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Decide whether the misconception explains the student's wrong answer.
Question context:
Rotate an object or point 180° about a point, where the point lies on the edge or outside of the object Rotation ![A pair of axes: x-axis is from -3 to 4; y-axis is from -4 to 4. A quadrilateral, labelled "P", is made by joining t... | NO_MATCH | null | NO_MATCH
**Reasoning:**
1. **Correct Transformation:** The question asks for a rotation of $180^{\circ}$ about the origin. The rule for this transformation is $(x, y) \rightarrow (-x, -y)$. Applying this to the red point $(-1, 3)$ gives $(1, -3)$, which corresponds to point **D**.
2. **Student's Answer:** The studen... |
Decide whether the misconception explains the student's wrong answer.
Question context:
Multiply a decimal by an integer Multiplying and Dividing with Decimals Work out:
\[
0.6 \times 11
\]
Student's wrong answer:
\( 66 \)
Candidate misconception:
When multiplying a decimal by an integer, ignores decimal point and j... | MATCH | null | MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
Identify the mode from a frequency table Averages and Range from Frequency Table This table shows the ages of people on a university running team.
What is the modal age? \begin{tabular}{|c|c|l|}
\hline Age & Frequency & \\
\hline ... | NO_MATCH | null | MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
Mark a point in the second quadrant of a 2D grid having been given its coordinates, where both values are integers Graphing Linear Inequalities (Shading Regions) Which region describes where \( \boldsymbol{x}>\mathbf{0} \) and \( \... | NO_MATCH | null | MATCH
To determine if the candidate misconception explains the student's wrong answer, let's analyze the question and the student's response.
1. **Analyze the Question:**
The question asks for the region where \( x > 0 \) and \( y < 0 \).
* \( x > 0 \) means the point is to the right of the y-axis.
* ... |
Decide whether the misconception explains the student's wrong answer.
Question context:
Complete the square for expressions that end up in the form (x + a)² + b Completing the Square When Sarah completes the square, what should replace the triangle?
\[
p^{2}-10 p-1 \equiv(p-5)^{2} \Delta
\]
Student's wrong answer:
\... | MATCH | null | MATCH
**Explanation:**
To complete the square for $p^2 - 10p - 1$, the correct process is:
1. Halve the coefficient of $p$: $-10 / 2 = -5$. This gives $(p - 5)^2$.
2. Expand $(p - 5)^2$ to find the constant term generated: $(-5)^2 = 25$.
3. Adjust the constant to match the original expression: $25 + \Delta = -1$, so $... |
Decide whether the misconception explains the student's wrong answer.
Question context:
Factorise a quadratic expression in the form x² + bx + c Factorising into a Double Bracket Factorise this expression, if possible:
\(
p^{2}+2 p+3
\)
Student's wrong answer:
\( (p+3)(p+1) \)
Candidate misconception:
Believes that ... | MATCH | null | MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
Construct a triangle using Side-Side-Side Construct Triangle What is the length of the side marked \( q \) ? ![Two, intersecting circles drawn with a compass and used to construct a triangle with one side labelled with q]()
Studen... | NO_MATCH | null | NO_MATCH
The student's answer of \( 2.5 \mathrm{~cm} \) suggests they likely measured or estimated the length of the side \( q \) directly from the diagram using a ruler, rather than identifying the length from the construction properties—specifically, the radius of the compass arc used to draw it.
The candidate mis... |
Decide whether the misconception explains the student's wrong answer.
Question context:
Express a non-linear equation as a function machine Function Machines Which function machine matches the equation \( y=x^{2}+4 ? \)
Student's wrong answer:
![A function machine which has 4 parts joined by arrows pointing from left... | NO_MATCH | null | MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
Describe the properties of an isosceles triangle Properties of Triangles An isosceles triangle must have ...
Student's wrong answer:
one pair of parallel sides.
Candidate misconception:
Does not know the meaning of corresponding
... | NO_MATCH | null | NO_MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
Given information about one part, work out other parts Sharing in a Ratio Jess and Heena share some sweets in the ratio \( 3\;: 5 \).
Jess gets \( 15 \) sweets.
How many sweets does Heena get?
Student's wrong answer:
\( 17 \)
Can... | NO_MATCH | null | NO_MATCH
**Explanation:**
1. **Analyze the Student's Error:**
- **Correct Method:** The ratio is 3:5. If Jess (3 parts) gets 15 sweets, then 1 part = 15 ÷ 3 = 5 sweets. Heena (5 parts) gets 5 × 5 = 25 sweets.
- **Student's Answer:** 17.
- **Likely Reasoning:** The student calculated the difference between th... |
Decide whether the misconception explains the student's wrong answer.
Question context:
Identify a unit of volume or capacity Volume of Prisms Which of the following is not a measure of volume?
