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

Question:
What is \( 16 \) out of \( 25 \) as a percentage?

Options:
A. \( 16 \% \)
B. \( 32 \% \)
C. \( 64 \% \)
D. \( 80 \% \)

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


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

Question:
What is the mode of the following numbers?
\(
0.4, \quad \frac{1}{4}, \quad 2.5, \quad \frac{2}{5}
\)

Options:
A. \( \frac{1}{4} \)
B. \( \frac{2}{5} \)
C. \( 0.4 \) and \( 2.5 \)
D. There is no mode

Solve the problem as a student with the misconception above.
You 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 is always smaller than a, ignoring the possibility that a is negative

Question:
Jo and Paul are talking about statements that can be made about the equation on the right. \( 2 x=y \) Jo says this is always true: \( 2 x+1>y \)
Paul says this is always true: \( -2 x<y \)
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:
Multiplies by 10 instead of 100 when converting decimal to percentage

Question:
\( 0.01+57 \%= \)

Options:
A. \( 0.58 \% \)
B. \( 58 \% \)
C. \( 57.1 \% \)
D. \( 67 \% \)

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


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

Question:
\( 0.01+57 \%= \)

Options:
A. \( 0.58 \% \)
B. \( 58 \% \)
C. \( 57.1 \% \)
D. \( 67 \% \)

Solve the problem as a student with the misconception above.
You 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:
The formula for the area of a triangle, \( A \), is
\(A=\frac{1}{2}(b \times h)\)

Rearrange this to make the height, \( h \), the subject. ![An image of a triangle with the base labelled b and the perpendicular height h.]()

Options:
A. \( h=\frac{1}{2}(b \times A) \)
B. \( h=\frac{2 A}{b} \)
C. \( h=\frac{A}{2 b} \)
D. They are all incorrect

Solve the problem as a student with the misconception above.
You 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:
The formula for the area of a triangle, \( A \), is
\(A=\frac{1}{2}(b \times h)\)

Rearrange this to make the height, \( h \), the subject. ![An image of a triangle with the base labelled b and the perpendicular height h.]()

Options:
A. \( h=\frac{1}{2}(b \times A) \)
B. \( h=\frac{2 A}{b} \)
C. \( h=\frac{A}{2 b} \)
D. They are all incorrect

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


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

Question:
Isaac is trying to solve the equation on the right.
Here are his steps.

Which steps, if any, are correct? ![\[
27=9(1+k)
\]

Step \( 1 \quad 3=1+k \)

Step \( 2 \)
\[
2=k
\]]()

Options:
A. Only step \( 1 \)
B. Only step \( 2 \)
C. Both steps are correct
D. Both steps are incorrect

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


Prompt:
Misconception:
Thinks the fraction bar means subtract rather than divide

Question:
When \( h=15 \)

\(
\frac{h}{3}=
\)

Options:
A. \( 12 \)
B. \( 5 \)
C. \( -9 \)
D. \( -5 \)

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


Prompt:
Misconception:
Believes dividing two positives will give a negative answer

Question:
When \( h=15 \)

\(
\frac{h}{3}=
\)

Options:
A. \( 12 \)
B. \( 5 \)
C. \( -9 \)
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 that the coefficient of x represents the gradient even when a line is not in the form y = mx+c

Question:
Which of the following lines is not parallel to
\[
y=-2 x+7 \text { ? }
\]

Options:
A. \( 3 y=-6 x-8 \)
B. \( y=-(8-2 x) \)
C. \( y=2-2 x \)
D. \( y=2(1-x) \)

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


Prompt:
Misconception:
When given the equation of a straight line, believes the first term always gives the gradient, even when the first term is actually c

Question:
Which of the following lines is not parallel to
\[
y=-2 x+7 \text { ? }
\]

Options:
A. \( 3 y=-6 x-8 \)
B. \( y=-(8-2 x) \)
C. \( y=2-2 x \)
D. \( y=2(1-x) \)

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

Question:
Which of the following lines is not parallel to
\[
y=-2 x+7 \text { ? }
\]

Options:
A. \( 3 y=-6 x-8 \)
B. \( y=-(8-2 x) \)
C. \( y=2-2 x \)
D. \( y=2(1-x) \)

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:
Gives the vertex instead of the 3-letter angle notation

Question:
Which of the following is a correct way to describe the marked angle? ![Trapezium PQRS with angle QPS highlighted in red]()

Options:
A. \( P \)
B. \( Q P \)
C. \( Q P S \)
D. QPRS

Solve the problem as a student with the misconception above.
You 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 2 letters to describe an angle

Question:
Which of the following is a correct way to describe the marked angle? ![Trapezium PQRS with angle QPS highlighted in red]()

Options:
A. \( P \)
B. \( Q P \)
C. \( Q P S \)
D. QPRS

Solve the problem as a student with the misconception above.
You 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 more than 3 letters to describe an angle

Question:
Which of the following is a correct way to describe the marked angle? ![Trapezium PQRS with angle QPS highlighted in red]()

Options:
A. \( P \)
B. \( Q P \)
C. \( Q P S \)
D. QPRS

Solve the problem as a student with the misconception above.
You 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 equivalent fractions

Question:
Express the following as a single fraction, writing your answer as simply as possible:
\(
\frac{1}{s+1}-\frac{t}{2}
\)

Options:
A. \( \frac{1-t}{2(s+1)} \)
B. \( \frac{1-s t}{2(s+1)} \)
C. \( \frac{1-t}{s-1} \)
D. \( \frac{2-t(s+1)}{2(s+1)} \)

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

Question:
Express the following as a single fraction, writing your answer as simply as possible:
\(
\frac{1}{s+1}-\frac{t}{2}
\)

Options:
A. \( \frac{1-t}{2(s+1)} \)
B. \( \frac{1-s t}{2(s+1)} \)
C. \( \frac{1-t}{s-1} \)
D. \( \frac{2-t(s+1)}{2(s+1)} \)

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 subtracting fractions, subtracts the numerators and denominators

Question:
Express the following as a single fraction, writing your answer as simply as possible:
\(
\frac{1}{s+1}-\frac{t}{2}
\)

Options:
A. \( \frac{1-t}{2(s+1)} \)
B. \( \frac{1-s t}{2(s+1)} \)
C. \( \frac{1-t}{s-1} \)
D. \( \frac{2-t(s+1)}{2(s+1)} \)

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


Prompt:
Misconception:
Does not realise that the order is important in a ratio

Question:
Write the following ratio in its simplest form so both sides of the ratio are integers:
\(
\frac{1}{8}: \frac{1}{2}
\)

Options:
A. \( 1: 4 \)
B. \( 4: 1 \)
C. \( 2: 8 \)
D. \( 8: 2 \)

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 fully simplify ratio

Question:
Write the following ratio in its simplest form so both sides of the ratio are integers:
\(
\frac{1}{8}: \frac{1}{2}
\)

Options:
A. \( 1: 4 \)
B. \( 4: 1 \)
C. \( 2: 8 \)
D. \( 8: 2 \)

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


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

Question:
A number, \( n \), has been rounded to \( 2 \) decimal places to give \( \mathbf{3 . 7 2} \)
What is the smallest \( n \) can be?

Options:
A. \( 3.7 \)
B. \( 3.71 \)
C. \( 3.715 \)
D. \( 3.719 \)

Solve the problem as a student with the misconception above.
You 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 which place value is the one that determines if a number rounds up or down

Question:
A number, \( n \), has been rounded to \( 2 \) decimal places to give \( \mathbf{3 . 7 2} \)
What is the smallest \( n \) can be?

Options:
A. \( 3.7 \)
B. \( 3.71 \)
C. \( 3.715 \)
D. \( 3.719 \)

Solve the problem as a student with the misconception above.
You 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 which place value is the one that determines if a number rounds up or down

Question:
A number, \( n \), has been rounded to \( 2 \) decimal places to give \( \mathbf{3 . 7 2} \)
What is the smallest \( n \) can be?

Options:
A. \( 3.7 \)
B. \( 3.71 \)
C. \( 3.715 \)
D. \( 3.719 \)

Solve the problem as a student with the misconception above.
You 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 term in a sequence and position of a term

Question:
![The first three terms of a sequence represented using boxes. The first term is made of 3 boxes arranged with 2 on the base and one box above the furthers left box. The second term is the same pattern as the first but with two additional boxes added to the left hand side of the shape, one on top of the other. The third pattern is the second pattern with an additional two boxes added to the left hand side of the shape, one above the other again.]() \begin{tabular}{|l|c|c|c|}
\hline Position & \( 1 \) & \( 2 \) & \( 3 \) \\
\hline Term & \(  \) & \( \bigstar \) & \(  \) \\
\hline
\end{tabular} What value should replace the star?

