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

Question:
Which of the following graphs is most likely to illustrate the time taken to complete a job \( (t) \) changes depending on the number of people working on it \( (p) \)

Options:
A. ![A straight line from bottom left to top right, starting from above the origin ]()
B. ![A straight line from top left to bottom right, starting from above the origin]()
C. ![A curved line from top left rapidly descending as it moves right before slowing down and levelling out ]()
D. ![A straight line from bottom left to top right, starting from the origin]()

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


Prompt:
Misconception:
When multiplying a decimal less than 1 by an integer, gives an answer 10 times smaller than it should be

Question:
Work out:
\[
0.03 \times 12
\]

Options:
A. \( 0.036 \)
B. \( 0.306 \)
C. \( 0.36 \)
D. \( 3.6 \)

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


Prompt:
Misconception:
When dividing decimals, does not realize that the order and position of the digits (relative to each other) has to remain constant.

Question:
Work out:
\[
0.03 \times 12
\]

Options:
A. \( 0.036 \)
B. \( 0.306 \)
C. \( 0.36 \)
D. \( 3.6 \)

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


Prompt:
Misconception:
When multiplying a decimal less than 1 by an integer, gives an answer 10 times bigger than it should be

Question:
Work out:
\[
0.03 \times 12
\]

Options:
A. \( 0.036 \)
B. \( 0.306 \)
C. \( 0.36 \)
D. \( 3.6 \)

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


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

Question:
\( 3000 \mathrm{ml} \) is the same as \(___\) litres

Options:
A. \( 3 \)
B. \( 30 \)
C. \( 300 \)
D. \( 3000000 \)

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


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

Question:
\( 3000 \mathrm{ml} \) is the same as \(___\) litres

Options:
A. \( 3 \)
B. \( 30 \)
C. \( 300 \)
D. \( 3000000 \)

Solve the problem as a student with the misconception above.
You 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:
\( 3000 \mathrm{ml} \) is the same as \(___\) litres

Options:
A. \( 3 \)
B. \( 30 \)
C. \( 300 \)
D. \( 3000000 \)

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


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

Question:
Which letter describes the region where \( \boldsymbol{x}+\boldsymbol{y} \leq \mathbf{3} \) and \( \boldsymbol{y} \geq \mathbf{1} \) ? ![Image is a set of axes with two straight lines drawn. One is x+y=3, which goes through (0,3) and (3,0). The other is y=1 which is a horizontal line going through (0,1). Letter A is in the region that is under x+y=3 and above y=1. Letter B is in the region above both lines. Letter C is in the region that is under y=1 and above x+y=3. Letter D is in the region below both lines.]()

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

Question:
\( 3 \) hours \( +700 \) minutes \( = \)

Options:
A. \( 11 \) hours and \( 40 \) minutes
B. \( 10 \) hours
C. \( 14 \) hours and \( 66 \) minutes
D. \( 14 \) hours and \( 40 \) minutes

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


Prompt:
Misconception:
Answers as if there are 100 minutes in an hour when writing minutes as decimals

Question:
\( 3 \) hours \( +700 \) minutes \( = \)

Options:
A. \( 11 \) hours and \( 40 \) minutes
B. \( 10 \) hours
C. \( 14 \) hours and \( 66 \) minutes
D. \( 14 \) hours and \( 40 \) minutes

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


Prompt:
Misconception:
When reading decimals on a number line, assumes each dash is 0.5

Question:
![A horizontal number-line with 9 vertical, equally spaced, dashes representing the position of numbers. "0" above the 1st dash and "2" above the last dash are the only numbers marked on the line. A red arrow is pointing to the 8th dash.]() What number is the arrow pointing to?

Options:
A. \( 1.5 \)
B. \( 1.8 \)
C. \( 1.9 \)
D. \( 1.75 \)

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:
Estimates a measurement on a diagram rather than working it out

Question:
![A horizontal number-line with 9 vertical, equally spaced, dashes representing the position of numbers. "0" above the 1st dash and "2" above the last dash are the only numbers marked on the line. A red arrow is pointing to the 8th dash.]() What number is the arrow pointing to?

Options:
A. \( 1.5 \)
B. \( 1.8 \)
C. \( 1.9 \)
D. \( 1.75 \)

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:
When reading decimals on a number line, assumes each dash is 0.1

Question:
![A horizontal number-line with 9 vertical, equally spaced, dashes representing the position of numbers. "0" above the 1st dash and "2" above the last dash are the only numbers marked on the line. A red arrow is pointing to the 8th dash.]() What number is the arrow pointing to?

Options:
A. \( 1.5 \)
B. \( 1.8 \)
C. \( 1.9 \)
D. \( 1.75 \)

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:
Believes constructing a perpendicular gives an angle of 60 degrees

Question:
Which of the following best describes how to construct an angle of \( 60^{\circ} \) using a ruler and a pair of compasses?

Options:
A. - Draw a straight line with a ruler
- Set the compasses to a width equal to the length of the line
- Draw an arc above the line from one end of the line
- Do the same from the other end of the line
- Draw a straight line from the ends of each line to where the arcs intersect
- Bisect the angle created
B. - Draw a straight line with a ruler
- Set the compasses to a width at least the length of the line
- Draw an arc above the line and below from one end of the line
- Do the same from the other end of the line
- Join up where the lines intersect
- Bisect the angle created
C. - Draw a straight line with a ruler
- Set the compasses to a width equal to the length of the line
- Draw an arc above the line from one end of the line
- Do the same from the other end of the line
- Draw a straight line from the ends of each line to where the arcs intersect
D. - Draw a straight line with a ruler
- Set the compasses to a width at least the length of the line
- Draw an arc above the line and below from one end of the line
- Do the same from the other end of the line
- Join up where the lines intersect

Solve the problem as a student with the misconception above.
You 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:
Tom and Katie are arguing about a first step to solve this equation:
\(
4(m-1)=20
\)
Tom says you can write: \( 4 m=21 \)
Katie says you can write: \( m-1=5 \)
Who is correct?

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

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


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

Question:
Tom and Katie are arguing about a first step to solve this equation:
\(
4(m-1)=20
\)
Tom says you can write: \( 4 m=21 \)
Katie says you can write: \( m-1=5 \)
Who is correct?

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

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


Prompt:
Misconception:
Does not understand how to solve linear two step equations

Question:
Tom and Katie are arguing about a first step to solve this equation:
\(
4(m-1)=20
\)
Tom says you can write: \( 4 m=21 \)
Katie says you can write: \( m-1=5 \)
Who is correct?

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

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


Prompt:
Misconception:
Thinks a factor of the final digit is also a factor of the whole number

Question:
Tom and Katie are discussing factors

Tom says \( 3 \) is a common factor of \( 18 x \) and \( 29 y \)

Katie says \( x \) is a common factor of \( 6 x \) and \( 9 y \)

Who is correct?

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

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


Prompt:
Misconception:
Believes an arrowhead has four equal sides

Question:
Tom and Katie have been asked to give the name of a quadrilateral with four equal sides
Tom says arrowhead
Katie says rhombus
Who do you agree with?

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

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


Prompt:
Misconception:
Believes an arrowhead has four equal sides

Question:
Tom and Katie have been asked to give the name of a quadrilateral with four equal sides
Tom says arrowhead
Katie says rhombus
Who do you agree with?

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

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


Prompt:
Misconception:
Believes an arrowhead has four equal sides

Question:
Tom and Katie have been asked to give the name of a quadrilateral with four equal sides
Tom says arrowhead
Katie says rhombus
Who do you agree with?

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

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


Prompt:
Misconception:
Fails to identify any rotational symmetry

Question:
![Q]() What is the order of rotational symmetry of this shape?

Options:
A. \( 0 \)
B. \( 1 \)
C. \( 2 \)
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:
Gives one fewer order of rotational symmetry than there is

Question:
![Q]() What is the order of rotational symmetry of this shape?

Options:
A. \( 0 \)
B. \( 1 \)
C. \( 2 \)
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 know how to find order of rotational symmetry

Question:
![Q]() What is the order of rotational symmetry of this shape?

