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

Question:
What is \( 637 \) rounded to the nearest \( 1000 \) ?

Options:
A. \( 500 \)
B. \( 1000 \)
C. \( 0 \)
D. \( 6000 \)

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


Prompt:
Misconception:
Rounds down instead of up

Question:
What is \( 637 \) rounded to the nearest \( 1000 \) ?

Options:
A. \( 500 \)
B. \( 1000 \)
C. \( 0 \)
D. \( 6000 \)

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


Prompt:
Misconception:
Thinks x^2 - a^2x is a valid form of difference of two squares

Question:
Tom and Katie are arguing about how to solve this equation:

\(
x^{2}+4 x=0
\)

Tom says one solution is \( x=2 \)

Katie says one solution is \( x=0 \)

Who is correct?

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

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


Prompt:
Misconception:
Does not know that units of volume are usually cubed

Question:
James has answered a question on volume. His answer is 8.5.
Behind the star he has written the units that he used.

\(
8.5 \,\bigstar
\)

Which of the following units is definitely wrong?

Options:
A. \( \mathrm{cm}^{3} \)
B. \( \mathrm{mm}^{2} \)
C. \( m^{3} \)
D. \( l \)

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


Prompt:
Misconception:
Does not know that units of volume are usually cubed

Question:
James has answered a question on volume. His answer is 8.5.
Behind the star he has written the units that he used.

\(
8.5 \,\bigstar
\)

Which of the following units is definitely wrong?

Options:
A. \( \mathrm{cm}^{3} \)
B. \( \mathrm{mm}^{2} \)
C. \( m^{3} \)
D. \( l \)

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


Prompt:
Misconception:
Does not recognise litres as a unit of volume

Question:
James has answered a question on volume. His answer is 8.5.
Behind the star he has written the units that he used.

\(
8.5 \,\bigstar
\)

Which of the following units is definitely wrong?

Options:
A. \( \mathrm{cm}^{3} \)
B. \( \mathrm{mm}^{2} \)
C. \( m^{3} \)
D. \( l \)

Solve the problem as a student with the misconception above.
You 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:
Which image completes a symmetric figure using the red line of symmetry? ![A shape composed of coloured squares is drawn on the left side of a vertical line of symmetry]()

Options:
A. ![The shape has been reflected in the line of symmetry, but the coloured squares are not in the corresponding places]()
B. ![The shape has been translated right by 4 squares so that it is now on the right hand side of the line of symmetry, but has not changed orientation]()
C. ![The shape has been reflected in the line of symmetry, The coloured squares have been shaded in their corresponding places]()
D. ![The shape has been reflected in the line of symmetry, but the coloured squares are not in the corresponding places]()

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


Prompt:
Misconception:
Translates rather than reflects across a line of symmetry

Question:
Which image completes a symmetric figure using the red line of symmetry? ![A shape composed of coloured squares is drawn on the left side of a vertical line of symmetry]()

Options:
A. ![The shape has been reflected in the line of symmetry, but the coloured squares are not in the corresponding places]()
B. ![The shape has been translated right by 4 squares so that it is now on the right hand side of the line of symmetry, but has not changed orientation]()
C. ![The shape has been reflected in the line of symmetry, The coloured squares have been shaded in their corresponding places]()
D. ![The shape has been reflected in the line of symmetry, but the coloured squares are not in the corresponding places]()

Solve the problem as a student with the misconception above.
You 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:
Which image completes a symmetric figure using the red line of symmetry? ![A shape composed of coloured squares is drawn on the left side of a vertical line of symmetry]()

Options:
A. ![The shape has been reflected in the line of symmetry, but the coloured squares are not in the corresponding places]()
B. ![The shape has been translated right by 4 squares so that it is now on the right hand side of the line of symmetry, but has not changed orientation]()
C. ![The shape has been reflected in the line of symmetry, The coloured squares have been shaded in their corresponding places]()
D. ![The shape has been reflected in the line of symmetry, but the coloured squares are not in the corresponding places]()

Solve the problem as a student with the misconception above.
You 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:
This is an incomplete net for a triangular prism.

What shapes do you add to complete this net? ![An incomplete net of a triangular prism comprising a rectangle (landscape) and an equilateral triangle. These 2 shapes are attached to each other along one side (the righthand shorter side of the rectangle, which is the same length as the sides of the triangle). ]()

Options:
A. \( 1 \) triangle and \( 2 \) rectangles
B. \( 3 \) triangles
C. \( 3 \) rectangles
D. \( 1 \) triangle and \( 3 \) rectangles

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


Prompt:
Misconception:
Confuses pyramid with prism

Question:
This is an incomplete net for a triangular prism.

What shapes do you add to complete this net? ![An incomplete net of a triangular prism comprising a rectangle (landscape) and an equilateral triangle. These 2 shapes are attached to each other along one side (the righthand shorter side of the rectangle, which is the same length as the sides of the triangle). ]()

Options:
A. \( 1 \) triangle and \( 2 \) rectangles
B. \( 3 \) triangles
C. \( 3 \) rectangles
D. \( 1 \) triangle and \( 3 \) rectangles

Solve the problem as a student with the misconception above.
You 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:
This is an incomplete net for a triangular prism.

What shapes do you add to complete this net? ![An incomplete net of a triangular prism comprising a rectangle (landscape) and an equilateral triangle. These 2 shapes are attached to each other along one side (the righthand shorter side of the rectangle, which is the same length as the sides of the triangle). ]()

Options:
A. \( 1 \) triangle and \( 2 \) rectangles
B. \( 3 \) triangles
C. \( 3 \) rectangles
D. \( 1 \) triangle and \( 3 \) rectangles

Solve the problem as a student with the misconception above.
You 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 solutions of a quadratic equation are the absolute values of the constants in the factorised form

Question:
The area of the trapezium on the right is \( 12 \mathrm{~cm}^{2} \). ![A trapezium with the parallel sides a and b labelled x -1 and x + 3 and the perpendicular height as x.]() Based on the information given, Adam writes this formula:
\(x^{2}+x=12\)

What are the two solutions to this equation?

Options:
A. \( \begin{array}{c}x=4 \\ \text { and } \\ x=3\end{array} \)
B. \( \begin{array}{c}x=-4 \\ \text { and } \\ x=-3\end{array} \)
C. \( \begin{array}{c}x=4 \\ \text { and } \\ x=-3\end{array} \)
D. \( \begin{array}{c}x=-4 \\ \text { and } \\ x=3\end{array} \)

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


Prompt:
Misconception:
Believes the solutions of a quadratic equation are the constants in the factorised form

Question:
The area of the trapezium on the right is \( 12 \mathrm{~cm}^{2} \). ![A trapezium with the parallel sides a and b labelled x -1 and x + 3 and the perpendicular height as x.]() Based on the information given, Adam writes this formula:
\(x^{2}+x=12\)

What are the two solutions to this equation?

Options:
A. \( \begin{array}{c}x=4 \\ \text { and } \\ x=3\end{array} \)
B. \( \begin{array}{c}x=-4 \\ \text { and } \\ x=-3\end{array} \)
C. \( \begin{array}{c}x=4 \\ \text { and } \\ x=-3\end{array} \)
D. \( \begin{array}{c}x=-4 \\ \text { and } \\ x=3\end{array} \)

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


Prompt:
Misconception:
Thinks x = ? is a horizontal line through ?

Question:
What is the equation of this line? ![A set of axes with a line drawn on. The lines passes through the points: (0,2) (1,2) (2,2) (3,2) and (4,2)]()

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

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

Question:
What is the equation of this line? ![A set of axes with a line drawn on. The lines passes through the points: (0,2) (1,2) (2,2) (3,2) and (4,2)]()

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

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

Question:
What is the equation of this line? ![A set of axes with a line drawn on. The lines passes through the points: (0,2) (1,2) (2,2) (3,2) and (4,2)]()

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

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


Prompt:
Misconception:
Confuses chord and radius

Question:
What is the correct name for the line marked on the circle? ![A circle with a line from the centre of the circle to the circumference.]()

Options:
A. Radius
B. Chord
C. Tangent
D. Diameter

Solve the problem as a student with the misconception above.
You 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 tangent and radius

Question:
What is the correct name for the line marked on the circle? ![A circle with a line from the centre of the circle to the circumference.]()

Options:
A. Radius
B. Chord
C. Tangent
D. Diameter

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


Prompt:
Misconception:
Confuses diameter and radius

Question:
What is the correct name for the line marked on the circle? ![A circle with a line from the centre of the circle to the circumference.]()

Options:
A. Radius
B. Chord
C. Tangent
D. Diameter

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


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

Question:
What is the area of the shaded section of this composite shape made from rectangles? ![A composite shape that makes a backwards "L" shape from 2 rectangles.  The base of the shape is horizontal and is 11cm long. The vertical height of the whole shape is 12cm. The horizontal width of the top part of the shape is 5cm. The vertical height of the bottom rectangle is labelled 4cm. The top rectangle is shaded.]()

