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

The nth term of a sequence is given by 9 − 4n Find the first 3 terms of this sequence …………… , …………… , ……………

Find the highest common factor (HCF) of 60, 126 and 648 Show your working clearly.

Express 325 millilitres as a fraction of 3.7 litres. Give your answer in its simplest form.

Without using a calculator and showing all your working, work out 1 2 3 ×2 4 3 Give your answer as a mixed number in its simplest form.

N = 254 × 583 Evaluate N, giving your answer

to 3 significant figures …………… , ……………

to 6 decimal places.

Find the size of each interior angle of a regular 18-sided polygon.

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A straight line passes through the points with coordinates (12, −4) and (−2, 3) Calculate the gradient of the line.

The diagram shows a sector OAB of a circle centre O and radius 7 cm. Given that the area of the sector OAB is 52 cm² calculate the size, to the nearest degree, of ∠AOB. °

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: B, A, O · Figure values: 7.

Factorise completely 6xy − 3x

Factorise completely 6ab − 2bc + 3ad − cd

Solve = 3 2 Show clear algebraic working. x = ……………Solve = 3 2 Show clear algebraic working. x =

A company makes two sizes of containers, small and large. Each small container is similar to each large container. The volume of each small container is 225 cm³ The volume of each large container is 650 cm³ Given that the height of each large container is 18 cm, calculate the height, in cm to 3 significant figures, of each small container cm

x is an integer such that 2(1 − 3x) > 25 − 2x Find the greatest possible value of x.

A and B are two matrices such that the determinant of A is equal to the determinant of B. ⎛ 3 2⎞ ⎛ 5 3⎞ Given that A = and B = 1 4 where a is a positive integer, ⎝ −1 a⎠ find the value of a. a =

The equation of the curve C is y = x³ − x² The point A lies on C such that the x coordinate of A is −1 Use differentiation to find the gradient of C at the point A.

The diagram shows △ABC and the straight line BMD such that M is the midpoint of AC. The points E and F lie on BMD such that AE and CF are each perpendicular to BMD. Prove that △AEM is congruent to △CFM.

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

A= B = 4 3 4 1 Find

A − B

3A + 2B

Show that ÷ 2 is equal to an integer. x + x − 12 3 x − 48 Show clear algebraic working.

y −2 −1 O 1 2 3 4 5 6 7 x −1 −2 −3

x = 4

2x + y = 8

y = 3x − 1

On the grid, show by shading, the region R defined by the inequalities x ≤ 4 and 2x + y ≥ 8 and y ≤ 3x – 1 Label the region R.

In the diagram, A, B and C are points on a circle with centre O and radius 5 cm. AOC is a diameter of the circle and PAQ is the tangent to the circle at A. ∠BAQ = 63° Calculate the length, in cm to 3 significant figures, of AB. AB = cm

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: C, B, O, Q, A, P · Figure values: 5, 63°.

2− 2 (1 + 2 ) 20 2 can be written in the form a + b 2 where a and b are integers. Find the value of a and the value of b. Show your working clearly. a = b =

y varies inversely as the cube of x and y = 3a when x = 2a Find an expression for y in terms of a when x = 4a2 Give your answer in its simplest form. y =

The diagram shows a solid made by fixing a solid hemisphere of radius 4 cm on the flat circular top face of a solid cylinder of radius 4 cm. The centre of the hemisphere coincides with the centre of the flat circular top face of the cylinder. 920 The total volume of the solid is π cm³ Find the total height, in cm, of the solid cm

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Figure values: 4.

a cm Diagram NOT accurately drawn R cm² h cm b cm The diagram shows a trapezium in which the parallel sides are of length a cm and b cm The height of the trapezium is h cm The area of the trapezium is R cm² Given that b = 14.5 to the nearest 0.5 h = 4.0 to the nearest 0.1 R = 50 to the nearest whole number calculate the lower bound, to 3 significant figures, of a

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

q = The vectors p and q are such that | p | = | p − 2q | Find the value of x. Show clear algebraic working. x =

There are 12 marbles in bag A and 15 marbles in bag B. In bag A, there are 7 yellow marbles and 5 red marbles. In bag B, there are 10 yellow marbles and 5 red marbles. Eugene takes at random one marble from bag A and without looking at the marble puts the marble into bag B. Eugene then takes at random one marble from bag A and takes at random two marbles from bag B. He places the three marbles on a table. Calculate the probability that the three marbles on the table all have the same colour. ( )

h cm B C 4a cm A 2a cm D The diagram shows a cuboid ABCDEFGH in which AD = 2a cm DC = 4a cm CH = h cm ( ) Given that AC = 2 a BH and that ∠HAC = 45° find the value of a. ( ) a =

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

Amrit recorded the time, in minutes, that he took to complete each of his homework tasks last term. The table shows information about these times. Time (t minutes) Frequency 15 ≤ t < 20 12 20 ≤ t < 25 10 25 ≤ t < 30 8 30 ≤ t < 40 28 40 ≤ t < 50 14

Find the class interval that contains the median of these times.

Calculate an estimate, to 3 significant figures, of the mean time it took Amrit to complete his homework tasks last term

The diagram below is an incomplete histogram for the information in the table. Frequency density 15 20 25 30 35 40 45 50 Time (minutes)

Use the information in the table to complete the histogram.

y Diagram NOT y = 4x + 8 accurately drawn B y = 2x2 + 3x − 2 A O x The diagram shows a sketch of part of the curve with equation y = 2x2 + 3x − 2 and part of the straight line with equation y = 4x + 8 The points of intersection of the line with the curve are A and B.

Find the length of AB, giving your answer in the form k 17 , where k is a rational number to be determined. Show your working clearly. ( ) The point C has coordinates (−5, 0)

Calculate the size, to the nearest degree, of ∠CAB.

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