Options:
A. \( 2 \)
B. \( 4 \)
C. \( 5 \)
D. \( 7 \)

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


Prompt:
Misconception:
Thinks the term in a sequence is double the position value

Question:
![The first three terms of a sequence represented using boxes. The first term is made of 3 boxes arranged with 2 on the base and one box above the furthers left box. The second term is the same pattern as the first but with two additional boxes added to the left hand side of the shape, one on top of the other. The third pattern is the second pattern with an additional two boxes added to the left hand side of the shape, one above the other again.]() \begin{tabular}{|l|c|c|c|}
\hline Position & \( 1 \) & \( 2 \) & \( 3 \) \\
\hline Term & \(  \) & \( \bigstar \) & \(  \) \\
\hline
\end{tabular} What value should replace the star?

Options:
A. \( 2 \)
B. \( 4 \)
C. \( 5 \)
D. \( 7 \)

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


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

Question:
![The first three terms of a sequence represented using boxes. The first term is made of 3 boxes arranged with 2 on the base and one box above the furthers left box. The second term is the same pattern as the first but with two additional boxes added to the left hand side of the shape, one on top of the other. The third pattern is the second pattern with an additional two boxes added to the left hand side of the shape, one above the other again.]() \begin{tabular}{|l|c|c|c|}
\hline Position & \( 1 \) & \( 2 \) & \( 3 \) \\
\hline Term & \(  \) & \( \bigstar \) & \(  \) \\
\hline
\end{tabular} What value should replace the star?

Options:
A. \( 2 \)
B. \( 4 \)
C. \( 5 \)
D. \( 7 \)

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


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

Question:
What is \( 5.5 \% \) of \( 400 \) ?

Options:
A. \( 22 \)
B. \( 11 \)
C. \( 5.5 \)
D. \( 220 \)

Solve the problem as a student with the misconception above.
You 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 dividing by 10 gives 1%

Question:
What is \( 5.5 \% \) of \( 400 \) ?

Options:
A. \( 22 \)
B. \( 11 \)
C. \( 5.5 \)
D. \( 220 \)

Solve the problem as a student with the misconception above.
You 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 left and right

Question:
If you translate the star \( 3 \) squares left and \( 2 \) squares down, which letter do you land on? ![Positive coordinate grid from 0 to 8 in the x and y directions with a gold star at (4,4), A at (7,2), B at (2,1), C at (2,2) and D at (1,2)]()

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:
When describing a translation, counts the corners of squares (including the starting one) rather than the number of jumps between squares.

Question:
If you translate the star \( 3 \) squares left and \( 2 \) squares down, which letter do you land on? ![Positive coordinate grid from 0 to 8 in the x and y directions with a gold star at (4,4), A at (7,2), B at (2,1), C at (2,2) and D at (1,2)]()

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

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


Prompt:
Misconception:
Does not know that angles on a straight line sum to 180 degrees

Question:
Which of the following cannot represent a straight line?

Options:
A. ![A straight line, separated into an angle of 53 degrees and an angle of 127 degrees]()
B. ![A straight line, separated into an angle of 150 degrees and an angle of 50 degrees]()
C. ![A straight line, separated into three angles. One is unmarked, one is 90 degrees and one is 45 degrees]()
D. ![A straight line, separated into two angles of 90 degrees]()

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


Prompt:
Misconception:
Misinterprets the meaning of angles on a straight line angle fact

Question:
Which of the following cannot represent a straight line?

Options:
A. ![A straight line, separated into an angle of 53 degrees and an angle of 127 degrees]()
B. ![A straight line, separated into an angle of 150 degrees and an angle of 50 degrees]()
C. ![A straight line, separated into three angles. One is unmarked, one is 90 degrees and one is 45 degrees]()
D. ![A straight line, separated into two angles of 90 degrees]()

Solve the problem as a student with the misconception above.
You 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 angles on a straight line sum to 180 degrees

Question:
Which of the following cannot represent a straight line?

Options:
A. ![A straight line, separated into an angle of 53 degrees and an angle of 127 degrees]()
B. ![A straight line, separated into an angle of 150 degrees and an angle of 50 degrees]()
C. ![A straight line, separated into three angles. One is unmarked, one is 90 degrees and one is 45 degrees]()
D. ![A straight line, separated into two angles of 90 degrees]()

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


Prompt:
Misconception:
Doubles side length for similar shape instead of using correct scale factor

Question:
These two shapes are similar (not drawn to scale).
What should replace the star? ![Two scalene triangles. The smaller one has sides 5cm and 4cm. On the bigger triangle, the side corresponding to the 5cm is 15cm, and the side corresponding to the 4cm is marked with a star.]()

Options:
A. \( 8 \mathrm{~cm} \)
B. \( 12 \mathrm{~cm} \)
C. \( 14 \mathrm{~cm} \)
D. Not enough information

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


Prompt:
Misconception:
Thinks adding the same value to each side makes shapes similar

Question:
These two shapes are similar (not drawn to scale).
What should replace the star? ![Two scalene triangles. The smaller one has sides 5cm and 4cm. On the bigger triangle, the side corresponding to the 5cm is 15cm, and the side corresponding to the 4cm is marked with a star.]()

Options:
A. \( 8 \mathrm{~cm} \)
B. \( 12 \mathrm{~cm} \)
C. \( 14 \mathrm{~cm} \)
D. Not enough information

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


Prompt:
Misconception:
Does not understand how to find a scale factor

Question:
These two shapes are similar (not drawn to scale).
What should replace the star? ![Two scalene triangles. The smaller one has sides 5cm and 4cm. On the bigger triangle, the side corresponding to the 5cm is 15cm, and the side corresponding to the 4cm is marked with a star.]()

Options:
A. \( 8 \mathrm{~cm} \)
B. \( 12 \mathrm{~cm} \)
C. \( 14 \mathrm{~cm} \)
D. Not enough information

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


Prompt:
Misconception:
Adds when calculating volume instead of multiplying

Question:
What is the volume of this cuboid? ![A cuboid with dimensions labelled 10cm, 4cm and 5cm]()

Options:
A. \( 19 \mathrm{~cm}^{3} \)
B. \( 50 \mathrm{~cm}^{3} \)
C. \( 200 \mathrm{~cm}^{3} \)
D. \( 220 \mathrm{~cm}^{3} \)

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


Prompt:
Misconception:
Finds area of one face when asked for volume

Question:
What is the volume of this cuboid? ![A cuboid with dimensions labelled 10cm, 4cm and 5cm]()

Options:
A. \( 19 \mathrm{~cm}^{3} \)
B. \( 50 \mathrm{~cm}^{3} \)
C. \( 200 \mathrm{~cm}^{3} \)
D. \( 220 \mathrm{~cm}^{3} \)

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


Prompt:
Misconception:
Finds surface area when asked for volume

Question:
What is the volume of this cuboid? ![A cuboid with dimensions labelled 10cm, 4cm and 5cm]()

Options:
A. \( 19 \mathrm{~cm}^{3} \)
B. \( 50 \mathrm{~cm}^{3} \)
C. \( 200 \mathrm{~cm}^{3} \)
D. \( 220 \mathrm{~cm}^{3} \)

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


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

Question:
![Arrow pointing to the left showing -18  and 3 arrows pointing to the left showing -18 in 3 equal parts]() Tom and Katie are trying to write different calculations for the diagram shown.
Tom writes: \( 3 \times(-6)=-18 \)
Katie writes: \( \frac{(-18)}{3}=-6 \)
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 multiplying a positive by a negative gives a positive answer

Question:
![Arrow pointing to the left showing -18  and 3 arrows pointing to the left showing -18 in 3 equal parts]() Tom and Katie are trying to write different calculations for the diagram shown.
Tom writes: \( 3 \times(-6)=-18 \)
Katie writes: \( \frac{(-18)}{3}=-6 \)
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 that when eliminating a variable, if the signs of the terms with matching coefficients are the same, we add the equations.

Question:
Eliza is trying to solve the pair of simultaneous equations below.

\( \begin{aligned} -6 g-2 h & = & -2 \\ g-2h & = & 10 \\ \end{aligned} \)

She decides to add them together.
What will she end up with?

