4MB1/02R — June 2025 (Edexcel IGCSE Maths): Past Paper

Solve the simultaneous equations 3x 4 y 4x 7 y Show clear algebraic working.

A B D C The diagram shows quadrilateral ABCD

Construct the locus of all points that are 4 cm from C

Using ruler and compasses only and showing all your construction lines, construct the perpendicular bisector of AD The region R consists of all the points inside the quadrilateral that are less than 4 cm from C and nearer to A than to D

Show, by shading, the region R Label the region R

Diagram NOT accurately drawn F G E D C B A Figure 1 Figure 1 shows part of a regular 20-sided polygon in which AB, BC, CD, DE, EF and FG are six of the sides.

Find the size, in degrees, of angle ABC

Find the size, in degrees, of angle EGA Sum of interior angles of a polygon 2n 4 right angles

The nth term of a sequence is given by 2n 2 − 5

Find the difference between the 3rd term and the 7th term of the sequence. A different sequence is generated. After the first term the sequence is generated by using the rule “multiply the previous term by d and then add 2” The first term of the sequence is 2 x 1 The second term of the sequence is 4 x 9 The third term of the sequence is 20 x 11 Given that 2 x 1

find the value of d Show all your working.

A large rental company has cars, vans and minibuses available to rent. The cost to rent a minibus from the company is found by adding $1000 rental fee $400 for each day the minibus is rented $0.8 per kilometre the minibus travels during the time it is rented This cost is reduced by n% if the minibus is a hybrid vehicle. The total cost of hiring 3 minibuses that are hybrid vehicles for 7 days is $10 584 Given that each minibus travels a total distance of 500 kilometres during these 7 days

find the value of n Show all your working. The number of cars the company owns is the Highest Common Factor (HCF) of 2 2 × 35 × 53 and 25 × 32 × 55 × 7

Find the number of cars the company owns. The number of cars that are hybrid vehicles is the least value of N such that when N is divided by 120 the remainder is 7 and when N is divided by 504 the remainder is 7

Find the number of cars that are hybrid vehicles. The company owns 200 vans and minibuses in total. Each van and each minibus is either an electric vehicle or a hybrid vehicle. The ratio of the number of vans to the number of minibuses is 5 : 3 40% of the vans are hybrid vehicles. of the minibuses are hybrid vehicles.

Express the total number of vans and minibuses which are hybrid vehicles as a percentage of the total number of vans and minibuses. Show your working clearly.

A group of 90 students were asked if they own any of a dog (D), a cat (C) or a horse (H) Of these 90 students 4 own all three 14 own a dog and a cat 7 own a cat and a horse 26 own a dog only 2 own a horse only 6 own none of these animals Let x be the number of these students who own a cat only.

Show all this information on the Venn diagram, giving the number of students in each appropriate subset, in terms of x where necessary. E C D H The number of these students who own a cat is 37 more than the number of these students who own a horse.

Find the value of x

Find n D H

Find n C D

Triangle A and triangle B are drawn on the grid opposite. Triangle A is transformed to triangle C under the translation

On the grid, draw and label triangle C Triangle A is transformed to triangle D under a reflection in the line with equation x = 4

On the grid, draw and label triangle D Triangle B is the image of triangle A under an enlargement with centre the origin and scale factor 5 followed by a clockwise rotation of θ° about the origin.

Calculate the value, to 4 significant figures, of θ Show your working.

Table 1 gives information about the probability that a biased red six-sided dice will land on each of the numbers 1, 2, 5, 7, 9, 11

Table 1

Calvin rolls the red dice once.

either the number 2 or the number 5

an odd number

a number less than 8 Pabel rolls the red dice twice.

Calculate the probability that the red dice lands on the numbers 2 and 5 Tai rolls the red dice 80 times.

Calculate the expected number of times the red dice lands on a number less than 5 A biased blue six-sided dice has faces numbered 2, 4, 6, 8, 10, 12 The probability that the blue dice lands on the number 2 is 0.24 The probability that the blue dice lands on the number 4 is 0.12 In a game Tai rolls the red dice once and the blue dice once. The number that the red dice lands on is added to the number that the blue dice lands on to give his score in the game. Given that his score is less than 6

find the probability that the red dice lands on the number 2

Diagram NOT accurately drawn E F D C G H A B Figure 2 Figure 2 shows a solid made by joining a half cylinder to a prism. The plane face of the half cylinder coincides with the top face of the prism. The rectangular base ABGH of the solid is horizontal. The cross section ABCD of the prism is a trapezium such that AB is parallel to DC AB = 26 cm DC = 10 cm BG = 20 cm AD = BC = 17 cm The perpendicular height of the trapezium ABCD is 15 cm

Calculate, in cm² to 2 significant figures, the total surface area of the solid. Show all your working. O is the midpoint of EF N is the point on the edge of the half cylinder vertically above O

Calculate the size, in degrees to 3 significant figures, of ∠AON Area of trapezium = 2 (a b)h

B Diagram NOT accurately drawn N C O M A Figure 3 Figure 3 shows triangle OAB where = 10a and = 5b M is the midpoint of OA The point N lies on the line AB such that AN = AB

Find an expression for in terms of a and b Give your answer in its simplest form. The point C lies on BM such that BC : BM = 3 : 4 The area of triangle OBM = 45 cm² Given that a= b= 2 cm

find the length, in cm to 3 significant figures, of OC a b c Sine Rule sin A sin B sin c Cosine Rule a b c 2bc cos A 2 2 2 Area of triangle ab sin C

The curve C has equation f x 2 x 3 x 2 5 x

Use the factor theorem to show that x 2 is a factor of f x

Hence find the x coordinate of each point where curve C crosses the x-axis. Show clear algebraic working. The curve C has two turning points. The x coordinates of the turning points are such that 6 x 2 2 x 5

Find the coordinates, to 2 decimal places, of these two turning points. Show your working clearly.

Complete the table of values for y f x x −1.5 −0.75 0 0.75 1.5 2.25 y 0.3 −2 −5.5 4.5

On the grid opposite, plot the points where curve C crosses the x-axis, the two turning points and all the points from your completed table.

Solutions of $ax^2 + bx + c = 0$ are $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Join all the points to form a smooth curve.

By drawing a suitable line on the grid, find estimates to one decimal place, of the solutions to the equation 2 x 3 x 2 3x 0 in the interval −1.5 ≤ x ≤ 2.25

Solutions of $ax^2 + bx + c = 0$ are $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

By drawing a suitable line (at least 3 cm long) on the grid, find the gradient of curve C at the point where x = 1.5.

Solutions of $ax^2 + bx + c = 0$ are $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

A particle P is moving along a straight line. At time t seconds, the displacement, x metres, of P from a fixed point O on the line is x k (48t t 3 ) where k is a constant. When t = 2 , the particle P is at the point A on the line. P is instantaneously at rest at the point B on the line. Given that AB = 5 metres calculate the distance, in metres, of P from O when t = 2 Show all your working.