O Level Mathematics 4024 Paper 12, May/June 2025

$6-2\times (-4)$

$80\times 0.2$

$\frac{2}{9}÷\frac{5}{6}$

yellow

not blue.

Find the actual distance between village A and village B.

Village C is on a bearing of 060° from village A. Village C is on a bearing of 320° from village B. Find and label the position of village C on the scale drawing.

$\sqrt[3]{125}$

4^{-2}

Complete the scatter diagram. The first 6 points have been plotted for you.

Draw a line of best fit.

Asha goes for another walk. She walks a distance of $6.8\text{ km}$. Use your line of best fit to estimate the time Asha takes for this walk.

Write 228 as a product of its prime factors.

228^2 = 51984 Write 51984 as a product of its prime factors.

The total mass of 4 small boxes and 6 large boxes is $30\text{ kg}$. Show that $2x+3y=15$.

The total mass of 6 small boxes and 1 large box is $13\text{ kg}$. Use this information to write down an equation in terms of $x$ and $y$.

Solve the simultaneous equations to find the mass of a small box and the mass of a large box. You must show all your working.

Describe fully the single transformation that maps triangle A onto triangle B.

Draw the image of triangle A after a reflection in the line $x=-1$.

Triangle A is enlarged with scale factor $k$ and centre $(0,0)$. Triangle C is the image of triangle A after the enlargement. The coordinates of one vertex of triangle C are $(12,3)$. Find the value of $k$.

Find the coordinates of the other two vertices of triangle C.

A coat costs $85 before the sale. Work out the sale price of the coat.

The sale price of a shirt is $40. Work out the cost of the shirt before the sale.

Find the column vector $\overrightarrow{AB}$.

Find the coordinates of point C.

ABCD is a trapezium. AB is parallel to DC and $AB=2DC$. Find the coordinates of point D.

Find the length of line AD. Give your answer as a surd in its simplest form.

Simplify. $$\sqrt{175}-\sqrt{28}$$

Rationalise the denominator. $$\frac{1}{\sqrt{5}}$$

Use the cumulative frequency diagram to find an estimate of the median

Use the cumulative frequency diagram to find an estimate of the interquartile range

Use the cumulative frequency diagram to find an estimate of the number of people who had a journey time of 40 minutes or more.

Each of the 80 people also record their journey time from work to home that day. The table shows the results.

Jay says: “The journey times from home to work are more consistent than the journey times from work to home.” Is Jay correct? Explain how you decide.

Rearrange $5y+3x=10$ to make $y$ the subject.

Line P is perpendicular to line L. Line P passes through the point $(6,7)$. Find the equation of line P.

Describe the motion of the cyclist between $t=40$ and $t=100$.

The acceleration of the cyclist between $t=0$ and $t=40$ is $0.25{\text{ m/s}}^2$. Show that $v=10$.

The total distance travelled by the cyclist between $t=0$ and $t=T$ is $1.4\text{ km}$. Find the value of $T$.

Find $\overrightarrow{AX}$. Give your answer in its simplest form in terms of $\mathbf{a}$ and $\mathbf{b}$.

Find $\overrightarrow{XC}$. Give your answer in its simplest form in terms of $\mathbf{a}$ and $\mathbf{b}$.

Write $x^2+4x-12$ in the form $(x+a{)}^2+b$.

Use your answer to part (a) to find the coordinates of the turning point of the graph of $y=x^2+4x-12$.

Sketch the graph of $y=x^2+4x-12$ indicating the values where the graph crosses the axes.