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

Factorise fully 9 x + 12 x 2 y

The diagram shows the position of two towns, J and K The bearing of J from K is 214° Find the bearing, in degrees, of K from J °

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: N, N, K, J · Figure values: 214°.

Make x the subject of t = 6(x + 4)

The price of a television is reduced by 8% in a sale. The price of the television in the sale is $1012 Calculate the price of the television before the sale. $

Simplify fully (4xy5)³ / 2xy

Given that, for all values of x, x 2 + 6 x − 15 = ( x + a )² − b where a and b are integers find the value of a and the value of b a = b =

In the diagram ABC and DEFG are parallel straight lines. ∠BEF = 56° and ∠CBF = 72° Find the size, in degrees, of ∠EBF Give reasons for each stage of your working. ∠EBF °

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: A, B, C, D, E, F, G · Figure values: 72°, 56°.

Here are the marks that 10 students scored in a test. 25 11 24 6 4 28 19 11 15 10

Write down the mode of these 10 marks.

Find the median of these 10 marks.

Solve the inequality 5 y < 20 + 3y 3 y

Represent the inequality x ≥ 1 on the number line below. x −5 −4 −3 −2 −1 0 1 2 3 4 5

The cost, including delivery, of a mobile phone in the UK is £624 The cost of an identical mobile phone in the USA is $448 plus an additional cost of $d for delivery. The cost, including delivery, of the mobile phone in the UK is £224 more than the cost, including delivery, of the mobile phone in the USA. Using the exchange rate £1 = $1.28 calculate the value of d d =

A and B are two points on horizontal ground. The distance from A to B is 1.5 kilometres BC is a vertical pole The angle CAB = 6° Calculate the height, in metres to 3 significant figures, of the pole metres

Solid A and solid B are similar. The surface area of solid A is 25 cm² The surface area of solid B is 900 cm² The volume of solid A is 50 cm³ Calculate the volume, in cm³, of solid B

…………… cm³

On a trip, a powerboat travels at an average speed of 40 km/h for 1 hour 18 minutes and then travels at an average speed of 22 km/h for 30 minutes. Calculate the average speed of the powerboat, in km/h, for the whole trip km/h

Xiou records the time, in minutes, it takes each of the 30 students in his class to complete the same puzzle. The table shows information about his results.

Calculate an estimate for the mean number of minutes that these students take to complete the puzzle

The points O, A and B are such that OA = (−1/5) and OB = (−4/2) The point C is such that |AC| = √125 and AC is parallel to OB Find BC Give your answer in the form (c/d) where c and d are integers such that c < 0 and d > 0 Show all your working. BC = ( )

OABC is a sector of a circle, centre O with ∠AOC = 120° The length of arc ABC is 17.2 cm Calculate the area, in cm² to 3 significant figures, of the sector cm²

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: A, B, O, C · Figure values: 120°.

Without using a calculator and showing all your working, express (4 + 2√7)/(3 − √7) in the form a + √b where a and b are integers.

B Diagram NOT accurately drawn 52° x° O A C D In the diagram A, B, C and D are points on a circle, centre O ∠ABC = 52° and the reflex angle AOC = x°

Find the size, in degrees, of ∠ADC Give a reason for your answer

…………… °

Find the value of x Give a reason for your answer. x =

Calculate 3.6 × 10103 × 7.5 × 10101 Give your answer in standard form. $c = 4 \times 10^{-8n}$ where n is an integer. −

Find an expression for $c^{-\frac{1}{2}}$ in terms of n Give your answer in standard form.

The width of a rectangle is x metres. The length of the rectangle is 8 metres longer than the width of the rectangle.

Find an expression in terms of x for the perimeter, in metres, of the rectangle. Simplify your answer m.

Factorise x 2 + 8 x − 20

Hence write down the range of values of x for which the area of the rectangle is greater than 20

…………… m²

The diagram shows a right solid pyramid ABCDE, made of silver, with horizontal rectangular base ABCD and vertex E AB = 9 cm to 1 significant figure. BC = 6.5 cm to the nearest 0.5 cm. The mass of the pyramid is 5080 grams to the nearest 10 grams. The density of the silver is 10.5 g/cm³ to 3 significant figures. mass Given that density = volume calculate the upper bound, in cm to 3 significant figures, of the perpendicular height of the pyramid. Show all your working cm

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

The weights, in grams, of tomatoes harvested by a gardener last month were measured. The incomplete table and incomplete histogram below give information about the weight, in grams, of each tomato harvested last month.

Show that y = 16 A tomato for which w ≤ 35 grams is classed as a small tomato. A small tomato is selected at random. The probability that this tomato weighs less than or equal to 15 grams is

Complete the histogram.

A = (−1/2 −2 / 0 1) BA⁻¹ = ( x −8 / 1 x ) where x > 0 Given that the determinant of matrix B⁻¹ is −1/6 find matrix B –1 Give the elements of this matrix as numbers. Show all your working. B⁻¹ = ( )

Solve the simultaneous equations 9 − xy = x² 4y − x = 11 Show clear algebraic working.

h cm H F G D X A C Y B A cube ABCDEFGH of side 6 cm is placed inside a hollow cone of height h cm. The face ABCD of the cube rests on the circular base of the cone. The vertices E, F, G and H of the cube touch the curved surface of the cone. X and Y are points on the circumference of the base of the cone such that XACY is a straight line. Given that XF = 134 cm find the value of h Show all your working. h =

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: E.

The function g is defined by g:x ↦ 3 − x < 0 x

Find g(−2)

Find the range of g

Express the inverse function g −1 in the form g −1 : x ↦ ... g −1 : x ↦ The function h is defined by h : x ↦ x<0 2x − 3 ax + b

Express the composite function gh in the form gh : x ↦ where a, b and c c are integers. gh : x ↦