Options:
A. \( 40 \mathrm{~cm}^{2} \)
B. \( 20 \mathrm{~cm}^{2} \)
C. \( 30 \mathrm{~cm}^{2} \)
D. \( 60 \mathrm{~cm}^{2} \)

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:
Does not know how to find missing lengths in a composite shape

Question:
What is the area of the shaded section of this composite shape made from rectangles? ![A composite shape that makes a backwards "L" shape from 2 rectangles.  The base of the shape is horizontal and is 11cm long. The vertical height of the whole shape is 12cm. The horizontal width of the top part of the shape is 5cm. The vertical height of the bottom rectangle is labelled 4cm. The top rectangle is shaded.]()

Options:
A. \( 40 \mathrm{~cm}^{2} \)
B. \( 20 \mathrm{~cm}^{2} \)
C. \( 30 \mathrm{~cm}^{2} \)
D. \( 60 \mathrm{~cm}^{2} \)

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:
Beileves you can use the full length when finding an area of part of a composite shape, when part of the length is needed

Question:
What is the area of the shaded section of this composite shape made from rectangles? ![A composite shape that makes a backwards "L" shape from 2 rectangles.  The base of the shape is horizontal and is 11cm long. The vertical height of the whole shape is 12cm. The horizontal width of the top part of the shape is 5cm. The vertical height of the bottom rectangle is labelled 4cm. The top rectangle is shaded.]()

Options:
A. \( 40 \mathrm{~cm}^{2} \)
B. \( 20 \mathrm{~cm}^{2} \)
C. \( 30 \mathrm{~cm}^{2} \)
D. \( 60 \mathrm{~cm}^{2} \)

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 the coefficent of x in an expanded quadratic comes from multiplying the two numbers in the brackets

Question:
If
\(
m^{2}+3 m-28 \equiv(m+a)(m+b)
\)
then \( a \times b= \)

Options:
A. \( -3 \)
B. \( 3 \)
C. \( -28 \)
D. \( 28 \)

Solve the problem as a student with the misconception above.
You 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 into double brackets, believes the product of the constants in the brackets is of the opposite sign to the constant in the expanded equation.

Question:
If
\(
m^{2}+3 m-28 \equiv(m+a)(m+b)
\)
then \( a \times b= \)

Options:
A. \( -3 \)
B. \( 3 \)
C. \( -28 \)
D. \( 28 \)

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


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

Question:
Use the graph to approximate the solution to \( x^{2}+2 x-3<-3 \) ![A set of axes with the quadratic graph y=x^2+2x-3 drawn on.]()

Options:
A. \( -2<x<0 \)
B. \( x<-2, x>0 \)
C. \( x=-2 \)
D. \( -3<x<1 \)

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


Prompt:
Misconception:
When collecting like terms, only simplifies when there is an addition

Question:
Simplify the following by collecting like terms.
\[
4 x+6 x-3 x
\]

Options:
A. \( 10 x-3 x \)
B. \( 13 x \)
C. \( 7 x \)
D. \( x \)

Solve the problem as a student with the misconception above.
You 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 collecting like terms, treats subtractions as if they are additions

Question:
Simplify the following by collecting like terms.
\[
4 x+6 x-3 x
\]

Options:
A. \( 10 x-3 x \)
B. \( 13 x \)
C. \( 7 x \)
D. \( x \)

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


Prompt:
Misconception:
Does not realise that subtracting a larger number will give a smaller answer

Question:
Tom and Katie are discussing related calculations
Tom says if you know that \( 4122+426=4548 \), then \( 4122+428 \) must equal \( \mathbf{4 5 5 0} \)

Katie says if you know that \( 4122-426=3696 \), then \( 4122-428 \) must equal \( \mathbf{3 6 9 4} \)
Who is correct?

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

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


Prompt:
Misconception:
Does not realise that adding a larger number gives a larger answer

Question:
Tom and Katie are discussing related calculations
Tom says if you know that \( 4122+426=4548 \), then \( 4122+428 \) must equal \( \mathbf{4 5 5 0} \)

Katie says if you know that \( 4122-426=3696 \), then \( 4122-428 \) must equal \( \mathbf{3 6 9 4} \)
Who is correct?

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

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


Prompt:
Misconception:
Does not understand what each part of a bar model represents as a fraction

Question:
What should replace the question mark? ![A bar split into 5 equal parts. Four parts are shaded pink. The total length of the shaded parts is labelled 4/5. One shaded part is labelled with a question mark.]()

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

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


Prompt:
Misconception:
Does not understand what each part of a bar model represents as a fraction

Question:
What should replace the question mark? ![A bar split into 5 equal parts. Four parts are shaded pink. The total length of the shaded parts is labelled 4/5. One shaded part is labelled with a question mark.]()

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

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


Prompt:
Misconception:
Does not understand what each part of a bar model represents as a fraction

Question:
What should replace the question mark? ![A bar split into 5 equal parts. Four parts are shaded pink. The total length of the shaded parts is labelled 4/5. One shaded part is labelled with a question mark.]()

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

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


Prompt:
Misconception:
Does not recognise the height of a trapezium as the perpendicular length between the parallel sides

Question:
Sally wants to calculate the area of this trapezium using the formula: Area \( =\left(\frac{a+b}{2}\right) h \) ![A trapezium with the parallel sides labelled 6cm and 2cm, the slant height labelled 7cm and the perpendicular height labelled 5cm.]() What is the values of \( h \) ?

Options:
A. \( 6 \mathrm{~cm} \)
B. \( 5 \mathrm{~cm} \)
C. \( 7 \mathrm{~cm} \)
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:
Uses slant height instead of perpendicular height to find area of a trapezium

Question:
Sally wants to calculate the area of this trapezium using the formula: Area \( =\left(\frac{a+b}{2}\right) h \) ![A trapezium with the parallel sides labelled 6cm and 2cm, the slant height labelled 7cm and the perpendicular height labelled 5cm.]() What is the values of \( h \) ?

Options:
A. \( 6 \mathrm{~cm} \)
B. \( 5 \mathrm{~cm} \)
C. \( 7 \mathrm{~cm} \)
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 recognise the height of a trapezium as the perpendicular length between the parallel sides

Question:
Sally wants to calculate the area of this trapezium using the formula: Area \( =\left(\frac{a+b}{2}\right) h \) ![A trapezium with the parallel sides labelled 6cm and 2cm, the slant height labelled 7cm and the perpendicular height labelled 5cm.]() What is the values of \( h \) ?

Options:
A. \( 6 \mathrm{~cm} \)
B. \( 5 \mathrm{~cm} \)
C. \( 7 \mathrm{~cm} \)
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 rather than subtracts when answering worded problems

Question:
Nick wants to subtract \( 98 \) from a number.
Which one of the following methods would give him the correct answer?

Options:
A. \( +100 \) then \( +2 \)
B. \( -100 \) then \( -2 \)
C. \( -100 \) then \( +2 \)
D. \( +100 \) then \( -2 \)

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 understand the effect of consecutive subtractions

Question:
Nick wants to subtract \( 98 \) from a number.
Which one of the following methods would give him the correct answer?

Options:
A. \( +100 \) then \( +2 \)
B. \( -100 \) then \( -2 \)
C. \( -100 \) then \( +2 \)
D. \( +100 \) then \( -2 \)

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:
Adds rather than subtracts when answering worded problems

Question:
Nick wants to subtract \( 98 \) from a number.
Which one of the following methods would give him the correct answer?

Options:
A. \( +100 \) then \( +2 \)
B. \( -100 \) then \( -2 \)
C. \( -100 \) then \( +2 \)
D. \( +100 \) then \( -2 \)

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 the arrows for parallel lines mean equal length

Question:
The arrows tell us that these two sides are... ![Parallelogram PQRS with sides QR and PS labelled with arrows]()

Options:
A. The same length
B. Opposite
C. Parallel
D. Equilateral

Solve the problem as a student with the misconception above.
You 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 sign for parallel lines just means opposite

Question:
The arrows tell us that these two sides are... ![Parallelogram PQRS with sides QR and PS labelled with arrows]()

Options:
A. The same length
B. Opposite
C. Parallel
D. Equilateral

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


Prompt:
Misconception:
Does not know the meaning of equilateral

Question:
The arrows tell us that these two sides are... ![Parallelogram PQRS with sides QR and PS labelled with arrows]()

Options:
A. The same length
B. Opposite
C. Parallel
D. Equilateral

Solve the problem as a student with the misconception above.
You 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 when to find a multiple from a worded question

Question:
Problem 1: What is the product of \( 17 \) and \(32\)?
Problem 2: Each person in a group of \( 17 \) people owns \( 32 \) pieces of art. How many pieces of art does the group own in total?
Which of these problems needs multiplication to solve it?

