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

Express 15 centimetres as a percentage of 3 metres.

…………… %

A B The diagram shows shape A and shape B. Write down …………… , …………… the number of lines of symmetry of shape A …………… , ……………

the order of rotational symmetry of shape B.

The bearing of ship P from ship Q is 057° Find the bearing of ship Q from ship P.

…………… °

A= B = −3 5⎠ ⎝ 3 −3 Calculate 3A + 2B

Without using a calculator and showing all your working, evaluate 1 2 2 ×2 4 3 Give your answer in its simplest form.

Given that y = 7x2 − x dy find dx dy = dx

Here are the first 4 terms of a sequence. 4096 −1024 256 −64

4096 −1024 256 −64 (i) Write down the next 2 terms of the sequence. , (ii) Explain how you found your answer.

Ying has 4 black counters and 3 white counters. There is a number on each counter. The mean of the numbers on the black counters is 11.5 The mean of the numbers on the white counters is 9 Calculate the mean, to 3 significant figures, of the numbers on all 7 counters.

Find the largest integer value of x such that 17 − 2x ≥ 4(x – 5) Show clear algebraic working.

A regular polygon has n sides. Each interior angle of the regular polygon is 135° greater than each exterior angle of the polygon. Find the value of n. n=

A piece of ribbon 9 metres long is cut into 3 parts in the ratios 3 : 5 : 7 by length. Calculate the length, in metres, of the longest piece. m

Write 9.6 × 10−7 as an ordinary number. 2.4 × 10199

Calculate 9.6 × 10 −7 Give your answer in standard form.

Without using a calculator and showing all your working, express 605 − 80 in the form n where n is an integer.

Solve the equation 5x2 = 7 − 9x Give your solutions to 3 significant figures. Show your working clearly.

A D B C The diagram shows quadrilateral ABCD. The point P lies inside the quadrilateral, such that P is 5.5 cm from C and equidistant from AD and AB. Using ruler and compasses only and showing all your construction lines, show the point P on the diagram.

t varies inversely as the square of a where a > 0 t = 14 when a = 5 Calculate the value of a when t = 224 a=

The diagram shows two similar jugs. The height of jug A is 20 cm and the height of jug B is 6 cm. Given that volume of jug A − volume of jug B = 1459.5 cm³ calculate the volume, in cm³, of jug B. cm³

Labels in the original figure: A, B · Figure values: 20, 6.

E = {positive integers from 1 to 15 inclusive} A = {multiples of 3} B = {even numbers}

Find A ∪ B A∪B={ }

Find A ∩ B A∩B={ }

Find n([A ∩ B]ʹ) n([A ∩ B]ʹ) = The set C has 8 elements and B ∩ C = ∅

Write down the elements of set C. C={ }

Solve the simultaneous equations 10x + 2y = 17 15x − 3y = 39 x= ,y=

The coordinates of point A are (7, 2) and the coordinates of point B are (−5, y). → The modulus of the vector AB is 13 Calculate the possible values of y. y=

The straight line joining the points with coordinates (−a, −22) and (3a, 38) has equation y = mx + a Calculate the value of a and the value of m. a= m=

In the diagram ACE and BCD are straight lines such that the point C is the midpoint of BD. AB is parallel to DE. Prove that the triangles ABC and EDC are congruent.

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

A right circular cone has a curved surface area of 136 π cm² The radius of the base of the cone is 8 cm The volume of the cone is k π cm³ Find the value of k. k=

Solve 3 − − =1 2x + 9x − 5 x+5 Show clear algebraic working. x=

There are 20 counters in a bag. There are 7 red counters. The rest of the counters are green or white. Bernard takes at random 2 counters from the bag. The probability that Bernard will take 2 white counters is Calculate the probability that Bernard will take 1 green counter and 1 white counter.

The table below gives information about the lengths of time that 50 people have been waiting for a train.

Find the modal class.

Find the class interval that contains the median waiting time.

Calculate an estimate for the mean waiting time. minutes

− 5) cm 30° (x + 5) cm A C The diagram shows △ ABC in which AB = (2x − 5) cm BC = (x + 5) cm ∠ ABC = 30° The area of △ ABC is 15.75 cm² Calculate the length, in cm to 3 significant figures, of AC. cm

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: 30° · Other figure text: (2x − 5) cm, (x + 5) cm.

Factorise fully 15x3 y − 20x2 y² (27 x ) 6 3

Simplify fully 18 x 3

Given that (x − 2) is a factor of 2x3 + 3x2 + kx − 6 find the value of k. k=