Options:
A. \( 0 \)
B. \( 1 \)
C. \( 2 \)
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 fully simplify fraction

Question:
Simplify fully (if possible): \( \frac{45}{60} \)

Options:
A. \( \frac{9}{12} \)
B. \( \frac{3}{4} \)
C. \( \frac{21}{28} \)
D. Cannot be simplified

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


Prompt:
Misconception:
Does not fully simplify fraction

Question:
Simplify fully (if possible): \( \frac{45}{60} \)

Options:
A. \( \frac{9}{12} \)
B. \( \frac{3}{4} \)
C. \( \frac{21}{28} \)
D. Cannot be simplified

Solve the problem as a student with the misconception above.
You 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 completed square form, confuses the x and y coordinates of the turning point

Question:
Sally wants to write the equation of the curve in the form \( y=(\boldsymbol{x}+\boldsymbol{p})^{2}+\boldsymbol{q} \).
What is the value of \( \boldsymbol{q} \) ? ![A set of axes with a quadratic curve drawn on. The curve is y=x^2 translated 2 squares to the right and 9 squares down.]()

Options:
A. \( -2 \)
B. \( 2 \)
C. \( -9 \)
D. \( 9 \)

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


Prompt:
Misconception:
Believes that in completed square form, they need to change the sign of the constant to get the turning point

Question:
Sally wants to write the equation of the curve in the form \( y=(\boldsymbol{x}+\boldsymbol{p})^{2}+\boldsymbol{q} \).
What is the value of \( \boldsymbol{q} \) ? ![A set of axes with a quadratic curve drawn on. The curve is y=x^2 translated 2 squares to the right and 9 squares down.]()

Options:
A. \( -2 \)
B. \( 2 \)
C. \( -9 \)
D. \( 9 \)

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


Prompt:
Misconception:
Does not recognise difference of two squares

Question:
When factorised, \( x^{2}-64 \) will become...

Options:
A. \( (x+8)(x-8) \)
B. \( x(x-64) \)
C. \( x(x-8) \)
D. \( (x-8)(x-8) \)

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


Prompt:
Misconception:
Does not recognise difference of two squares

Question:
When factorised, \( x^{2}-64 \) will become...

Options:
A. \( (x+8)(x-8) \)
B. \( x(x-64) \)
C. \( x(x-8) \)
D. \( (x-8)(x-8) \)

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


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

Question:
When factorised, \( x^{2}-64 \) will become...

Options:
A. \( (x+8)(x-8) \)
B. \( x(x-64) \)
C. \( x(x-8) \)
D. \( (x-8)(x-8) \)

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


Prompt:
Misconception:
Thinks the interior angles of any polygon add up to 360

Question:
What do all the interior angles of this shape add up to? ![Image of an irregular pentagon]()

Options:
A. \( 360^{\degree} \)
B. \( 540^{\degree} \)
C. \( 720^{\degree} \)
D. Not enough information to work it out

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


Prompt:
Misconception:
Subtracts 1 rather than 2 from the number of sides when finding the sum of interior angles

Question:
What do all the interior angles of this shape add up to? ![Image of an irregular pentagon]()

Options:
A. \( 360^{\degree} \)
B. \( 540^{\degree} \)
C. \( 720^{\degree} \)
D. Not enough information to work it out

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


Prompt:
Misconception:
Thinks rule for calculating interior angles only applies to regular polygons

Question:
What do all the interior angles of this shape add up to? ![Image of an irregular pentagon]()

Options:
A. \( 360^{\degree} \)
B. \( 540^{\degree} \)
C. \( 720^{\degree} \)
D. Not enough information to work it out

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


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

Question:
What fraction replaces the question mark? ![A bar split into 7 equal pieces. 3 are shaded, and one of these is labelled with a question mark.]()

Options:
A. \( \frac{1}{3} \)
B. \( \frac{1}{4} \)
C. \( \frac{1}{6} \)
D. \( \frac{1}{7} \)

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

Question:
Jo and Paul are arguing about a first step to solve this equation:
\(2 v-5=6 v-3\)

Jo says you can write: \( 2 v-8=6 v \)

Paul says you can write: \( 2 v=6 v-8 \)

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

Question:
Jo and Paul are arguing about a first step to solve this equation:
\(2 v-5=6 v-3\)

Jo says you can write: \( 2 v-8=6 v \)

Paul says you can write: \( 2 v=6 v-8 \)

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

Question:
Jo and Paul are arguing about a first step to solve this equation:
\(2 v-5=6 v-3\)

Jo says you can write: \( 2 v-8=6 v \)

Paul says you can write: \( 2 v=6 v-8 \)

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 that in completed square form, they need to change the signs of both values to get the turning point

Question:
What are the co-ordinates of the turning point of the graph of \( y=(x-1)^{2}+4 \) ?

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

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


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

Question:
What are the co-ordinates of the turning point of the graph of \( y=(x-1)^{2}+4 \) ?

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

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


Prompt:
Misconception:
Believes that in completed square form, they need to change the sign of the constant to get the turning point

Question:
What are the co-ordinates of the turning point of the graph of \( y=(x-1)^{2}+4 \) ?

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

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


Prompt:
Misconception:
When adding fractions, adds the numerators and denominators

Question:
Work out:
\(
\frac{3}{10}+\frac{5}{10}
\)
Write your answer in its simplest form.

Options:
A. \( \frac{8}{20} \)
B. \( \frac{8}{10} \)
C. \( \frac{4}{5} \)
D. \( \frac{4}{10} \)

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


Prompt:
Misconception:
Forgot to simplify the fraction

Question:
Work out:
\(
\frac{3}{10}+\frac{5}{10}
\)
Write your answer in its simplest form.

Options:
A. \( \frac{8}{20} \)
B. \( \frac{8}{10} \)
C. \( \frac{4}{5} \)
D. \( \frac{4}{10} \)

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


Prompt:
Misconception:
When adding fractions, adds the numerators and denominators

Question:
Work out:
\(
\frac{3}{10}+\frac{5}{10}
\)
Write your answer in its simplest form.

Options:
A. \( \frac{8}{20} \)
B. \( \frac{8}{10} \)
C. \( \frac{4}{5} \)
D. \( \frac{4}{10} \)

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


Prompt:
Misconception:
Believes a line of reflection must be touching the original shape

Question:
![A grid of 8 squares across and 7 squares up.  A blue isosceles triangle, labelled "P", is drawn on the grid. Its corners are at points: 4 squares up from the bottom left corner of the grid; 2 squares right and 3 squares up from the bottom left corner of the grid; 2 squares right and 5 squares up from the bottom left corner of the grid.   Another blue isosceles triangle (identical shape and size to P), labelled "Q", is also drawn on the grid. Its corners are at points: 6 squares right and 3 squares up from the bottom left corner of the grid; 6 squares right and 5 squares up from the bottom left corner of the grid; 8 squares right and 4 squares up from the bottom left corner of the grid.
A light blue vertical line, labelled "A" goes from top to bottom of the grid, 2 squares to the right of the left-hand side of the grid. A dark blue vertical line, labelled "B" goes from top to bottom of the grid, 4 squares to the right of the left-hand side of the grid. A green vertical line, labelled "C" goes from top to bottom of the grid, 5 squares to the right of the left-hand side of the grid. ]() Which is the correct line of reflection to map triangle \( \mathrm{P} \) to triangle \( \mathrm{Q} \) ?

Options:
A. A
B. B
C. C
D. None of these lines are 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:
Starts at the wrong end of the dividend when dividing

Question:
When using long-division to solve this problem, what digit should replace the triangle to give the correct answer (quotient)? ![Division sum written out in Bus Stop format with dividend = 92, divisor = 4, the digits of the quotient are represented by a yellow star and a purple triangle.]()

Options:
A. \( 3 \)
B. \( 0 \)
C. \( 2 \)
D. \( 1 \)

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


Prompt:
Misconception:
When dividing, confuses the remainder with the quotient

Question:
When using long-division to solve this problem, what digit should replace the triangle to give the correct answer (quotient)? ![Division sum written out in Bus Stop format with dividend = 92, divisor = 4, the digits of the quotient are represented by a yellow star and a purple triangle.]()

Options:
A. \( 3 \)
B. \( 0 \)
C. \( 2 \)
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:
Mixes up the value of two terms when substituting

Question:
This is a part of the table of values for the equation
\[
2 x+3 y=12
\] \begin{tabular}{|c|c|}
\hline\( x \) &  \( \bigstar \) \\
\hline\( y \) & \( 0 \) \\
\hline
\end{tabular} What should replace the star?

Options:
A. \( 2 \)
B. \( 3 \)
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:
Confuses midpoint and distance between two points

Question:
Amy is trying to work out the distance between these two points: \( (1,-6) \) and \( (-5,2) \) She wants to use a formula.

