4MB1/01R — June 2026 (Edexcel IGCSE Maths): Past Paper

Noah travels 18 km on his bicycle. The journey time is 45 minutes. Work out Noah’s average speed, in km/h, for the journey km/h

Without using a calculator and showing all your working, work out 2 1 1 +2 3 4 Give your answer as a mixed number in its simplest form.

E = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} A = {1, 3, 5, 7, 9} B = {3, 6, 9} Show all this information on the Venn diagram. E A B

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

A straight line L passes through the points with coordinates 6, 0 and 0, 8 Find an equation of L Give your answer in the form y mx c

Find the value of $\frac{a-b}{a^2+b^2}$ when a = 3 and b = −4

x cm accurately drawn D C 5 cm A B 10 cm The diagram shows trapezium ABCD where AB is parallel to DC AB = 10cm and DC = x cm The vertical height of the trapezium is 5 cm Given that the area of the trapezium is 45 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: D, C, A, B · Figure values: 5, 10.

A = $\begin{pmatrix} 1 & -1 \\ 3 & -4 \end{pmatrix}$ B = $\begin{pmatrix} 3 & 3 \\ -1 & 5 \end{pmatrix}$ C = $\begin{pmatrix} x & 2 \\ -2 & x \end{pmatrix}$ D = $\begin{pmatrix} 4 & 1 \\ 1 & -1 \end{pmatrix}$

(a) Find A + B

Given that A + C = D

(b) find the value of x

find the value of $x$ x =

Find the Highest Common Factor (HCF) of 24 and 54 Show all your working.

Find the Lowest Common Multiple (LCM) of 24 and 54

Solve the inequality 3 4 x

On the number line below, represent the inequality y < 2 y −5 −4 −3 −2 −1 0 1 2 3 4 5

y y=x+3 R x=4 x+y=4 O x Write down three inequalities that define the shaded region R in the diagram above.

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

OAB is a sector of a circle, centre O and radius 5 cm AOB 80° Calculate the perimeter, in cm to 2 significant figures, of the sector OAB cm

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: A, B, O · Figure values: 80°, 5.

The incomplete table and the incomplete histogram give information about the length of time, in minutes, that each of 100 students worked in a library.

Complete the table and the histogram.

The diagram shows a triangle. Diagram NOT accurately drawn x cm The vertical height of the triangle is 6 2 7 cm The length of the base of the triangle is x cm The area of the triangle is 1 7 cm Without using a calculator find the value of x Give your answer in the form a + b c where a, b and c are prime numbers. Show all your working. x =

The value of an investment increases by 20% to $1926

Find the value of the investment before the increase. $ Using an exchange rate of 1 euro = $1.07

change $1926 into euros euros

Calculate 9 10100 1.2 10101 Give your answer in standard form.

Calculate 9 10100 1.2 10101 Give your answer in standard form.

A large solid cylinder has a diameter of 12 cm and a height of 12 cm

Show that the volume of the cylinder is 432π cm³ Diagram NOT accurately drawn 12 cm 12 cm The diagram shows a large solid cylinder from which a small cylinder is removed. The volume of the solid formed is 416π cm³ Given that the small cylinder is similar to the large cylinder …………… , ……………

calculate the diameter of the small cylinder cm

Simplify fully $\left(2x^2y^3\right)^3$

Write $\left(\frac{125p^{11}q}{375p^{15}q^3}\right)^{-2}$ in the form $ap^mq^n$ where a, m and n are integers.

The diagram shows triangle ABC

AC = (x + 1) cm BC = x cm ∠ABC = 90° ∠BAC = 20°

Calculate the length, in cm to 2 significant figures, of BC

cm

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: C, A, B · Figure values: 20° · Other figure text: 1).

Express as a single fraction in its simplest terms $\frac{x-5}{x-2}$ + $\frac{2x^2+9x+9}{3x^2+9x}$

f(x) = x³ + 7x² + 17x + 14

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

Given that f(x) = (x + 2)Q(x) where Q(x) is a quadratic expression in x

(b) find Q(x)

find $Q(x)$ $Q(x) =$

Shape A is transformed to shape B under the transformation with matrix M where 1 1 M Shape B is transformed to shape C under the transformation with matrix N where N Shape C is transformed to shape A under the transformation with matrix P Find the matrix P P

A bag contains only red buttons, green buttons, blue buttons and yellow buttons. The table shows information about the probability that when a button is taken at random from the bag it is red or green or blue or yellow.

Find the value of x x = There are 340 buttons in the bag.

Find the number of red buttons in the bag. Roya takes at random two buttons from the bag without replacement. Given that the first button Roya takes is not green …………… , ……………

calculate the probability that both buttons Roya takes are red. Show all your working.

The curve with equation y = x³ − 15x + 5 has two stationary points.

Find the exact coordinates of each of these stationary points.

Diagram NOT accurately drawn B O A P 12 cm C Q In the diagram, A, B and C are points on a circle, centre O PCQ is the tangent to the circle at C QB is the tangent to the circle at B PAOB is a straight line. PB = 18cm PC = 12 cm

Calculate the radius, in cm, of the circle cm

Calculate the length, in cm, of QB cm

The points O, A, B and C are such that OB = 13 AB is parallel to OC Given that the x coordinate of B is negative, find the exact coordinates of the point B ( …………… , …………… )

The diagram shows a right pyramid ABCDE with horizontal rectangular base ABCD O is the centre of the base. Vertex E is vertically above O such that AE = BE = CE = DE AB = 64cm BC = 48cm EO = 9cm M is the midpoint of AD Calculate the size, to the nearest degree, of angle CEM °

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: E, D, C, M, O, A, B · Figure values: 9, 48, 64.

A regular polygon P has (x + 2) sides.

(a) Write down, in terms of x, an expression for the size, in degrees, of each exterior angle of P

A regular polygon Q has x sides.

The size of each exterior angle of polygon Q is 9° greater than the size of each exterior angle of polygon P

Show that $x^2 + 2x - 80 = 0$

Calculate the value of x Show clear algebraic working.