4MB1/01 — October 2025 (Edexcel IGCSE Maths): Past Paper

The nth term of a sequence is given by 5n2 – 2n Find the difference between the 3rd term and the 4th term of this sequence.

Make h the subject of k

Without using a calculator and showing all your working, evaluate 5 2 1 ×2 6 5 Give your answer as a mixed number in its simplest form.

Write down the order of rotational symmetry of a regular hexagon. A shape is made from a regular hexagon and a square. The vertices of the square lie on the sides of the hexagon.

For this shape, write down the number of lines of symmetry.

Using ruler and compasses only and showing all your construction lines, construct the perpendicular bisector of AB A B

The bearing of point P from point Q is 304° Calculate the bearing of point Q from point P

…………… °

Find the value of when p = 2 and q = –5 2 p

Given that y = x³ + 2x2 – 15x + 7 dy find dx dy = ……………dx

Given that y = x³ + 2x2 – 15x + 7 dy find dx dy = dx

Here are eight numbers. 15 30 18 12 23 19 16 23

Write down the mode.

Find the median.

The probability that Charlie arrives late to school is 0.35

Write down the probability that Charlie does not arrive late to school. Charlie attends school 20 times during January.

Calculate the expected number of times that Charlie arrives late to school during January.

A B 7m 4 Find 3A – B Give each element of the matrix in terms of m where appropriate.

A straight line L passes through the points with coordinates (4, 3) and (6, –8) Find an equation of L in the form y = mx + c

P, Q and R are three points on a circle, centre O ∠POR = 124° Calculate the size, in degrees, of ∠PQR Give reasons for each stage of your working. ∠PQR = °

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: O, P, R, Q · Figure values: 124.

The diagram shows a square ABCD M is the midpoint of AD N is the midpoint of AB Prove that △DAN is congruent to △CDM

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

Without using a calculator and showing all your working, express 11 2 3 2 in the form a + b 2 where a and b are integers.

Write 3x2 + 24x + 1 in the form a(x + b)² + c where a, b and c are integers.

Expand and simplify 3c(2 – 5c) – 2c(5c + 1)

Factorise fully 2de5 – 9de2

C x cm D Diagram NOT accurately drawn A 6 cm B E 6 cm F 14 cm 10 cm 10 cm H 5x cm G The diagram shows a shape ABCDEFGH HG = 5x cm CD = x cm AH = FG = 10 cm AB = EF = 6 cm ∠BAH = ∠AHG = ∠HGF = ∠GFE = 90° CD is parallel to HG The perpendicular height of the shape is 14 cm The area of the shape ABCDEFGH is 534 cm² Find the value of x x =

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: C, D, A, B, E, F, H, G · Figure values: 6, 6, 14, 10, 10 · Other figure text: 5x.

Find the two values of x such that 2 81x 2 x 4x 6 8x Show clear algebraic working. x =

Emma asks 420 students to choose one type of movie from Horror, Adventure and Comedy. 5% of the students choose Horror. of the students choose Adventure. The remaining students choose Comedy. The students who choose Comedy are put into either group A or group B For the students who choose Comedy number in group A : number in group B = 1 : 6 Calculate the number of students who choose Comedy and are in group B Show all your working.

The table shows information about the number of points scored by people in a game.

Given that the mean number of points scored is 15.6 seconds

calculate the value of x Show all your working. x = One of the people is chosen at random.

Calculate the probability that this person scored more than 16 points.

E = {3, 4, 5, 6, 7, 8, 9, 10, 11, 12} A = {multiples of 4} B = {factors of 12} C = {prime numbers}

Complete the Venn diagram for this information showing the position of each of the numbers in the universal set. E B A C

Find n(A′∩ B′ ∩ C′)

Find n(A ∪ B′) A number is chosen at random from the universal set, E

Find the probability that this number is in the set A ∪ C

Diagram NOT accurately drawn B A C 24 cm The diagram shows a semicircle with diameter 24 cm The diagram also shows three congruent circles A, B and C inside the semicircle. All three circles touch the circumference of the semicircle and circle B touches both circle A and circle C The diameter of the semicircle is a tangent to circle A and circle C The radius of each of the circles is r cm

Show that r = 4

Calculate the total area, in cm² to 3 significant figures, of the shaded region

…………… cm²

Express 2 2 as a single fraction in its simplest form. x 3x 2 x 1 2 x x 1 Show clear algebraic working.

The diagram shows a solid shape made by fixing the flat circular face of a solid hemisphere, with radius 5 cm, to a solid right circular cone with base radius 5 cm The centre of the circular face of the hemisphere coincides with the centre of the base of the cone. 550 The total volume of the solid is π cm³ Find the total surface area, in cm² to 3 significant figures, of the solid. Show all your working cm²

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Figure values: 5.

D Diagram NOT accurately drawn B A P O C The diagram shows a quadrilateral OABC → → → OA = 2a OC = 3b AB = a + 2b The point P is on the line CB such that CP : PB = 4 : 1 The point D is such that ABD and OPD are straight lines. →

Find AC in terms of a and b → AC = →

Find OP in terms of a and b Give your answer in its simplest form. → OP =

Using a vector method find the ratio OP : PD Show all your working.

(2x – 1) is a factor of 6x3 + 17x2 + ax – 8 where a is a constant.

Use the factor theorem to show that a = 6

Hence, factorise fully 6x3 + 17x2 + 6x – 8 Show all your working.

Hence, solve 6(3y + 1)³ + 17(3y + 1)² + 6(3y + 1) – 8 = 0 Show all your working. y =