Student's wrong answer:
Centimetres cubed
Candidate misconception:
Does not recognise a unit of volume
Does this misconcep... | NO_MATCH | null | MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
Recognise the notation for parallel lines Properties of Quadrilaterals The arrows tell us that these two sides are... ![Parallelogram PQRS with sides QR and PS labelled with arrows]()
Student's wrong answer:
Opposite
Candidate mi... | MATCH | null | MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
Recognise square roots Square Roots, Cube Roots, etc Which of the following is the square root of \( 36 \) ?
Student's wrong answer:
\( 72 \)
Candidate misconception:
Mixes up squaring and multiplying by 2 or doubling
Does this ... | NO_MATCH | null | MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
Interpret continuous data using a line graph Time Series and Line Graphs 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. Vertica... | NO_MATCH | null | NO_MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
Calculate the square root of a number Square Roots, Cube Roots, etc What is the square root of sixteen?
Student's wrong answer:
\( 32 \)
Candidate misconception:
Confuses square rooting and halving the number
Does this misconcep... | NO_MATCH | null | NO_MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
Calculate the median as an average from an odd numbered list of data Averages (mean, median, mode) from a List of Data What is the median of the following numbers?
\( 2,2,4,7,10 \)
Student's wrong answer:
\( 2 \)
Candidate miscon... | NO_MATCH | null | NO_MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
Rearrange formulae to change the subject where the subject appears once and three or more steps are needed Rearranging Formula and Equations Tom and Katie are discussing rearranging \( t=\sqrt{u+9} \) to make \( u \) the subject
To... | NO_MATCH | null | NO_MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
Factorise a quadratic expression in the form x² + bx + c Factorising into a Double Bracket When \( x^{2}+12 x+32 \) is factorised, what will appear in the box below? ![\( (x+4) \square \)]()
Student's wrong answer:
\( (x+28) \)
C... | NO_MATCH | null | NO_MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
Given the area of a parallelogram, calculate a missing dimension Area of Simple Shapes The area of this parallelogram is \( 24 \mathrm{~cm}^{2} \)
What measurement should replace the star? ![Parallelogram with base length 6cm and ... | NO_MATCH | null | MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
Calculate the square of a number Estimation Which is the best estimate for \( (4.2)^{2} \) ?
Student's wrong answer:
\( 8 \)
Candidate misconception:
Multiplies by the index
Does this misconception explain the wrong answer? Answ... | MATCH | null | MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
Calculate the range from a list of data Range and Interquartile Range from a List of Data What is the range of the following numbers?
\[
2,2,4,17,-10
\]
Student's wrong answer:
\( 12 \)
Candidate misconception:
To find the range ... | NO_MATCH | null | MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
Given a negative x value, find the corresponding y value for curves in the form y = x² + bx + c Plotting Quadratics from Tables of Values This is a part of the table of values for the equation
\[y=x^{2}-x\] \begin{tabular}{|c|c|}
\... | NO_MATCH | null | MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
Identify whether two shapes are similar or not Length Scale Factors in Similar Shapes Tom and Katie are discussing similarity. Who is correct? Tom says these two rectangles are similar ![Two rectangles of different sizes. One recta... | NO_MATCH | null | NO_MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
Given the sector angle on a pie chart, calculate the frequency of a group Pie Chart A class of students were surveyed about how many siblings they have.
A selection of results are shown in the table. \begin{tabular}{|c|c|c|}
\hlin... | NO_MATCH | null | MATCH
**Reasoning:**
1. **Analyze the Student's Answer:** The student calculated \( 165 \div 24 \). In the context of the problem, \( 165 \) is the **Angle** and \( 24 \) is the **Total Frequency**. So, the student calculated \( \text{Angle} \div \text{Total Frequency} \).
2. **Analyze the Misconception:** The candi... |
Decide whether the misconception explains the student's wrong answer.
Question context:
Round integers to the nearest 100 Rounding to the Nearest Whole (10, 100, etc) What is \( 356,958 \) rounded to the nearest \( 100 \) ?
Student's wrong answer:
\( 356,900 \)
Candidate misconception:
Rounds every number down when ... | NO_MATCH | null | MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
For a given output find the input of a function machine Function Machines ![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" abov... | MATCH | null | **Step 1 — Compare: Analyze all responses across three dimensions:**
- **Content accuracy & completeness:** All responses correctly conclude with "MATCH". Responses 1 and 2 provide a complete, step-by-step mathematical breakdown. They accurately identify the correct input (5) and successfully simulate the student's er... |
Decide whether the misconception explains the student's wrong answer.
Question context:
Select the correct answer to an iteration question to the required degree of accuracy Trial and Improvement and Iterative Methods The area of the rectangle on the right is \( 8 \mathrm{~cm}^{2} \).
To find the value of \( x \), Sa... | NO_MATCH | null | To determine if the misconception matches, we must first find the correct answer and then analyze the student's error.
**1. Correct Calculation:**
The iteration formula is $x_{n+1} = \frac{8}{9} - \frac{x_n^3}{9}$ with $x_0 = 0$.
- $x_1 = \frac{8}{9} - \frac{0^3}{9} \approx 0.888889$
- $x_2 = \frac{8}{9} - \frac{(0.88... |
Decide whether the misconception explains the student's wrong answer.
