4MB1/01 — January 2022 (Edexcel IGCSE Maths): Past Paper

Find the Lowest Common Multiple (LCM) of 180 and 198 Show your working clearly.

Factorise fully 6 p 3 q 5 r − 15 pq 3

Find the value of when a = − 2 and b = −3 b

The diagram shows the right-angled triangle in which AB = 15 cm BC = 8 cm ∠ ACB = 90° Calculate the size, in degrees to 3 significant figures, of ∠ ABC ° ∠ ABC =

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: A, C, B · Figure values: 15, 8.

B = Calculate 4A − 3B

The nth term of a sequence is given by 3n − 5

Write down the first two terms of this sequence , The mth term of this sequence is 103

Find the value of m m =

A straight line L passes through the points with coordinates (4, 8) and (0, −6) Find an equation of L Give your answer in the form y = mx + c

OAB is a sector of a circle, centre O and radius 6.5 cm ∠ AOB = 55° Calculate the perimeter, in cm to 3 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, O, B · Figure values: 6.5, 55°.

Simplify (25 x 4 y 2 ) 2 25 x 3

In the diagram, triangles ABC and ABD are such that AD = BC and ∠ BAD = ∠ ABC Prove that AC = BD

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

solid is made by joining a hemisphere, of diameter 18 cm, to a right circular cone whose base has a diameter of 18 cm. The height of the cone is 24 cm. The plane face of the cone coincides with the plane face of the hemisphere. Calculate the volume, in cm³, of the solid. Give your answer in terms of π cm³

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: A · Figure values: 24, 18.

Given that y = where x ≠ 0 x dy find dx dy = ……………dx

Given that y = where x ≠ 0 x dy find dx dy = dx

Without using a calculator and showing your working clearly, express 432 − 147 in the form n where n is an integer.

A and B are two similar solids. The volume of A is 500 cm³ The volume of B is 32 cm³ The total surface area of A is 250 cm² Calculate the total surface area, in cm², of B

…………… cm²

The table gives information about the weights, in grams, of 40 adult mice.

Calculate an estimate for the mean weight, in grams to 3 significant figures, of these adult mice grams One of these adult mice is selected at random.

Find the probability that this mouse weighs less than 22 grams.

Andrew borrowed some money from Sarah. He borrowed $21 250 on 1st January 2018 On 31st December each year, starting on 31st December 2018, Sarah charged Andrew interest of 4% on the amount of money that he owed her. This interest was added to the amount of money that Andrew owed Sarah. On 1st January each year, starting on 1st January 2019, Andrew repaid $4000 to Sarah.

Show that before Andrew had repaid $4000 to Sarah on 1st January 2019, he owed Sarah $22 100 After Andrew had repaid $4000 to Sarah on 1st January 2020 …………… , ……………

calculate how much money Andrew now owed Sarah. $

fountain D C Scale: 1 cm represents 1 m The diagram shows a scale drawing of a garden in the shape of the rectangle ABCD. The position of a fountain in the garden is marked by a cross. Tarik is going to plant a tree in the garden. The tree must be less than 2 metres from AB, greater than 3 metres from the fountain, closer to AB than to AC. Using ruler and compasses only and showing all your construction lines, construct and show by shading the region in which Tarik can plant the tree. Label the region R.

Figure not shown in this reconstruction — the printed paper includes a diagram. Labels in the original figure: A, B.

The diagram shows a trapezium ABCD. ∠ ABC = ∠ BCD = 90° AB = 5 cm DC = 9 cm The area of the trapezium ABCD is 29.4 cm² Calculate the length, in cm, of AD cm

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: A, B, D, C · Figure values: 5, 9.

The sum of the interior angles of a regular polygon is 8280° Calculate the size, in degrees, of each exterior angle of the regular polygon.

…………… °

The numbers p and q are positive such that p is inversely proportional to q p = 420 when q = 9 Calculate the value of q when p = 28 q =

a cm A cm² C° b cm The diagram shows a triangle of area A cm² in which a = 5.2 to 1 decimal place b = 8.4 to 1 decimal place A = 13 to 2 significant figures. Given that the angle marked C ° is an acute angle, calculate the lower bound, to 3 significant figures, of C.

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

Express ÷⎜ − ⎟ as a single fraction in its simplest form. 6 x + 7 x − 10 ⎝ 5 x − 1 x + 2 ⎠ Show clear algebraic working.

A bag contains 20 balls. Each ball has either the number 5 on it or the number 6 on it. 5 6 There are 12 balls with the number 5 There are 8 balls with the number 6 Ben takes at random 2 balls from the bag.

Complete the probability tree diagram. First ball Second ball

Calculate the probability that the sum of the numbers on the two balls is greater than 10 Give your answer as a fraction.

The two digit number M has tens digit p and units digit q The two digit number N has tens digit q and units digit p Given that N − M = 9 and that p + q = 13 find the value of M Show clear algebraic working. M =

By writing 8x 2 − 56x + 17 in the form p (x + q) 2 + r find the exact solutions of the equation 8x 2 − 56x + 17 = 0 a±b 2 Give your answer in the form where a, b and c are integers. c Show your working clearly. x =

The diagram shows a solid pyramid with a triangular base ABC, which is an equilateral triangle of side 8 3 cm. The base of the pyramid is on a horizontal surface and the vertex V of the pyramid is vertically above the point O of the base. The edges AV, BV and CV of the pyramid are the same length and O lies on AM, where M is the midpoint of CB and AO : OM = 2 : 1 Given that the total surface area of the pyramid is 150 3 cm², find the length, in cm, of VO cm

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

Egan cycled 168 km at an average speed of x km/h, Rohan cycled the 168 km at an average speed that was 2 km/h less than Egan’s average speed. Given that it took Rohan 12 minutes longer than Egan to cycle the 168 km, calculate the value of x x =