4MB1/01 — June 2021 (Edexcel IGCSE Maths): Past Paper

Factorise fully 8 xy 2 − 18 xy

A pattern is made using a four by four grid with both grey squares and white squares.

Shade one more square to make a pattern with exactly one line of symmetry.

Shade two more squares to make a pattern that has rotational symmetry of order 2

Make x the subject of y = t x + 4 y 2

Each time Arhan plays a game of chess, the probability that he does not win is 0.64 Arhan plays 75 games of chess. Calculate an estimate for the number of games he wins.

Solve the simultaneous equations 4 x + 4 y = 18 4 x + 6 y = 35 Show clear algebraic working. x = y =

The diagram shows a quadrilateral ABCD in which BC = 25 cm AB = 50 cm CD = 35 cm angle BAD = angle CDA = 90° Calculate the perimeter, in cm, of quadrilateral ABCD cm

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: B, C, A, D · Figure values: 25, 50, 35.

Michael’s age is n years. Navtej’s age is three times Michael’s age. Indre is 8 years younger than Navtej and 20 years older than Michael. Find the value of n. Show clear algebraic working. n =

The diagram shows the rectangle ABCD. The region R consists of all the points inside the rectangle that are

A D The diagram shows the rectangle ABCD. The region R consists of all the points inside the rectangle that are (i) greater than 4 cm from B, (ii) closer to BA than to CD. Using ruler and compasses only and showing all your construction lines, show, by shading, the region R. Label the region R.

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

A shopkeeper sells a radio for $27 For this selling price, the shopkeeper makes a profit of 8% Calculate the selling price of the radio so that the shopkeeper would make a profit of 35% $

The integer N is greater than 120 When N is divided by 28 the remainder is 3 When N is divided by 120 the remainder is 3 Find the least value of N. You must show your working.

Greg is organising a day out for his students. Each of his students has to choose to take part in at least one activity chosen from rock climbing (R) and canoeing (C ). The cost for rock climbing is $42 The cost for canoeing is $34 The total cost for all the activities chosen by the students is $3702 Given that n(R ∩ C ʹ ) = 32 and that n(R ∪ C ) = 68 find the number of Greg’s students who chose to take part in both rock climbing and canoeing.

Write as a single fraction in its simplest form x − 6 8x + 2 − 3 4 Show clear algebraic working.

In the diagram, A, B, C and D are points on a circle. BED and AEC are straight lines. Prove that triangle ABE is similar to triangle DCE.

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

The diagram shows a square based right pyramid ABCDE. The point X is the centre of the base so that the point E is vertically above X. EX = 15 cm AB = 8 cm Calculate the size, in degrees to 3 significant figures, of the acute angle between AE and AX. °

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

Without using a calculator and showing all your working, express 4 − 12 4 + 12 in the form a − b where a and b are integers.

Simplify fully (5a²b³)²

Simplify fully (9 x 4 y 2 ) 2 3 x 2 y −4

Find the set of values of x for which −2x + 4 ≤ 3x − 6 < 2x + 2

On the number line below, represent the set of values of x for which −2x + 4 ≤ 3x − 6 < 2x + 2 x 0 1 2 3 4 5 6 7 8 9 10

In the diagram, AB represents a vertical cliff of height 25 m. The points C and D are buoys on the surface of the sea so that CDA is a horizontal straight line. The angle of elevation of B from C is 33° and CD = 20 m. Calculate the size, in degrees to 3 significant figures, of the angle of depression of D from B. °

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: B, C, D, A · Figure values: 25, 20.

ABCD is a rectangle in which AB = x 3 cm and BC = x cm. EFG is an equilateral triangle with sides of length y cm. The area of rectangle ABCD is equal to the area of triangle EFG. Find the ratio the perimeter of the rectangle ABCD : the perimeter of the triangle EFG. Give your answer in the form (a + b ) : b where a and b are integers.

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

A solid right circular cone is made of brass. The mass of the cone is 5080 grams, to the nearest 10 grams. The radius of the base of the cone is 8.5 cm, to 2 significant figures. The density of the brass is 8.73 g / cm³, to 3 significant figures. Given that mass density = volume and taking the value of π as 3.142 calculate the upper bound of the height of the cone. Give your answer to one decimal place cm

A and B are two mathematically similar containers. Container A has surface area of 1550 mm² and container B has surface area of 10 478 mm² Given that volume of container B − volume of container A = 62 160 mm³ calculate the volume, in mm³, of container A

…………… mm³

In the diagram AB, BC, CD, DE, EF, FG and GH are seven sides of a regular n-sided polygon. ABP and HGP are straight lines. The size of each exterior angle of the polygon is x° The size of each interior angle of the polygon is 7 x° Calculate the size of ∠GPB Show your working clearly. °

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, P, F, G, H.

In a region of a country, two types of eagle, type A and type B, can be found. In 2003 the ratio of the number of type A eagles to the number of type B eagles was 2 : 5 In 2015 the ratio of the number of type A eagles to the number of type B eagles was 4 : 3 From 2003 to 2015, the number of type A eagles had increased by 16 From 2003 to 2015, the number of type B eagles had decreased by 107 Calculate the number of type B eagles in this region in 2015

One solution of the equation 6x3 + 17x2 − 5x − 6 = 0 is − Find the other 2 solutions of the equation. Show clear algebraic working.

A particle P is moving along a straight line. At time t seconds, t ≥ 0, the displacement, x metres, of P from a fixed point O on the line is given by x = k + 6t − 2kt2 where k is a constant. When t = 0, P is at the point A on the line. When P is at the point B on the line, P is instantaneously at rest. Given that AB = 0.9 m, calculate the value of k. Show your working clearly. k =

There are 30 students in a class. All the students in the class take a test. Here are the marks in the test for the 12 girls in the class. 35 42 67 83 21 24 56 32 69 98 x 49 where x > 70

Find the median of the girls’ marks. The mean mark for the 12 girls is 54.5

Find the value of x. x = The mean mark for the boys is 56

Calculate the mean mark for the 30 students in the class.

⎛ 3 −1⎞ A= 2 −2 1 ⎛ 2 −1⎞

Given that the inverse of matrix A is a 2 −3 find the value of a. a = ⎛ 9 −11⎞

Hence find the matrix B such that ABA−1 = 8 −11