Question context:
Write the next term of a descending integer linear sequence Sequences-Others What is the next term in this sequence?
\[
23, \quad 13, \quad 3, \quad \ldots
\]
Student's wrong answer:
\( -10 \)
Candidate misconception:
Uses term... | NO_MATCH | null | To determine if the misconception explains the student's answer, let's analyze the sequence and the context of the error.
1. **Analyze the sequence:** The sequence is $23, 13, 3, \ldots$ The common difference (term-to-term rule) is $13 - 23 = -10$. To find the next term, we add this difference to the last term: $3 + (... |
Decide whether the misconception explains the student's wrong answer.
Question context:
Convert between cm³ and mm³ Volume and Capacity Units \( 1 \mathrm{~cm}^{3} \) is the same as _______ \( \mathrm{mm}^{3} \)
Student's wrong answer:
\( 100 \)
Candidate misconception:
Does not convert measurements to have the same... | NO_MATCH | null | NO_MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
Compare the lengths of diagonal line segments without calculating the exact length Translation and Vectors $ to $(4, 3)$. The horizontal change is $4 - (-1) = 5$ and the vertical change is $3 - 2 = 1$. The components are $(5, 1)$, and the squared length is $5^2 + 1^2 = 26$.
* **Segment L:** From $(-3, -4)$ to $(-2, 0)$. The ... |
Decide whether the misconception explains the student's wrong answer.
Question context:
Convert fractions to ratios Writing Ratios \( \frac{3}{7} \) of a group of students are boys.
What would be a possible ratio of boys to girls?
Student's wrong answer:
\( 3: 10 \)
Candidate misconception:
When converting ratio to ... | NO_MATCH | null | NO_MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
Reflect an object or a point in a horizontal line with the line of reflection drawn, where the line of reflection lies on the edge or outside the object Reflection If you reflect the rectangle in the horizontal line, where does the... | MATCH | null | MATCH
**Reasoning:**
The question asks the student to reflect the top-left vertex of a rectangle across a horizontal mirror line. A correct reflection requires the point to "flip" to the opposite side of the line, maintaining its horizontal position and moving an equal perpendicular distance away.
Based on the descr... |
Decide whether the misconception explains the student's wrong answer.
Question context:
Carry out addition problems involving two negative integers Adding and Subtracting Negative Numbers \( (-3)+(-5)= \)
Student's wrong answer:
\( 8 \)
Candidate misconception:
Believes multiplying two positives gives a negative an... | NO_MATCH | null | NO_MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
Convert from mixed number fractions to improper fractions Converting Mixed Number and Improper Fractions Convert this into an improper fraction:
\(
4 \frac{2}{3}
\)
Student's wrong answer:
\( \frac{42}{3} \)
Candidate misconcepti... | NO_MATCH | null | NO_MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
Convert decimals less than 1 with 2 decimal place to percentages Converting between Decimals and Percentages Write \( 0.15 \) as a percentage.
Student's wrong answer:
\( 1.5 \% \)
Candidate misconception:
Divides by 10 instead of... | NO_MATCH | null | NO_MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
Expand two brackets with linear terms in the form (x + a)² Expanding Double Brackets Which of the following answers shows a correct expansion and simplification of the expression below? \( (x-4)^{2} \)
Student's wrong answer:
\( x... | NO_MATCH | null | NO_MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
Add integers up to 4 digits using a written method where carrying is needed Written Addition What number should replace the star? \begin{tabular}{|c|c|c|c|c|}
\hline & \( 4 \) & \( 2 \) & \(5\) & \(4\)\\
\hline+ & \( 2 \) & \(\bigs... | NO_MATCH | null | NO_MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
Rotate an object or point 900 clockwise or anticlockwise about a point, where the point lies on the edge or outside of the object Rotation The blue shape is rotated \( 90^{\circ} \) anticlockwise about \( (-2,2) \). Which shape giv... | NO_MATCH | null | The correct answer is Shape D, which results from rotating the blue shape 90° anticlockwise about the point (-2, 2). The student incorrectly chose Shape A, which likely corresponds to a rotation in the wrong direction (clockwise) or a misplacement of the center of rotation.
The candidate misconception is "Confuses ver... |
Decide whether the misconception explains the student's wrong answer.
Question context:
Factorise a quadratic expression in the form ax² - c Difference of Two Squares When factorised, \( 9 x^{2}-16 \) will become...
Student's wrong answer:
\( 9 x(x-16) \)
Candidate misconception:
Believes only the first term needs t... | MATCH | null | NO_MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
Solve quadratic inequalities from the graph of the quadratic Solving Quadratic Inequalities Using the graph of
\(
y=x^{2}-x-6
\)
What is the correct way to write the solution to
\(
y=x^{2}-x-6 \geq 0 ?
\) ![The is a parabolic grap... | MATCH | null | MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
Add surds in the form mva + nvb Operations with Surds \(
2 \sqrt{5}+2 \sqrt{45} \equiv d \sqrt{5}
\)
What is the value of \( d \) ?