Options:
A. Only
Problem \( 1 \)
B. Only Problem \( 2 \)
C. Both problems
D. Neither problem

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


Prompt:
Misconception:
Believes that product means add rather than multiply

Question:
Problem 1: What is the product of \( 17 \) and \(32\)?
Problem 2: Each person in a group of \( 17 \) people owns \( 32 \) pieces of art. How many pieces of art does the group own in total?
Which of these problems needs multiplication to solve it?

Options:
A. Only
Problem \( 1 \)
B. Only Problem \( 2 \)
C. Both problems
D. Neither problem

Solve the problem as a student with the misconception above.
You 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:
\( \frac{7}{6}, \frac{4}{3}, \frac{3}{2}, \frac{5}{3}, \ldots \) When calculating the nth-term rule of this sequence, what should replace the star? ![Text: "nth-term rule:" followed by a star, n and a purple rectangle. ]()

Options:
A. \( 2 \)
B. \( 1 \)
C. \( \frac{4}{3} \)
D. \( \frac{1}{6} \)

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:
Reverses the order of operations but does not apply the inverse operations when finding the input of a function machine

Question:
\( input\Rightarrow(+1) \Rightarrow(\times2) \Rightarrow9\) What is the input of this function machine?

Options:
A. \( 19 \)
B. \( 3.5 \)
C. \( 19 \)
D. \( 4 \)

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


Prompt:
Misconception:
Reverses the order of operations but does not apply the inverse operations when finding the input of a function machine

Question:
\( input\Rightarrow(+1) \Rightarrow(\times2) \Rightarrow9\) What is the input of this function machine?

Options:
A. \( 19 \)
B. \( 3.5 \)
C. \( 19 \)
D. \( 4 \)

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


Prompt:
Misconception:
Does not reverse the order of operations when finding the input of a function machine

Question:
\( input\Rightarrow(+1) \Rightarrow(\times2) \Rightarrow9\) What is the input of this function machine?

Options:
A. \( 19 \)
B. \( 3.5 \)
C. \( 19 \)
D. \( 4 \)

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


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

Question:
Convert this decimal to a percentage
\(
0.07
\)

Options:
A. \( 0.07 \% \)
B. \( 0.7 \% \)
C. \( 7 \% \)
D. \( 70 \% \)

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


Prompt:
Misconception:
Multiplies by 10 instead of 100 when converting decimal to percentage

Question:
Convert this decimal to a percentage
\(
0.07
\)

Options:
A. \( 0.07 \% \)
B. \( 0.7 \% \)
C. \( 7 \% \)
D. \( 70 \% \)

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


Prompt:
Misconception:
Multiplies by 1000 instead of 100 when converting a decimal to a percentage

Question:
Convert this decimal to a percentage
\(
0.07
\)

Options:
A. \( 0.07 \% \)
B. \( 0.7 \% \)
C. \( 7 \% \)
D. \( 70 \% \)

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


Prompt:
Misconception:
Believes the constant gives the y-intercept even when a line is not written in the form y = mx + c

Question:
In which region would \( x-y=2 \) belong? ![A Venn diagram with two overlapping sets. The set on the left is 'Crosses the y-axis at (0,-2)' and the set on the right is 'Has a positive gradient'. A is in only 'Crosses the y-axis at (0,-2)' set, B is in the intersection, C is in only  'Has a positive gradient' set and D is outside both sets.]()

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

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


Prompt:
Misconception:
Believes you divide 1 by the number of values, rather than the total, when finding the mean

Question:
What is the mean of the following numbers?
\( 1, \quad 0.1, \quad 0.01 \)

Options:
A. \( 0.333 \)
B. \( 0.33 \)
C. \( 0.1 \)
D. \( 0.37 \)

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


Prompt:
Misconception:
Believes you divide 1 by the number of values, rather than the total, when finding the mean

Question:
What is the mean of the following numbers?
\( 1, \quad 0.1, \quad 0.01 \)

Options:
A. \( 0.333 \)
B. \( 0.33 \)
C. \( 0.1 \)
D. \( 0.37 \)

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


Prompt:
Misconception:
Finds the median instead of the mean

Question:
What is the mean of the following numbers?
\( 1, \quad 0.1, \quad 0.01 \)

Options:
A. \( 0.333 \)
B. \( 0.33 \)
C. \( 0.1 \)
D. \( 0.37 \)

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


Prompt:
Misconception:
Confuses an expression with a variable

Question:
Which of the following is the most appropriate word to describe \( t \) in this: \( 9-3 t \)

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

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


Prompt:
Misconception:
Confuses a variable with an equation

Question:
Which of the following is the most appropriate word to describe \( t \) in this: \( 9-3 t \)

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

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


Prompt:
Misconception:
Confuses a term with a variable

Question:
Which of the following is the most appropriate word to describe \( t \) in this: \( 9-3 t \)

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

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


Prompt:
Misconception:
Does not think that the compensation strategy for the multiplication of 2 numbers is valid.

Question:
Sara has \( £ 2.79 \).
Rhys has \( 3 \) times as much as Sara.
How much do they have altogether?
Which calculation would not find the answer?

Options:
A. \( £ 2.79 \times 4 \)
B. \( (£ 2.79 \times 3)+£ 2.79 \)
C. \( £ 2.80 \times 4-£ 0.04 \)
D. \( £ 2.79 \times 3 \)

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


Prompt:
Misconception:
Multiplies up without finding unit price in proportion question

Question:
\( \frac{4}{9} \) of a litre of paint can cover \( 1 \mathrm{~m}^{2} \).
What area can \( 4 \) litres of paint cover?

Options:
A. \( 4 m^{2} \)
B. \( 9 \mathrm{~m}^{2} \)
C. \( \frac{16}{9} \mathrm{~m}^{2} \)
D. \( \frac{36}{16} \mathrm{~m}^{2} \)

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:
Confuses factors and multiples

Question:
What is the lowest common multiple of \( 8 \) and \( 4 \) ?

Options:
A. \( 32 \)
B. \( 4 \)
C. \( 8 \)
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 unrelated acute/obtuse angles in a diagram are supplementary

Question:
Calculate the unknown angle, \( x \). ![\( A \)]()

Options:
A. \( 56^{\circ} \)
B. \( 146^{\circ} \)
C. \( 124^{\circ} \)
D. \( 236^{\circ} \)

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


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

Question:
![A bar chart with blue vertical bars. The x-axis is titled "Fruits" and the y-axis is titled "Number of Children" and its scale is from 0 to 50 in steps of 10. The bars represent the following numbers of children: Banana, 30; Apple, 20; Kiwi, 30; Orange, 35; Pineapple, 10.]() \begin{tabular}{|c|c|}
\hline Type of Fruit & Number of Children\\
\hline Banana & \( 30 \) \\
\hline Apple & \\
\hline Kiwi & \( 30 \) \\
\hline Orange & \\
\hline Pineapple & \( 10 \) \\
\hline
\end{tabular} Using the bar chart, what two numbers are missing from the table?

Options:
A. \( 20 \) and \( 30 \)
B. \( 30 \) and \( 35 \)
C. Orange, Apple
D. \( 20 \) and \( 35 \)

Solve the problem as a student with the misconception above.
You 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:
Expand:
\[
6(p-2)
\]

Options:
A. \( 6 p-2 \)
B. \( 6 p-12 \)
C. \( p-12 \)
D. \( 6 p-4 \)

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


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

Question:
Expand:
\[
6(p-2)
\]

Options:
A. \( 6 p-2 \)
B. \( 6 p-12 \)
C. \( p-12 \)
D. \( 6 p-4 \)

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


Prompt:
Misconception:
When expanding brackets, multiplies out the first term correctly but adds together the number outside the bracket with the second term inside the bracket.

Question:
Expand:
\[
6(p-2)
\]

Options:
A. \( 6 p-2 \)
B. \( 6 p-12 \)
C. \( p-12 \)
D. \( 6 p-4 \)

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


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

Question:
If \( x=2.5 \) and \( z=2 \) what is the value of \( y \) when \( \mathrm{z}=4 x-2 y \) ?

Options:
A. \( 8 \)
B. \( -8 \)
C. \( 6 \)
D. \( 4 \)

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


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

Question:
If \( x=2.5 \) and \( z=2 \) what is the value of \( y \) when \( \mathrm{z}=4 x-2 y \) ?

Options:
A. \( 8 \)
B. \( -8 \)
C. \( 6 \)
D. \( 4 \)

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


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

Question:
Jo and Paul are arguing about the solution to this inequality:
\(t+3>-0.3\)

Jo says \( t \) could be \( -3.4 \)

Paul says \( t \) could be \( 3.4 \)

Who is correct?

