4MB1/02 — June 2023 (Edexcel IGCSE Maths): Past Paper

Colour Number of bricks red red 72° yellow green 50 Total 130 A bag contains red bricks, yellow bricks and green bricks only. The incomplete table and an incomplete pie chart give information about the colours of the bricks in the bag.

Find the number of red bricks. A box contains 9 red bricks and 6 green bricks only. Asha takes a brick from the bag and a brick from the box.

Complete the tree diagram opposite.

Calculate the probability that exactly one of the bricks is green. Bag Box 15 green green 130 not green green not green not green

A farmer grows 300 pumpkins. The pumpkins are small or medium or giant. It cost the farmer $1.25 to grow each small pumpkin. He sells each small pumpkin for $1.30

Calculate the percentage profit the farmer makes on each small pumpkin he sells. The farmer sells each medium pumpkin for 20% more than he sells each small pumpkin.

Calculate the price, in $, that the farmer sells each medium pumpkin for. Of the 300 pumpkins, 28% are small.

Calculate the number of small pumpkins the farmer grows. The remaining pumpkins are medium or giant. The ratio of medium pumpkins to giant pumpkins is 3 : 5

Calculate the number of giant pumpkins the farmer grows. The farmer sells all of his giant pumpkins for the same price. The farmer’s profit from giant pumpkins is 30% of the selling price of the first 50 giant pumpkins sold, 60% of the selling price of the next 40 giant pumpkins sold, 90% of the selling price of the remaining giant pumpkins sold.

Calculate the percentage of the total selling price of the giant pumpkins that is the farmer’s profit from giant pumpkins. Give your answer to the nearest whole number.

The table below shows information about the prices of secondhand cars for sale at a garage.

Calculate an estimate, in dollars, for the mean price of a secondhand car at this garage.

Each interior angle of a regular polygon is 172°

Calculate the number of sides of the polygon. The length of each side of the regular polygon is 5.2 cm to 2 significant figures.

Calculate, in cm² to 3 significant figures, the upper bound of the area of the polygon. Sum of interior angles of polygon 2n 4 right angles

Part of the curve C with equation y x 2 x is drawn on the grid. 2 2

By drawing a suitable straight line on the grid, find estimates, to one decimal place, for the solutions of the equation 1 1 x x 1 2 2 The equation of curve D is given by y x³ x 2 3x

Complete the table of values for y x³ x 2 3 x, giving your values to 2 decimal places where necessary. x −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 y 2 3 1.63 0 −1.13 6

On the grid opposite, plot the points from your completed table and join them to form a smooth curve. Curve C and curve D intersect twice in the range −2 ≤ x ≤ 2

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Use the text description to work through it.

Write down the coordinates, to one decimal place, of these 2 points of intersection.

Work out the equation of the line that passes through these 2 points of intersection. Give your answer in the form y = mx + c where the values of m and c are given to one decimal place. Show your working clearly.

The Venn diagram shows information about the numbers of students who play Rugby (R), Basketball (B) or Hockey (H). The number of students who do not play Basketball is 35

Use this information to complete the Venn diagram. E R B 4 6 H

n H B

n H B

n R B H One of the students is selected at random. Given that this student plays Hockey …………… , ……………

calculate the probability that they also play Rugby. m Give your answer in the form where m and n are integers. n

The functions f, g and h are defined as f : x ↦ x 2 − 2 x g : x 1 x 0 x 5x 4 h : x ↦ x x

Find f (−3)

Find the inverse function h 1, xgiving your answer in the form h −1 : x ↦ ... x

Solve fg(x) = −1 54

Figure 1 Figure 1 shows three points A, B and C on a circle with centre O where AOC is a diameter of the circle. The length of AB is 2 cm less than the length of BC Given that AC ≤ BC calculate the range of possible values for the length, in cm to one decimal place, of BC

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: A, B, O, C.

f ( x) 3 x³ ax 2 20 x b where a and b are integers. (x + 4) is a factor of f(x) (x − 2) is a factor of f(x)

Use the factor theorem to find the value of a and the value of b One solution of the equation 8 x³ 18 x 2 5 x 0 is

Without using a calculator and showing all your working, find the other 2 solutions of the equation. Give your answers in exact form.

Triangle A and triangle B are drawn on the grid opposite.

Describe fully the single transformation that maps triangle A onto triangle B Triangle A is transformed to triangle C under an enlargement with scale factor 3 and centre of enlargement (6, −2)

On the grid, draw and label triangle C Triangle A is transformed to triangle D under a reflection in the line with equation y = −3

On the grid, draw and label triangle D Triangle B is transformed to triangle E under the transformation with matrix P where k 1 P= k 3 0 Triangle E is transformed to triangle F under the transformation with matrix Q where k 1 Q= k 1 k Triangle F is the image of triangle B under the matrix N Given that the determinant of N is 2

find the coordinates of the vertices of triangle F.

[Determinant of matrix $\begin{pmatrix} a & b \\ c & d \end{pmatrix} = ad-bc$]

Differentiate 4 10t 6t 2 A rocket moves vertically so that at time t seconds, the velocity, v m/s is given by v 4 10t 6t 2

Find the time, in seconds, when the rocket stops accelerating vertically. The vertical displacement, d metres, of the rocket at time t seconds, is given by d 4t 5t 2 2t 3 t≥0 The rocket is launched from a height of k metres above horizontal ground. The height, in metres, above ground when the rocket is first instantaneously at rest is 20 metres.

Find the value of k

O Diagram NOT accurately drawn M N A C B Figure 2 → → Figure 2 shows the triangle OAB in which OA = 3a and OB = 15b → 1 → C is the point on AB such that AC AC == ABAB → 3 → N is the point on OC such that ON ON == OC OC →

Find and simplify an expression for BN in terms of a and b M is the point on OA such that B, N and M are collinear.

Find the ratio OM : MA Show your working clearly.