Student's wrong answer:
\( 7 \)
Candidate misconception:
When simplifying surds, does not unders... | NO_MATCH | null | To determine if the misconception explains the student's answer, let's analyze the correct working and how the student might have arrived at 7.
**Correct Working:**
\( 2 \sqrt{5} + 2 \sqrt{45} \)
\( = 2 \sqrt{5} + 2 \sqrt{9 \times 5} \)
\( = 2 \sqrt{5} + 2(3 \sqrt{5}) \)
\( = 2 \sqrt{5} + 6 \sqrt{5} = 8 \sqrt{5} \)
Th... |
Decide whether the misconception explains the student's wrong answer.
Question context:
Expand double brackets with an extra variable outside Expanding Double Brackets When you multiply out the brackets and simplify, what replaces the triangle?
\(
m(m+5)(m-5) \equiv m^{3} \bigstar \ m^{2} \triangle \ m \bigcirc
\)
St... | NO_MATCH | null | The correct expansion of the expression is:
$m(m+5)(m-5) = m(m^2 - 25) = m^3 - 25m$
In the target form $m^3 \bigstar m^2 \triangle m \bigcirc$, the triangle ($\triangle$) represents the coefficient of $m$. The correct value for $\triangle$ is $-25$.
The student's answer is $\triangle = +0$. For the coefficient of $m$... |
Decide whether the misconception explains the student's wrong answer.
Question context:
Carry out missing number subtraction problems where a written method is needed Adding and Subtracting with Decimals \(\square\quad -\quad 1.534=2.7 \)
Student's wrong answer:
\( 1.166 \)
Candidate misconception:
Subtracts instead... | NO_MATCH | null | NO_MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
Identify a rectangle when presented non-conventionally Naming Co-ordinates in 2D ![A rhombus drawn on a grid]() What shape do you get if you join up the midpoints of the sides of this shape?
Student's wrong answer:
Rhombus
Candid... | NO_MATCH | null | NO_MATCH
The correct answer to the question is a **Rectangle** (according to Varignon's Theorem, the midpoints of any quadrilateral form a parallelogram; because a rhombus has perpendicular diagonals, the resulting shape is specifically a rectangle). The student answered **Rhombus**.
The candidate misconception is "*... |
Decide whether the misconception explains the student's wrong answer.
Question context:
Subtract decimals from integers Adding and Subtracting with Decimals How should you line up the digits to calculate \( 7-0.612 \) ?
Student's wrong answer:
![A column subtraction written as 0.007 - 0.612 with the decimal points li... | NO_MATCH | null | The student's error is a place value alignment mistake. When calculating 7 - 0.612, the student rewrote the integer 7 as 0.007, placing the digit in the thousandths column to match the number of decimal places in 0.612, rather than correctly writing it as 7.000.
The candidate misconception describes a failure to unde... |
Decide whether the misconception explains the student's wrong answer.
Question context:
Substitute numbers into a SUVAT equation to work out distance Substitution into Formula \( s=u t+\frac{1}{2} a t^{2} \) What is the value of \( s \) when
a=6
u=3
t=4
Student's wrong answer:
\( 576 \)
Candidate misconception:
W... | MATCH | null | MATCH
**Reasoning:**
1. **Correct Calculation:**
Using the formula \( s = ut + \frac{1}{2}at^2 \) with \( u=3, a=6, t=4 \):
\( s = (3 \times 4) + \frac{1}{2} \times 6 \times 4^2 \)
\( s = 12 + 3 \times 16 \)
\( s = 12 + 48 = 60 \)
2. **Student's Answer:** 576.
3. **Analyzing the Misconception:**
... |
Decide whether the misconception explains the student's wrong answer.
Question context:
Identify the net of a non-prism Nets This is the net of a... ![A circle touching a sector]()
Student's wrong answer:
Triangular prism
Candidate misconception:
Struggles to visualise the new position of an object after transformat... | NO_MATCH | null | NO_MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
Calculate the median as an average from an even numbered list of data Averages (mean, median, mode) from a List of Data What is the median of the following numbers?
\[
3,5,6,18,18,-4
\]
Student's wrong answer:
\( 6 \)
Candidate m... | NO_MATCH | null | NO_MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
Complete multi-step mental calculations Mental Addition and Subtraction What is the value of:
\(
\frac{54+58}{2}
\)
Student's wrong answer:
\( 224 \)
Candidate misconception:
Multiplies rather than divides when answering worded p... | NO_MATCH | null | NO_MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
Read a fraction on a scale where the required number is marked by a dash between two numbers Ordering Fractions What fraction is the arrow pointing to? ![An image of a numberline with 5 dashes. On the leftmost dash is the number 1/... | MATCH | null | MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
For a given output find the input of a function machine Function Machines \( input\Rightarrow(+1) \Rightarrow(\times2) \Rightarrow9\) What is the input of this function machine?
Student's wrong answer:
\( 19 \)
Candidate misconce... | NO_MATCH | null | MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
Interpret remainders from written division problems Written Division \( 321 \) children are going on a school trip. One adult is needed for every seven children.