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

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


Prompt:
Misconception:
Believes negative numbers with a larger absolute value are greater

Question:
Jo and Paul are arguing about the solution to this inequality:
\(t+3>-0.3\)

Jo says \( t \) could be \( -3.4 \)

Paul says \( t \) could be \( 3.4 \)

Who is correct?

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

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


Prompt:
Misconception:
Estimated when not appropriate

Question:
These two shapes are similar.

What is the value of \( y \) ? ![The diagram is of two trapeziums. The base of each trapezium is parallel with its top side.
The smaller trapezium has base 60cm and top labelled y.
The larger trapezium has base 150cm and top 70cm.]()

Options:
A. \( 28 \mathrm{~cm} \)
B. \( 20 \mathrm{~cm} \)
C. \( 25 \mathrm{~cm} \)
D. \( 30 \mathrm{~cm} \)

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:
Estimated when not appropriate

Question:
These two shapes are similar.

What is the value of \( y \) ? ![The diagram is of two trapeziums. The base of each trapezium is parallel with its top side.
The smaller trapezium has base 60cm and top labelled y.
The larger trapezium has base 150cm and top 70cm.]()

Options:
A. \( 28 \mathrm{~cm} \)
B. \( 20 \mathrm{~cm} \)
C. \( 25 \mathrm{~cm} \)
D. \( 30 \mathrm{~cm} \)

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:
Estimated when not appropriate

Question:
These two shapes are similar.

What is the value of \( y \) ? ![The diagram is of two trapeziums. The base of each trapezium is parallel with its top side.
The smaller trapezium has base 60cm and top labelled y.
The larger trapezium has base 150cm and top 70cm.]()

Options:
A. \( 28 \mathrm{~cm} \)
B. \( 20 \mathrm{~cm} \)
C. \( 25 \mathrm{~cm} \)
D. \( 30 \mathrm{~cm} \)

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:
Calculates area when asked for perimeter

Question:
What is an expression for the perimeter of this rectangle? ![Yellow rectangle with base length 5a and side length a]()

Options:
A. \( 12 a \)
B. \( 5 a^{2} \)
C. \( 6 a \)
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 calculating perimeter, only adds the marked lengths

Question:
What is an expression for the perimeter of this rectangle? ![Yellow rectangle with base length 5a and side length a]()

Options:
A. \( 12 a \)
B. \( 5 a^{2} \)
C. \( 6 a \)
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 recall rectangle side length property

Question:
What is an expression for the perimeter of this rectangle? ![Yellow rectangle with base length 5a and side length a]()

Options:
A. \( 12 a \)
B. \( 5 a^{2} \)
C. \( 6 a \)
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:
Reflects in an axis, instead of the given mirror line

Question:
Which is the correct description of the transformation that maps shape A onto shape \( B \) ? ![A coordinate grid with two triangles drawn on it. Triangle A has the coordinates: (6,4) (4,4) and (4,5). Triangle B has the coordinates: (-4,4) (-2,4) and (-2,5).]()

Options:
A. Reflection in \( y \)-axis
B. Reflection in \( x \)-axis
C. Reflection in \( \mathrm{y}=1 \)
D. Reflection in \( x=1 \)

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


Prompt:
Misconception:
Thinks y = ? is a vertical line through ?

Question:
Which is the correct description of the transformation that maps shape A onto shape \( B \) ? ![A coordinate grid with two triangles drawn on it. Triangle A has the coordinates: (6,4) (4,4) and (4,5). Triangle B has the coordinates: (-4,4) (-2,4) and (-2,5).]()

Options:
A. Reflection in \( y \)-axis
B. Reflection in \( x \)-axis
C. Reflection in \( \mathrm{y}=1 \)
D. Reflection in \( x=1 \)

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


Prompt:
Misconception:
Believes vertically opposite angles sum to 180 degrees

Question:
What is the relationship between these two angles? ![A pair of lines crossing to form an X shape. Two angles are marked, with one blank angle between them on each side.]()

Options:
A. They add together to make
\[
180^{\circ}
\]
B. They add together to make
\[
360^{\circ}
\]
C. They are equal
D. They are parallel

Solve the problem as a student with the misconception above.
You 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 vertically opposite angles sum to 360 degrees

Question:
What is the relationship between these two angles? ![A pair of lines crossing to form an X shape. Two angles are marked, with one blank angle between them on each side.]()

Options:
A. They add together to make
\[
180^{\circ}
\]
B. They add together to make
\[
360^{\circ}
\]
C. They are equal
D. They are parallel

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


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

Question:
What is the relationship between these two angles? ![A pair of lines crossing to form an X shape. Two angles are marked, with one blank angle between them on each side.]()

Options:
A. They add together to make
\[
180^{\circ}
\]
B. They add together to make
\[
360^{\circ}
\]
C. They are equal
D. They are parallel

Solve the problem as a student with the misconception above.
You 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 if shapes have rotational symmetry they must have line symmetry

Question:
Which of the combinations of properties are not possible for a polygon?

Options:
A. Rotation symmetry order \( 3 \) and \( 0 \) line of symmetry
B. Rotation symmetry order \( 1 \) and \( 2 \) lines of symmetry
C. Rotation symmetry order \( 4 \) and \( 4 \) lines of symmetry
D. Rotation symmetry order \( 2 \) and \( 0 \) lines of symmetry

Solve the problem as a student with the misconception above.
You 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 if shapes have rotational symmetry they must have line symmetry

Question:
Which of the combinations of properties are not possible for a polygon?

Options:
A. Rotation symmetry order \( 3 \) and \( 0 \) line of symmetry
B. Rotation symmetry order \( 1 \) and \( 2 \) lines of symmetry
C. Rotation symmetry order \( 4 \) and \( 4 \) lines of symmetry
D. Rotation symmetry order \( 2 \) and \( 0 \) lines of symmetry

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


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

Question:
The graph can be used to work out how much Kay's company pays her for travel.

Kay’s company paid her \( £ 100 \)

How many miles did she travel? ![The graph shows distance in miles on the x axis and amount in pounds on the y axis. The graph consists of a straight line, starting at the origin (0,0) and passing through the points (20,16) and (25,20)]()

Options:
A. \( 80 \)
B. \( 100 \)
C. \( 125 \)
D. \( 120 \)

Solve the problem as a student with the misconception above.
You 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 direct proportion means a 1:1 ratio

Question:
The graph can be used to work out how much Kay's company pays her for travel.

Kay’s company paid her \( £ 100 \)

How many miles did she travel? ![The graph shows distance in miles on the x axis and amount in pounds on the y axis. The graph consists of a straight line, starting at the origin (0,0) and passing through the points (20,16) and (25,20)]()

Options:
A. \( 80 \)
B. \( 100 \)
C. \( 125 \)
D. \( 120 \)

Solve the problem as a student with the misconception above.
You 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 compare decimal numbers

Question:
Tom and Katie are discussing how to order decimals.

Tom says \( 0.60 \) is greater than \( 0.06 \)

Katie says \( 0.5993 \) is greater than \( 0.5399 \)

Who is correct?

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

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


Prompt:
Misconception:
Does not know how to compare decimal numbers

Question:
Tom and Katie are discussing how to order decimals.

Tom says \( 0.60 \) is greater than \( 0.06 \)

Katie says \( 0.5993 \) is greater than \( 0.5399 \)

Who is correct?

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

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


Prompt:
Misconception:
Does not know how to compare decimal numbers

Question:
Tom and Katie are discussing how to order decimals.

Tom says \( 0.60 \) is greater than \( 0.06 \)

Katie says \( 0.5993 \) is greater than \( 0.5399 \)

Who is correct?

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

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


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

Question:
Here are the first \( 4 \) terms of a sequence ![\( \begin{array}{lllll}11 & 15 & 19 & 23 & \ldots\end{array} \)]() What position in the sequence is the number \( 87 ? \)

Options:
A. \( 355 \)
B. \( 20 \)
C. \( 4 n+7 \)
D. \( 21.75 \)

Solve the problem as a student with the misconception above.
You 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 naming structure of polygons

Question:
A ten sided polygon is also known as...

Options:
A. An octagon
B. A hexagon
C. A decagon
D. A dodecagon

Solve the problem as a student with the misconception above.
You 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 naming structure of polygons

Question:
A ten sided polygon is also known as...

Options:
A. An octagon
B. A hexagon
C. A decagon
D. A dodecagon

Solve the problem as a student with the misconception above.
You 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 naming structure of polygons

Question:
A ten sided polygon is also known as...