Which formula should she use?

Options:
A. \( \sqrt{\left(x_{2}+x_{1}\right)^{2}-\left(y_{2}+y_{1}\right)^{2}} \)
B. \( \sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}} \)
C. \( \left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right) \)
D. \( \frac{y_{2}-y_{1}}{x_{2}-x_{1}} \)

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:
Confuses the method for finding the gradient and length of a line segment

Question:
Amy is trying to work out the distance between these two points: \( (1,-6) \) and \( (-5,2) \) She wants to use a formula.

Which formula should she use?

Options:
A. \( \sqrt{\left(x_{2}+x_{1}\right)^{2}-\left(y_{2}+y_{1}\right)^{2}} \)
B. \( \sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}} \)
C. \( \left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right) \)
D. \( \frac{y_{2}-y_{1}}{x_{2}-x_{1}} \)

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 that probabilities of an event occurring or not occurring must be equal

Question:
A bag contains some strawberry sweets, some orange sweets and some blackcurrant sweets.

The probability of choosing a strawberry sweet is \( 0.8 \).

What is the probability of choosing an orange sweet?

Options:
A. \( \frac{1}{3} \)
B. \( 0.1 \)
C. \( 0.2 \)
D. Impossible to know

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


Prompt:
Misconception:
Does not understand that the probability of something not happening is 1 minus the probability of it happening

Question:
A bag contains some strawberry sweets, some orange sweets and some blackcurrant sweets.

The probability of choosing a strawberry sweet is \( 0.8 \).

What is the probability of choosing an orange sweet?

Options:
A. \( \frac{1}{3} \)
B. \( 0.1 \)
C. \( 0.2 \)
D. Impossible to know

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


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

Question:
Amy is collecting shells on the beach. She collected \( 16 \) shells on Monday. She collected \( 11 \) less shells on Tuesday than on Monday.
How many shells does Amy have altogether?

Options:
A. \( 43 \)
B. \( 27 \)
C. \( 21 \)
D. \( 5 \)

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


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

Question:
\( 12^{2}= \)

Options:
A. \( 24 \)
B. \( 122 \)
C. \( 144 \)
D. \( 1212 \)

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


Prompt:
Misconception:
Writes the index as a digit on the end of a number

Question:
\( 12^{2}= \)

Options:
A. \( 24 \)
B. \( 122 \)
C. \( 144 \)
D. \( 1212 \)

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


Prompt:
Misconception:
Repeats the digits twice when squaring a number

Question:
\( 12^{2}= \)

Options:
A. \( 24 \)
B. \( 122 \)
C. \( 144 \)
D. \( 1212 \)

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


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

Question:
Tom and Katie are discussing \( \boldsymbol{y}=\mathbf{3}^{\boldsymbol{x}} \)
Tom says there is no value of \( x \) that can make \( y \) negative.
Katie says there is no value of \( x \) that can make \( y \) equal to \( 0 \).
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:
Ignores negative sign when expanding bracket

Question:
John is expanding these two brackets.

What should he get when he multiplies the two terms indicated by the arrows? ![\( (x+5)(x-3) \)]()

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

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:
Adds instead of multiplying when expanding bracket

Question:
John is expanding these two brackets.

What should he get when he multiplies the two terms indicated by the arrows? ![\( (x+5)(x-3) \)]()

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

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:
Adds instead of subtracts

Question:
\( \frac{5}{12}-\frac{1}{6}= \)

Options:
A. \( \frac{7}{12} \)
B. \( \frac{3}{12} \)
C. \( \frac{4}{6} \)
D. \( \frac{4}{12} \)

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


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

Question:
\( \frac{5}{12}-\frac{1}{6}= \)

Options:
A. \( \frac{7}{12} \)
B. \( \frac{3}{12} \)
C. \( \frac{4}{6} \)
D. \( \frac{4}{12} \)

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


Prompt:
Misconception:
Does not understand how to maintain equivalence in fractions

Question:
\( \frac{5}{12}-\frac{1}{6}= \)

Options:
A. \( \frac{7}{12} \)
B. \( \frac{3}{12} \)
C. \( \frac{4}{6} \)
D. \( \frac{4}{12} \)

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


Prompt:
Misconception:
Does not think that a variable with no coefficient has a coefficient of 1.

Question:
![Two angles around a point, labelled 2y and y]() What is the size of angle \( y \) ?

Options:
A. \( 180^{\circ} \)
B. \( 120^{\circ} \)
C. \( 90^{\circ} \)
D. Not enough information

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


Prompt:
Misconception:
Assumes an angle is the size that it looks in the (not to scale) diagram

Question:
![Two angles around a point, labelled 2y and y]() What is the size of angle \( y \) ?

Options:
A. \( 180^{\circ} \)
B. \( 120^{\circ} \)
C. \( 90^{\circ} \)
D. Not enough information

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


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

Question:
![Two angles around a point, labelled 2y and y]() What is the size of angle \( y \) ?

Options:
A. \( 180^{\circ} \)
B. \( 120^{\circ} \)
C. \( 90^{\circ} \)
D. Not enough information

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


Prompt:
Misconception:
Ignores a more than question and just states one of the values

Question:
The frequency table shows the grade achieved by some students in a maths exam.
How many more students achieved a grade \( 5 \) than a grade \( 1 \) ? ![\begin{tabular}{|c|c|}
\hline Grade & Frequency \\
\hline \( 1 \) & \( 4 \) \\
\hline \( 2 \) & \( 5 \) \\
\hline \( 3 \) & \( 1 \) \\
\hline \( 4 \) & \( 8 \) \\
\hline \( 5 \) & \( 10 \) \\
\hline
\end{tabular}]()

Options:
A. \( 5 \)
B. \( 6 \)
C. \( 10 \)
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:
Ignores a more than question and just states one of the values

Question:
The frequency table shows the grade achieved by some students in a maths exam.
How many more students achieved a grade \( 5 \) than a grade \( 1 \) ? ![\begin{tabular}{|c|c|}
\hline Grade & Frequency \\
\hline \( 1 \) & \( 4 \) \\
\hline \( 2 \) & \( 5 \) \\
\hline \( 3 \) & \( 1 \) \\
\hline \( 4 \) & \( 8 \) \\
\hline \( 5 \) & \( 10 \) \\
\hline
\end{tabular}]()

Options:
A. \( 5 \)
B. \( 6 \)
C. \( 10 \)
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 multiplying a fraction by an integer, multiplies the denominator instead of the numerator

Question:
Solve the equation:
\(
\frac{t+1}{3}=\frac{5}{4}
\)

Options:
A. \( t=2 \frac{3}{4} \)
B. \( t=-\frac{7}{12} \)
C. \( t=\frac{3}{4} \)
D. \( t=\frac{11}{12} \)

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


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

Question:
Solve the equation:
\(
\frac{t+1}{3}=\frac{5}{4}
\)

Options:
A. \( t=2 \frac{3}{4} \)
B. \( t=-\frac{7}{12} \)
C. \( t=\frac{3}{4} \)
D. \( t=\frac{11}{12} \)

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


Prompt:
Misconception:
Fails to reflect across mirror line

Question:
The triangle is reflected in the \( x \)-axis
What are the new coordinates of point \( P \) ? ![A set of axes: x-axis from -1 to 6, y-axis from -4 to 2. Three points are plotted and joined to make a triangle: (2, 0), (4, 0), (3, 1). Point (3, 1) is labelled with the letter "P". ]()

Options:
A. \( (3,1) \)
B. \( (3,0) \)
C. \( (3,-1) \)
D. \( (1,3) \)

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:
Fails to reflect across mirror line

Question:
The triangle is reflected in the \( x \)-axis
What are the new coordinates of point \( P \) ? ![A set of axes: x-axis from -1 to 6, y-axis from -4 to 2. Three points are plotted and joined to make a triangle: (2, 0), (4, 0), (3, 1). Point (3, 1) is labelled with the letter "P". ]()

Options:
A. \( (3,1) \)
B. \( (3,0) \)
C. \( (3,-1) \)
D. \( (1,3) \)

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:
Fails to reflect across mirror line

Question:
The triangle is reflected in the \( x \)-axis
What are the new coordinates of point \( P \) ? ![A set of axes: x-axis from -1 to 6, y-axis from -4 to 2. Three points are plotted and joined to make a triangle: (2, 0), (4, 0), (3, 1). Point (3, 1) is labelled with the letter "P". ]()

Options:
A. \( (3,1) \)
B. \( (3,0) \)
C. \( (3,-1) \)
D. \( (1,3) \)

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:
When asked to solve simultaneous equations, believes they can just find values that work in one equation

Question:
![\( \begin{array}{l}\square \square \square \circ \circ=22 \\ \square \square \circ \circ=18\end{array} \)]() What is the value of a square?

