4MB1/01R — January 2020 (Edexcel IGCSE Maths): Past Paper

Express 7 minutes as a fraction of 24 hours. Give your answer in its simplest form.

The nth term of a sequence is given by the expression 2n2 − 5 Find the first term of the sequence and the third term of the sequence. First term = Third term =

Solve − = x 3 2 x = ……………Solve − = x 3 2 x =

Factorise completely 2x2 − 6xy + 5wx − 15wy

The function g where g: x ↦ 16 − x² is defined for all values of x. Write down

Write down (i) the maximum value of g(x), (ii) the range of g.

Find the value of 16 × 1050 Give your answer in standard form.

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

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

Write down

the number of lines of symmetry of the figure …………… , ……………

the order of rotational symmetry of the figure.

Find the range of values of x for which x − 10 < 3x + 4 ≤ 20 − 5x

A factory produces 2500 plates. There are large plates and small plates. There are 800 large plates which have a mean weight of 600 grams. The small plates have a mean weight of 450 grams. Calculate the mean weight, in grams, of all 2500 plates grams

Find, showing your working clearly …………… , …………… (i) the lowest common multiple (LCM) of 42, 54 and 66 (ii) the highest common factor (HCF) of 42, 54 and 66 (i) LCM = (ii) HCF =

During a week, 500 trains will arrive at a station. Each train will be late, on time or early. The probability of a train arriving late is 0.85 The probability of a train arriving on time is 0.07 Calculate an estimate for the number of trains that will arrive early during the week.

y 3y − 2x = 3 O 1 2 3 4 5 6 x y = 6 − 3x x + y =6 Write down the three inequalities that define the shaded region in the diagram.

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

P = { a, b, c, d } Write down all of the subsets of P that have 2 elements.

Simplify fully (7x − 3) − (5x − 9) 6 3

ABCD is a rectangle with perimeter 28 m. The length of AB is 8 m. Calculate the length, in m, of the diagonal AC of the rectangle m

The diagram shows the trapezium ABCD in which AD and BC are parallel. AC = 20 cm BC = 30 cm ∠ACD = 50° ∠ADC = 90° Calculate the area, in cm² to 3 significant figures, of the trapezium ABCD cm²

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: B, A, D, C · Figure values: 30, 20, 50°.

Express 5−2 in the form m + n, where m and n are integers. Show your working clearly.

Given that 1 mile = 1.609 kilometres and 1 gallon = 4.546 litres, change 35 miles per gallon into litres per 100 kilometres. Give your answer correct to 3 significant figures litres per 100 kilometres

A = 5 −7

Find A2 −1 2⎞ B = ⎜ −3 5 4 −3⎠

Find BA

The weights of 710 passengers boarding buses at a bus station were recorded. The incomplete table and histogram give information about these passengers.

Complete the table.

Complete the histogram.

In a survey of 55 farmers who keep animals, the numbers of farmers who keep cattle (C ), goats (G ) and sheep (S ) were recorded. The Venn diagram shows information about the results of the survey. The numbers shown in the Venn diagram are the number of farmers in the given subset of E. E S G C 22 5 10 3 15

Find n(C ∩ G ∩ S )

Describe the members of the subset C ∩ G ∩ S

Find n(C ′ ∩ G ′ ∩ S )

Describe the members of the subset C ′ ∩ G ′ ∩ S

A particle is dropped from rest and falls a distance of s metres in time t seconds. In the first 4 seconds after it has been dropped, the particle falls a distance of 96 metres. At time 5 seconds after it has been dropped, the particle is at the point A. At time 6 seconds after it has been dropped, the particle is at the point B. Given that s is directly proportional to the cube of t, calculate, in metres, the distance AB m

The scale of a map is 1 : 40 000 The actual area of a field is 2.4 km²

Calculate the area, in cm², of the field on the map cm² Given that n is an integer, the scale of another map is 1 : n The length of a road shown on this map is 8 cm. The actual length of this road is 2 km.

Find the value of n. n =

Given that w = 5x + y − 1 express x in terms of y and w. Give your answer as a single fraction. x =

The diagram shows part of a circle through the points A, B, C and D. AD is parallel to BC, AD = DC and ∠CAD = 30° Giving your reasons, prove that BC is a diameter of the circle.

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: A, D, B, C · Figure values: 30°.

At time t = 0 seconds, a cyclist passed the point P on a straight horizontal road. The cyclist was moving with a constant speed of 5 m/s. The cyclist travelled a distance of 35 m at this speed to the point Q on the road. On reaching Q, the cyclist decelerated at a constant rate, coming to rest at the point R on the road such that PQR is a straight line and QR = 10 m. Represent, on the grid, the information for the journey of the cyclist from P to R as a speed-time graph. Speed (m/s) 3 O 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Time (seconds)

The diagram shows circle ABCD with centre O, diameter AMONC and radius r. The diagram also shows circle AFOG, with centre M, and circle OHCJ, with centre N.

Find and simplify an expression, in terms of r and π, for the perimeter of the shaded region in the diagram. The line FH is the tangent to the circle AFOG at the point F. The line FH is also the tangent to the circle OHCJ at the point H. The point P on circle ABCD is such that OFP is a straight line. The point Q on circle ABCD is such that OHQ is a straight line. The region FPBQH inside circle ABCD is bounded by the straight line FP, the arc PBQ of circle ABCD and the two straight lines QH and HF.

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

Find and simplify an expression, in terms of r and π, for the area of FPBQH.

D Diagram NOT accurately drawn B 8 cm A 7 cm 6 cm C The diagram shows a pyramid ABCD with a horizontal triangular base ABC. The face ADB of the pyramid is perpendicular to the base ABC. In ΔABC, AB = 8 cm, BC = 7 cm and CA = 6 cm.

Calculate the size, in degrees to 3 significant figures, of ∠ACB. ∠ACB = ° In ΔADB, AD = DB and ∠ADB = 50°

Calculate the volume, in cm³ to 3 significant figures, of the pyramid ABCD

…………… cm³