Options:
A. An octagon
B. A hexagon
C. A decagon
D. A dodecagon

Solve the problem as a student with the misconception above.
You 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 the distributive property

Question:
What word do we use to describe the relationship:
\(
7 \times 9=5 \times 9+2 \times 9
\)

Options:
A. Commutativity
B. Factors
C. Associativity
D. Distributivity

Solve the problem as a student with the misconception above.
You 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 splitting a multiplication using the distributive property is the same as splitting it into factors

Question:
What word do we use to describe the relationship:
\(
7 \times 9=5 \times 9+2 \times 9
\)

Options:
A. Commutativity
B. Factors
C. Associativity
D. Distributivity

Solve the problem as a student with the misconception above.
You 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 the distributive property

Question:
What word do we use to describe the relationship:
\(
7 \times 9=5 \times 9+2 \times 9
\)

Options:
A. Commutativity
B. Factors
C. Associativity
D. Distributivity

Solve the problem as a student with the misconception above.
You 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 into double brackets, finds the sum of two values which give the non variable term in the expression rather than the product

Question:
When \( x^{2}+9 x+14 \) is factorised, what will appear in the box below? ![Bracket (x+2) and a rectangular box beside it where the second bracket should be.]()

Options:
A. \( (x+12) \)
B. \( (x+8) \)
C. \( (x-7) \)
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:
Believes multiplying a positive by a negative gives a positive answer

Question:
When \( x^{2}+9 x+14 \) is factorised, what will appear in the box below? ![Bracket (x+2) and a rectangular box beside it where the second bracket should be.]()

Options:
A. \( (x+12) \)
B. \( (x+8) \)
C. \( (x-7) \)
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:
Thinks there are 100g in a kilogram

Question:
A \( 0.5 \) kilogram weight has \( 10 \) grams shaved off it.

What is the mass of the weight that remains?
Give your answer in grams.

Options:
A. \( 490 \mathrm{~g} \)
B. \( 40 \mathrm{~g} \)
C. \( 499 \mathrm{~g} \)
D. \( 0.49 g \)

Solve the problem as a student with the misconception above.
You 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:
\( 0.1 \div 4= \)

Options:
A. \( 0.3 \)
B. \( 0.025 \)
C. \( 0.4 \)
D. \( 0.25 \)

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


Prompt:
Misconception:
When dividing a decimal by a whole number, ignores decimal point and just divides the digits

Question:
\( 0.1 \div 4= \)

Options:
A. \( 0.3 \)
B. \( 0.025 \)
C. \( 0.4 \)
D. \( 0.25 \)

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


Prompt:
Misconception:
Believes that in the nth term of a descending sequence, b is the difference between the term and the positive multiple of n

Question:
Here are the first three terms of a sequence ![\( \begin{array}{llll}98 & 92 & 86 & \ldots\end{array} \)]() Find an expression for the nth term of this sequence.

Options:
A. \( -6 n+104 \)
B. \( -6 n+92 \)
C. \( -6 n \)
D. \( 6 n+92 \)

Solve the problem as a student with the misconception above.
You 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 terms in linear sequence are in direct proportion

Question:
Here are the first three terms of a sequence ![\( \begin{array}{llll}98 & 92 & 86 & \ldots\end{array} \)]() Find an expression for the nth term of this sequence.

Options:
A. \( -6 n+104 \)
B. \( -6 n+92 \)
C. \( -6 n \)
D. \( 6 n+92 \)

Solve the problem as a student with the misconception above.
You 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 nth term of a descending sequence will have a positive coefficient of n

Question:
Here are the first three terms of a sequence ![\( \begin{array}{llll}98 & 92 & 86 & \ldots\end{array} \)]() Find an expression for the nth term of this sequence.

Options:
A. \( -6 n+104 \)
B. \( -6 n+92 \)
C. \( -6 n \)
D. \( 6 n+92 \)

Solve the problem as a student with the misconception above.
You 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:
A sphere has a volume of
\[
V \mathrm{~cm}^{3} \text {. }
\] ![A sphere with the radius labelled '?']() What is its radius?

Options:
A. \( \sqrt[3]{\frac{4 V \pi}{3}} \mathrm{~cm} \)
B. \( \sqrt[3]{\frac{4 V}{3 \pi}} \mathrm{cm} \)
C. \( \sqrt[3]{\frac{3 V}{4 \pi}} \mathrm{cm} \)
D. \( \frac{3 \sqrt[3]{V}}{4 \pi} \mathrm{cm} \)

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:
When dividing by a fraction, switches to multiplication without also using the reciprocal

Question:
A sphere has a volume of
\[
V \mathrm{~cm}^{3} \text {. }
\] ![A sphere with the radius labelled '?']() What is its radius?

Options:
A. \( \sqrt[3]{\frac{4 V \pi}{3}} \mathrm{~cm} \)
B. \( \sqrt[3]{\frac{4 V}{3 \pi}} \mathrm{cm} \)
C. \( \sqrt[3]{\frac{3 V}{4 \pi}} \mathrm{cm} \)
D. \( \frac{3 \sqrt[3]{V}}{4 \pi} \mathrm{cm} \)

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 reverse the order of operations when solving an equation

Question:
A sphere has a volume of
\[
V \mathrm{~cm}^{3} \text {. }
\] ![A sphere with the radius labelled '?']() What is its radius?

Options:
A. \( \sqrt[3]{\frac{4 V \pi}{3}} \mathrm{~cm} \)
B. \( \sqrt[3]{\frac{4 V}{3 \pi}} \mathrm{cm} \)
C. \( \sqrt[3]{\frac{3 V}{4 \pi}} \mathrm{cm} \)
D. \( \frac{3 \sqrt[3]{V}}{4 \pi} \mathrm{cm} \)

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

Question:
Alisha is using cups and counters to help her solve an equation. Which would be the correct start to work it out? ![Three diagrams of equations shown with cups and counters.
Step 1 is one cup plus four counters equals two cups and two counters.
Step 2 is four counters equals one cup plus two counters.
Step 3 is two counters equals one cup.]()

Options:
A. \( \begin{array}{c}x+4=2 x+2 \\ x=2\end{array} \)
B. \( 3 x=6 \)
C. \( \begin{array}{c}x+4=2 x+2 \\ 3 x=2\end{array} \)
D. \( \begin{array}{c}x+4=2 x+2 \\ 3 x=6\end{array} \)

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


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

Question:
Alisha is using cups and counters to help her solve an equation. Which would be the correct start to work it out? ![Three diagrams of equations shown with cups and counters.
Step 1 is one cup plus four counters equals two cups and two counters.
Step 2 is four counters equals one cup plus two counters.
Step 3 is two counters equals one cup.]()

Options:
A. \( \begin{array}{c}x+4=2 x+2 \\ x=2\end{array} \)
B. \( 3 x=6 \)
C. \( \begin{array}{c}x+4=2 x+2 \\ 3 x=2\end{array} \)
D. \( \begin{array}{c}x+4=2 x+2 \\ 3 x=6\end{array} \)

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


Prompt:
Misconception:
Believes 0 is not a real solution to an equation

Question:
Which of the following pairs of simultaneous equations would have no solutions?
\begin{array}{ccc}
Pair \( 1 \) & Pair \( 2 \) \\
\( 2 y-2 x=7 \) & & \( 2 x+2 y=7 \) \\
\( 2 x-2 y=7 \) & & \( 2 x-2 y=7 \)
\end{array}

Options:
A. Only Pair \( 1 \)
B. Only Pair \( 2 \)
C. Both Pair \( 1 \) and Pair \( 2 \)
D. Neither Pair \( 1 \) nor 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:
Uses dividing fractions method for multiplying fractions

Question:
\( \frac{6}{7} \times \frac{2}{3}=? \)

Options:
A. \( 1 \frac{11}{21} \)
B. \( \frac{9}{7} \)
C. \( \frac{8}{21} \)
D. \( \frac{4}{7} \)

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


Prompt:
Misconception:
When multiplying fractions, adds the numerators and multiplies the denominators

Question:
\( \frac{6}{7} \times \frac{2}{3}=? \)

Options:
A. \( 1 \frac{11}{21} \)
B. \( \frac{9}{7} \)
C. \( \frac{8}{21} \)
D. \( \frac{4}{7} \)

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:
Assumes a fact without considering enough examples

Question:
Jo and Paul are discussing quadratic equations.

Jo says there is no value of \( x \) that can make \( (1-x)^{2} \) negative.

Paul says there is no value of \( x \) that can make \( 1-x^{2} \) positive.
Who is correct?

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

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


Prompt:
Misconception:
Believes the square of a negative will also be negative

Question:
Jo and Paul are discussing quadratic equations.

Jo says there is no value of \( x \) that can make \( (1-x)^{2} \) negative.

Paul says there is no value of \( x \) that can make \( 1-x^{2} \) positive.
Who is correct?