Options:
A. \( 3 \)
B. \( 4 \)
C. \( 5 \)
D. \( 6 \)

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


Prompt:
Misconception:
Starts at the wrong end of the dividend when dividing

Question:
When using long-division to solve this problem, what digit should replace the triangle to give the correct answer (quotient)? ![Division sum written out in Bus Stop format with dividend = 84, divisor = 6, quotient is represented by a yellow star and a purple triangle.]()

Options:
A. \( 1 \)
B. \( 2 \)
C. \( 4 \)
D. \( 0 \)

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


Prompt:
Misconception:
Believes they can multiply/divide through by a negative number without changing the direction of the inequality

Question:
Solve the inequality:
\(-\frac{1}{3} y \leq-6\)

Options:
A. \( y \leq 18 \)
B. \( y \geq 2 \)
C. \( y \leq 2 \)
D. \( y \geq 18 \)

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


Prompt:
Misconception:
Believes dividing by a unit fraction is equivalent to dividing by its reciprocal

Question:
Solve the inequality:
\(-\frac{1}{3} y \leq-6\)

Options:
A. \( y \leq 18 \)
B. \( y \geq 2 \)
C. \( y \leq 2 \)
D. \( y \geq 18 \)

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:
When using the formula to solve a quadratic equation, believes that a, b and c are always taken from the 1st, 2nd and 3rd terms, respectively, of the quadratic.

Question:
Vera wants to solve this equation using the quadratic formula.
\(
h^{2}+4=5 h
\)

What should replace the star? \( \frac{ \bigstar\pm \sqrt{?-?}}{?} \)

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

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


Prompt:
Misconception:
Does not realise a quadratic must be in the form ax^2+bx+c=0 to be factorised

Question:
Vera wants to solve this equation using the quadratic formula.
\(
h^{2}+4=5 h
\)

What should replace the star? \( \frac{ \bigstar\pm \sqrt{?-?}}{?} \)

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

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


Prompt:
Misconception:
Believes a polygon can have curved sides

Question:
Tom and Katie are discussing polygons Tom says this is a polygon: ![Triangle]() Katie says this is a polygon: ![Semi-circle]() Who is correct?

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

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


Prompt:
Misconception:
Thinks the term polygons only applies to shapes with more than 3 sides

Question:
Tom and Katie are discussing polygons Tom says this is a polygon: ![Triangle]() Katie says this is a polygon: ![Semi-circle]() Who is correct?

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

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


Prompt:
Misconception:
When solving an equation, subtracts instead of dividing

Question:
Step \( 2 \)

Which is the correct next step rearrangement of the following formula, making \( u \) the subject?
\[
7 t-13=u(5+2 t)
\]

Options:
A. \( u=5 t-8 \)
B. \( u=\frac{7 t-13}{5+2 t} \)
C. \( u=\frac{5+2 t}{7 t-13} \)
D. \( u=9 t-8 \)

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:
Misunderstands the process of making a variable the subject of an equation

Question:
Step \( 2 \)

Which is the correct next step rearrangement of the following formula, making \( u \) the subject?
\[
7 t-13=u(5+2 t)
\]

Options:
A. \( u=5 t-8 \)
B. \( u=\frac{7 t-13}{5+2 t} \)
C. \( u=\frac{5+2 t}{7 t-13} \)
D. \( u=9 t-8 \)

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

Question:
\( 1.5 \) hours \( = _______\) minutes

Options:
A. \( 150 \)
B. \( 105 \)
C. \( 90 \)
D. \( 65 \)

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


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

Question:
\( 1.5 \) hours \( = _______\) minutes

Options:
A. \( 150 \)
B. \( 105 \)
C. \( 90 \)
D. \( 65 \)

Solve the problem as a student with the misconception above.
You 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 10 minutes in an hour

Question:
\( 1.5 \) hours \( = _______\) minutes

Options:
A. \( 150 \)
B. \( 105 \)
C. \( 90 \)
D. \( 65 \)

Solve the problem as a student with the misconception above.
You 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:
If you know the first term of a linear sequence and you multiply it by \( 10 \), you get the \( 10^{\text {th }} \) term of that sequence.
Is this statement...

Options:
A. always true
B. sometimes true
C. never true
D. Need more 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:
Assumes a fact without considering enough examples

Question:
If you know the first term of a linear sequence and you multiply it by \( 10 \), you get the \( 10^{\text {th }} \) term of that sequence.
Is this statement...

Options:
A. always true
B. sometimes true
C. never true
D. Need more information

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


Prompt:
Misconception:
Believes distance is the area under the graph on a displacement time graph

Question:
This displacement-time graph shows the first \( 10 \) seconds of Mo's journey.

During that time he travelled at a speed of \( 6 \mathrm{~m} / \mathrm{s.} \)

What distance should replace the star? ![A graph showing Time in seconds on the x axis and Distance in metres on the y axis. A straight line is drawn from the origin to the point (10, \(\bigstar \))]()

Options:
A. \( 30 \mathrm{~m} \)
B. \( 6 \mathrm{~m} \)
C. \( 60 \mathrm{~m} \)
D. \( 16 \mathrm{~m} \)

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


Prompt:
Misconception:
Believes scales on graphs must match on both axes

Question:
This displacement-time graph shows the first \( 10 \) seconds of Mo's journey.

During that time he travelled at a speed of \( 6 \mathrm{~m} / \mathrm{s.} \)

What distance should replace the star? ![A graph showing Time in seconds on the x axis and Distance in metres on the y axis. A straight line is drawn from the origin to the point (10, \(\bigstar \))]()

Options:
A. \( 30 \mathrm{~m} \)
B. \( 6 \mathrm{~m} \)
C. \( 60 \mathrm{~m} \)
D. \( 16 \mathrm{~m} \)

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


Prompt:
Misconception:
Believes distance = speed + time

Question:
This displacement-time graph shows the first \( 10 \) seconds of Mo's journey.

During that time he travelled at a speed of \( 6 \mathrm{~m} / \mathrm{s.} \)

What distance should replace the star? ![A graph showing Time in seconds on the x axis and Distance in metres on the y axis. A straight line is drawn from the origin to the point (10, \(\bigstar \))]()

Options:
A. \( 30 \mathrm{~m} \)
B. \( 6 \mathrm{~m} \)
C. \( 60 \mathrm{~m} \)
D. \( 16 \mathrm{~m} \)

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


Prompt:
Misconception:
Assumes the item has not been replaced in a probability question where it has actually been replaced

Question:
There are \( 4 \) red balls and \( 3 \) yellow balls in a cup. ![The image shows the cup with the 4 red balls and 3 yellow balls.]() Kate picks a yellow ball out and then replaces it.

She then has a second pick.
What is the probability the second pick is also a yellow ball?

Options:
A. \( \frac{3}{7} \)
B. \( \frac{3}{6} \)
C. \( \frac{2}{7} \)
D. \( \frac{2}{6} \)

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:
Assumes the item has not been replaced in a probability question where it has actually been replaced

Question:
There are \( 4 \) red balls and \( 3 \) yellow balls in a cup. ![The image shows the cup with the 4 red balls and 3 yellow balls.]() Kate picks a yellow ball out and then replaces it.

She then has a second pick.
What is the probability the second pick is also a yellow ball?

Options:
A. \( \frac{3}{7} \)
B. \( \frac{3}{6} \)
C. \( \frac{2}{7} \)
D. \( \frac{2}{6} \)

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


Prompt:
Misconception:
When reading decimals on a number line, assumes each dash is 0.1

Question:
![A horizontal number-line with 9 vertical, equally spaced, dashes representing the position of numbers. "0" above the 1st dash and "2" above the 9th dash are the only numbers marked on the line. A red arrow is pointing to the 7th dash.]() What number is the arrow pointing to?

