4MB1/02R — November 2020 (Edexcel IGCSE Maths): Past Paper

The manufacturer’s price for a Jinko car is $x Ben was given a 7% discount on the manufacturer’s price when he bought a Jinko. Ben paid $23 622 when he bought his Jinko.

Calculate the value of x. After a year Ben sold his Jinko for $19 880

Calculate the percentage loss, to 3 significant figures, on the price Ben paid for his Jinko. During the year that Ben owned the Jinko, he travelled d km in the car. The average fuel consumption of the car was 10 km per litre. The average cost of the fuel he used was $1.40 per litre. Other costs for the car in the year came to $938 The cost per km, including the loss in value, of his Jinko to Ben during the year that he owned the car was $0.40

Calculate the value of d.

Find the Highest Common Factor (HCF) of 75, 90 and 120 . Bhu sets the alarm on her phone to sound at 09 10 Her alarm then sounds every 12 minutes. Dax sets the alarm on his phone to sound at 09 30 His alarm then sounds every 8 minutes. Bhu’s alarm sounds at 09 10 and Dax’s alarm sounds at 09 30

Find the first time after 09 30 that both alarms will sound at the same time.

Solve the equation 3a + 6 = 4 – 5a

Solve the inequality 3p > 6p + 12 An inequality, in w, is shown on a number line below. –3 –2 –1 0 1 2 3 4 5 6 7 w

Write down the inequality.

Write down the 3 inequalities that define the shaded region R in Figure 1 y 1 R –4 –3 –2 –1 O 1 2 3 4 5 x –1 –2 –3 Figure 1

A youth club has introduced three new activities badminton (B), cookery (C) and drama (D). Each of the 75 members of the youth club is asked to say in which of these activities they have participated. Their answers showed that of the 75 members all have participated in at least one of these activities 27 have participated in badminton and drama 31 have participated in badminton and cookery 23 have participated in cookery and drama 48 have participated in badminton 49 have participated in cookery 40 have participated in drama. Let x be the number of members of the youth club who have participated in all three activities.

Using all this information, complete the Venn diagram opposite to show, in terms of x, the number of elements in each appropriate subset.

Find the value of x.

n (B ∩ C ʹ)

n B C D One of the members of the youth club is picked at random. Given that this member has participated in cooking …………… , ……………

find the probability that this member has not participated in any other activity. E C D B for a spare Venn diagram if you need to redraw your diagram. Only use this diagram if you need to redraw your Venn diagram. E C D B

Factorise x² + 5x − 6

Express as a single fraction in its simplest form x 3 2x 5 4

The points with coordinates (1, 1), (3, 1) and (4, 3) are the vertices of triangle A.

On the grid opposite, draw and label triangle A. Triangle B is the image of triangle A under the transformation with matrix M where 2 0 M = 0 2

On the grid opposite, draw and label triangle B. Triangle C is the image of triangle B under a reflection in the line with equation y = 0

On the grid opposite, draw and label triangle C. Triangle A is transformed to triangle C under the transformation with matrix N.

Find matrix N. Triangle D is the image of triangle C under a rotation through 180º about the point (1, 1)

On the grid opposite, draw and label triangle D.

Describe fully the single transformation that maps triangle D onto triangle A. y –10 –8 –6 –4 –2 O 2 4 6 8 10 x –2 –4 –6 –8 for a spare copy of the grid if you need to redraw your triangles. Only use this grid if you need to redraw your triangles. y –10 –8 –6 –4 –2 O 2 4 6 8 10 x –2 –4 –6 –8

The table gives information about the length of time, in seconds, that each of 28 birds spent on Ali’s bird table on Monday.

Find the class interval that contains the median length of time that the birds spent on the bird table on Monday.

Calculate an estimate, in seconds to one decimal place, for the mean length of time that the birds spent on the bird table on Monday. The incomplete histogram below gives some information about the length of time, in seconds, that each of 35 birds spent on Ali’s bird table on Tuesday. On Tuesday 9 of the birds spent between 5 seconds and 8 seconds on the bird table 6 of the birds spent between 8 seconds and 10 seconds on the bird table no bird spent longer than 40 seconds on the bird table.

Use this information to complete the histogram.

Find the proportion of birds on Tuesday that spent longer than 15 seconds on the bird table. for a spare copy of the histogram if you need to redraw your bar. Only use this histogram if you need to redraw your bar.

Jenny ran a road race. The distance Jenny ran was 5 km, to the nearest 20 m. Jenny’s time for the race was 34 minutes, to the nearest minute. Colin ran a different road race. The distance Colin ran was 10 km, to the nearest 200 m. Colin’s time for the race was 1 hour 8 minutes, to the nearest minute. Colin’s average speed for his race is greater than Jenny’s average speed for her race. Calculate the upper bound for the difference, in km/h, between Colin’s average speed and Jenny’s average speed. Show your working clearly.

Figure 2 shows two shapes A and B. All the lengths are in metres. Diagram NOT accurately drawn P 2x x 2y A 6y – 3 B 4y + 4 4y Q 2x + 4 R Figure 2 The corners of shape A are all right angles. The area of shape A is 400 m² Shape B is triangle PQR. The perimeter of shape A is equal to the perimeter of shape B.

Show that $4y^2$ – x² = 200 and that 2y = 2x + 5

Find the value of x and the value of y. Show clear algebraic working.

f(x) = 3x3 – 7x2 + 5x – 1

Use the factor theorem to show that (3x – 1) is a factor of f(x).

Hence solve the equation f(x) = 0 Show clear algebraic working. The curve C has equation y = f(x)

Find the exact coordinates of the turning points on C. The curve C crosses the y-axis at the point P.

Find the gradient of C at P.

Hence find an equation of the tangent to C at P.

Cone B 20 cm 100 cm Cone A F 30 cm Figure 3 A right circular cone, A, has height 100 cm and base radius 30 cm. The shaded solid, F, is formed by removing the right circular cone, B, of height 20 cm from the top of A, as shown in Figure 3 The volume of F is k π cm³ where k is an integer.

Find the value of k. Diagram NOT 20 cm accurately drawn 102 cm Figure 4 Figure 4 shows a solid circular cylinder. The cylinder has a radius of 20 cm, a height of 102 cm and a volume of V cm³

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 of V. Give your answer in terms of π. Volume of a cylinder πr 2 h Volume of a cone 1 2 = πr h Figure 5 below shows a door stop made from a hollow hemisphere and a hollow right circular cone. Diagram NOT accurately drawn 108 cm h cm 30 cm Figure 5 The radius of the base of the cone and the radius of the hemisphere are both 30 cm. The centre of the base of the cone coincides with the centre of the hemisphere. The height of the cone is 108 cm. The door stop rests on horizontal ground with the cone on top of the hemisphere and the axis of symmetry of the door stop vertical. The door stop contains sand to a height of h cm. Given that the volume of sand in the door stop is V cm³, where V cm³ is the volume of the cylinder in Figure 4

calculate the value of h. 4 3 Volume of a sphere 3 πr

A Diagram NOT B accurately drawn C F E O Figure 6 Figure 6 shows triangle OAB. The point E lies on OB such that OE : OB = 1 : 2 → 1 → The point F lies on OA such that OF = OA → → 5 Given that OA = a and OB = b →

find FE in terms of a and b The point C is such that ABC is a straight line and AB = BC.

Show that F, E and C are not collinear. Given that ABG and FEG are straight lines, →

find OG in terms of a and b