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

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


Prompt:
Misconception:
When factorising into single brackets, only factors out the numerical values and forgets to factorise possible variables

Question:
What should replace the circle when this expression is fully factorised? \( 9 y^{2}+4 y \equiv \bigstar(\triangle y+\bigcirc) \)

Options:
A. \( \bigcirc=4 y \)
B. \( \bigcirc=y \)
C. \( \bigcirc=4 \)
D. \( \bigcirc=5 \)

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


Prompt:
Misconception:
Believes that addition should be used when finding the difference between two values on a time series graph

Question:
![Graph titled height of rocket with Height in metres versus time in seconds]() How many metres did the rocket travel between \( 10 \) and \( 40 \) seconds?

Options:
A. \( 60 \)
B. \( 50 \)
C. \( 30 \)
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 finding the difference between two points on a time series graph, only uses one of the points.

Question:
![Graph titled height of rocket with Height in metres versus time in seconds]() How many metres did the rocket travel between \( 10 \) and \( 40 \) seconds?

Options:
A. \( 60 \)
B. \( 50 \)
C. \( 30 \)
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 finding the difference between two points on a time series graph, only uses one of the points.

Question:
![Graph titled height of rocket with Height in metres versus time in seconds]() How many metres did the rocket travel between \( 10 \) and \( 40 \) seconds?

Options:
A. \( 60 \)
B. \( 50 \)
C. \( 30 \)
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:
Does not recognise difference of two squares

Question:
Which of the following answers shows a correct factorisation of the expression below? \( 2 x^{2}-50 \)

Options:
A. \( 2\left(x^{2}-25\right) \)
B. \( 2(x-5)(x-5) \)
C. \( 2(x-5)(x+5) \)
D. \( 2(x-12.5)^{2} \)

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:
Factorises difference of two squares with the same sign in both brackets

Question:
Which of the following answers shows a correct factorisation of the expression below? \( 2 x^{2}-50 \)

Options:
A. \( 2\left(x^{2}-25\right) \)
B. \( 2(x-5)(x-5) \)
C. \( 2(x-5)(x+5) \)
D. \( 2(x-12.5)^{2} \)

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:
Ignores the negative signs when adding positive and negative numbers

Question:
\( (-6)-(-8)= \)

Options:
A. \( 14 \)
B. \( -14 \)
C. \( 2 \)
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:
When subtracting a negative number, subtracts the absolute value rather than adding it

Question:
\( (-6)-(-8)= \)

Options:
A. \( 14 \)
B. \( -14 \)
C. \( 2 \)
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:
When subtracting a negative thinks the answer must be negative

Question:
\( (-6)-(-8)= \)

Options:
A. \( 14 \)
B. \( -14 \)
C. \( 2 \)
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:
In repeated percentage change, believes the second change is only a percentage of the first change, without including the original

Question:
I increase \( £ 200 \) by \( 50 \% \).
Then, I increase the new amount by \( 10 \% \).
What percentage of the original amount do I have now?

Options:
A. \( 155 \% \)
B. \( 60 \% \)
C. \( 165 \% \)
D. \( 330 \% \)

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


Prompt:
Misconception:
Thinks numbers are a multiple of their index

Question:
Which of these is a cube number?

Options:
A. \( 8 \)
B. \( 15 \)
C. \( 100 \)
D. \( 3 \)

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


Prompt:
Misconception:
Mixes up square numbers and cube numbers

Question:
Which of these is a cube number?

Options:
A. \( 8 \)
B. \( 15 \)
C. \( 100 \)
D. \( 3 \)

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


Prompt:
Misconception:
Thinks numbers are a multiple of their index

Question:
Which of these is a cube number?

Options:
A. \( 8 \)
B. \( 15 \)
C. \( 100 \)
D. \( 3 \)

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


Prompt:
Misconception:
Confuses the terms faces and edges

Question:
![An orange cube]() How many faces does this cube have?

Options:
A. \( 4 \)
B. \( 12 \)
C. \( 6 \)
D. \( 8 \)

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


Prompt:
Misconception:
Confuses the terms faces and vertices

Question:
![An orange cube]() How many faces does this cube have?

Options:
A. \( 4 \)
B. \( 12 \)
C. \( 6 \)
D. \( 8 \)

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


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

Question:
![Two arrows in a line, both pointing right. The first one has '- 3' in it, the second one has 'x 5' in it. ]() The rule above is used to generate a term-to-term sequence.
If the third term is \( 35 \), what is the first term?

Options:
A. \( 10 \)
B. \( -10 \)
C. \( 5 \)
D. \( 1 \)

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


Prompt:
Misconception:
Does not know the definition of term or term-to-term rule

Question:
![Two arrows in a line, both pointing right. The first one has '- 3' in it, the second one has 'x 5' in it. ]() The rule above is used to generate a term-to-term sequence.
If the third term is \( 35 \), what is the first term?

Options:
A. \( 10 \)
B. \( -10 \)
C. \( 5 \)
D. \( 1 \)

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


Prompt:
Misconception:
Thinks the first term of a sequence must be 1

Question:
![Two arrows in a line, both pointing right. The first one has '- 3' in it, the second one has 'x 5' in it. ]() The rule above is used to generate a term-to-term sequence.
If the third term is \( 35 \), what is the first term?

Options:
A. \( 10 \)
B. \( -10 \)
C. \( 5 \)
D. \( 1 \)

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


Prompt:
Misconception:
Does not understand a percentage is out of 100

Question:
Convert this fraction to a percentage
\(
\frac{27}{200}
\)

Options:
A. \( 13.5 \% \)
B. \( 27 \% \)
C. \( 54 \% \)
D. This fraction does not convert to a percentage

Solve the problem as a student with the misconception above.
You 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 a percentage is out of 100

Question:
Convert this fraction to a percentage
\(
\frac{27}{200}
\)

Options:
A. \( 13.5 \% \)
B. \( 27 \% \)
C. \( 54 \% \)
D. This fraction does not convert to a percentage

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


Prompt:
Misconception:
Converted hours to minutes instead of hours to seconds

Question:
Which of the following would correctly calculate the number of seconds in \( 1 \) day?

Options:
A. \( 24 \times 60 \)
B. \( 24 \times 60 \times 60 \)
C. \( 12 \times 60 \)
D. \( 12 \times 60 \times 60 \)

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


Prompt:
Misconception:
Thinks there are 12 hours in 1 day

Question:
Which of the following would correctly calculate the number of seconds in \( 1 \) day?

Options:
A. \( 24 \times 60 \)
B. \( 24 \times 60 \times 60 \)
C. \( 12 \times 60 \)
D. \( 12 \times 60 \times 60 \)

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


Prompt:
Misconception:
Does not understand the value of zeros as placeholders

Question:
What is \( \mathbf{2 . 5 0 6 7 1 0} \) rounded to three significant figures?

Options:
A. \( 2.51 \)
B. \( 2.507 \)
C. \( 2.50 \)
D. \( 3.00 \)

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


Prompt:
Misconception:
Rounds down instead of up

Question:
What is \( \mathbf{2 . 5 0 6 7 1 0} \) rounded to three significant figures?

Options:
A. \( 2.51 \)
B. \( 2.507 \)
C. \( 2.50 \)
D. \( 3.00 \)

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


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

Question:
What is \( \mathbf{2 . 5 0 6 7 1 0} \) rounded to three significant figures?

Options:
A. \( 2.51 \)
B. \( 2.507 \)
C. \( 2.50 \)
D. \( 3.00 \)

Solve the problem as a student with the misconception above.
You 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:
A diver wants to make a pie chart of his trip. \begin{tabular}{|c|c|c|}
\hline & Frequency & Degrees \\
\hline Manta Ray & \( 16 \) & \( 180 \) \\
\hline Hammerhead & \( 4 \) & \( 45 \) \\
\hline Conger Eel & \( 12 \) & \( \mathrm{~F} \) \\
\hline
\end{tabular} Which one of these is a correct method for finding F?

Options:
A. \( 360-180+45 \)
B. \( \frac{12}{20} \times 360 \)
C. \( 360-180-45 \)
D. \( \frac{360}{32} \)

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


Prompt:
Misconception:
Believes to find the proportion of a pie chart sector you do frequency/sum of other frequencies rather than frequency/overall total

Question:
A diver wants to make a pie chart of his trip. \begin{tabular}{|c|c|c|}
\hline & Frequency & Degrees \\
\hline Manta Ray & \( 16 \) & \( 180 \) \\
\hline Hammerhead & \( 4 \) & \( 45 \) \\
\hline Conger Eel & \( 12 \) & \( \mathrm{~F} \) \\
\hline
\end{tabular} Which one of these is a correct method for finding F?