Options:
A. \( 1.8 \)
B. \( 1.5 \)
C. \( 1 \)
D. \( 1.6 \)

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


Prompt:
Misconception:
Believes the arrow on a number line points to the middle value

Question:
![A horizontal number-line with 9 vertical, equally spaced, dashes representing the position of numbers. "0" above the 1st dash and "2" above the 9th dash are the only numbers marked on the line. A red arrow is pointing to the 7th dash.]() What number is the arrow pointing to?

Options:
A. \( 1.8 \)
B. \( 1.5 \)
C. \( 1 \)
D. \( 1.6 \)

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


Prompt:
Misconception:
Estimates a measurement on a diagram rather than working it out

Question:
![A horizontal number-line with 9 vertical, equally spaced, dashes representing the position of numbers. "0" above the 1st dash and "2" above the 9th dash are the only numbers marked on the line. A red arrow is pointing to the 7th dash.]() What number is the arrow pointing to?

Options:
A. \( 1.8 \)
B. \( 1.5 \)
C. \( 1 \)
D. \( 1.6 \)

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


Prompt:
Misconception:
Does not understand a percentage can be applied to something not out of 100

Question:
\( 20 \% \) of \( \pounds 140= \)

Options:
A. \( £ 280 \)
B. \( £ 20 \)
C. \( £ 120 \)
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:
Has taken the percentage from the original

Question:
\( 20 \% \) of \( \pounds 140= \)

Options:
A. \( £ 280 \)
B. \( £ 20 \)
C. \( £ 120 \)
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 adding decimals, just adds the digits and ignores place value

Question:
This is how Dora calculates the answer to \( 12.3+4.5 \) mentally ![Image showing a cartoon girl with three thought bubbles above her head. The first bubble states 'I added the whole part first 12+4=16'. The second states 'I then added the decimal part 0.3+0.5=0.8'. The third bubble states 'I then added 16 and 0.8 to get 16.8.So 12.3+4.5=16.8']() Dora uses the same method to calculate \( 3.5+21.8 \). Which of the following shows how she would do this?

Options:
A. \( \begin{array}{c}3+21=24 \\ 0.5+0.8=0.13 \\ 24+0.13=24.13\end{array} \)
B. \( \begin{array}{c}3.5+21=24.5 \\ 24.5+0.8=25.3\end{array} \)
C. \( \begin{array}{c}3+21=24 \\ 0.5+0.8=1.3 \\ 24+1.3=24.13\end{array} \)
D. \( \begin{array}{c}3+21=24 \\ 0.5+0.8=1.3 \\ 24+1.3=25.3\end{array} \)

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:
Does not interpret the correct order of operations from a worded problem

Question:
This is how Dora calculates the answer to \( 12.3+4.5 \) mentally ![Image showing a cartoon girl with three thought bubbles above her head. The first bubble states 'I added the whole part first 12+4=16'. The second states 'I then added the decimal part 0.3+0.5=0.8'. The third bubble states 'I then added 16 and 0.8 to get 16.8.So 12.3+4.5=16.8']() Dora uses the same method to calculate \( 3.5+21.8 \). Which of the following shows how she would do this?

Options:
A. \( \begin{array}{c}3+21=24 \\ 0.5+0.8=0.13 \\ 24+0.13=24.13\end{array} \)
B. \( \begin{array}{c}3.5+21=24.5 \\ 24.5+0.8=25.3\end{array} \)
C. \( \begin{array}{c}3+21=24 \\ 0.5+0.8=1.3 \\ 24+1.3=24.13\end{array} \)
D. \( \begin{array}{c}3+21=24 \\ 0.5+0.8=1.3 \\ 24+1.3=25.3\end{array} \)

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:
Ignores place value when adding a whole number and a decimal

Question:
This is how Dora calculates the answer to \( 12.3+4.5 \) mentally ![Image showing a cartoon girl with three thought bubbles above her head. The first bubble states 'I added the whole part first 12+4=16'. The second states 'I then added the decimal part 0.3+0.5=0.8'. The third bubble states 'I then added 16 and 0.8 to get 16.8.So 12.3+4.5=16.8']() Dora uses the same method to calculate \( 3.5+21.8 \). Which of the following shows how she would do this?

Options:
A. \( \begin{array}{c}3+21=24 \\ 0.5+0.8=0.13 \\ 24+0.13=24.13\end{array} \)
B. \( \begin{array}{c}3.5+21=24.5 \\ 24.5+0.8=25.3\end{array} \)
C. \( \begin{array}{c}3+21=24 \\ 0.5+0.8=1.3 \\ 24+1.3=24.13\end{array} \)
D. \( \begin{array}{c}3+21=24 \\ 0.5+0.8=1.3 \\ 24+1.3=25.3\end{array} \)

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:
Does not divide by 2 when calculating the area of a trapezium

Question:
The area of this trapezium is \( 63 \mathrm{~cm}^{2} \).

What is the value of \( a \) ? ![A trapezium with the parallel sides labelled with 3cm and a and the height labelled with 9cm]()

Options:
A. \( 125 \mathrm{~cm} \)
B. \( 4 \mathrm{~cm} \)
C. \( 6 \mathrm{~cm} \)
D. \( 11 \mathrm{~cm} \)

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

Question:
\( \frac{1}{20} \) of \( 7=? \times 7 \)

Options:
A. \( 0.5 \)
B. \( 0.05 \)
C. \( 0.2 \)
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:
Multiplies by the denominator instead of dividing when finding a fraction of an amount

Question:
\( \frac{1}{20} \) of \( 7=? \times 7 \)

Options:
A. \( 0.5 \)
B. \( 0.05 \)
C. \( 0.2 \)
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 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:
Does not realise that subtracting a negative is the same as adding it's additive inverse

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:
Rounds up instead of down

Question:
A distance has been rounded to the nearest \( \mathrm{km} \), giving \( 106 \) \( \mathrm{km} \).
Which of these values could the distance \( \underline{not} \) be?

Options:
A. \( 106220 \mathrm{~m} \)
B. \( 105605 \mathrm{~m} \)
C. \( 105698 \mathrm{~m} \)
D. \( 106502 \mathrm{~m} \)

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


Prompt:
Misconception:
Rounds down instead of up

Question:
A distance has been rounded to the nearest \( \mathrm{km} \), giving \( 106 \) \( \mathrm{km} \).
Which of these values could the distance \( \underline{not} \) be?

Options:
A. \( 106220 \mathrm{~m} \)
B. \( 105605 \mathrm{~m} \)
C. \( 105698 \mathrm{~m} \)
D. \( 106502 \mathrm{~m} \)

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


Prompt:
Misconception:
Rounds down instead of up

Question:
A distance has been rounded to the nearest \( \mathrm{km} \), giving \( 106 \) \( \mathrm{km} \).
Which of these values could the distance \( \underline{not} \) be?

Options:
A. \( 106220 \mathrm{~m} \)
B. \( 105605 \mathrm{~m} \)
C. \( 105698 \mathrm{~m} \)
D. \( 106502 \mathrm{~m} \)

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


Prompt:
Misconception:
Expands when asked to simplify

Question:
Write this as a single fraction as simply as possible
\(
\frac{2}{m^{2}-4 m+3} \times \frac{m-3}{4}
\)

Options:
A. \( \frac{8}{m-1} \)
B. \( \frac{1}{2(m-1)} \)
C. \( \frac{2 m-6}{4 m^{2}-16 m+12} \)
D. \( \frac{2}{m-1} \)

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:
Confuses reciprocal and exponential graphs

Question:
Which of the following is most likely to be the graph of a exponential function?

Options:
A. ![A curved graph that starts just above the x-axis on the left and travels right and very gradually up. Just before it reaches the y-axis it travels more steeply up and right, going through a point on the y-axis above the origin and continually steeply rising up and right.]()
B. ![A graph with two curves, in the top right and bottom left quadrants. The top right curves starts up and right of the origin and travels steeply down and right, it then levels off to travel alongside the x-axis without touching it. The bottom left curve starts down and left of the origin, travels steeply up and left, it then levels off just below the x-axis without touching it.]()
C. ![A curved graph that starts in the top left, travels steeply down and right, turns to travel steeply up and right, to the origin, where it turns around to travel down and right again.]()
D. ![A curved graph, an upside down symmetrical U shape. It starts in the bottom left, travels steeply up and right, turns at a point on the y-axis above the origin and travels steeply right and down.]()

Solve the problem as a student with the misconception above.
You 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 cubic and exponential graphs

Question:
Which of the following is most likely to be the graph of a exponential function?

