4MA1 Mathematics A: May/June 2022 Paper 2HHigher Tier Paper 2

Here are some integers where a < b < c < d

The mode of the integers is 9 The median of the integers is 8 The range of the integers is 4

Work out the value of a, the value of b, the value of c and the value of d

a =

b =

c =

d = [3]

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

(i)y = 1 (ii) x = 2 (iii) x + y = 7

[3]

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

Label the region R.[1]

An aeroplane travelled from New York City to Los Angeles.

The aeroplane travelled a distance of 3980 kilometres in 5 hours 24 minutes.

Work out the average speed of the aeroplane. Give your answer in kilometres per hour correct to the nearest whole number.

_{kilometresperhour}[3]

Show that 5 13 − 2 67 = 2 1021[3]

The diagram shows an 8-sided shape ABCDEFGH.

The height of the shape is 20 cm CD is parallel to HG

The area of shape ABCDEFGH is 434 cm²

Find the length of CD.

_cm[4]

The diagram shows triangle PQR.

Work out the value of x Give your answer correct to one decimal place.

x = [3]

Change a speed of 81 kilometres per hour to a speed in metres per second.

_{metrespersecond}[3]

Behnaz makes 300 celebration cards so that

birthday cards anniversary cards congratulations cards

25 of the birthday cards have numbers on them.

36% of the anniversary cards have numbers on them. None of the congratulations cards have numbers on them.

Work out what fraction of the 300 cards have numbers on them. Give your answer in its simplest form.

[5]

Pasha invests 50 000 dollars in a savings account for 4 years. He gets 1.3% per year compound interest.

Work out how much money Pasha will have in his savings account at the end of 4 years. Give your answer correct to the nearest dollar.

_dollars[3]

Solve the simultaneous equations

Show clear algebraic working.

x =

y = [3]

(i)Factorise x²+ 5x − 24

[2]

(ii)Hence, solve x²+ 5x − 24 = 0

[1]

Larry is a delivery man.

He has 7 parcels to deliver. The mean weight of the 7 parcels is 2.7 kg

Larry delivers 3 of the parcels. Each of these 3 parcels has a weight of W kg

The mean weight of the other 4 parcels is 3.3 kg

Work out the value of W

W = [3]

The table gives information about the ages, in years, of 80 people in a train carriage.

(a)Complete the cumulative frequency table.

[1]

(b)On the grid opposite, draw a cumulative frequency graph for your table.[2]

(c)Use your graph to find an estimate for the median age of the 80 people.

_years[1]

Of the people in the train carriage, 60% of those who are aged between 18 and 65 are going to work. None of the other people in the train carriage are going to work.

(d)Use your graph to find an estimate for the number of people in the train carriage who are going to work.

[3]

(a)Expand and simplify (5 − x)(2x + 3)(x + 4) Show your working clearly.

[3]

(b)Make c the subject of g = c + 34 + c − 7

[4]

(a)Solve 4x + 53 − 3 − 2x2 = 13

Show clear algebraic working.

x = [4]

(b)Solve the inequality 2y² − 7y − 30  0 Show your working clearly.

[3]

100 farmers are asked if they have goats (G), sheep (S) or chickens (C) on their farms.

Of these farmers 31 have sheep 53 have chickens

11 have sheep and goats 17 have sheep and chickens 18 have goats and chickens 20 do not have any goats, sheep or chickens

(a)Using this information, complete the Venn diagram to show the number of farmers in each appropriate subset.

[3]

(b)Find

(i)n(G)

[1]

(ii)n([G ∪ S]ʹ)

[1]

(iii)n(Gʹ ∩ C )

[1]

One of the farmers who has chickens is chosen at random.

(c)Find the probability that this farmer also has goats.

[2]

M varies directly as the cube of h M = 4 when h = 0.5

Find the value of h when M = 500

[4]

X =

a = 7.5 correct to 1 decimal place. b = 3.42 correct to 2 decimal places. f = 2 correct to the nearest whole number.

Work out the upper bound of the value of X Show your working clearly.

14 7[3]

a = x =

Express a in the form where p, q, r and s are integers.

Give your answer in its simplest form.

a = [3]

The diagram shows four identical circles drawn inside a square.

Each circle touches two other circles and two sides of the square.

The region inside the square that is outside the circles, shown shaded in the diagram, has a total area of 40 cm²

Work out the perimeter of the square. Give your answer correct to 3 significant figures.

_cm[4]

OAB is a triangle. Q is the point on AB such that OQP is a straight line.

Using a vector method, find the ratio AQ : QB

AQ : QB = [5]

ABCD is a kite, with diagonals AC and BD, drawn on a centimetre square grid, with a scale of 1 cm for 1 unit on each axis.

A is the point with coordinates (−3, 4)

The diagonals of the kite intersect at the point M with coordinates (0, 2)

Given that AB = AD = 6.5 cm and the x coordinate of B is positive,

find the coordinates of the points B and D.

( , )

( , )

°[7]

The diagram shows a sketch of the graph of y = cos  x 2

y = cos  x 2

(i)Find the coordinates of the point A

( , )[1]

(ii)Find the coordinates of the point B

( , )[1]

Express x in terms of n Show your working clearly and simplify your expression.

x = [3]