Options:
A. \( -5 g-4 h=12 \)
B. \( 5 g=8 \)
C. \( -7 g=8 \)
D. \( -5 g-4 h=8 \)

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:
Misreads scale

Question:
This graph shows the temperature in Dan's garden in a \( 24 \) hour period.
What was the temperature at 12:00? ![Time series graph titled Temperature. Vertical axis is labelled Degrees Centigrade, and horizontal axis is Time. Points plotted are (00:00, -2), (04:00, -4), (08:00, 0), (12:00, 5), (16:00, 8) and (00:00, 0)]()

Options:
A. \( 4^{\circ} \mathrm{C} \)
B. \( 4.5^{\circ} \mathrm{C} \)
C. \( 5^{\circ} \mathrm{C} \)
D. \( 2.5^{\circ} \mathrm{C} \)

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


Prompt:
Misconception:
Misreads scale

Question:
This graph shows the temperature in Dan's garden in a \( 24 \) hour period.
What was the temperature at 12:00? ![Time series graph titled Temperature. Vertical axis is labelled Degrees Centigrade, and horizontal axis is Time. Points plotted are (00:00, -2), (04:00, -4), (08:00, 0), (12:00, 5), (16:00, 8) and (00:00, 0)]()

Options:
A. \( 4^{\circ} \mathrm{C} \)
B. \( 4.5^{\circ} \mathrm{C} \)
C. \( 5^{\circ} \mathrm{C} \)
D. \( 2.5^{\circ} \mathrm{C} \)

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


Prompt:
Misconception:
Misreads scale

Question:
This graph shows the temperature in Dan's garden in a \( 24 \) hour period.
What was the temperature at 12:00? ![Time series graph titled Temperature. Vertical axis is labelled Degrees Centigrade, and horizontal axis is Time. Points plotted are (00:00, -2), (04:00, -4), (08:00, 0), (12:00, 5), (16:00, 8) and (00:00, 0)]()

Options:
A. \( 4^{\circ} \mathrm{C} \)
B. \( 4.5^{\circ} \mathrm{C} \)
C. \( 5^{\circ} \mathrm{C} \)
D. \( 2.5^{\circ} \mathrm{C} \)

Solve the problem as a student with the misconception above.
You 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:
John's flat is on floor \( 4 \).

The gym is on floor \( -1 \).

How many floors does John need to go down to get from his flat to the gym? ![A vertical number line from -8 to 7 increasing in 1 digit increments]()

Options:
A. \( 5 \)
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:
Does not count end number when counting

Question:
John's flat is on floor \( 4 \).

The gym is on floor \( -1 \).

How many floors does John need to go down to get from his flat to the gym? ![A vertical number line from -8 to 7 increasing in 1 digit increments]()

Options:
A. \( 5 \)
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:
Answers order of operations questions with brackets as if the brackets are not there

Question:
When \( h=10 \)
Which of the following pairs of statements is true?

Options:
A. \( 3 h^{2}=300 \)
\( (3 h)^{2}=300 \)
B. \( \begin{array}{l}3 h^{2}=300 \\ (3 h)^{2}=900\end{array} \)
C. \( \begin{array}{l}3 h^{2}=900 \\ (3 h)^{2}=900\end{array} \)
D. \( \begin{array}{l}3 h^{2}=900 \\ (3 h)^{2}=300\end{array} \)

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:
Multiplies before applying a power

Question:
When \( h=10 \)
Which of the following pairs of statements is true?

Options:
A. \( 3 h^{2}=300 \)
\( (3 h)^{2}=300 \)
B. \( \begin{array}{l}3 h^{2}=300 \\ (3 h)^{2}=900\end{array} \)
C. \( \begin{array}{l}3 h^{2}=900 \\ (3 h)^{2}=900\end{array} \)
D. \( \begin{array}{l}3 h^{2}=900 \\ (3 h)^{2}=300\end{array} \)

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:
Rounds down instead of up

Question:
\( 58.2684 \) to \( 1 \) decimal place is....

Options:
A. \( 58.3 \)
B. \( 58.2 \)
C. \( 59.3 \)
D. \( 59.2 \)

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 incorrectly by changing multiple place values

Question:
\( 58.2684 \) to \( 1 \) decimal place is....

Options:
A. \( 58.3 \)
B. \( 58.2 \)
C. \( 59.3 \)
D. \( 59.2 \)

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 incorrectly by changing multiple place values

Question:
\( 58.2684 \) to \( 1 \) decimal place is....

Options:
A. \( 58.3 \)
B. \( 58.2 \)
C. \( 59.3 \)
D. \( 59.2 \)

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 recognise that the intersection of a Venn diagram represents those belonging to both sets

Question:
\( \begin{array}{c}\xi=\{\text { integers between } 1 \\ \text { and } 10 \text { inclusive }\} \\ P=\{\text { odd numbers }\} \\ Q=\{\text { factors of } 30\}\end{array} \) ![A Venn diagram with two circles labelled P and Q. P without the intersection is labelled A, Q without the intersection is labelled C, the intersection of the two sets is labelled B, and outside the circles is labelled D.]() In which region does \( \mathbf{5} \) belong?

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

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


Prompt:
Misconception:
Does not recognise that the intersection of a Venn diagram represents those belonging to both sets

Question:
\( \begin{array}{c}\xi=\{\text { integers between } 1 \\ \text { and } 10 \text { inclusive }\} \\ P=\{\text { odd numbers }\} \\ Q=\{\text { factors of } 30\}\end{array} \) ![A Venn diagram with two circles labelled P and Q. P without the intersection is labelled A, Q without the intersection is labelled C, the intersection of the two sets is labelled B, and outside the circles is labelled D.]() In which region does \( \mathbf{5} \) belong?

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:
Simplifies a fraction by adding or subtracting the same amount from the numerator  and denominator

Question:
Simplify fully (if possible):
\(
\frac{13}{78}
\) Simplify fully (if possible): \( \frac{13}{78} \)

Options:
A. \( \frac{1}{7} \) \( \frac{1}{7} \)
B. \( \frac{1}{6} \) \( \frac{1}{6} \)
C. \( \frac{1}{66} \) \( \frac{1}{66} \)
D. Cannot be simplified 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:
Assumes fractions with prime numerators cannot be simplified

Question:
Simplify fully (if possible):
\(
\frac{13}{78}
\) Simplify fully (if possible): \( \frac{13}{78} \)

Options:
A. \( \frac{1}{7} \) \( \frac{1}{7} \)
B. \( \frac{1}{6} \) \( \frac{1}{6} \)
C. \( \frac{1}{66} \) \( \frac{1}{66} \)
D. Cannot be simplified 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:
Believes an upward line has a negative gradient

Question:
Which diagram shows the graphical solution to: \( \begin{array}{c}3 x+2 y=12 \\ y=3-x\end{array} \)

Options:
A. ![A four quadrant plane. Y axis -15 to 30 and x axis -15 to 25. A blue line goes from bottom left to top right sloping upwards. It goes through (-10, -7) and (10, 12). A red line goes from bottom left to top right sloping upwards. It goes through (0, -6) and (10, 9) ]()
B. ![A four quadrant plane. Y axis --3 to 6 and x axis -4 to 7. A blue line goes from bottom left to top right sloping upwards. It goes through (-3, 0) and (0, 3). A red line goes from top left to bottom right sloping downwards. It goes through (0, 6) and (4, 0) ]()
C. ![A four quadrant plane. Y axis --2 to 7 and x axis -4 to 7. A blue line goes from top left to bottom right sloping downwards. It goes through (0, 6) and (6, 0). A red line goes from top left to bottom right sloping downwards. It goes through (0, 6) and (4, 0) ]()
D. ![A four quadrant plane. Y axis --3 to 3 and x axis -2 to 8. A blue line goes from top left to bottom right sloping downwards. It goes through (0, 3) and (3, 0). A red line goes from top left to bottom right sloping downwards. It goes through (2, 3) and (4, 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 an upward line has a negative gradient

Question:
Which diagram shows the graphical solution to: \( \begin{array}{c}3 x+2 y=12 \\ y=3-x\end{array} \)

Options:
A. ![A four quadrant plane. Y axis -15 to 30 and x axis -15 to 25. A blue line goes from bottom left to top right sloping upwards. It goes through (-10, -7) and (10, 12). A red line goes from bottom left to top right sloping upwards. It goes through (0, -6) and (10, 9) ]()
B. ![A four quadrant plane. Y axis --3 to 6 and x axis -4 to 7. A blue line goes from bottom left to top right sloping upwards. It goes through (-3, 0) and (0, 3). A red line goes from top left to bottom right sloping downwards. It goes through (0, 6) and (4, 0) ]()
C. ![A four quadrant plane. Y axis --2 to 7 and x axis -4 to 7. A blue line goes from top left to bottom right sloping downwards. It goes through (0, 6) and (6, 0). A red line goes from top left to bottom right sloping downwards. It goes through (0, 6) and (4, 0) ]()
D. ![A four quadrant plane. Y axis --3 to 3 and x axis -2 to 8. A blue line goes from top left to bottom right sloping downwards. It goes through (0, 3) and (3, 0). A red line goes from top left to bottom right sloping downwards. It goes through (2, 3) and (4, 0) ]()

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


Prompt:
Misconception:
Does not recognise that a linear sequence must increase or decrease by same amount

Question:
Tom and Katie are discussing sequences
Tom says \( (\boldsymbol{n}+\mathbf{1})^{3} \) would produce a linear sequence.
Katie says \( 3-\frac{n}{3} \) would produce a linear sequence
Who is correct?