Options:
A. \( 360-180+45 \)
B. \( \frac{12}{20} \times 360 \)
C. \( 360-180-45 \)
D. \( \frac{360}{32} \)

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


Prompt:
Misconception:
Finds the degrees for 1 person rather than the required number of people for a pie chart sector

Question:
A diver wants to make a pie chart of his trip. \begin{tabular}{|c|c|c|}
\hline & Frequency & Degrees \\
\hline Manta Ray & \( 16 \) & \( 180 \) \\
\hline Hammerhead & \( 4 \) & \( 45 \) \\
\hline Conger Eel & \( 12 \) & \( \mathrm{~F} \) \\
\hline
\end{tabular} Which one of these is a correct method for finding F?

Options:
A. \( 360-180+45 \)
B. \( \frac{12}{20} \times 360 \)
C. \( 360-180-45 \)
D. \( \frac{360}{32} \)

Solve the problem as a student with the misconception above.
You 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 isosceles and scalene triangles

Question:
An isosceles triangle must have ...

Options:
A. no equal side lengths.
B. two sides of equal length and two equal angles.
C. one pair of parallel sides.
D. three equal angles.

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


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

Question:
An isosceles triangle must have ...

Options:
A. no equal side lengths.
B. two sides of equal length and two equal angles.
C. one pair of parallel sides.
D. three equal angles.

Solve the problem as a student with the misconception above.
You 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 isosceles and equilateral triangles

Question:
An isosceles triangle must have ...

Options:
A. no equal side lengths.
B. two sides of equal length and two equal angles.
C. one pair of parallel sides.
D. three equal angles.

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


Prompt:
Misconception:
Does not understand that a point on the line of reflection will stay the same when reflected

Question:
The triangle is reflected in the dashed line.
What are the new coordinates of point \( P \) ? ![A set of axes: x-axis from -1 to 7, y-axis from -2 to 8. Three points are plotted and joined to make a triangle: (2, 4), (4, 4), (2, 7). Point (2, 4) is labelled with the letter "P". The line y=4 is shown with a blue dashed line.]()

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

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


Prompt:
Misconception:
Does not understand that a point on the line of reflection will stay the same when reflected

Question:
The triangle is reflected in the dashed line.
What are the new coordinates of point \( P \) ? ![A set of axes: x-axis from -1 to 7, y-axis from -2 to 8. Three points are plotted and joined to make a triangle: (2, 4), (4, 4), (2, 7). Point (2, 4) is labelled with the letter "P". The line y=4 is shown with a blue dashed line.]()

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

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:
Reflects in an axis, instead of the given mirror line

Question:
The triangle is reflected in the dashed line.
What are the new coordinates of point \( P \) ? ![A set of axes: x-axis from -1 to 7, y-axis from -2 to 8. Three points are plotted and joined to make a triangle: (2, 4), (4, 4), (2, 7). Point (2, 4) is labelled with the letter "P". The line y=4 is shown with a blue dashed line.]()

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

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:
Thinks the inverse of subtraction is multiplication

Question:
This is a part of the table of values for the equation
\[
y=6 x
\] \begin{tabular}{|l|l|}
\hline\( x \) & \(\bigstar\) \\
\hline\( y \) & \( 0 \) \\
\hline
\end{tabular} What should replace the star?

Options:
A. \( -6 \)
B. \( 0 \)
C. \( \frac{10}{6} \)
D. There is no possible solution

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


Prompt:
Misconception:
Doesn't believe that when you divide by 0 the answer will always be 0

Question:
This is a part of the table of values for the equation
\[
y=6 x
\] \begin{tabular}{|l|l|}
\hline\( x \) & \(\bigstar\) \\
\hline\( y \) & \( 0 \) \\
\hline
\end{tabular} What should replace the star?

Options:
A. \( -6 \)
B. \( 0 \)
C. \( \frac{10}{6} \)
D. There is no possible solution

Solve the problem as a student with the misconception above.
You 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 triangle? ![The image is a set of axes with three points marked. One point is (1,7). The midpoint is (-1, 0.5). The third point is given as (star, triangle), so the triangle is the y value of the point.]()

Options:
A. \( \Delta=-7 \)
B. \( \Delta=-6 \)
C. \( \Delta=-6.5 \)
D. \( \Delta=3.25 \)

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


Prompt:
Misconception:
Believes midpoint calculation is just half of the difference

Question:
Here are two points and their midpoint.
What should replace the triangle? ![The image is a set of axes with three points marked. One point is (1,7). The midpoint is (-1, 0.5). The third point is given as (star, triangle), so the triangle is the y value of the point.]()

Options:
A. \( \Delta=-7 \)
B. \( \Delta=-6 \)
C. \( \Delta=-6.5 \)
D. \( \Delta=3.25 \)

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


Prompt:
Misconception:
Ignores negative sign when expanding bracket

Question:
Ori is expanding these three brackets:
\(
(x+2)(x-4)(x-7)
\)

He finds it helpful to split the first bracket and view the problem as follows:
\(
x(x-4)(x-7)+2(x-4)(x-7)
\)

He expands the brackets further. Before he simplifies, what are the terms than contain an \( x^{2} \) ?

Options:
A. \( \begin{array}{l}+7 x^{2} \\ +4 x^{2} \\ +2 x^{2}\end{array} \)
B. \( \begin{array}{l}+7 x^{2} \\ -4 x^{2} \\ +2 x^{2}\end{array} \)
C. \( -7 x^{2} \)
D. \( \begin{array}{l}-7 x^{2} \\ -4 x^{2} \\ +2 x^{2}\end{array} \)

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


Prompt:
Misconception:
Divides rather than multiplies when answering worded problems

Question:
Which of the following calculations would solve this problem?
Fred is monitoring the growth of his plant. The plant grew \( 7 \mathrm{~cm} \) every week for \( 35 \) weeks.
By how much did the plant grow in total?

Options:
A. \( 35 \div 7 \)
B. \( 35-7 \)
C. \( 35+7 \)
D. \( 35 \times 7 \)

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:
Subtracts rather than multiplies when answering worded problems

Question:
Which of the following calculations would solve this problem?
Fred is monitoring the growth of his plant. The plant grew \( 7 \mathrm{~cm} \) every week for \( 35 \) weeks.
By how much did the plant grow in total?

Options:
A. \( 35 \div 7 \)
B. \( 35-7 \)
C. \( 35+7 \)
D. \( 35 \times 7 \)

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


Prompt:
Misconception:
Adds rather than multiplies when asked for a total

Question:
Which of the following calculations would solve this problem?
Fred is monitoring the growth of his plant. The plant grew \( 7 \mathrm{~cm} \) every week for \( 35 \) weeks.
By how much did the plant grow in total?

Options:
A. \( 35 \div 7 \)
B. \( 35-7 \)
C. \( 35+7 \)
D. \( 35 \times 7 \)

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

Question:
What fraction replaces the question mark? ![A bar split into 5 equal parts, with two shaded. One of the shaded parts is labelled with a question mark.]()

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

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


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

Question:
Which calculation should you do first?
\(
((0.5 \div(0.2+0.4)-0.3) \times 0.6)
\)

Options:
A. \( 0.5 \div 0.2 \)
B. \( 0.2+0.4 \)
C. \( 0.4-0.3 \)
D. \( 0.3 \times 0.6 \)

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

Question:
Which calculation should you do first?
\(
((0.5 \div(0.2+0.4)-0.3) \times 0.6)
\)

Options:
A. \( 0.5 \div 0.2 \)
B. \( 0.2+0.4 \)
C. \( 0.4-0.3 \)
D. \( 0.3 \times 0.6 \)

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:
Performs subtraction in wrong order

Question:
\[
12 \times 6-1+2
\]
Where do the brackets need to go to make the answer equal \( 36 \) ?

Options:
A. \( 12 \times 6-(1+2) \)
B. \( 12 \times(6-1+2) \)
C. \( 12 \times(6-(1+2)) \)
D. Does not need brackets

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


Prompt:
Misconception:
Applies BIDMAS in strict order (does not realize addition and subtraction, and multiplication and division, are of equal priority)

Question:
\[
12 \times 6-1+2
\]
Where do the brackets need to go to make the answer equal \( 36 \) ?

Options:
A. \( 12 \times 6-(1+2) \)
B. \( 12 \times(6-1+2) \)
C. \( 12 \times(6-(1+2)) \)
D. Does not need brackets

Solve the problem as a student with the misconception above.
You 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 right to left regardless of priority order

Question:
\[
12 \times 6-1+2
\]
Where do the brackets need to go to make the answer equal \( 36 \) ?