Options:
A. ![A curved graph that starts just above the x-axis on the left and travels right and very gradually up. Just before it reaches the y-axis it travels more steeply up and right, going through a point on the y-axis above the origin and continually steeply rising up and right.]()
B. ![A graph with two curves, in the top right and bottom left quadrants. The top right curves starts up and right of the origin and travels steeply down and right, it then levels off to travel alongside the x-axis without touching it. The bottom left curve starts down and left of the origin, travels steeply up and left, it then levels off just below the x-axis without touching it.]()
C. ![A curved graph that starts in the top left, travels steeply down and right, turns to travel steeply up and right, to the origin, where it turns around to travel down and right again.]()
D. ![A curved graph, an upside down symmetrical U shape. It starts in the bottom left, travels steeply up and right, turns at a point on the y-axis above the origin and travels steeply right and down.]()

Solve the problem as a student with the misconception above.
You 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 quadratic and exponential graphs

Question:
Which of the following is most likely to be the graph of a exponential function?

Options:
A. ![A curved graph that starts just above the x-axis on the left and travels right and very gradually up. Just before it reaches the y-axis it travels more steeply up and right, going through a point on the y-axis above the origin and continually steeply rising up and right.]()
B. ![A graph with two curves, in the top right and bottom left quadrants. The top right curves starts up and right of the origin and travels steeply down and right, it then levels off to travel alongside the x-axis without touching it. The bottom left curve starts down and left of the origin, travels steeply up and left, it then levels off just below the x-axis without touching it.]()
C. ![A curved graph that starts in the top left, travels steeply down and right, turns to travel steeply up and right, to the origin, where it turns around to travel down and right again.]()
D. ![A curved graph, an upside down symmetrical U shape. It starts in the bottom left, travels steeply up and right, turns at a point on the y-axis above the origin and travels steeply right and down.]()

Solve the problem as a student with the misconception above.
You 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 intersection on a Venn diagram represents the total of one set

Question:
\( 60 \) people completed an online survey about the car they own.
The results are shown in the Venn Diagram.

How many people own a black car? ![A Venn diagram with two circles labelled Owns a 4x4 and Owns a Black Car. The number 27 is in the Owns a 4x4 only region, 15 is in the intersection, and 8 is in the Owns a Black Car only region.]()

Options:
A. \( 27 \)
B. \( 15 \)
C. \( 8 \)
D. \( 23 \)

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


Prompt:
Misconception:
Forgets to include the intersection value when asked for total value of a set in a Venn diagram

Question:
\( 60 \) people completed an online survey about the car they own.
The results are shown in the Venn Diagram.

How many people own a black car? ![A Venn diagram with two circles labelled Owns a 4x4 and Owns a Black Car. The number 27 is in the Owns a 4x4 only region, 15 is in the intersection, and 8 is in the Owns a Black Car only region.]()

Options:
A. \( 27 \)
B. \( 15 \)
C. \( 8 \)
D. \( 23 \)

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


Prompt:
Misconception:
Counts on by 1, when asked to count forward/backwards in a step other than 1

Question:
Amelie is counting backwards in steps of \( 4 \).
She starts at the number \( 24,993 \)
what is the next number she will say?

Options:
A. \( 24,988 \)
B. \( 24,992 \)
C. \( 24,990 \)
D. \( 24,989 \)

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


Prompt:
Misconception:
Counts the starting number when counting backwards

Question:
Amelie is counting backwards in steps of \( 4 \).
She starts at the number \( 24,993 \)
what is the next number she will say?

Options:
A. \( 24,988 \)
B. \( 24,992 \)
C. \( 24,990 \)
D. \( 24,989 \)

Solve the problem as a student with the misconception above.
You 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 numbers are divisible by numbers which sum to their factors

Question:
If \( 12 \) is a factor of a number, then another factor of that number must be...

Options:
A. \( 5 \) and \( 7 \)
B. \( 4 \)
C. \( 24 \)
D. Impossible to say

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


Prompt:
Misconception:
Thinks numbers are divisible by all multiples of their factors

Question:
If \( 12 \) is a factor of a number, then another factor of that number must be...

Options:
A. \( 5 \) and \( 7 \)
B. \( 4 \)
C. \( 24 \)
D. Impossible to say

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


Prompt:
Misconception:
When multiplying a decimal by an integer, ignores decimal point and just multiplies the digits

Question:
\( 9.4 \times 50= \)

Options:
A. \( 4700 \)
B. \( 420 \)
C. \( 940 \)
D. \( 470 \)

Solve the problem as a student with the misconception above.
You 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 fractions with prime numerators cannot be simplified

Question:
Jo and Paul are arguing about simplifying fractions.

Jo says you can never simplify a fraction if either the numerator or denominator is a prime number.

Paul says you will always be able to simplify a fraction if neither the numerator or denominator is prime.

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:
Assumes a fact without considering enough examples

Question:
Jo and Paul are arguing about simplifying fractions.

Jo says you can never simplify a fraction if either the numerator or denominator is a prime number.

Paul says you will always be able to simplify a fraction if neither the numerator or denominator is prime.

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:
Does not understand a percentage can be applied to something not out of 100

Question:
\( 30 \% \) of \( £ 120= \)

Options:
A. \( £ 30 \)
B. \( £ 36 \)
C. \( £ 90 \)
D. \( £ 360 \)

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


Prompt:
Misconception:
Believes adding two negatives gives a positive answer

Question:
Multiply out the brackets:
\[
(m-3)(m-2)
\]

Options:
A. \( m^{2}-5 m+6 \)
B. \( m^{2}-m-6 \)
C. \( m^{2}+5 m+6 \)
D. \( m^{2}-5 m-6 \)

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


Prompt:
Misconception:
Believes multiplying two negatives gives a negative answer

Question:
Multiply out the brackets:
\[
(m-3)(m-2)
\]

Options:
A. \( m^{2}-5 m+6 \)
B. \( m^{2}-m-6 \)
C. \( m^{2}+5 m+6 \)
D. \( m^{2}-5 m-6 \)

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


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

Question:
This is a part of the table of values for the equation
\[
2 x+3 y=12
\] \begin{tabular}{|l|l|}
\hline\( x \) & \( 0.3 \) \\
\hline\( y \) & \( \bigstar \) \\
\hline
\end{tabular} What should replace the star?

Options:
A. \( 4.1 \)
B. \( 3.9 \)
C. \( 4.2 \)
D. \( 3.8 \)

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


Prompt:
Misconception:
When asked for factors of an algebraic expression, thinks any part of a term will be a factor

Question:
Which of the following is a factor of: \( 6 p^{2}+11 p \)

Options:
A. \( 6 \)
B. \( 11 \)
C. \( p^{2} \)
D. \( p \)

Solve the problem as a student with the misconception above.
You 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 factors of an algebraic expression, thinks any part of a term will be a factor

Question:
Which of the following is a factor of: \( 6 p^{2}+11 p \)

Options:
A. \( 6 \)
B. \( 11 \)
C. \( p^{2} \)
D. \( p \)

Solve the problem as a student with the misconception above.
You 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 factors of an algebraic expression, thinks any part of a term will be a factor

Question:
Which of the following is a factor of: \( 6 p^{2}+11 p \)

Options:
A. \( 6 \)
B. \( 11 \)
C. \( p^{2} \)
D. \( p \)

Solve the problem as a student with the misconception above.
You 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 when calculating volume instead of multiplying

Question:
What is the volume of this cube? ![A cube with one edge labelled 5cm]()

Options:
A. \( 125 \mathrm{~cm}^{3} \)
B. \( 15 \mathrm{~cm}^{3} \)
C. \( 25 \mathrm{~cm}^{3} \)
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:
Finds area of one face when asked for volume

Question:
What is the volume of this cube? ![A cube with one edge labelled 5cm]()

Options:
A. \( 125 \mathrm{~cm}^{3} \)
B. \( 15 \mathrm{~cm}^{3} \)
C. \( 25 \mathrm{~cm}^{3} \)
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 recognise that all lengths on a cube are equal

Question:
What is the volume of this cube? ![A cube with one edge labelled 5cm]()

Options:
A. \( 125 \mathrm{~cm}^{3} \)
B. \( 15 \mathrm{~cm}^{3} \)
C. \( 25 \mathrm{~cm}^{3} \)
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:
Fails to reflect across mirror line