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

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


Prompt:
Misconception:
Does not recognise that a linear sequence must increase or decrease by same amount

Question:
Tom and Katie are discussing sequences
Tom says \( (\boldsymbol{n}+\mathbf{1})^{3} \) would produce a linear sequence.
Katie says \( 3-\frac{n}{3} \) would produce a linear sequence
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 linear sequences cannot include fractions

Question:
Tom and Katie are discussing sequences
Tom says \( (\boldsymbol{n}+\mathbf{1})^{3} \) would produce a linear sequence.
Katie says \( 3-\frac{n}{3} \) would produce a linear sequence
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:
Mixes up sides of a ratio

Question:
To make green paint, you mix blue paint with yellow paint in the ratio \( 5: 3 \).
What should replace the star? \begin{tabular}{|c|c|c|}
\hline Blue & Yellow & Total \\
\hline \( \mathrm{1500 ml} \) & \( \bigstar \)
\hline
\end{tabular}

Options:
A. \( 2500 \mathrm{ml} \)
B. \( 1502 \mathrm{ml} \)
C. \( 900 \mathrm{ml} \)
D. \( 4500 \mathrm{ml} \)

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


Prompt:
Misconception:
Thinks a difference of one part in a ratio means the quantities will differ by one unit

Question:
To make green paint, you mix blue paint with yellow paint in the ratio \( 5: 3 \).
What should replace the star? \begin{tabular}{|c|c|c|}
\hline Blue & Yellow & Total \\
\hline \( \mathrm{1500 ml} \) & \( \bigstar \)
\hline
\end{tabular}

Options:
A. \( 2500 \mathrm{ml} \)
B. \( 1502 \mathrm{ml} \)
C. \( 900 \mathrm{ml} \)
D. \( 4500 \mathrm{ml} \)

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


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

Question:
To make green paint, you mix blue paint with yellow paint in the ratio \( 5: 3 \).
What should replace the star? \begin{tabular}{|c|c|c|}
\hline Blue & Yellow & Total \\
\hline \( \mathrm{1500 ml} \) & \( \bigstar \)
\hline
\end{tabular}

Options:
A. \( 2500 \mathrm{ml} \)
B. \( 1502 \mathrm{ml} \)
C. \( 900 \mathrm{ml} \)
D. \( 4500 \mathrm{ml} \)

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


Prompt:
Misconception:
Believes to find the angle for a pie chart sector you calculate 360 divided by the frequency of that sector

Question:
Which calculation is correct to find the number of degrees representing comedy in a pie chart showing the following information? \begin{tabular}{|c|c|c|c|}
\hline Film Genre & Comedy & Romance & Action \\
\hline Number of teachers & \( 9 \) & \( 4 \) & \( 7 \) \\
\hline
\end{tabular}

Options:
A. \( 360 \div 9 \)
B. \( 360 \div 13 \times 9 \)
C. \( 360 \div 9+4+7 \times 4 \)
D. \( \frac{9}{9+7+4} \times 360 \)

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 that when finding area under graph you can use the upper y value rather than average of upper and lower

Question:
![A speed-time graph. At 6 seconds, the car is travelling at a speed of 8 metres per second. After 8 seconds, the car is travelling at a speed of 15 metres per second. ]() Here is a speed-time graph for a car.

Which of the following gives the best estimate for the distance travelled between \( 6 \) and \( 8 \) seconds?

Options:
A. \( 30 m \)
B. \( 11 \mathrm{~m} \)
C. \( 24 m \)
D. \( 66 m \)

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

Question:
\( 0.32+0.8= \)

Options:
A. \( 1.2 \)
B. \( 0.4 \)
C. \( 1.12 \)
D. \( 0.328 \)

Solve the problem as a student with the misconception above.
You 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 with a different number of decimal places, lines up the digits incorrectly

Question:
\( 0.32+0.8= \)

Options:
A. \( 1.2 \)
B. \( 0.4 \)
C. \( 1.12 \)
D. \( 0.328 \)

Solve the problem as a student with the misconception above.
You 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 angles which look the same on diagram will be equal

Question:
What is the size of angle \( q \) ? ![A long straight line with two shorter lines joining it, but not crossing it. Where the line on the left joins it forms two angles, q on the left, 126 degrees on the right. Where the line on the right joins it forms two angles, the left is unmarked, 37 degrees on the right.]()

Options:
A. \( 37^{\circ} \)
B. \( 54^{\circ} \)
C. \( 17^{\circ} \)
D. \( 64^{\circ} \)

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


Prompt:
Misconception:
Misinterprets the meaning of angles on a straight line angle fact

Question:
What is the size of angle \( q \) ? ![A long straight line with two shorter lines joining it, but not crossing it. Where the line on the left joins it forms two angles, q on the left, 126 degrees on the right. Where the line on the right joins it forms two angles, the left is unmarked, 37 degrees on the right.]()

Options:
A. \( 37^{\circ} \)
B. \( 54^{\circ} \)
C. \( 17^{\circ} \)
D. \( 64^{\circ} \)

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


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

Question:
What is the size of angle \( q \) ? ![A long straight line with two shorter lines joining it, but not crossing it. Where the line on the left joins it forms two angles, q on the left, 126 degrees on the right. Where the line on the right joins it forms two angles, the left is unmarked, 37 degrees on the right.]()

Options:
A. \( 37^{\circ} \)
B. \( 54^{\circ} \)
C. \( 17^{\circ} \)
D. \( 64^{\circ} \)

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


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

Question:
A \( 4 \) digit number belongs in this box to make the calculation true
\(
\square-6027=1253
\)
What is the \( 4^{\text {th }} \) digit of the number that belongs in the box?

Options:
A. \( 0 \)
B. \( 4 \)
C. \( 5 \)
D. Not possible

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


Prompt:
Misconception:
Does not understand the effect of consecutive operations

Question:
Nick wants to add \( 97 \) to a number.
Which one of the following methods would give him the correct answer?

Options:
A. \( +100 \) then \( +3 \)
B. \( +100 \) then \( -3 \)
C. \( -100 \) then \( +3 \)
D. \( -100 \) then \( -3 \)

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:
Subtracts instead of adds when answering worded problems

Question:
Nick wants to add \( 97 \) to a number.
Which one of the following methods would give him the correct answer?

Options:
A. \( +100 \) then \( +3 \)
B. \( +100 \) then \( -3 \)
C. \( -100 \) then \( +3 \)
D. \( -100 \) then \( -3 \)

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


Prompt:
Misconception:
Does not understand that a probability of 1 represents something that is certain

Question:
The probability of an event occurring is \( 0.9 \).

Which of the following most accurately describes the likelihood of the event occurring?

Options:
A. Certain
B. Likely
C. Unlikely
D. Impossible

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


Prompt:
Misconception:
Does not understand that a probability of 1 represents something that is certain

Question:
The probability of an event occurring is \( 0.9 \).

Which of the following most accurately describes the likelihood of the event occurring?

Options:
A. Certain
B. Likely
C. Unlikely
D. Impossible

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


Prompt:
Misconception:
Does not understand that a probability of 0 represents something that is impossible

Question:
The probability of an event occurring is \( 0.9 \).

Which of the following most accurately describes the likelihood of the event occurring?

Options:
A. Certain
B. Likely
C. Unlikely
D. Impossible

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


Prompt:
Misconception:
Has used slant height and base to find area of a triangle rather than perpendicular height and base

Question:
What is the area of this triangle? ![A right angled triangle with base length 12 cm, slant length 15cm and perpendicular height 9cm.]()

Options:
A. \( 54 \mathrm{~cm}^{2} \)
B. \( 67.5 \mathrm{~cm}^{2} \)
C. \( 810 \mathrm{~cm}^{2} \)
D. \( 108 \mathrm{~cm}^{2} \)

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


Prompt:
Misconception:
Multiplies all given dimensions when calculating an area

Question:
What is the area of this triangle? ![A right angled triangle with base length 12 cm, slant length 15cm and perpendicular height 9cm.]()

Options:
A. \( 54 \mathrm{~cm}^{2} \)
B. \( 67.5 \mathrm{~cm}^{2} \)
C. \( 810 \mathrm{~cm}^{2} \)
D. \( 108 \mathrm{~cm}^{2} \)

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


Prompt:
Misconception:
Does not divide by 2 when calculating the area of a triangle

Question:
What is the area of this triangle? ![A right angled triangle with base length 12 cm, slant length 15cm and perpendicular height 9cm.]()

Options:
A. \( 54 \mathrm{~cm}^{2} \)
B. \( 67.5 \mathrm{~cm}^{2} \)
C. \( 810 \mathrm{~cm}^{2} \)
D. \( 108 \mathrm{~cm}^{2} \)

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:
In a worded problem, does not complete all calculations

Question:
Sunita wants to buy a soup and a coffee.
How much change should she get from f20? \begin{tabular}{|c|}
\hline Joe's Café \\
Sandwich \( £ 3.25 \) \\
Pasty \( £ 2.99 \) \\
Cake \( £ 2.25 \) \\
Soup \( £ 3.19 \) \\
Tea \( £ 1.55 \) \\
Coffee \( £ 1.95 \) \\
Orange \( 89 p \) \\
\hline
\end{tabular}

Options:
A. \( £ 5.14 \)
B. \( £ 15.86 \)
C. \( £ 14.86 \)
D. \( £ 14.96 \)

Solve the problem as a student with the misconception above.
You 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 discussing the sequence \( \mathbf{7 n}+\mathbf{5} \)

Jo says \( \mathbf{1 4 9} \) is a term in the sequence.

