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

Calculate the value of 12.3 − 9.91 Give your answer as a decimal to 5 significant figures.

The nth term of a sequence is given by 7 – 4n Determine whether –123 is a term of this sequence. Show your working clearly.

x° C B The diagram shows the position of two ports, A and B, and the position of a ship C The bearing of port B from port A is 133° Given that C is due west of B calculate 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: N, A, N · Figure values: 133°.

Without using a calculator and showing all your working, calculate 7 5 2 ×3 10 9 Give your answer as a mixed number in its simplest form. ………………………

Make h the subject of 2(h – 6) = 4g + 2

Solve the inequality 3 – 2x < 5 + 6x

Here is a list of six numbers. 20 4π 24 5 18 −3 5 9π 42 2 3 Write down the two numbers in the list that are natural numbers …………… , ……………

cm Diagram NOT accurately drawn 10 cm The diagram shows a right circular solid cylinder of diameter 8 cm and height 10 cm. Calculate, to the nearest cm³, the volume of the cylinder cm³

9 1 second = 106 microseconds. Change 4.5 × 1014 microseconds into hours. Give your answer in standard form hours

Patrick sells a painting for 557.75 euros. He makes a profit of 15% on the price he paid for the painting. Calculate the price Patrick paid for the painting euros

Here are the marks that Srinjoy scored in each of 7 tests. 21 24 25 18 28 25 20

Write down the mode of these 7 marks. After taking an 8th test, Srinjoy’s mean mark for all 8 tests is 22.5

Calculate his mark for the 8th test.

Find the value of 12xy – 15y when x = 2 and y = –3

Factorise completely 12xy – 15y

The diagram shows a trapezium. (2x – 1) cm Diagram NOT accurately drawn 4 cm (3x + 2) cm The lengths of the parallel sides of the trapezium are (3x + 2) cm and (2x – 1) cm. The height of the trapezium is 4 cm. Given that the area of the trapezium is 28 cm² find the value of x x =

The diagram shows a farmer’s field that is in the shape of a ΔABC The farmer is going to grow carrots in the region of the field which is • nearer to A than to B and • nearer to AB than to AC Using ruler and compasses only and showing all your construction lines, construct the region T inside the field in which the farmer is going to grow his carrots. Shade the region and label it T

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

y y–x=2 Diagram NOT accurately drawn R O x 3x + y = 15 The diagram shows part of the shaded infinite region R which has three straight boundary lines. Write down the three inequalities that define the shaded region R

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

The diagram shows the square ACEF and the equilateral triangles ABC and CDE Prove that ΔECB is congruent to ΔACD

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

Without using a calculator and showing all your working, express 4−2 3 3 +1 in the form a 3 + b where a and b are integers.

In the diagram, P, Q and R are points on a circle with centre O PRS is a straight line and ∠QRS = 118° Calculate, in degrees, the size of ∠OQP Give reasons for each stage of your working. ∠OQP = °

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: O, S, R, P, Q · Figure values: 118°.

6m B 24° O D A In the diagram A, B and C are points on a circle with centre O and radius 6 m. AD and CD are tangents to the circle. OBD is a straight line such that ∠ODC = 24° Calculate the perimeter, in m to 3 significant figures, of the shaded region m

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

The incomplete table and incomplete histogram give information about the length of time, in minutes, that each of 105 runners took to complete a half marathon.

None of the 105 runners took longer than 190 minutes to complete the half marathon.

Use this information and the information in the histogram to complete the table.

Use the information in the table to complete the histogram.

The points A and B are such that the coordinates of A are (3, –2) and BA = 4

Find the coordinates of point B ( …………… , …………… ) The point C has coordinates (m, n) where m > 3 → Given that ½ AC ½ = 5

find an expression for m in terms of n m =

G H Diagram NOT accurately drawn F E cm³ − 8x B C 18 x cm A 3 cm D 1 − 2x The diagram shows cuboid ABCDEFGH in which 18 x 6 AD = 3 cm DC = cm AH = cm 1 − 2x 3 − 8x where 0 < x < k Given that the length of CH is L cm, where L = and k is a positive integer, (3 − 8 x)(1 − 2 x)

find the value of k Show your working clearly. k = Given that x = 0.3

calculate the volume, in cm³, of the cuboid

…………… cm³

A dice has eight faces numbered 1, 2, 3, 4, 5, 6, 7 and 8 The table shows information about the probability that, when the dice is rolled once, it will land on each of the possible numbers.

When the dice is rolled once, the probability that the dice will land on the number 5 is 0.2 The dice is rolled 250 times. Calculate an estimate for the number of times the dice will land on an odd number.

A= B= −3 4 2 2 Find

A – B

3A + 2B The matrix C is such that A = BC

Find C C=

A Diagram NOT accurately drawn 5 cm B E x cm 15 cm 120° y cm D 7x cm C A, B, C and D are four points on a circle. The chord AC intersects the chord BD at E AE = 5 cm EC = y cm DE = 15 cm EB = x cm DC = 7x cm ∠DEC = 120°

Find the value of x and the value of y Show your working clearly. x = y = Given that area of ΔABE : area of ΔCDE = 1 : n

find the value of n n =

The equation of a curve C is y = (kx 2 – 2)(x + 3), where k is a constant. The point A on C has x coordinate equal to –1 The tangent to C at A has gradient equal to –8

Show that the x coordinates of the stationary points on C satisfy the equation 3x2 + 6x – 1 = 0

Write 3x 2 + 6x – 1 in the form a(x + b)² + c where a, b and c are integers.

Hence find the exact x coordinate of each of the stationary points on C Show your working clearly.

x is directly proportional to w 3 y is inversely proportional to w y = 2 when x = Find the value of p and the value of q such that xy p = q p = q =