Question:
The triangle is reflected in the dashed line.
What are the new coordinates of point \( P \) ? ![Four quadrant, coordinate grid with the reflection line y=x drawn and a triangle. The triangle has coordinates: (3,3) (2,1) and (4,1). The point P is the coordinate (2,1)]()

Options:
A. \( (2,2) \)
B. \( (2,0) \)
C. \( (0,1) \)
D. \( (1,2) \)

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


Prompt:
Misconception:
Fails to reflect across mirror line

Question:
The triangle is reflected in the dashed line.
What are the new coordinates of point \( P \) ? ![Four quadrant, coordinate grid with the reflection line y=x drawn and a triangle. The triangle has coordinates: (3,3) (2,1) and (4,1). The point P is the coordinate (2,1)]()

Options:
A. \( (2,2) \)
B. \( (2,0) \)
C. \( (0,1) \)
D. \( (1,2) \)

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


Prompt:
Misconception:
Reflects horizontally or vertically instead of across a diagonal line of symmetry

Question:
The triangle is reflected in the dashed line.
What are the new coordinates of point \( P \) ? ![Four quadrant, coordinate grid with the reflection line y=x drawn and a triangle. The triangle has coordinates: (3,3) (2,1) and (4,1). The point P is the coordinate (2,1)]()

Options:
A. \( (2,2) \)
B. \( (2,0) \)
C. \( (0,1) \)
D. \( (1,2) \)

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


Prompt:
Misconception:
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 \( x^{2}+12 x+32 \) is factorised, what will appear in the box below? ![\( (x+4) \square \)]()

Options:
A. \( (x+7) \)
B. \( (x+28) \)
C. \( (x+8) \)
D. \( (x-8) \)

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


Prompt:
Misconception:
Believes multiplying a positive by a negative gives a positive answer

Question:
When \( x^{2}+12 x+32 \) is factorised, what will appear in the box below? ![\( (x+4) \square \)]()

Options:
A. \( (x+7) \)
B. \( (x+28) \)
C. \( (x+8) \)
D. \( (x-8) \)

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


Prompt:
Misconception:
Added rather than multiplied by a scale factor

Question:
\( 1 \mathrm{~km} \approx 0.6 \) miles \( 3 \mathrm{~km} \approx \square \) miles

Options:
A. \( 1.8 \)
B. \( 2.6 \)
C. \( 3.6 \)
D. \( 0.18 \)

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:
When multiplying decimals, ignores place value and just multiplies the digits

Question:
\( 1 \mathrm{~km} \approx 0.6 \) miles \( 3 \mathrm{~km} \approx \square \) miles

Options:
A. \( 1.8 \)
B. \( 2.6 \)
C. \( 3.6 \)
D. \( 0.18 \)

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:
Writes fraction rather than fraction of amount

Question:
\( 24 \) people went to an local ice hockey match.
The pie chart shows the colours of their shirts.
How many people wore red? ![Pie chart divided into 8 equal sections. 4 sections are yellow, 2 sections are red, 1 section is black and 1 section is white.]()

Options:
A. \( 6 \)
B. \( \frac{1}{4} \)
C. \( 3 \)
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:
Finds the unit fraction when asked to find a non-unit fraction of an amount

Question:
\( 24 \) people went to an local ice hockey match.
The pie chart shows the colours of their shirts.
How many people wore red? ![Pie chart divided into 8 equal sections. 4 sections are yellow, 2 sections are red, 1 section is black and 1 section is white.]()

Options:
A. \( 6 \)
B. \( \frac{1}{4} \)
C. \( 3 \)
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:
Gives number of sections of pie chart rather than the amount it represents

Question:
\( 24 \) people went to an local ice hockey match.
The pie chart shows the colours of their shirts.
How many people wore red? ![Pie chart divided into 8 equal sections. 4 sections are yellow, 2 sections are red, 1 section is black and 1 section is white.]()

Options:
A. \( 6 \)
B. \( \frac{1}{4} \)
C. \( 3 \)
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:
Does not realise addition is commutative

Question:
\[
\text { When } h=10 \text { and } j=4
\]

Which of the following pairs of statements is true?

Options:
A. \( \begin{array}{l}h(j+2)=60 \\ h(2+j)=-60\end{array} \)
B. \( \begin{array}{l}h(j+2)=42 \\ h(2+j)=24\end{array} \)
C. \( \begin{array}{l}h(j+2)=24 \\ h(2+j)=42\end{array} \)
D. \( \begin{array}{l}h(j+2)=60 \\ h(2+j)=60\end{array} \)

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 realise addition is commutative

Question:
\[
\text { When } h=10 \text { and } j=4
\]

Which of the following pairs of statements is true?

Options:
A. \( \begin{array}{l}h(j+2)=60 \\ h(2+j)=-60\end{array} \)
B. \( \begin{array}{l}h(j+2)=42 \\ h(2+j)=24\end{array} \)
C. \( \begin{array}{l}h(j+2)=24 \\ h(2+j)=42\end{array} \)
D. \( \begin{array}{l}h(j+2)=60 \\ h(2+j)=60\end{array} \)

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 realise addition is commutative

Question:
\[
\text { When } h=10 \text { and } j=4
\]

Which of the following pairs of statements is true?

Options:
A. \( \begin{array}{l}h(j+2)=60 \\ h(2+j)=-60\end{array} \)
B. \( \begin{array}{l}h(j+2)=42 \\ h(2+j)=24\end{array} \)
C. \( \begin{array}{l}h(j+2)=24 \\ h(2+j)=42\end{array} \)
D. \( \begin{array}{l}h(j+2)=60 \\ h(2+j)=60\end{array} \)

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:
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 compound shape making an upside down T shape where there is a rectangle across the bottom and a rectangle attached above this, slightly to the left of the centre. The full width across the bottom is 16m, the partial width on the left is 2m, the partial width on the top block is 7m. The full height on the right is 9m, the partial height on the left is 3m. The shaded section is the right hand rectangle from the right edge up to where the top rectangle begins.]()

Options:
A. \( 48 \mathrm{~m}^{2} \)
B. \( 21 \mathrm{~m}^{2} \)
C. \( 15 \mathrm{~m}^{2} \)
D. \( 10 \mathrm{~cm}^{2} \)

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


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

Question:
What is the area of the shaded section of this composite shape made from rectangles? ![A compound shape making an upside down T shape where there is a rectangle across the bottom and a rectangle attached above this, slightly to the left of the centre. The full width across the bottom is 16m, the partial width on the left is 2m, the partial width on the top block is 7m. The full height on the right is 9m, the partial height on the left is 3m. The shaded section is the right hand rectangle from the right edge up to where the top rectangle begins.]()

Options:
A. \( 48 \mathrm{~m}^{2} \)
B. \( 21 \mathrm{~m}^{2} \)
C. \( 15 \mathrm{~m}^{2} \)
D. \( 10 \mathrm{~cm}^{2} \)

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 area of a rectangle is calculated by length add width

Question:
What is the area of the shaded section of this composite shape made from rectangles? ![A compound shape making an upside down T shape where there is a rectangle across the bottom and a rectangle attached above this, slightly to the left of the centre. The full width across the bottom is 16m, the partial width on the left is 2m, the partial width on the top block is 7m. The full height on the right is 9m, the partial height on the left is 3m. The shaded section is the right hand rectangle from the right edge up to where the top rectangle begins.]()

Options:
A. \( 48 \mathrm{~m}^{2} \)
B. \( 21 \mathrm{~m}^{2} \)
C. \( 15 \mathrm{~m}^{2} \)
D. \( 10 \mathrm{~cm}^{2} \)

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:
Mixes up greater than and less than symbols

Question:
Which signs belong in the boxes to make the statement correct?
\( 76426 \)\[ {\color{blue}\square} \]\( 76462 \)\[ {\color{orange}\square} \]\( 74662 \)

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

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


Prompt:
Misconception:
Assumes that a list is given in size order

Question:
Which signs belong in the boxes to make the statement correct?
\( 76426 \)\[ {\color{blue}\square} \]\( 76462 \)\[ {\color{orange}\square} \]\( 74662 \)

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

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


Prompt:
Misconception:
Assumes that a list is given in size order

Question:
Which signs belong in the boxes to make the statement correct?
\( 76426 \)\[ {\color{blue}\square} \]\( 76462 \)\[ {\color{orange}\square} \]\( 74662 \)

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

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


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

Question:
Tom and Katie are discussing how to solve:
\(
\frac{8 x}{5}=40
\)

Tom says a correct next line of working could be: \( 8 x=8 \)
Katie says a correct next line of working could be: \( \frac{x}{5}=5 \)
Who is correct?