Paul says \( \mathbf{1 5 0} \) is a term in the sequence.

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:
Is not able to spot a proportional relationship pictorially unless they are laid out in groups

Question:
Tom says for every one circle there are two squares
\(\bigcirc\bigcirc\bigcirc\)
\(\square\;\square\;\square\;\square\;\square\;\square\) Katie says for every one circle there are two squares
\(\square\quad\square\quad\square\quad\square\quad\square\)
\(\bigcirc\bigcirc\bigcirc\bigcirc\bigcirc\)
\(\square\quad\square\quad\square\quad\square\quad\square\) Who is correct?

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

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


Prompt:
Misconception:
Does not believe you can scale up a proportional statement

Question:
Tom says for every one circle there are two squares
\(\bigcirc\bigcirc\bigcirc\)
\(\square\;\square\;\square\;\square\;\square\;\square\) Katie says for every one circle there are two squares
\(\square\quad\square\quad\square\quad\square\quad\square\)
\(\bigcirc\bigcirc\bigcirc\bigcirc\bigcirc\)
\(\square\quad\square\quad\square\quad\square\quad\square\) 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 multiplying numbers with different bases, multiplies the powers and multiplies the base numbers.

Question:
Jo and Paul are discussing \( 3^{2} \times 4^{2} \)
Jo says \( 3^{2} \times 4^{2}=12^{4} \)
Paul says \( 3^{2} \times 4^{2}=12^{2} \)
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 realise that multiplication can be broken down into factors

Question:
Jo and Paul are discussing \( 3^{2} \times 4^{2} \)
Jo says \( 3^{2} \times 4^{2}=12^{4} \)
Paul says \( 3^{2} \times 4^{2}=12^{2} \)
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:
Identifies the term-to-term rule rather than the next term in a sequence

Question:
What is the next term in this sequence?

\[
32, \quad 28, \quad 24, \quad \ldots
\]

Options:
A. \( 4 \)
B. \( 18 \)
C. \( 20 \)
D. Not enough information

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


Prompt:
Misconception:
Does not know that a solid is a 3D shape

Question:
This is the uniform cross-section of solid \( Q \).

Which of the following could shape \( Q \) be? ![A rectangle.]()

Options:
A. Rectangle
B. Cube
C. Cuboid
D. Cylinder

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


Prompt:
Misconception:
Mixes up cubes and cuboids

Question:
This is the uniform cross-section of solid \( Q \).

Which of the following could shape \( Q \) be? ![A rectangle.]()

Options:
A. Rectangle
B. Cube
C. Cuboid
D. Cylinder

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


Prompt:
Misconception:
Does not know the meaning of uniform cross section

Question:
This is the uniform cross-section of solid \( Q \).

Which of the following could shape \( Q \) be? ![A rectangle.]()

Options:
A. Rectangle
B. Cube
C. Cuboid
D. Cylinder

Solve the problem as a student with the misconception above.
You 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 outlier is a value that does not fit the same characteristics as the other values

Question:
\( \begin{array}{llllll}\frac{8}{10} & \frac{41}{50} & \frac{7}{20} & 0.77 & \frac{4}{5} & \frac{79}{100}\end{array} \) Which value is the outlier in this set of data?

Options:
A. \( \frac{41}{50} \)
B. \( \frac{7}{20} \)
C. \( 0.77 \)
D. \( \frac{79}{100} \)

Solve the problem as a student with the misconception above.
You 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 outlier is a value that does not fit the same characteristics as the other values

Question:
\( \begin{array}{llllll}\frac{8}{10} & \frac{41}{50} & \frac{7}{20} & 0.77 & \frac{4}{5} & \frac{79}{100}\end{array} \) Which value is the outlier in this set of data?

Options:
A. \( \frac{41}{50} \)
B. \( \frac{7}{20} \)
C. \( 0.77 \)
D. \( \frac{79}{100} \)

Solve the problem as a student with the misconception above.
You 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 outlier is the value in a data set with the biggest denominator, even if this value is close to the mean

Question:
\( \begin{array}{llllll}\frac{8}{10} & \frac{41}{50} & \frac{7}{20} & 0.77 & \frac{4}{5} & \frac{79}{100}\end{array} \) Which value is the outlier in this set of data?

Options:
A. \( \frac{41}{50} \)
B. \( \frac{7}{20} \)
C. \( 0.77 \)
D. \( \frac{79}{100} \)

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


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

Question:
Which of the following would correctly calculate the number of seconds in \( 2 \) days?

Options:
A. \( 2 \times 12 \times 60 \)
B. \( 2 \times 12 \times 60 \times 60 \)
C. \( 2 \times 24 \times 60 \)
D. \( 2 \times 24 \times 60 \times 60 \)

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


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

Question:
Which of the following would correctly calculate the number of seconds in \( 2 \) days?

Options:
A. \( 2 \times 12 \times 60 \)
B. \( 2 \times 12 \times 60 \times 60 \)
C. \( 2 \times 24 \times 60 \)
D. \( 2 \times 24 \times 60 \times 60 \)

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


Prompt:
Misconception:
Thinks a positive y value in a column vector means to move down rather than up

Question:
Which of the following vectors describes how to get from point \( P \) to point \( Q \)? ![The image shows a square grid and 2 points, P and Q. Point P is 4 squares left and 2 squares up from point Q. ]()

Options:
A. \( \left(\begin{array}{l}2 \\ 4\end{array}\right) \)
B. \( \left(\begin{array}{l}4 \\ 2\end{array}\right) \)
C. \( \left(\begin{array}{c}4 \\ -2\end{array}\right) \)
D. \( \left(\begin{array}{c}-2 \\ 4\end{array}\right) \)

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


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

Question:
Which of the following vectors describes how to get from point \( P \) to point \( Q \)? ![The image shows a square grid and 2 points, P and Q. Point P is 4 squares left and 2 squares up from point Q. ]()

Options:
A. \( \left(\begin{array}{l}2 \\ 4\end{array}\right) \)
B. \( \left(\begin{array}{l}4 \\ 2\end{array}\right) \)
C. \( \left(\begin{array}{c}4 \\ -2\end{array}\right) \)
D. \( \left(\begin{array}{c}-2 \\ 4\end{array}\right) \)

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


Prompt:
Misconception:
When adding an integer to a fraction, thinks you add the integer to the numerator

Question:
Solve the equation:
\(
p-3=\frac{1}{12}
\)

Options:
A. \( p=\frac{4}{15} \)
B. \( p=\frac{4}{12} \)
C. \( p=\frac{3}{36} \)
D. \( p=\frac{37}{12} \)

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


Prompt:
Misconception:
When solving an equation, multiplies instead of adding

Question:
Solve the equation:
\(
p-3=\frac{1}{12}
\)

Options:
A. \( p=\frac{4}{15} \)
B. \( p=\frac{4}{12} \)
C. \( p=\frac{3}{36} \)
D. \( p=\frac{37}{12} \)

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 divide by 2 when calculating the area of a triangle

Question:
To work out the area of a triangle you multiply the base by the perpendicular height and then halve your answer.
What is the area of this triangle? ![Triangle with base b=5cm and perpendicular height h=3cm]()

Options:
A. \( 15 \mathrm{~cm}^{2} \)
B. \( 4 \mathrm{~cm}^{2} \)
C. \( 30 \mathrm{~cm}^{2} \)
D. \( 7.5 \mathrm{~cm}^{2} \)

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:
Adds instead of multiples

Question:
To work out the area of a triangle you multiply the base by the perpendicular height and then halve your answer.
What is the area of this triangle? ![Triangle with base b=5cm and perpendicular height h=3cm]()

Options:
A. \( 15 \mathrm{~cm}^{2} \)
B. \( 4 \mathrm{~cm}^{2} \)
C. \( 30 \mathrm{~cm}^{2} \)
D. \( 7.5 \mathrm{~cm}^{2} \)

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


Prompt:
Misconception:
Thinks halving is the same as multiplying by 2

Question:
To work out the area of a triangle you multiply the base by the perpendicular height and then halve your answer.
What is the area of this triangle? ![Triangle with base b=5cm and perpendicular height h=3cm]()

Options:
A. \( 15 \mathrm{~cm}^{2} \)
B. \( 4 \mathrm{~cm}^{2} \)
C. \( 30 \mathrm{~cm}^{2} \)
D. \( 7.5 \mathrm{~cm}^{2} \)

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


Prompt:
Misconception:
Believes you can have decimals in a simplified fraction

Question:
Simplify fully (if possible):

\( \frac{18}{30} \)

Options:
A. \( \frac{4.5}{7.5} \)
B. \( \frac{9}{15} \)
C. \( \frac{3}{5} \)
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):

\( \frac{18}{30} \)

Options:
A. \( \frac{4.5}{7.5} \)
B. \( \frac{9}{15} \)
C. \( \frac{3}{5} \)
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 understand how to simplify fractions

Question:
Simplify fully (if possible):

\( \frac{18}{30} \)

Options:
A. \( \frac{4.5}{7.5} \)
B. \( \frac{9}{15} \)
C. \( \frac{3}{5} \)
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:
Mixes up squaring and multiplying by 2 or doubling

Question:
What is the value of \( 4^{2} \) ?

