4MB1/01 — June 2019 (Edexcel IGCSE Maths): Past Paper

Write 8693 to 2 significant figures.

Write 0.0374 to 2 significant figures.

Find the Lowest Common Multiple (LCM) of 18, 30 and 48 Show your working clearly.

A pattern is made with white squares and shaded squares.

Shade one more square to make a pattern with exactly 1 line of symmetry.

Shade one more square to make a pattern with rotational symmetry of order 2

Work out 2 ÷3 4 6 Show your working clearly and give your answer as a fraction in its simplest form.

Given that y = 2 x 4 − 2 x dy find dx dy ……………= dx

Given that y = 2 x 4 − 2 x dy find dx dy = dx

A straight line passes through the points with coordinates (2, –10) and (–3, 5) Calculate the gradient of the line.

Expand and simplify (4x – 5)(2x + 3)

The nth term of a sequence is given by 24 – 5n Find the sum of the 3rd term and the 10th term of the sequence.

Each exterior angle of a regular polygon is 9° Calculate the number of sides of the polygon.

In a sale, the price of a book is reduced by 15% The price of the book before the sale was £7.60 Calculate the sale price of the book. £

Simplify 2x2 q 3x5

Simplify (4a2b3)³

The function f is defined for all values of x by f : x 6 x² – 2

Write down the range of f. The function g is given by g : x 6 3 where x ≠ 3 − 4 x +4

Calculate fg(2)

Find the value of 3c2 when c = –8

Factorise completely 3c2 + 6c

Simplify fully 4 x 2 − 36

The diagram shows △ABC. APQR is a parallelogram where P is the midpoint of AB, Q is the midpoint of BC and R is the midpoint of AC. Prove that △PBQ and △RQC are congruent.

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

Here is a biased spinner labelled 1, 2, 3, 4, 5, 6

The table below shows information about the probability that when the spinner is spun once it will land on each of the numbers 1, 2, 3, 4, 5, 6

Abdul is going to spin the spinner 300 times.

Calculate an estimate for the number of times the spinner will land on number 1

Calculate the probability that when the spinner is spun once it lands on number 6

Here is △ABC. C Diagram NOT accurately drawn 6 cm 30° A 2 cm B

Calculate the area, in cm², of △ABC cm² Here is △PQR. Q Diagram NOT accurately drawn 12 cm x° R 4 cm P

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

Calculate the value, to 3 significant figures, of x. x =

There are 9 marbles in bag A and 11 marbles in bag B. In bag A, there are 3 red marbles, 2 yellow marbles and 4 green marbles. In bag B, there are 2 red marbles, 4 yellow marbles and 5 purple marbles. Ted takes at random one marble from bag A and one marble from bag B. Calculate the probability that the two marbles are not the same colour.

The period, T seconds, of a simple pendulum of length L metres is given by the formula L T = 6.28 g L = 1.32 to 3 significant figures. g = 9.8 to 2 significant figures. Calculate the upper bound, to 3 significant figures, of T.

The incomplete histogram and the incomplete table give information about the time taken, in minutes, for some students to each complete a piece of homework. No student took less than 10 minutes to complete the homework and no student took longer than 60 minutes to complete the homework.

Complete the histogram and the table.

Make x the subject of x x + 2y −5= 3 3w − 2 y Give your answer as a single fraction.

ABCDEF is a right triangular prism in which AB = 1.2 m BC = 2.3 m AF = 0.5 m ∠FAB = 90° Calculate the total surface area, in m², of the prism m²

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: E, C, D, F, A, B · Figure values: 2.3, 0.5, 1.2.

In a survey, 60 students were asked whether they study any of History (H), Geography (G) or Latin (L). Of these students 27 study History 25 study Geography 18 study Latin 13 study both History and Latin 2 study both Geography and Latin 8 study History only No students study History and Geography and Latin.

Use the information to complete the Venn diagram. E H G L

Find the number of students who study History but not Latin.

Find n(H′ ∩ [L ∪ G])

Y Diagram NOT Z accurately drawn –3a + 5b X 2a + 3b O → → The diagram shows △OXY where OX = 2a + 3b and OY = –3a + 5b →

Find and simplify an expression, in terms of a and b, for YX . → 2 35 The point Z on YX is such that OZ = − a + b 9 9

Calculate, in its simplest form, the ratio of YZ : ZX

A Diagram NOT B accurately drawn 62° C 126° O D In the diagram, A, B, C and D are points on a circle, centre O. ∠CBO = 62° and ∠BCD = 126°

Find the size, in degrees, of ∠BAD. Give a reason for your answer. ° ∠BAD =

Find the size, in degrees, of ∠ODC. Give reasons for your working. ° ∠ODC =

A= B= −5 1 1 −1 The determinant of the matrix A2 – AB is equal to 3k + 28 Find the value of k. k =

A 2x cm B Diagram NOT accurately drawn The diagram shows a semicircle, with diameter AB, where AB = 2x cm. The diagram also shows a circle, which is the circle with the greatest possible radius that can be drawn inside the semicircle. The perimeter of the shaded region is P cm and the area of the shaded region is A cm2. Given that P = A, find an expression for x in terms of π. x =

A particle P is moving along a straight line. At time t seconds, the displacement, x metres, of P from a fixed point O on the line is given by x = –3t3 + 6t2 + kt + 4 t.0 At time t seconds, the velocity of P is v m/s such that v = 9 when t = 2

Show that k = 21 Particle P comes to instantaneous rest at the point A.

Using k = 21, find the value of t when P is at A. t =

Find, to the nearest metre, the distance OA m