How many adults are needed?
Student's wrong answer:
\( 45 \) r6
Ca... | NO_MATCH | null | NO_MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
Solve quadratic equations using the quadratic formula where the coefficient of x² is not 1 Quadratic Equations Which option gives a correct substitution into the quadratic formula to solve the quadratic equation? \( 2 x^{2}-8 x+7=... | NO_MATCH | null | NO_MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
Calculate the range from a list of data Range and Interquartile Range from a List of Data What is the range of the following numbers?
\[
1,5,5,17,-6
\]
Student's wrong answer:
\( 5 \)
Candidate misconception:
Finds the median ins... | NO_MATCH | null | NO_MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
Solve coordinate geometry questions involving ratio Sharing in a Ratio What is the ratio of
\[
A B: B C \text { ? }
\] ![A line AC which is 10 units long. B is on it so that AB:BC is 1:2]()
Student's wrong answer:
\( 1: 3 \)
Cand... | NO_MATCH | null | MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
Identify unit fractions when part of a shape Fractions of an Amount What fraction of the shape is shaded? ![A rectangle split in half. One half is split in half again, and one half of that is split in half again, with one of those ... | MATCH | null | MATCH
The shape is a rectangle divided recursively into halves, resulting in four unequal parts: one 1/2, one 1/4, and two 1/8 pieces. One of the 1/8 pieces is shaded, making the correct answer 1/8.
The student answered 1/3. The candidate misconception is "Does not understand a denominator represents equal parts." If... |
Decide whether the misconception explains the student's wrong answer.
Question context:
Round numbers between 0 and 1 to one significant figure Rounding to Significant Figures Round this number to \( 1 \) significant figure:
\( 0.8532 \)
Student's wrong answer:
\( 0.8 \)
Candidate misconception:
Rounds every number ... | NO_MATCH | null | MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
Carry out a subtraction problem with positive integers where the answer is less than 0 Place Value \( 598-1000= \)
Student's wrong answer:
\( 402 \)
Candidate misconception:
Believes the smaller number is always subtracted from t... | MATCH | null | MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
Can write Roman numerals between 100 and 1000 Place Value Which of the following is the correct way to write \( 900 \) using Roman numerals?
Student's wrong answer:
DCCCC
Candidate misconception:
Writes more than three repeated s... | NO_MATCH | null | MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
Divide proper fractions in the form: Integer ÷ Fraction Dividing Fractions How many times does \( \frac{3}{5} \) go into \( 15 \) ?
Student's wrong answer:
\( 9 \)
Candidate misconception:
when dividing a fraction by an integer, ... | NO_MATCH | null | NO_MATCH
**Explanation:**
1. **Analyze the Problem:** The question asks to calculate \( 15 \div \frac{3}{5} \) ("How many times does \( \frac{3}{5} \) go into \( 15 \)?"). The correct calculation is \( 15 \times \frac{5}{3} = 25 \).
2. **Analyze the Student's Answer:** The student answered \( 9 \). This result is obta... |
Decide whether the misconception explains the student's wrong answer.
Question context:
Divide two decimals with a different number of decimal places Multiplying and Dividing with Decimals \( 70.04 \div 0.1= \)
Student's wrong answer:
\( 700.04 \)
Candidate misconception:
When multiplying decimals, does not realize ... | NO_MATCH | null | NO_MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
Carry out subtraction problems involving two negative integers Adding and Subtracting Negative Numbers What number belongs in the box?
\(
(-8)-(-5)=
\square\)
Student's wrong answer:
\( 3 \)
Candidate misconception:
Thinks subtr... | NO_MATCH | null | NO_MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
Read values off a displacement-time graph Time Series and Line Graphs This graph shows the displacement of a ball from a starting point at various times.
How far did the ball travel between \( 1 \) and \( 2 \) seconds? ![A displace... | NO_MATCH | null | To determine if the misconception explains the student's answer, we must analyze the question and the typical values found on a displacement-time graph.
1. **Analyzing the Question:** The question asks for the distance traveled between $t = 1\text{s}$ and $t = 2\text{s}$. This requires calculating the change in displa... |
Decide whether the misconception explains the student's wrong answer.
Question context:
Find missing angles using angles on a straight line Basic Angle Facts (straight line, opposite, around a point, etc) ![Two angles meeting on a straight line labelled n and 48 degrees, one angle further down the straight line labell... | NO_MATCH | null | MATCH
The student's answer of \( 102^{\circ} \) is calculated as \( 180^{\circ} - 48^{\circ} - 30^{\circ} = 102^{\circ} \).
The correct calculation for angles on a straight line would be to only subtract the adjacent angle from \( 180^{\circ} \) (\( 180^{\circ} - 48^{\circ} = 132^{\circ} \)), as the \( 30^{\circ} \) ... |
Decide whether the misconception explains the student's wrong answer.
Question context:
Substitute negative integer values into formulae involving powers or roots Substitution into Formula \(
F=3^{a}
\)
What is the value of \( F \) when \( a=-5 \) ?