Options:
A. \( 16 \)
B. \( 8 \)
C. \( 6 \)
D. \( 4 \)

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


Prompt:
Misconception:
Adds the index to the number

Question:
What is the value of \( 4^{2} \) ?

Options:
A. \( 16 \)
B. \( 8 \)
C. \( 6 \)
D. \( 4 \)

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


Prompt:
Misconception:
Believes a power of 2 has no impact on its value

Question:
What is the value of \( 4^{2} \) ?

Options:
A. \( 16 \)
B. \( 8 \)
C. \( 6 \)
D. \( 4 \)

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


Prompt:
Misconception:
Does not understand the difference between a value on a graph and the gradient of a graph

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

Which of the following is the best estimate for the gradient of the curve when \( t=6 \) ![The image is of a velocity-time graph. There is a straight line, a tangent, drawn so that it is touching the curve at t=6. The tangent goes through (2, 31), (6, 47) and (8,55). ]()

Options:
A. \( 0.1875 \)
B. \( 46 \)
C. \( 7.66 \ldots \)
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:
Believes gradient at a point = y coordinate/x coordinate

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

Which of the following is the best estimate for the gradient of the curve when \( t=6 \) ![The image is of a velocity-time graph. There is a straight line, a tangent, drawn so that it is touching the curve at t=6. The tangent goes through (2, 31), (6, 47) and (8,55). ]()

Options:
A. \( 0.1875 \)
B. \( 46 \)
C. \( 7.66 \ldots \)
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:
Has multiplied by the root power

Question:
\( \sqrt[4]{16}=? \)

Options:
A. \( 64 \)
B. \( 16 \)
C. \( 4 \)
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 understand the root power of 4

Question:
\( \sqrt[4]{16}=? \)

Options:
A. \( 64 \)
B. \( 16 \)
C. \( 4 \)
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:
Divides by the order of the root

Question:
\( \sqrt[4]{16}=? \)

Options:
A. \( 64 \)
B. \( 16 \)
C. \( 4 \)
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:
\begin{tabular}{llll|l|l}
\( x \) & \( -1 \) & \( 0 \) & \( 1 \) & \( 2 \) & \( 3 \) \\
\hline\( y \) & \( \bigstar \) &  & \( -1 \) &
\end{tabular} This is a table of values for \( y=x^{2}-x+1 \) What should replace the star?

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

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


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

Question:
What is the gradient of this line?
\(4 x-5 y=20\)

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

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


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

Question:
What is the gradient of this line?
\(4 x-5 y=20\)

Options:
A. \( 4 \)
B. \( \frac{4}{5} \)
C. \( -\frac{4}{5} \)
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 reading value from graph, reads from the wrong axes.

Question:
This is a conversion graph between pints and litres.
Which of the following is the best estimate for the number of pints equivalent to \( 50 \) litres? ![A graph on gridded paper showing litres on the y axis from 0 to 50 and pints on the x axis from 0 to 90. A straight line goes from the origin and passes through (35,20) (not marked - just a point it goes through) but extends the whole way up the graph.]()

Options:
A. \( 87 \) pints
B. \( 23 \) pints
C. \( 28 \) pints
D. \( 85 \) pints

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


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

Question:
This is a conversion graph between pints and litres.
Which of the following is the best estimate for the number of pints equivalent to \( 50 \) litres? ![A graph on gridded paper showing litres on the y axis from 0 to 50 and pints on the x axis from 0 to 90. A straight line goes from the origin and passes through (35,20) (not marked - just a point it goes through) but extends the whole way up the graph.]()

Options:
A. \( 87 \) pints
B. \( 23 \) pints
C. \( 28 \) pints
D. \( 85 \) pints

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


Prompt:
Misconception:
Thinks the inverse of subtraction is multiplication

Question:
This is a part of the table of values for the equation \( y=3 x \) ![A table with two rows and two columns. The top left box has 'x', with a star in the top right box. The bottom left box has 'y' with a 9 in the bottom right box. ]() What should replace the star?

Options:
A. \( 6 \)
B. \( 39 \)
C. \( 27 \)
D. \( 3 \)

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


Prompt:
Misconception:
Mixes up 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', with a star in the top right box. The bottom left box has 'y' with a 9 in the bottom right box. ]() What should replace the star?

Options:
A. \( 6 \)
B. \( 39 \)
C. \( 27 \)
D. \( 3 \)

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


Prompt:
Misconception:
Mixes up quantitative and qualitative data types

Question:
Leanne has written a questionnaire on the topic of holidays. One of her questions is,

"Describe how you feel when you are about to go on holiday."

What type of data is she collecting by asking this question?

Options:
A. Primary
Quantitative
data
B. Secondary
Quantitative data
C. Attribute data
D. Primary
Qualitative data

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


Prompt:
Misconception:
Does not know the meaning of attribute data

Question:
Leanne has written a questionnaire on the topic of holidays. One of her questions is,

"Describe how you feel when you are about to go on holiday."

What type of data is she collecting by asking this question?

Options:
A. Primary
Quantitative
data
B. Secondary
Quantitative data
C. Attribute data
D. Primary
Qualitative data

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


Prompt:
Misconception:
When completing the square, believes the constant in the bracket is the coefficient of x

Question:
\( m^{2}+6 m+1 \equiv(m \bigstar )^{2} \triangle \)

Options:
A. \(\bigstar =+6 \)
B. \(\bigstar =+12 \)
C. \(\bigstar =+3 \)
D. \(\bigstar =+2 \)

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

Question:
\( m^{2}+6 m+1 \equiv(m \bigstar )^{2} \triangle \)

Options:
A. \(\bigstar =+6 \)
B. \(\bigstar =+12 \)
C. \(\bigstar =+3 \)
D. \(\bigstar =+2 \)

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:
Which calculation is equal to \( -20 \) ?

Options:
A. \( 2 \times(-2)-(-4) \times 4 \)
B. \( -28-(-4) \times 2 \)
C. \( (-5)^{2}+5 \)
D. \( (-42) \div(-2)+1 \)

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


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

Question:
Which calculation is equal to \( -20 \) ?

Options:
A. \( 2 \times(-2)-(-4) \times 4 \)
B. \( -28-(-4) \times 2 \)
C. \( (-5)^{2}+5 \)
D. \( (-42) \div(-2)+1 \)

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


Prompt:
Misconception:
Believes dividing a negative by a negative gives a negative answer

Question:
Which calculation is equal to \( -20 \) ?

Options:
A. \( 2 \times(-2)-(-4) \times 4 \)
B. \( -28-(-4) \times 2 \)
C. \( (-5)^{2}+5 \)
D. \( (-42) \div(-2)+1 \)

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


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

Question:
\( (-5)+(-2)= \)

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

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


Prompt:
Misconception:
Believes that adding a negative will increase the value of the original number

Question:
\( (-5)+(-2)= \)

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

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


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

Question:
\[
5,12,19,26, \ldots ?
\]

What number comes next in this sequence?

Options:
A. \( 32 \)
B. \( 31 \)
C. \( 33 \)
D. \( 40 \)

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


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

Question:
This velocity-time graph shows the first \( 5 \) seconds of Mo's journey which starts at home.

At what time did he first start travelling at \( 4 \mathrm{~m} / \mathrm{s} \) ? ![The image is of a graph. Its vertical axis labelled Velocity (m/s) and has the scale 0, 2, 4, 6 marked in even steps. Its horizontal axis is labelled Time (secs) and has the scale 0, 1, 2, 3, 4, 5 marked in even steps.
The graph is in three sections. The first section is a straight slanted line from (0,0) to (1, 4). The second section is a horizontal line from (1, 4) to (3, 4). The third section is a slanted line from (3, 4) to (5, 0).]()

Options:
A. \( 1 \mathrm{sec} \)
B. \( 2 \mathrm{sec} \)
C. \( 3 \) secs
D. \( 4 \) secs

Solve the problem as a student with the misconception above.
You 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 connect rotational symmetry to number of sides/vertices

Question:
Tom and Katie are arguing about the order of rotational symmetry of quadrilaterals.

Tom says some quadrilaterals have an order of rotational symmetry of \( 1 \).
Katie says some quadrilaterals have an order of rotational symmetry of \( 3 \).
Who is correct?

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

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


Prompt:
Misconception:
Does not connect rotational symmetry to number of sides/vertices

Question:
Tom and Katie are arguing about the order of rotational symmetry of quadrilaterals.

Tom says some quadrilaterals have an order of rotational symmetry of \( 1 \).
Katie says some quadrilaterals have an order of rotational symmetry of \( 3 \).
Who is correct?

