4MA1 Mathematics A: January 2021 Paper 2HHigher Tier Paper 2

A train takes 6 hours 39 minutes to travel from New Delhi to Kanpur. The train travels a distance of 429 km.

Work out the average speed of the train. Give your answer in km/h correct to one decimal place.

km/h[3]

Ava writes down five whole numbers.

For these five numbers

the median is 7

the mode is 8

the range is 5

Find a possible value for each of the five numbers that Ava writes down.

[3]

Gladys buys a table for $465 to sell in her shop.

She sells the table for $520

(a)Work out the percentage profit that Gladys makes from the sale of the table. Give your answer correct to 3 significant figures.

%[3]

Gladys has a sale in her shop.

She decreases all the normal prices by 12% The normal price of an armchair was $550

(b)Work out the sale price of the armchair.

$ [3]

(a)On the grid, draw and label the straight line with equation

(i)x = 1.5

(ii)y = x

(iii)x + y = 6[3]

(b)Show, by shading on the grid, the region that satisfies all three of the inequalities

Label the region R.[1]

(a)Expand and simplify 4x(2x + 5) – 3x(2x – 3)

[2]

Given that × yy₆ = y¹³

(b)work out the value of n.

n = [2]

(c)(i)Solve the inequality 7t – 8 < 2t + 7

[2]

(ii)On the number line below, represent the solution set of the inequality solved in part (c)(i)

[1]

(a)Write down the value of y⁰

[1]

(b)Work out 9.6 × 103.2 × 10₁₆

Give your answer in standard form.

[3]

There are 5 cocoa pods in a bag. The mean weight of the 5 cocoa pods is 398 grams.

A sixth cocoa pod is put into the bag. The mean weight of the 6 cocoa pods is 401 grams.

Work out the weight of the sixth cocoa pod that is put into the bag.

_grams[3]

A, B and C are points on a circle with centre O.

AOC is a diameter of the circle.

AB = 8 cm BC = 15 cm

Angle ABC = 90°

Work out the total area of the regions shown shaded in the diagram. Give your answer correct to 3 significant figures.

cm²[5]

Find the lowest common multiple (LCM) of A and B. Give your answer as a product of powers of prime numbers.

[2]

The people working for a company work in Team A or in Team B.

number of people in Team A: number of people in Team B = 3 : 4

45 of Team A work full time.

24% of Team B work full time.

Work out what fraction of the people working for the company work full time. Give your fraction in its simplest form.

[3]

Simplify fully ₆₁₀   18t w 

[3]

15 people were asked how long, in minutes, they had been waiting for a bus.

Here are the results.

Find the interquartile range of these times.

_minutes[2]

P, Q, R, S and T are points on a circle with centre O.

QOS is a diameter of the circle.

(a)Find the value of

(i)m

(ii)n

[2]

(b)Find the size of angle QPO.

[1]

(a)Solve 9a − 75 − 3a − 74 = 4.55

Show clear algebraic working.

a = [3]

(b)Make c the subject of the formula p =

[4]

A postman records the weight of each parcel that he delivers.

The histogram shows information about the weights of all the parcels that the postman delivered last Monday. No parcels weighed more than 6 kg.

Frequency density

63 of the parcels that the postman delivered last Monday each had a weight between 0.5 kg and 2 kg.

(a)Work out the total number of parcels the postman delivered last Monday.

[3]

The postman picks at random two of the records of the parcels he delivered last Monday.

(b)Work out an estimate for the probability that each parcel weighed more than 2.25 kg.

[3]

Some students were asked the following question.

“Which of the subjects Russian (R), French (F) and German (G) do you study?”

Of these students

4 study all three of Russian, French and German 10 study Russian and French 13 study French and German 6 study Russian and German 24 study German 11 study none of the three subjects the number who study Russian only is twice the number who study French only.

Let x be the number of students who study French only.

(a)Show all this information on the Venn diagram, giving the number of students in each appropriate subset, in terms of x where necessary.

E

[3]

Given that the number of students who were asked the question was 80

(b)work out the number of these students that study Russian.

[3]

The diagram shows a solid prism ABCDEFGH.

The trapezium ABCD, in which AD is parallel to BC, is a cross section of the prism. The base ADEH of the prism is a horizontal plane. ADEH and BCFG are rectangles. The midpoint of BC is vertically above the midpoint of AD so that BA = CD.

The perpendicular distance between edges AD and BC is 20 cm.

(a)Work out the total surface area of the prism.

cm²[4]

(b)Calculate the size of the angle between AF and the plane ADEH. Give your answer correct to one decimal place.

[3]

A rectangle ABCD is to be drawn on a centimetre grid such that

A has coordinates (–4, –2) B has coordinates (1, 10) C has coordinates (19, a) D has coordinates (b, c)

(a)Work out the value of a, the value of b and the value of c.

a =

b =

c = [4]

(b)Calculate the perimeter, in centimetres, of rectangle ABCD.

cm[3]

A particle P is moving along a straight line. The fixed point O lies on this line.

At time t seconds where t  0, the displacement, s metres, of P from O is given by

Find the displacement of P from O when P is instantaneously at rest.

Give your answer in the form ab where a and b are integers.

metres[5]

The diagram shows a shaded region T formed by removing an equilateral triangle PQR from a regular hexagon ABCDEF.

The points P and Q lie on AB such that AB = 1.5 × PQ

Given that the area of region T is 72 3 cm²

work out the length of PQ.

cm

[4]

Write 25x5x₂ − 64− 13x − 6 × − 8x + 155x + 8 − (x − 7)

as a single fraction in its simplest form. Show clear algebraic working.

[4]

The diagram shows a sector OBC of a circle with centre O and radius (6 + x) cm.

A is the point on OB and D is the point on OC such that OA = OD = 6 cm

Angle BOC = 50°

Given that

the perimeter of sector OBC = 2 × the perimeter of triangle OAD

find the value of x. Give your answer correct to 3 significant figures.

x = [6]