Student's wrong answer:
\( -15 \)
Candidate misconception:
Has mul... | MATCH | null | MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
Calculate the square root of a number Squares, Cubes, etc What is the value of the missing number? ![\begin{tabular}{|c|c|}
\hline \multicolumn{2}{|c|}{\( 15^{2} \)} \\
\hline\( \square^{2} \) & \( 2 \) \\
\hline
\end{tabular}]()
... | NO_MATCH | null | NO_MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
Solve one-step linear inequalities in one variable where the variable appears on one side of the equation Solving Linear Inequalities Tom and Katie are arguing about the solution to this inequality:
\[
20 \geq 8 m
\]
Tom says \( m... | NO_MATCH | null | To determine if the candidate misconception explains the student's wrong answer, let's analyze the problem and the student's logic.
**1. Analyze the Problem:**
The inequality is $20 \geq 8m$.
To solve for $m$, divide both sides by 8:
$20 / 8 \geq m$
$2.5 \geq m$ (or $m \leq 2.5$)
* **Tom's claim:** $m = 2.5$. Since... |
Decide whether the misconception explains the student's wrong answer.
Question context:
Recognise and name a variable Writing Expressions Which of the following is the most appropriate word to describe \( p \) in this:
\(
3 p+7
\)
Student's wrong answer:
Expression
Candidate misconception:
Confuses a term with a var... | NO_MATCH | null | NO_MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
Use the order of operations to carry out calculations involving powers BIDMAS \( 8-7 \div 6^{3}= \) Which calculation should you do first?
Student's wrong answer:
\( 7 \div 6 \)
Candidate misconception:
Believes when dividing num... | NO_MATCH | null | NO_MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
Solve length problems involving similar shapes where the missing length is the shorter one Length Scale Factors in Similar Shapes These two shapes are similar (not drawn to scale).
What should replace the star? ![Two scalene triang... | NO_MATCH | null | **Step 1 — Compare**
* **Content accuracy & completeness:** Responses 0, 1, and 2 correctly identify the proper scale factor (6/9 = 2/3) to find the correct answer of 5 cm. They accurately deduce that the student's answer of 3.75 cm comes from incorrectly using a scale factor of 1/2 (halving 7.5 cm). This demonstrat... |
Decide whether the misconception explains the student's wrong answer.
Question context:
Calculate coordinates of points on the graph of y = ax, where x is a positive non-integer Graphs of Exponentials and Other Powers of x This is a part of the table of values for the equation \( \boldsymbol{y}=\mathbf{8}^{\boldsymbol... | NO_MATCH | null | The correct calculation for the table value is \( y = 8^{1/3} = \sqrt[3]{8} = 2 \).
The student's answer is \( 24 \). To arrive at \( 24 \) from the base \( 8 \) and the exponent \( \frac{1}{3} \) (where the root order is \( 3 \)), the student likely performed the operation \( 8 \times 3 = 24 \). This indicates a misc... |
Decide whether the misconception explains the student's wrong answer.
Question context:
Calculate the mean from a frequency table Averages and Range from Frequency Table This table shows the number of pets a group of students owns.
If calculating the mean number of pets owned, what would replace the star? \begin{tabul... | NO_MATCH | null | NO_MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
Round numbers greater than 1 to one significant figure Rounding to Significant Figures Round this number to \( 1 \) significant figure:
\( 95365 \)
Student's wrong answer:
\( 10000 \)
Candidate misconception:
When two digits mult... | NO_MATCH | null | NO_MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
Fill in regions of a double Venn diagram with numbers from given information Venn Diagrams \( \begin{array}{c}\xi=\{\text { integers between } 1 \\ \text { and } 10 \text { inclusive }\} \\ P=\{\text { odd numbers }\} \\ Q=\{\text ... | NO_MATCH | null | **1. Analyze the sets:**
* $\xi = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$
* $P = \{\text{odd numbers}\} = \{1, 3, 5, 7, 9\}$
* $Q = \{\text{factors of 30 within } \xi\} = \{1, 2, 3, 5, 6, 10\}$
**2. Identify the regions of the Venn diagram:**
* **Region A (P only):** Elements in $P$ but not in $Q$ $\rightarrow \{7,... |
Decide whether the misconception explains the student's wrong answer.
Question context:
Given a situation sketch an appropriate real life graph Currency Conversions \( £ 1 \) is \( 1.5 \) US dollars.
Which of these graphs shows the value of up to \( £ 10 \) in US dollars?
Student's wrong answer:
![A straight horizont... | NO_MATCH | null | NO_MATCH
The student's answer is a horizontal line at $y = 15$. This indicates that the student calculated the maximum value (£10 = $15) and plotted it as a constant, failing to understand that the value in US dollars should increase proportionally with the amount in Pounds.
The candidate misconception is "Believes a... |
Decide whether the misconception explains the student's wrong answer.