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

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


Prompt:
Misconception:
When reading integers on a number line, assumes each dash is 1

Question:
What temperature does the thermometer show? ![A thermometer showing the temperature in degrees Celsius. There are five steps on the scale between 10 and 0, and five steps between 0 and -10. The temperature is shown at 4 steps below 0.]()

Options:
A. \( -8^{\circ} \mathrm{C} \)
B. \( -9^{\circ} \mathrm{C} \)
C. \( -4^{\circ} \mathrm{C} \)
D. \( -11^{\circ} \mathrm{C} \)

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


Prompt:
Misconception:
When reading integers on a number line, assumes each dash is 1

Question:
What temperature does the thermometer show? ![A thermometer showing the temperature in degrees Celsius. There are five steps on the scale between 10 and 0, and five steps between 0 and -10. The temperature is shown at 4 steps below 0.]()

Options:
A. \( -8^{\circ} \mathrm{C} \)
B. \( -9^{\circ} \mathrm{C} \)
C. \( -4^{\circ} \mathrm{C} \)
D. \( -11^{\circ} \mathrm{C} \)

Solve the problem as a student with the misconception above.
You 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 surface area, only includes visible faces

Question:
Which of the following calculations would give you the total surface area of this cuboid in \( \mathrm{cm}^{2} \) ? ![A cuboid. The top measures 4cm by 2cm, and the height is 7cm.]()

Options:
A. \( (2 \times 7)+(4 \times 2)+(4 \times 7) \)
B. \( [(2 \times 7)+(4 \times 2)+(4 \times 7)] \times 2 \)
C. \( (2 \times 7) \times(4 \times 2) \times(4 \times 7) \)
D. \( 2 \times 4 \times 7 \)

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


Prompt:
Misconception:
Finds volume when asked for surface area

Question:
Which of the following calculations would give you the total surface area of this cuboid in \( \mathrm{cm}^{2} \) ? ![A cuboid. The top measures 4cm by 2cm, and the height is 7cm.]()

Options:
A. \( (2 \times 7)+(4 \times 2)+(4 \times 7) \)
B. \( [(2 \times 7)+(4 \times 2)+(4 \times 7)] \times 2 \)
C. \( (2 \times 7) \times(4 \times 2) \times(4 \times 7) \)
D. \( 2 \times 4 \times 7 \)

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


Prompt:
Misconception:
When multiplying involving a multiple of 10, just multiplies the digits and ignores the zeros

Question:
What should replace the star when solving the following problem using the grid method?
\(52 \times 326\) \begin{tabular}{|c|c|c|c|}
\hline\( \times \) & \( 300 \) & \( 20 \) & \( 6 \) \\
\hline \( 50 \) &  &  \( \bigstar \) & \\
\hline \( 2 \) &  & \\
\hline
\end{tabular}

Options:
A. \( 10 \)
B. \( 1000 \)
C. \( 70 \)
D. \( 100 \)

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

Question:
What should replace the star when solving the following problem using the grid method?
\(52 \times 326\) \begin{tabular}{|c|c|c|c|}
\hline\( \times \) & \( 300 \) & \( 20 \) & \( 6 \) \\
\hline \( 50 \) &  &  \( \bigstar \) & \\
\hline \( 2 \) &  & \\
\hline
\end{tabular}

Options:
A. \( 10 \)
B. \( 1000 \)
C. \( 70 \)
D. \( 100 \)

Solve the problem as a student with the misconception above.
You 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 involving a multiple of 10, gives an answer 10 times smaller than it should be

Question:
What should replace the star when solving the following problem using the grid method?
\(52 \times 326\) \begin{tabular}{|c|c|c|c|}
\hline\( \times \) & \( 300 \) & \( 20 \) & \( 6 \) \\
\hline \( 50 \) &  &  \( \bigstar \) & \\
\hline \( 2 \) &  & \\
\hline
\end{tabular}

Options:
A. \( 10 \)
B. \( 1000 \)
C. \( 70 \)
D. \( 100 \)

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


Prompt:
Misconception:
Mixes up odd and even numbers

Question:
In which region would \( \mathbf{3 6} \) belong? ![A Venn diagram with two sets, one labelled Square number and one labelled Odd number. Square Number without the intersection is labelled A, Odd Number without the intersection is labelled C, the intersection of the two sets is labelled B, and outside the circles is labelled D.]()

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

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


Prompt:
Misconception:
Mixes up odd and even numbers

Question:
In which region would \( \mathbf{3 6} \) belong? ![A Venn diagram with two sets, one labelled Square number and one labelled Odd number. Square Number without the intersection is labelled A, Odd Number without the intersection is labelled C, the intersection of the two sets is labelled B, and outside the circles is labelled D.]()

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

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


Prompt:
Misconception:
Mixes up odd and even numbers

Question:
In which region would \( \mathbf{3 6} \) belong? ![A Venn diagram with two sets, one labelled Square number and one labelled Odd number. Square Number without the intersection is labelled A, Odd Number without the intersection is labelled C, the intersection of the two sets is labelled B, and outside the circles is labelled D.]()

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

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


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

Question:
A \( 3 \) digit number belongs in this box to make the calculation true
\(
258+\square=1162
\)
What is the \( 3^{\text {rd }} \) digit of the number that belongs in the box?

Options:
A. \( 0 \)
B. \( 2 \)
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:
Subtracts the smallest digit from the largest digit

Question:
A \( 3 \) digit number belongs in this box to make the calculation true
\(
258+\square=1162
\)
What is the \( 3^{\text {rd }} \) digit of the number that belongs in the box?

Options:
A. \( 0 \)
B. \( 2 \)
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:
Believes the constant in an expanded quadratic comes from adding the two numbers in the brackets

Question:
What should replace the circle when these two brackets are expanded and simplified?
\(
(p-5)(p+2) \equiv p^{2} \triangle p \bigcirc
\)

Options:
A. \( \bigcirc=-7 \)
B. \( \bigcirc=-3 \)
C. \( \bigcirc=-10 \)
D. \( \bigcirc=+10 \)

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 multiplying a positive by a negative gives a positive answer

Question:
What should replace the circle when these two brackets are expanded and simplified?
\(
(p-5)(p+2) \equiv p^{2} \triangle p \bigcirc
\)

Options:
A. \( \bigcirc=-7 \)
B. \( \bigcirc=-3 \)
C. \( \bigcirc=-10 \)
D. \( \bigcirc=+10 \)

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


Prompt:
Misconception:
Thinks x = ? is the y axis

Question:
A point, \( Q \), has coordinates \( (2,5) \)
The point is reflected in the line \( x=2 \)
What are the new coordinates of point \( Q \) ?

Options:
A. \( (2,5) \)
B. \( (-2,5) \)
C. \( (5,2) \)
D. \( (2,-5) \)

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


Prompt:
Misconception:
Thinks x = ? or y = ? is y = x

Question:
A point, \( Q \), has coordinates \( (2,5) \)
The point is reflected in the line \( x=2 \)
What are the new coordinates of point \( Q \) ?

Options:
A. \( (2,5) \)
B. \( (-2,5) \)
C. \( (5,2) \)
D. \( (2,-5) \)

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


Prompt:
Misconception:
Thinks y = ? is the x axis

Question:
A point, \( Q \), has coordinates \( (2,5) \)
The point is reflected in the line \( x=2 \)
What are the new coordinates of point \( Q \) ?

Options:
A. \( (2,5) \)
B. \( (-2,5) \)
C. \( (5,2) \)
D. \( (2,-5) \)

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:
Answers order of operations questions with brackets as if the brackets are not there

Question:
When \( h=5 \)
Which of the following pairs of statements is true?

Options:
A. \( \begin{array}{l}3 h^{2}=75 \\ (3 h)^{2}=75\end{array} \)
B. \( \begin{array}{l}3 h^{2}=75 \\ (3 h)^{2}=225\end{array} \)
C. \( \begin{array}{l}3 h^{2}=225 \\ (3 h)^{2}=225\end{array} \)
D. \( \begin{array}{l}3 h^{2}=225 \\ (3 h)^{2}=75\end{array} \)

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:
Multiplies before applying a power

Question:
When \( h=5 \)
Which of the following pairs of statements is true?

Options:
A. \( \begin{array}{l}3 h^{2}=75 \\ (3 h)^{2}=75\end{array} \)
B. \( \begin{array}{l}3 h^{2}=75 \\ (3 h)^{2}=225\end{array} \)
C. \( \begin{array}{l}3 h^{2}=225 \\ (3 h)^{2}=225\end{array} \)
D. \( \begin{array}{l}3 h^{2}=225 \\ (3 h)^{2}=75\end{array} \)

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:
Multiplies before applying a power

Question:
When \( h=5 \)
Which of the following pairs of statements is true?

