4MB1/01 — June 2018 (Edexcel IGCSE Maths): Past Paper

The nth term of a sequence is given by 5n – 7 Write down the second, third and fourth terms of the sequence …………… , …………… , ……………

The bearing of town A from town B is 054° Find the bearing of town B from town A.

…………… °

At the beginning of the summer, Amrit’s weight was 75 kg. At the end of the summer, his weight was 69 kg. Calculate the percentage loss in Amrit’s weight

…………… %

The point A is mapped onto the point (–1, 3) under the translation −5 Find the coordinates of A. ( …………… , …………… )

BEARING Write down all the letters of the above word that have

exactly two lines of symmetry

rotational symmetry of order 2

Write down which two of the following six numbers are equivalent to irrational numbers. 7 27 1 2π 16 4 4 2 0.3 12 3

Without using a calculator and showing all your working, calculate 7 ⎛1 1⎞ −⎜ ×2 ⎟ 8 ⎝3 4⎠ Give your answer as a fraction in its simplest form.

Solve the equation 4x + (5.2 × 10⁵) = (7.1 × 10⁷) – 12x Give your answer in standard form.

Showing all your working, express 3 180 − 2 80 in the form a b where a is an integer and b is a prime number.

The determinant of the matrix is equal to 9 5 x 4 Find the value of x. x =

Express as a single fraction in its simplest form 3 4 − 2x − 1 x + 2

Diagram NOT accurately drawn A O 32° C B ABC is a triangle such that the points A, B and C lie on a circle, centre O. BC = BA and ∠CAB = 32° Find the size, in degrees, of

∠COB

…………… °

∠OCA

…………… °

Prove that (4n + 3)² – (4n – 3)² is a multiple of 12 for all positive integer values of n.

⎛ 2 x − 1⎞ a= −3 Given that a = 5 find the possible values of x.

A, B and D are three points on a circle. The point C is such that CD and CB are tangents to the circle. ∠ADB = ∠ABD Prove that △ABC and △ADC are congruent.

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

Simplify (4x5)²

Simplify (27 y 9 ) 3

The lengths of the sides of a rectangular piece of paper, measured to the nearest mm, are 296 mm and 210 mm. Calculate

the lower bound, in mm, for the perimeter of the piece of paper, mm

the upper bound, to the nearest mm², for the area of the piece of paper

…………… mm²

y varies inversely as the cube of x. y = 297 when x = Find the value of x² when y = 704 x² =

Simplify fully 10 x + 5 y − 2 x 2 − xy 4 x² − y 2

The table shows information about the number of hours for which each of 100 children used a computer one week.

The diagram below is an incomplete histogram representing this information. Use the information in the table to complete the histogram.

The diagram shows a sector, AOB, of a circle centre O and radius 8 cm. The angle AOB is 35° Find the area, in cm² to 3 significant figures, of the segment shaded in the diagram cm²

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: 35°, 8.

Two containers, A and B, are mathematically similar. Container A has a volume of 4500 cm³ and a total surface area of 1500 cm² Container B has a volume of 972 cm³ Calculate the total surface area, in cm², of container B

…………… cm²

Jenny has 18 sweets in a bag. There are 11 orange sweets and 7 green sweets in the bag. Jenny takes at random 3 sweets from the bag. Calculate the probability that the 3 sweets are not all of the same colour.

Diagram NOT accurately drawn O The diagram shows a circle and a square. The circle has centre O and diameter k cm and each vertex of the square lies on the circle. The total area of the regions shown shaded in the diagram is A cm²

Show that 8A = 2λN 2 – 3k2

Hence find an expression for k in terms of A and λ. k =

A particle is moving along a straight line. At time t seconds, the displacement, x metres, of the particle from a fixed point O on the line is given by x = t3 – 6t2 + 15t t.0 At time t seconds, the acceleration of the particle is a m/s2

Find an expression for a in terms of t. a =

Find the least speed of the particle m/s

The straight line L has equation 2x + y = 8

Find the gradient of L. L meets the y-axis at the point A and the x-axis at the point B.

Find the area of triangle AOB, where O is the origin.

(x + 3) cm 2x cm A (3x + 1) cm C The diagram shows triangle ABC in which AB = (x + 3) cm BC = 2x cm AC = (3x + 1) cm ∠ABC = 120° Find the size, in degrees to 3 significant figures, of ∠ACB. ∠ACB = °

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: 120° · Other figure text: (x + 3) cm, 2x cm, (3x + 1) cm.

Solve the inequality 4(x – 2) 1 + x

Without using a calculator and showing all your working, solve the inequality 2x2 - 7x + 9

Hence find the range of values of x for which both 4(x – 2) 1 + x and 2x2 - 7x + 9