Options:
A. \( 12 \times 6-(1+2) \)
B. \( 12 \times(6-1+2) \)
C. \( 12 \times(6-(1+2)) \)
D. Does not need brackets

Solve the problem as a student with the misconception above.
You 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 \( 4 \) red balls and \( 3 \) yellow balls in a cup ![A cup with 4 red and 3 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. \( 7 \)
B. \( 210 \)
C. \( 343 \)
D. \( 18 \)

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


Prompt:
Misconception:
Does not recognise that choosing 2 items at once means the first item does not get replaced in a probability question

Question:
There are \( 4 \) red balls and \( 3 \) yellow balls in a cup ![A cup with 4 red and 3 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. \( 7 \)
B. \( 210 \)
C. \( 343 \)
D. \( 18 \)

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


Prompt:
Misconception:
Adds rather than multiplies for combined probabilities

Question:
There are \( 4 \) red balls and \( 3 \) yellow balls in a cup ![A cup with 4 red and 3 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. \( 7 \)
B. \( 210 \)
C. \( 343 \)
D. \( 18 \)

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


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

Question:
Which of the following pairs of function machines are correct?

Options:
A. \( \begin{array}{l}a\rightarrow\times 3\rightarrow+4\rightarrow4+3 a \\ a\rightarrow+4\rightarrow\times 3\rightarrow3(4+a)\end{array} \)
B. \( \begin{array}{l}a\rightarrow\times 3\rightarrow+4\rightarrow4+3 a \\ a\rightarrow \times 3\rightarrow+4\rightarrow3(4+a)\end{array} \)
C. \( \begin{array}{l}a\rightarrow+4 \rightarrow\times 3\rightarrow4+3 a \\ a \rightarrow\times 3\rightarrow+4\rightarrow-3(4+a)\end{array} \)
D. \( \begin{array}{l}a\rightarrow4 \rightarrow\times 3\rightarrow4+3 a \\ a\rightarrow+4\rightarrow\times 3\rightarrow3(4+a)\end{array} \)

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


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

Question:
Which of the following pairs of function machines are correct?

Options:
A. \( \begin{array}{l}a\rightarrow\times 3\rightarrow+4\rightarrow4+3 a \\ a\rightarrow+4\rightarrow\times 3\rightarrow3(4+a)\end{array} \)
B. \( \begin{array}{l}a\rightarrow\times 3\rightarrow+4\rightarrow4+3 a \\ a\rightarrow \times 3\rightarrow+4\rightarrow3(4+a)\end{array} \)
C. \( \begin{array}{l}a\rightarrow+4 \rightarrow\times 3\rightarrow4+3 a \\ a \rightarrow\times 3\rightarrow+4\rightarrow-3(4+a)\end{array} \)
D. \( \begin{array}{l}a\rightarrow4 \rightarrow\times 3\rightarrow4+3 a \\ a\rightarrow+4\rightarrow\times 3\rightarrow3(4+a)\end{array} \)

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


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

Question:
Which of the following pairs of function machines are correct?

Options:
A. \( \begin{array}{l}a\rightarrow\times 3\rightarrow+4\rightarrow4+3 a \\ a\rightarrow+4\rightarrow\times 3\rightarrow3(4+a)\end{array} \)
B. \( \begin{array}{l}a\rightarrow\times 3\rightarrow+4\rightarrow4+3 a \\ a\rightarrow \times 3\rightarrow+4\rightarrow3(4+a)\end{array} \)
C. \( \begin{array}{l}a\rightarrow+4 \rightarrow\times 3\rightarrow4+3 a \\ a \rightarrow\times 3\rightarrow+4\rightarrow-3(4+a)\end{array} \)
D. \( \begin{array}{l}a\rightarrow4 \rightarrow\times 3\rightarrow4+3 a \\ a\rightarrow+4\rightarrow\times 3\rightarrow3(4+a)\end{array} \)

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


Prompt:
Misconception:
Confuses factors and multiples

Question:
Which of the following numbers is a common multiple of \( 4,6 \) and \( 12 \) ?

Options:
A. \( 2 \)
B. \( 12 \)
C. \( 18 \)
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:
Identifies a common multiple of two numbers when asked to consider a common multiple of three numbers

Question:
Which of the following numbers is a common multiple of \( 4,6 \) and \( 12 \) ?

Options:
A. \( 2 \)
B. \( 12 \)
C. \( 18 \)
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:
Identifies a multiple of a number but not a common multiple of a group of numbers

Question:
Which of the following numbers is a common multiple of \( 4,6 \) and \( 12 \) ?

Options:
A. \( 2 \)
B. \( 12 \)
C. \( 18 \)
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:
When subtracting a negative number, subtracts the absolute value rather than adding it

Question:
\( \fbox{-5} \) x\( \hspace{0.2cm} \fbox{4} = \hspace{0.2cm} \fbox{-12} - \hspace{0.2cm}\fbox{ ? } \)

Options:
A. \( -8 \)
B. \( 8 \)
C. \( -32 \)
D. \( 32 \)

Solve the problem as a student with the misconception above.
You 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:
\( \fbox{-5} \) x\( \hspace{0.2cm} \fbox{4} = \hspace{0.2cm} \fbox{-12} - \hspace{0.2cm}\fbox{ ? } \)

Options:
A. \( -8 \)
B. \( 8 \)
C. \( -32 \)
D. \( 32 \)

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


Prompt:
Misconception:
Thinks a power raised to a power leads to addition of the powers

Question:
\(\frac{\left(5^{6}\right)^{4}}{5^{2}} \equiv 5^{n}\)

What is the value of \( n \) ?

Options:
A. \( 5 \)
B. \( 8 \)
C. \( 12 \)
D. \( 22 \)

Solve the problem as a student with the misconception above.
You 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 when dividing numbers with the same base you divide the powers, rather than subtracting

Question:
\(\frac{\left(5^{6}\right)^{4}}{5^{2}} \equiv 5^{n}\)

What is the value of \( n \) ?

Options:
A. \( 5 \)
B. \( 8 \)
C. \( 12 \)
D. \( 22 \)

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


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

Question:
\(
x_{n+1}=10-\frac{1}{x_{n}}
\)

Using a starting value of \( x_{1}=4 \), what is the solution to \( x=10-\frac{1}{x} \) to \( 2 \) decimal places?

Options:
A. \( 9.8989 \ldots \)
B. \( 9.75 \)
C. \( 9.90 \)
D. \( 9.9 \)

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


Prompt:
Misconception:
Believes substituting the starting value into an iteration formula immediately gives the solution

Question:
\(
x_{n+1}=10-\frac{1}{x_{n}}
\)

Using a starting value of \( x_{1}=4 \), what is the solution to \( x=10-\frac{1}{x} \) to \( 2 \) decimal places?

Options:
A. \( 9.8989 \ldots \)
B. \( 9.75 \)
C. \( 9.90 \)
D. \( 9.9 \)

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


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

Question:
\(
x_{n+1}=10-\frac{1}{x_{n}}
\)

Using a starting value of \( x_{1}=4 \), what is the solution to \( x=10-\frac{1}{x} \) to \( 2 \) decimal places?

Options:
A. \( 9.8989 \ldots \)
B. \( 9.75 \)
C. \( 9.90 \)
D. \( 9.9 \)

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 understand the term factor

Question:
\begin{tabular}{|c|c|c|}
      & Multiple of \( 4 \) & Not a multiple of \( 4 \) \\
\hline Factor of \( 60 \) & A & B \\
\hline Not a factor of \( 60 \) & C & D \\
\hline
\end{tabular} In which box should you place \( \mathbf{3 0} \) ?

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

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


Prompt:
Misconception:
Does not know the meaning of consecutive

Question:
Which of these always produces consecutive numbers if \( n \) is a positive integer?

Options:
A. \( n, n+1, n+2 \)
B. \( n, 2 n, 3 n \)
C. \( 3 n, 2 n, n \)
D. \( n, n+2, n+4 \)

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


Prompt:
Misconception:
Does not know the meaning of consecutive

Question:
Which of these always produces consecutive numbers if \( n \) is a positive integer?

Options:
A. \( n, n+1, n+2 \)
B. \( n, 2 n, 3 n \)
C. \( 3 n, 2 n, n \)
D. \( n, n+2, n+4 \)

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


Prompt:
Misconception:
Does not know the meaning of consecutive

Question:
Which of these always produces consecutive numbers if \( n \) is a positive integer?

Options:
A. \( n, n+1, n+2 \)
B. \( n, 2 n, 3 n \)
C. \( 3 n, 2 n, n \)
D. \( n, n+2, n+4 \)

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:
Halves when asked to find the square root

Question:
Which of the following is the square root of \( 36 \) ?

Options:
A. \( 18 \)
B. \( 1296 \)
C. \( 6 \)
D. \( 72 \)

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:
Squares when asked to find the square root

Question:
Which of the following is the square root of \( 36 \) ?

Options:
A. \( 18 \)
B. \( 1296 \)
C. \( 6 \)
D. \( 72 \)

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}.