Options:
A. \( \begin{array}{l}3 h^{2}=75 \\ (3 h)^{2}=75\end{array} \)
B. \( \begin{array}{l}3 h^{2}=75 \\ (3 h)^{2}=225\end{array} \)
C. \( \begin{array}{l}3 h^{2}=225 \\ (3 h)^{2}=225\end{array} \)
D. \( \begin{array}{l}3 h^{2}=225 \\ (3 h)^{2}=75\end{array} \)

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


Prompt:
Misconception:
Thinks the fraction bar means subtract rather than divide

Question:
This is a part of the table of values for the equation \( y=\frac{3}{x} \) \begin{tabular}{|l|l|}
\hline\( x \) & \( 0.1 \) \\
\hline\( y \) & \(\color{gold}\bigstar\) \\
\hline
\end{tabular} What should replace the star?

Options:
A. \( 2.9 \)
B. \( 0.3 \)
C. \( 30 \)
D. \( 3.1 \)

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:
Multiplies instead of divides when division is written as a fraction

Question:
This is a part of the table of values for the equation \( y=\frac{3}{x} \) \begin{tabular}{|l|l|}
\hline\( x \) & \( 0.1 \) \\
\hline\( y \) & \(\color{gold}\bigstar\) \\
\hline
\end{tabular} What should replace the star?

Options:
A. \( 2.9 \)
B. \( 0.3 \)
C. \( 30 \)
D. \( 3.1 \)

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


Prompt:
Misconception:
Believes the fraction line represents addition

Question:
This is a part of the table of values for the equation \( y=\frac{3}{x} \) \begin{tabular}{|l|l|}
\hline\( x \) & \( 0.1 \) \\
\hline\( y \) & \(\color{gold}\bigstar\) \\
\hline
\end{tabular} What should replace the star?

Options:
A. \( 2.9 \)
B. \( 0.3 \)
C. \( 30 \)
D. \( 3.1 \)

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:
Added rather than multiplied by a scale factor

Question:
\( 1 \mathrm{~km} \approx 0.6 \) miles \( 4 \mathrm{~km} \approx \square \) miles

Options:
A. \( 4.6 \)
B. \( 0.24 \)
C. \( 2.4 \)
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 decimals, ignores place value and just multiplies the digits

Question:
\( 1 \mathrm{~km} \approx 0.6 \) miles \( 4 \mathrm{~km} \approx \square \) miles

Options:
A. \( 4.6 \)
B. \( 0.24 \)
C. \( 2.4 \)
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:
Subtracted rather than divided by a scale factor

Question:
\( 1 \mathrm{~km} \approx 0.6 \) miles \( 4 \mathrm{~km} \approx \square \) miles

Options:
A. \( 4.6 \)
B. \( 0.24 \)
C. \( 2.4 \)
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 you add the number of wholes to the numerator when converting a mixed number to an improper fraction.

Question:
\(
1 \frac{2}{3}+\frac{1}{3}
\)
Which of the following is a correct way to write the answer to this calculation?

Options:
A. \( \frac{4}{3} \)
B. \( 4 \)
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:
Believes you add the whole to the numerators, ignoring denominators, when adding a mixed number to a proper fraction with the same denominator.

Question:
\(
1 \frac{2}{3}+\frac{1}{3}
\)
Which of the following is a correct way to write the answer to this calculation?

Options:
A. \( \frac{4}{3} \)
B. \( 4 \)
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:
Has not realised that the answer may be changed by the insertion of brackets

Question:
Write the following using correct algebraic notation \( m \) multiplied by the cube of \( n \)

Options:
A. \( (m n)^{3} \)
B. \( m n^{3} \)
C. \( m n+3 \)
D. \( 3 m n \)

Solve the problem as a student with the misconception above.
You 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 cubing a number means adding 3 to that number

Question:
Write the following using correct algebraic notation \( m \) multiplied by the cube of \( n \)

Options:
A. \( (m n)^{3} \)
B. \( m n^{3} \)
C. \( m n+3 \)
D. \( 3 m n \)

Solve the problem as a student with the misconception above.
You 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 cubing a number means you multiply it by 3

Question:
Write the following using correct algebraic notation \( m \) multiplied by the cube of \( n \)

Options:
A. \( (m n)^{3} \)
B. \( m n^{3} \)
C. \( m n+3 \)
D. \( 3 m n \)

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


Prompt:
Misconception:
Believes all quadratic equations have a solution of 0

Question:
In which region would \( x^{2}-10 x-25=0 \) belong? ![A Venn diagram made up of two overlapping circles. One is labelled 'Factorises' and the other is labelled 'Has one solution equal to 0'.
A is in the 'Factorises' circle only, B is in the overlap of the two circles, C is in the 'Has one solution equal to 0' circle only, and D is outside the circles.]()

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

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


Prompt:
Misconception:
Does not notice all changes in a sequence of visual patterns

Question:
What is the next pattern in this linear sequence? ![A sequence of 4 patterns. The first pattern is a rectangle, made of 3 squares stacked vertically. The second pattern is the same as the first pattern but with 2 more squares added, to the right of the bottom 2 squares of Pattern 1. The 3rd pattern is the same as the second pattern but with 2 more squares added, to the right of the bottom 2 squares of Pattern 2. The 4th pattern is the same as the 3rd pattern but with 2 more squares added, to the right of the bottom 2 squares of Pattern 3.]()

Options:
A. ![This pattern is the same as Pattern 4: it is made up of 9 squares as a 4 (width) by 2 (height) rectangle and then an extra square on top of the top left square of the rectangle.]()
B. ![This pattern is made up of 11 squares as a 5 (width) by 2 (height) rectangle and then an extra square on top of the top left square of the rectangle.]()
C. ![This pattern is made up of 12 squares as a 5 (width) by 2 (height) rectangle and then 2 extra squares on top of the top left square of the rectangle.]()
D. ![This pattern is made up of 12 squares as a 5 (width) by 2 (height) rectangle and then an extra square on top of the top left square of the rectangle, and one more square to the right of that one.]()

Solve the problem as a student with the misconception above.
You 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 notice all changes in a sequence of visual patterns

Question:
What is the next pattern in this linear sequence? ![A sequence of 4 patterns. The first pattern is a rectangle, made of 3 squares stacked vertically. The second pattern is the same as the first pattern but with 2 more squares added, to the right of the bottom 2 squares of Pattern 1. The 3rd pattern is the same as the second pattern but with 2 more squares added, to the right of the bottom 2 squares of Pattern 2. The 4th pattern is the same as the 3rd pattern but with 2 more squares added, to the right of the bottom 2 squares of Pattern 3.]()

Options:
A. ![This pattern is the same as Pattern 4: it is made up of 9 squares as a 4 (width) by 2 (height) rectangle and then an extra square on top of the top left square of the rectangle.]()
B. ![This pattern is made up of 11 squares as a 5 (width) by 2 (height) rectangle and then an extra square on top of the top left square of the rectangle.]()
C. ![This pattern is made up of 12 squares as a 5 (width) by 2 (height) rectangle and then 2 extra squares on top of the top left square of the rectangle.]()
D. ![This pattern is made up of 12 squares as a 5 (width) by 2 (height) rectangle and then an extra square on top of the top left square of the rectangle, and one more square to the right of that one.]()

Solve the problem as a student with the misconception above.
You 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 notice all changes in a sequence of visual patterns

Question:
What is the next pattern in this linear sequence? ![A sequence of 4 patterns. The first pattern is a rectangle, made of 3 squares stacked vertically. The second pattern is the same as the first pattern but with 2 more squares added, to the right of the bottom 2 squares of Pattern 1. The 3rd pattern is the same as the second pattern but with 2 more squares added, to the right of the bottom 2 squares of Pattern 2. The 4th pattern is the same as the 3rd pattern but with 2 more squares added, to the right of the bottom 2 squares of Pattern 3.]()

Options:
A. ![This pattern is the same as Pattern 4: it is made up of 9 squares as a 4 (width) by 2 (height) rectangle and then an extra square on top of the top left square of the rectangle.]()
B. ![This pattern is made up of 11 squares as a 5 (width) by 2 (height) rectangle and then an extra square on top of the top left square of the rectangle.]()
C. ![This pattern is made up of 12 squares as a 5 (width) by 2 (height) rectangle and then 2 extra squares on top of the top left square of the rectangle.]()
D. ![This pattern is made up of 12 squares as a 5 (width) by 2 (height) rectangle and then an extra square on top of the top left square of the rectangle, and one more square to the right of that one.]()

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


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

Question:
![A function machine with 4 rectangles in a row, joined by arrows pointing from left to right. The first rectangle on the left is empty and says "input" above it. The next rectangle has "− 1" written inside it, the next rectangle has "✕ 2" written inside it and the final rectangle on the right has "output" written above it and "8" written inside it.]() What is the input of this function machine?

Options:
A. \( 15 \)
B. \( 5 \)
C. \( 14 \)
D. \( 4.5 \)

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


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

Question:
![A function machine with 4 rectangles in a row, joined by arrows pointing from left to right. The first rectangle on the left is empty and says "input" above it. The next rectangle has "− 1" written inside it, the next rectangle has "✕ 2" written inside it and the final rectangle on the right has "output" written above it and "8" written inside it.]() What is the input of this function machine?

Options:
A. \( 15 \)
B. \( 5 \)
C. \( 14 \)
D. \( 4.5 \)

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