Question context:
Solve one-step linear inequalities in one variable where the variable appears on one side of the equation Solving Linear Inequalities Solve the inequality:
\(-\frac{1}{3} y \leq-6\)
Student's wrong answer:
\( y \geq 2 \)
Candidat... | NO_MATCH | null | NO_MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
Solve problems that combine addition and subtraction Written Subtraction At the start of the day, there was \( £ 1,456 \) in the till. \( £ 7,347 \) was taken and \( £ 4,377 \) was handed out. How much money was left?
Student's wr... | MATCH | null | MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
Identify mathematical instruments and their functions Construct Angle What is the name of the mathematical instrument used to construct circles?
Student's wrong answer:
Slide rule
Candidate misconception:
Does not know the meanin... | NO_MATCH | null | NO_MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
Solve two-step linear equations, with the variable on one side, with all positive integers Linear Equations Jo and Paul are arguing about a first step to solve this equation:
\(
\frac{m}{6}-4=24
\)
Jo says you can write: \( \frac{m... | NO_MATCH | null | NO_MATCH
The student's answer "Both Jo and Paul" indicates they believe both proposed first steps are algebraically valid. Jo's step ($\frac{m}{6}=28$) is correct, as she added 4 to both sides. Paul's step ($m-4=144$) is incorrect because he multiplied $\frac{m}{6}$ and $24$ by $6$, but failed to multiply the $-4$ by ... |
Decide whether the misconception explains the student's wrong answer.
Question context:
Solve quadratic equations using the quadratic formula where the coefficient of x² is not 1 Quadratic Equations Which option gives a correct substitution into the quadratic formula to solve the quadratic equation? \( 2 x^{2}-8 x+7=... | NO_MATCH | null | NO_MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
Use a linear sequence expressed as a pattern to make a prediction about another term in the sequence other than the next one Sequences-Others What is the 7th pattern in this sequence? ![Three consecutive patterns in a sequence. The... | NO_MATCH | null | The sequence follows the pattern of odd numbers: 1, 3, 5, ...
The formula for the $n$-th term is $2n - 1$.
The question asks for the **7th** pattern.
The correct answer is $2(7) - 1 = 13$ squares.
The student's answer shows **11** squares.
Using the formula: $2n - 1 = 11 \Rightarrow 2n = 12 \Rightarrow n = 6$.
This me... |
Decide whether the misconception explains the student's wrong answer.
Question context:
Identify a radius Parts of a Circle What is the correct name for the line marked on the circle? ![A circle with a line from the centre of the circle to the circumference.]()
Student's wrong answer:
Diameter
Candidate misconceptio... | NO_MATCH | null | NO_MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
Factorise a quadratic expression in the form x² + bx + c Factorising into a Double Bracket Factorise \( x^{2}+20 x+64 \)
Student's wrong answer:
\( (x+14)(x+6) \)
Candidate misconception:
Believes that when factorising a quadrati... | NO_MATCH | null | MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
Identify the line of symmetry of curves in the form (x + a)(x + b) Quadratic Graphs-Others This is the graph of
\(y=(x+1)(x-3)\) ![A set of axes with the graph y=(x+1)(x-3) drawn on.]() What is the equation of the line of symmetry?... | NO_MATCH | null | MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
Given the area of a trapezium, calculate a missing dimension Area of Simple Shapes The area of this trapezium is \( 40 \mathrm{~cm}^{2} \). What would the perpendicular height, \( h \), of the trapezium be? ![Trapezium with paralle... | NO_MATCH | null | NO_MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
Recognise when a square root is a surd and when it is not Simplifying Surds Which of the following is not a surd?
Student's wrong answer:
\( \sqrt{45} \)
Candidate misconception:
When simplifying surds, does not understand that t... | NO_MATCH | null | NO_MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
Rotate an object or point 900 clockwise or anticlockwise about a point, where the point lies on the edge or outside of the object Rotation John rotates rectangle \( A B C D 90^{\circ} \) clockwise from the centre \( (3,2) \). What ... | MATCH | null | **Step 1 — Compare: Analyze all responses across three dimensions:**
- **Content accuracy & completeness:** All four responses correctly identify the answer as "MATCH". They all accurately analyze the coordinates to note the change in orientation (from a vertical to a horizontal rectangle) and correctly link this to t... |
Decide whether the misconception explains the student's wrong answer.
Question context:
Solve quadratic equations using balancing Quadratic Equations One of these equations has no real solutions.
Which is it?
Student's wrong answer:
\( t^{3}=-45 \)
Candidate misconception:
Believes a negative power results in a nega... | NO_MATCH | null | NO_MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
Simplify an algebraic fraction by factorising both the numerator and denominator Simplifying Algebraic Fractions Write the following as simply as possible: \( \frac{6 p-9}{6 p-3} \)
Student's wrong answer:
\( \frac{p-3}{p-1} \)
C... | NO_MATCH | null | MATCH
**Analysis:**
1. **Correct Simplification:**
The expression is $\frac{6p - 9}{6p - 3}$.
Factor out the greatest common divisor from the numerator and denominator:
Numerator: $3(2p - 3)$
Denominator: $3(2p - 1)$
Simplified fraction: $\frac{3(2p - 3)}{3(2p - 1)} = \frac{2p - 3}{2p - 1}$.
