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

Calculate the value of 7.1 Give your answer as a decimal to 5 significant figures.

The nth term of a sequence is given by 12 − 7 n Find the first 3 terms of this sequence …………… , …………… , ……………

Find the size of an interior angle of a regular polygon with 30 sides

…………… °

Without using a calculator and showing all your working, evaluate 2 4 5 −2 3 5 Give your answer as a mixed number in its simplest form.

The diagram shows the right-angled triangle ABC AB = 20 cm BC = 42.5 cm BAC Calculate the length of AC cm

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: B, A, C · Figure values: 42.5, 20.

Make d the subject of g 5d 4e 2

On the number line below represent the inequality 4 ≤ x x −5 −4 −3 −2 −1 0 1 2 3 4 5

Write down the value of p 0 where p > 0

Simplify fully 32q r 20 5 5

Students travel to college by bus or by car or by train so that the number who travel by bus : the number who travel by train = 9 : 2 the number who travel by train : the number who travel by car = 3 : 5 Given that 600 students travel to college by car, calculate the number of students who travel to college by bus.

The numbers $D$, $E$ and $F$ are given as products of their prime factors

$D = 2^9 \times 3^x$

$E = 2^2 \times 3^{x+1}$

$F = 2^4 \times 3^{2x+1} \times 7^{x+1}$

where $x$ is a positive integer.

Find the Highest Common Factor (HCF) of $D$ and $E$

Give your answer in terms of $x$ as a product of prime factors.

Find the Lowest Common Multiple (LCM) of $E$ and $F$

Give your answer in terms of $x$ as a product of prime factors.

Given that $x$ is even,

find the least number that $F$ must be multiplied by to give a square number.

Without using a calculator and showing all your working, find the value of the integer m such that 675 108 m m =

Solve 4 3 Show clear algebraic working. x = ……………Solve 4 3 Show clear algebraic working. x =

In the diagram A, B, C and D are points on a circle. AEC is a diameter of the circle. BED is a chord of the circle. AE = 5 cm BE = 7 cm ED = 13 cm Calculate, in cm, the radius of the circle cm

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: B, C, E, A, D · Figure values: 7, 5, 13.

Distance travelled (metres) 60 0 1 2 3 4 5 6 Time (t seconds) The graph shows the distance travelled by a car at time t seconds. By drawing a suitable straight line, estimate the speed of the car when t = 5 Give your answer in m/s to 2 significant figures m/s

Figure not shown in this reconstruction — the printed paper includes a diagram. Figure values: 120, 100.

x° U S T R and T are two points on a circle, centre O STU is the tangent to the circle at the point T ROS is a straight line. OTR OST x Calculate the value of x Give reasons for each stage of your working. x =

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: R, O · Figure values: 28°.

Factorise fully $10p^2q^4 - 15p^3q$

Factorise $2x^2 - 9x - 5$

The diagram shows six solid spheres placed inside a hollow cuboid. The cuboid measures 16 cm by 24 cm by 8 cm Each sphere has a diameter of 8 cm Calculate the volume, in cm³ to 3 significant figures, of the space inside the cuboid that is not occupied by the spheres cm³

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Figure values: 8, 16, 24.

The incomplete table and the incomplete histogram give information about the number of minutes that 900 flights arrived late at an airport.

Complete the table and the histogram. Sam selects at random one of the 900 flights.

Find the probability that this flight was late by greater than 120 minutes.

f is directly proportional to g 2 f = 9 when g = 5 g is inversely proportional to h g = 5 when h = 4 Find a formula for f in terms of h

A solid right cylinder is made of wood. The mass of the cylinder is 2140 g, to the nearest 10 g The radius of the cylinder is 8.5 cm, to the nearest 0.5 cm The density of the wood is 0.7 g/cm³, to the nearest 0.1 g/cm³ mass Given that density = volume and taking the value of π as 3.142 calculate the lower bound, in cm to one decimal place, of the height of the cylinder. Show all your working cm

$\mathbf{A} = \begin{pmatrix} 2 & -3 \\ -5 & 10 \end{pmatrix}\qquad \mathbf{A} - \mathbf{B} = \begin{pmatrix} 1 & p \\ -2p & 4 \end{pmatrix}\qquad \mathbf{C} = \begin{pmatrix} 4 & -5 & 2 \\ -1 & 3 & 8 \end{pmatrix}$

Find matrix $\mathbf{B}$, giving the elements of $\mathbf{B}$ in terms of $p$ where appropriate.

Find $\mathbf{A}^{-1}$

Find $\mathbf{AC}$

Solve the simultaneous equations

$3x^2 - \dfrac{10}{3}x + 3 = 2y$

$2x + 3y = 4$

Show clear algebraic working.

The table shows information about the monthly wages of 100 employees at a company.

Calculate an estimate for the mean wage of the 100 employees. £ The mean number of hours worked by the 100 employees last week is 33 hours. The total number of hours worked by 91 of these employees last week is 2976 hours.

Find the mean number of hours worked last week by the remaining 9 employees hours

The diagram shows the position of two boats, A and B, and the position of a lighthouse L, which are all in the same horizontal plane. The bearing of A from L is 050° The bearing of B from L is 125° The distance of A from L is 15 km The distance of B from L is 22 km Calculate the bearing, to the nearest degree, of A from B Show your working clearly °

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: N, A, L, B · Figure values: 15, 22.

A Diagram NOT accurately drawn M N X O B The diagram shows triangle OAB such that = a and = 3b M is the midpoint of OA N is the point on AB such that AN : NB = 4 : 1

Express in terms of a and b

Express in terms of a and b Give your answer in its simplest form. Given that the point X is such that OXN and MXB are straight lines …………… , ……………

find a simplified expression for in terms of a and b

Solve the inequality $3x - 5 < 15 - 2x$

Solve the inequality $x(x - 1) > 6$ Show clear algebraic working.

Hence find the range of values of $x$ for which both $3x - 5 < 15 - 2x$ and $x(x - 1) > 6$