4MB1/02R — June 2026 (Edexcel IGCSE Maths): Past Paper

Anne owns 2400 grams of an alloy made of gold, silver and copper such that weight of gold : weight of silver : weight of copper = 15 : 3 : 2

Calculate the weight of gold in 2400 grams of the alloy. Anne sells 2400 grams of the alloy to Geoff at a rate of £29.51 per gram. Of the money Anne receives, she is charged 10% commission.

Show that Anne receives £63 700 to 3 significant figures, after she pays commission. Anne originally paid £56 000 for the alloy.

Calculate the percentage profit, to 3 significant figures, that Anne makes. Geoff uses 3600 grams of a different alloy to make n pieces of jewellery. of the pieces he makes are rings each weighing 6 grams. of the pieces he makes are bracelets each weighing 24 grams. The remainder of the 3600 grams of alloy is used to make necklaces each weighing 78 grams.

Find the value of n Diagram NOT accurately drawn h mm a mm a mm Figure 1 Figure 1 shows a solid made from an alloy by fixing a small cuboid on the flat top face of a large cuboid. The total volume of the solid is V mm³ The base of the large cuboid is a square with sides of length a mm The height of the large cuboid is h mm The volume of the small cuboid is U mm³ Given that a = 73.2 to 1 decimal place U = 900 to the nearest 10 V = 51860 to 4 significant figures

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

calculate the upper bound, to 3 significant figures, of h Show all your working.

Akine notices that the rate at which water leaves the hot tap of his bath is different to the rate at which water leaves the cold tap of his bath. The rate at which water leaves each tap is constant. When full, the bath holds 240 litres of water. It takes 12 minutes to fill the bath using just the cold tap. It takes 15 minutes to fill the bath using just the hot tap.

Calculate the time taken to fill Akine’s bath with water using both the hot tap and the cold tap at the same time. Give your answer in minutes and seconds. Water leaves the bath at a constant rate of 100 litres per minute.

Calculate the time taken for the 240 litres of water to leave the bath. Give your answer in minutes and seconds.

Diagram NOT E F accurately drawn D C G H 5 cm A 6 cm B Figure 2 Figure 2 shows a cuboid ABCDEFGH with horizontal base ABGH AB = 6cm BG = 5cm Given that the surface area of the cuboid is 236 cm²

show that the length of BC is 8 cm

Calculate, in cm to one decimal place, the length of AF

A particle P is moving along a straight line. At time t seconds the displacement, s metres, of P from a fixed point O on the line is given by s 5t 3 t 4 t ≥ 0 At time t seconds the acceleration of P is a m/s2 Find the value of a at the instant when P changes direction and starts moving towards the point O Show all your working.

Figure 3 shows two shapes, A and B 2x cm Diagram NOT accurately drawn 10 cm A 13 cm B x cm 10 cm 12 cm Figure 3 The corners of shape A are all right angles. Shape B is a right-angled triangle. The area of shape A is equal to the area of shape B Find, to 3 significant figures, the value of x

Diagram NOT accurately drawn D E 45° C 85° A B F Figure 4 In Figure 4 ABCD is a quadrilateral such that the points A, B, C and D lie on a circle. EAF is the tangent to the circle at the point A ∠BDC = 45° ∠ABC = 85° BD = 22 cm BC = 17 cm

Find the size, to the nearest degree, of the obtuse angle BCD

Find the size, to the nearest degree, of ∠BAD

Find the size, to the nearest degree, of ∠BAF Give a reason for each stage of your working. a b c Sine rule : sin A sin B sin C

Given that 33a =

show that 3a 4b Given that 4 a 2 b

show that 2a 3b

Solve the simultaneous equations 3x 4 y 2x 3y Show clear algebraic working.

Hence write down the value of a and the value of b that satisfy 3a 9 2b 1 3 = and 4 a 2 b 27 8

A bag contains only red counters, blue counters and green counters. The bag contains 15 counters. There are 5 red counters and 3 blue counters. A counter is taken at random from the bag.

Show that the probability of this counter being green is 15 A second counter is taken at random from the same bag without replacing the first counter.

Complete the tree diagram on the opposite page.

Calculate the probability that at least one of the two counters taken is green. first counter second counter Red Blue Red 5 Green Red Blue Blue Green Red Green Blue Green

Diagram NOT C accurately drawn M B N A E D Figure 5 Figure 5 shows a quadrilateral ABCD such that = 7a 4a 2b = 5b M is the midpoint of BC and N is the midpoint of CD

MC

CD

MN The point E is such that MNE and ADE are straight lines.

Using a vector method, find BE as a simplified expression in terms of a and b

Triangles A and B are drawn on the grid opposite. Triangle C has vertices at coordinates 1, 1 , 2, 1 and 2, 3

On the grid, draw and label triangle C Triangle A is transformed to triangle D under the translation

On the grid, draw and label triangle D Triangle B is transformed to triangle E by a rotation of 90° anticlockwise about the point 1, 0

On the grid, draw and label triangle E

Describe fully the single transformation that maps triangle A onto triangle B Triangle C is transformed to triangle F by an enlargement with scale factor −2 and centre of enlargement 0, 2

On the grid, draw and label triangle F

The functions f and h are defined as f : x ↦ 4 x 2 4 x 15 x x 2 h:xα x x 1

Find f 2

Solve the equation f x ax + b

Express hh x in the form where a, b, c and d are integers. cx + d

Find the inverse of the function f Give your answer in the form f −1 : x ↦ …

Find the domain of f −1

Complete the following table of values for $y = 5x^2 - 10 + \frac{1}{2x^2}$ Give values to 2 decimal places.

On the grid opposite, plot the points from your completed table and join them to form a smooth curve.

By drawing a straight line on the grid, find estimates, to one decimal place, of the solutions to the equation 5 x 2 9 x 13 2 0 in the interval 0.2 ≤ x ≤ 1.6