2. ... |
Decide whether the misconception explains the student's wrong answer.
Question context:
Recognise cube numbers Square Roots, Cube Roots, etc What is the first cube number greater than \( 100 ? \)
Student's wrong answer:
\( 121 \)
Candidate misconception:
Mixes up square numbers and prime numbers
Does this misconcep... | NO_MATCH | null | NO_MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
Calculate the mode as an average from a list of data when there are two or more modes Averages (mean, median, mode) from a List of Data What is the mode of the following numbers?
\[
1,1,4,6,7,7
\]
Student's wrong answer:
\( 4 \)
... | NO_MATCH | null | NO_MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
Find missing angles using angles on a straight line Basic Angle Facts (straight line, opposite, around a point, etc) What is the size of angle \( q \) ? ![A long straight line with two shorter lines joining it, but not crossing it.... | NO_MATCH | null | MATCH
**Explanation:**
1. **Correct Method:** The angle \(q\) and the \(126^\circ\) angle are adjacent angles on a straight line. Therefore, they add up to \(180^\circ\). The correct calculation is \(q = 180^\circ - 126^\circ = 54^\circ\).
2. **Student's Answer:** The student answered \(37^\circ\), which is the value ... |
Decide whether the misconception explains the student's wrong answer.
Question context:
Round integers to the nearest other power of 10 Rounding to the Nearest Whole (10, 100, etc) What is \( 875,599 \) rounded to the nearest \( 10,000 \) ?
Student's wrong answer:
\( 870,000 \)
Candidate misconception:
Rounds up ins... | NO_MATCH | null | NO_MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
Identify alternate angles Angle Facts with Parallel Lines Tom and Katie are arguing about alternate angles.
Tom says angles \( p \) and \( q \) are alternate.
Katie says angles \( p \) and \( q \) are equal.
Who is correct? ![Show... | NO_MATCH | null | NO_MATCH
**Reasoning:**
1. **The Question:** The student is asked who is correct between Tom and Katie. Tom identifies angles \( p \) and \( q \) as "alternate," while Katie identifies them as "equal." Since the lines are **not parallel**, the angles are alternate (Tom is correct) but they are **not equal** (Katie is ... |
Decide whether the misconception explains the student's wrong answer.
Question context:
Convert two digit integer percentages to fractions Converting between Fractions and Percentages Convert this percentage to a fraction
\( 62 \% \)
Student's wrong answer:
None of these
Candidate misconception:
Does not understand ... | NO_MATCH | null | NO_MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
Use a linear sequence expressed as a pattern to make a prediction about another term in the sequence other than the next one Linear Sequences (nth term) Without drawing any more terms, how many circles do you predict will be in the... | NO_MATCH | null | MATCH
**Reasoning:**
1. **Analyze the Sequence:** The sequence of circles is 6, 10, 14. This is an arithmetic sequence with a common difference of 4.
* Term 1: 6
* Term 2: 10
* Term 3: 14
* Term 4: 18
* Term 5: 22
2. **Analyze the Question Requirement:** The question asks for the **5th ... |
Decide whether the misconception explains the student's wrong answer.
Question context:
Understand the relationship between different factors of a number Factors and Highest Common Factor If you can connect dots to draw a regular octagon in a ring of equally spaced dots, which other regular shape can you definitely dr... | MATCH | null | NO_MATCH
The student's wrong answer is "Hexagon" (6 sides). The correct answer is a "Square" (4 sides), because if a regular octagon (8 sides) can be drawn on a ring of equally spaced dots, the total number of dots must be a multiple of 8. Since 4 is a factor of 8, the number of dots is also a multiple of 4, meaning a... |
Decide whether the misconception explains the student's wrong answer.
Question context:
Answer fraction problems that require the use of BIDMAS BIDMAS \( \frac{3}{4}-\frac{1}{4} \times \frac{1}{5}= \)
Student's wrong answer:
\( \frac{1}{10} \)
Candidate misconception:
Carries out operations from left to right regard... | NO_MATCH | null | MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
Interpret a pictogram involving fractions of symbols Pictogram ![A pictogram where one smiley face =8 people. Game 1 has 4 faces. Game 2 has 3 faces. Game 3 has 2 faces. Game 4 has 2.75 faces.]() The pictogram shows the number of p... | MATCH | null | MATCH |
Decide whether the misconception explains the student's wrong answer.
Question context:
Given the solution to one problem, deduce the answer to a related problem using the same operation Mental Addition and Subtraction Tom and Katie are discussing related calculations
Tom says if you know that \( 3748+426=4174 \), the... | MATCH | null | To determine if the misconception explains the student's wrong answer, let's analyze the problem and the student's response.
**1. Analyze the Question:**
* **Tom's claim:** If $3748 + 426 = 4174$, then $3748 + 427 = 4175$.
* Tom is adding 1 to the second addend ($426 \to 427$), so he adds 1 to the result ($417... |
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