
Misconception:
Reflects instead of rotates

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

Where will the red point be on the rotated shape?

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

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


Prompt:
Misconception:
Includes the x variable when giving the equation of a horizontal line

Question:
What is the equation of this line? ![A coordinate grid from 0 to 10 in the y direction and -5 to 10 in the x direction. There is a line drawn passing through the coordinates: (-5,7) (0,7) (5,7) (10,7)]()

Options:
A. \( y=7 x \)
B. \( x=7 y \)
C. \( y=7 \)
D. \( x=7 \)

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:
Confuses the equations of vertical and horizontal lines

Question:
What is the equation of this line? ![A coordinate grid from 0 to 10 in the y direction and -5 to 10 in the x direction. There is a line drawn passing through the coordinates: (-5,7) (0,7) (5,7) (10,7)]()

Options:
A. \( y=7 x \)
B. \( x=7 y \)
C. \( y=7 \)
D. \( x=7 \)

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:
Multiplies rather than divides

Question:
\( 0.2 \div 0.4= \)

Options:
A. \( 0.08 \)
B. \( 0.5 \)
C. \( 0.8 \)
D. \( 2 \)

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:
Multiplies rather than divides

Question:
\( 0.2 \div 0.4= \)

Options:
A. \( 0.08 \)
B. \( 0.5 \)
C. \( 0.8 \)
D. \( 2 \)

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 division is commutative

Question:
\( 0.2 \div 0.4= \)

Options:
A. \( 0.08 \)
B. \( 0.5 \)
C. \( 0.8 \)
D. \( 2 \)

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:
Doubles the diameter when finding the radius

Question:
If the diameter of a circle is \( 5.4 \mathrm{~cm} \), the radius is...

Options:
A. \( 2.2 \mathrm{~cm} \)
B. \( 10.8 \mathrm{~cm} \)
C. \( 2.7 \mathrm{~cm} \)
D. \( 5.4 \mathrm{~cm} \)

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


Prompt:
Misconception:
Confuses diameter and radius

Question:
If the diameter of a circle is \( 5.4 \mathrm{~cm} \), the radius is...

Options:
A. \( 2.2 \mathrm{~cm} \)
B. \( 10.8 \mathrm{~cm} \)
C. \( 2.7 \mathrm{~cm} \)
D. \( 5.4 \mathrm{~cm} \)

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


Prompt:
Misconception:
Gets their constants and coefficients the wrong way around when writing a formula from a given situation

Question:
A taxi driver charges an initial \( £ 2.50 \) plus \( £ 1.20 \) per mile travelled. Which of the following expressions is correct for the total cost, \( T \), of a journey of \( \boldsymbol{m} \) miles?

Options:
A. \( \mathrm{T}=2.50 \mathrm{~m}+1.20 \)
B. \( \mathrm{T}=1.20 \mathrm{~m}+2.50 \)
C. \( \mathrm{T}=1.20(2.50+m) \)
D. \( \mathrm{T}=3.70 \mathrm{~m} \)

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


Prompt:
Misconception:
Has made an order of operations mistake when writing a formula from a given situation

Question:
A taxi driver charges an initial \( £ 2.50 \) plus \( £ 1.20 \) per mile travelled. Which of the following expressions is correct for the total cost, \( T \), of a journey of \( \boldsymbol{m} \) miles?

Options:
A. \( \mathrm{T}=2.50 \mathrm{~m}+1.20 \)
B. \( \mathrm{T}=1.20 \mathrm{~m}+2.50 \)
C. \( \mathrm{T}=1.20(2.50+m) \)
D. \( \mathrm{T}=3.70 \mathrm{~m} \)

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


Prompt:
Misconception:
Combines variables with constants when writing a formula from a given situation

Question:
A taxi driver charges an initial \( £ 2.50 \) plus \( £ 1.20 \) per mile travelled. Which of the following expressions is correct for the total cost, \( T \), of a journey of \( \boldsymbol{m} \) miles?

Options:
A. \( \mathrm{T}=2.50 \mathrm{~m}+1.20 \)
B. \( \mathrm{T}=1.20 \mathrm{~m}+2.50 \)
C. \( \mathrm{T}=1.20(2.50+m) \)
D. \( \mathrm{T}=3.70 \mathrm{~m} \)

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


Prompt:
Misconception:
Does not realise that the area of a triangle is half the area of the contatining rectangle

Question:
What is the area of this shape? ![Right angled triangle on square grid with area of 3 square units]()

Options:
A. \( 3 \)
B. \( 3.5 \)
C. \( 4 \)
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 realise that the area of a triangle is half the area of the contatining rectangle

Question:
What is the area of this shape? ![Right angled triangle on square grid with area of 3 square units]()

Options:
A. \( 3 \)
B. \( 3.5 \)
C. \( 4 \)
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}.