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

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


Prompt:
Misconception:
When dividing a fraction by an integer, divides both the numerator and denominator by the integer

Question:
Tom and Katie are discussing how to solve:
\(
\frac{8 x}{5}=40
\)

Tom says a correct next line of working could be: \( 8 x=8 \)
Katie says a correct next line of working could be: \( \frac{x}{5}=5 \)
Who is correct?

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

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


Prompt:
Misconception:
Fails to consider all possible outcomes

Question:
These spinners are spun and the two scores are added together.

Bob records the results in a sample space diagram.
How many cells would contain a score of \( 4 \) ? ![Two 6-sided spinners. Both spinners are split into 6 equal sections with the numbers 1, 3, 3, 5, 5, and 5 in them.]() \begin{tabular}{|l|l|l|l|l|l|l|}
\hline & \( 1 \) & \( 3 \) & \( 3 \) & \( 5 \) & \( 5 \) & \( 5 \) \\
\hline \( 1 \) \\
\hline \( 3 \)  \\
\hline \( 3 \)  \\
\hline \( 5 \)\\
\hline \( 5 \)  \\
\hline \( 5 \) \\
\hline
\end{tabular}

Options:
A. \( 1 \)
B. \( 2 \)
C. \( 4 \)
D. \( 0 \)

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


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

Question:
Convert \( \frac{4}{20} \) into a decimal

Options:
A. \( 5.0 \)
B. \( 0.4 \)
C. \( 0.2 \)
D. \( 4.20 \)

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

Question:
Convert \( \frac{4}{20} \) into a decimal

Options:
A. \( 5.0 \)
B. \( 0.4 \)
C. \( 0.2 \)
D. \( 4.20 \)

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

Question:
Convert \( \frac{4}{20} \) into a decimal

Options:
A. \( 5.0 \)
B. \( 0.4 \)
C. \( 0.2 \)
D. \( 4.20 \)

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:
Thinks congruent shapes are the same shape but can be different sizes

Question:
Tom and Katie are discussing congruent shapes. Who is correct? Tom says these two shapes are congruent ![An image of two triangles. The triangles are the same shape and size but have different orientations.]() Katie says these two shapes are congruent ![An image of two triangles. A big one and a small one.]()

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

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


Prompt:
Misconception:
Thinks congruent shapes are the same shape but can be different sizes

Question:
Tom and Katie are discussing congruent shapes. Who is correct? Tom says these two shapes are congruent ![An image of two triangles. The triangles are the same shape and size but have different orientations.]() Katie says these two shapes are congruent ![An image of two triangles. A big one and a small one.]()

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 that shapes are congruent if they have the same size and shape

Question:
Tom and Katie are discussing congruent shapes. Who is correct? Tom says these two shapes are congruent ![An image of two triangles. The triangles are the same shape and size but have different orientations.]() Katie says these two shapes are congruent ![An image of two triangles. A big one and a small one.]()

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

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


Prompt:
Misconception:
When calculating perimeter, only adds the marked lengths

Question:
What is the difference between the perimeters of these two shapes? ![Beige rectangle with base length 13cm and side length 5cm]() ![Pink, isosceles triangle with base length 4cm and side length 16cm]()

Options:
A. \( 4 \mathrm{~cm} \)
B. \( 48 \mathrm{~cm} \)
C. \( 0 \mathrm{~cm} \)
D. \( 72 \mathrm{~cm} \)

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 calculating perimeter, only adds the marked lengths

Question:
What is the difference between the perimeters of these two shapes? ![Beige rectangle with base length 13cm and side length 5cm]() ![Pink, isosceles triangle with base length 4cm and side length 16cm]()

Options:
A. \( 4 \mathrm{~cm} \)
B. \( 48 \mathrm{~cm} \)
C. \( 0 \mathrm{~cm} \)
D. \( 72 \mathrm{~cm} \)

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


Prompt:
Misconception:
Adds instead of subtracts when asked to find the difference

Question:
What is the difference between the perimeters of these two shapes? ![Beige rectangle with base length 13cm and side length 5cm]() ![Pink, isosceles triangle with base length 4cm and side length 16cm]()

Options:
A. \( 4 \mathrm{~cm} \)
B. \( 48 \mathrm{~cm} \)
C. \( 0 \mathrm{~cm} \)
D. \( 72 \mathrm{~cm} \)

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


Prompt:
Misconception:
Does not understand that base angles in an isosceles are equal

Question:
A triangle has the following angles: \( 90\degree, 50\degree, 40\degree \)
Tom says the triangle is right-angled
Katie says the triangle is isosceles
Who is correct?

Options:
A. Only Tom
B. Both Tom and Katie
C. Only Katie
D. Neither are 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 a right angle is 90 degrees

Question:
A triangle has the following angles: \( 90\degree, 50\degree, 40\degree \)
Tom says the triangle is right-angled
Katie says the triangle is isosceles
Who is correct?

Options:
A. Only Tom
B. Both Tom and Katie
C. Only Katie
D. Neither are 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 correctly apply the distributive property of multiplication

Question:
Tom and Katie are trying to calculate the answer to \( 19 \times 8 \)
Tom does this: \( 20 \times 8-1 \times 8 \)
Katie does this: \( 10 \times 8+9 \times 8 \)
Who is correct?

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

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


Prompt:
Misconception:
When factorising a quadratic without a non variable term, tries to double bracket factorise

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

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

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


Prompt:
Misconception:
When factorising a quadratic without a non variable term, tries to double bracket factorise

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

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

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


Prompt:
Misconception:
Confuses the calculations for HCF and LCM

Question:
Here is the completed Venn diagram from earlier in the quiz.
What calculation works out the lowest common multiple of \( 36 \) and \( 90 \) ? ![A Venn diagram showing the Prime factors of 36 set and the Prime factors of 90 set. There is a 2 in the prime factors of 36 set, there is 2, 3, 3 in the intersection and there is a 5 in the prime factors of 50 set.]()

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

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:
forgets to include the common factors when calculating the lowest common multiple

Question:
Here is the completed Venn diagram from earlier in the quiz.
What calculation works out the lowest common multiple of \( 36 \) and \( 90 \) ? ![A Venn diagram showing the Prime factors of 36 set and the Prime factors of 90 set. There is a 2 in the prime factors of 36 set, there is 2, 3, 3 in the intersection and there is a 5 in the prime factors of 50 set.]()

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

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


Prompt:
Misconception:
When finding the value of a number given in roman numerals, adds the value of all letters together without considering the position of the letter.

Question:
What number is this CCXLIX?

Options:
A. \( 271 \)
B. \( 269 \)
C. \( 249 \)
D. \( 259 \)

Solve the problem as a student with the misconception above.
You 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 value of a number given in roman numerals, adds the value of all letters together without considering the position of the letter.

Question:
What number is this CCXLIX?

Options:
A. \( 271 \)
B. \( 269 \)
C. \( 249 \)
D. \( 259 \)

Solve the problem as a student with the misconception above.
You 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:
Jo and Paul are discussing the table of values for \( \boldsymbol{y}=\boldsymbol{x}^{2} \) \begin{tabular}{|l|c|}
\hline\( x \) & \(\bigstar\) \\
\hline\( y \) & \( 4 \) \\
\hline
\end{tabular} Jo says the star could be \( 16 \).
Paul says the star could be \( -2 \).
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:
Does not understand the value of zeros as placeholders

Question:
Write \( 0.07 \) as a percentage.

Options:
A. \( 7 \% \)
B. \( \frac{7}{100} \)
C. \( 70 \% \)
D. \( 0.07 \% \)

Solve the problem as a student with the misconception above.
You 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:
Write \( 0.07 \) as a percentage.

Options:
A. \( 7 \% \)
B. \( \frac{7}{100} \)
C. \( 70 \% \)
D. \( 0.07 \% \)

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


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

Question:
This is a part of the table of values for the equation
\[
y=3 x
\] ![A table with two rows and two columns. The top left box has 'x', top right has a star, the bottom left box has 'y', bottom right has '-1'. ]() What should replace the star?

Options:
A. \( -3 \)
B. \( -0.3 \)
C. \( -\frac{1}{3} \)
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}.