4MA1 Mathematics A: May/June 2021 Paper 2HHigher Tier Paper 2

Write 600 as a product of powers of its prime factors. Show your working clearly.

[3]

Show that 2 47 ÷ 1 18 = 2 27[3]

The bearing of Paris from London is 149°

Work out the bearing of London from Paris.

[2]

E = {letters of the alphabet} B = {b, r, a, z, i, l} I = {i, r, e, l, a, n, d}

(a)List the members of the set

(i)B ∪ I

(ii)B ∩ Iʹ

[2]

K = {k, e, n, y, a}

Cody writes down the statement B ∩ K = ∅ Cody’s statement is wrong.

(b)Explain why.

[1]

ABCD and FGHI are parallel straight lines. EBGJ and ECH are straight lines.

BE = CE Angle BEC = 44°

Work out the size of angle JGH. Give a reason for each stage of your working.

[5]

Mariana sells bags of bird food.

The bags that Mariana sold last week each contained 12 kg of seeds.

The bags that she is going to sell next week will each contain a mixture of nuts and seeds where for each bag

The total weight of the nuts and the seeds in each bag will be 19.35 kg

The weight of seeds in each bag that Mariana sells next week will be less than the weight of seeds in each bag that Mariana sold last week.

Work out this decrease as a percentage of the weight of seeds in each bag that Mariana sold last week. Give your answer correct to one decimal place.

_%[4]

Here is a right-angled triangle.

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

x = [3]

Solve the simultaneous equations

Show clear algebraic working.

a =

c = [3]

(i)Factorise x²+ 2x – 24

[2]

(ii)Hence solve x²+ 2x – 24 = 0

[1]

Here is a triangular prism.

Work out the volume of the prism. Give your answer correct to 3 significant figures.

_cm³[5]

Chengbo sold a house for 180 000 yuan.

The amount for which he sold the house is 24% more than the amount he paid for the house.

(a)Work out how much Chengbo paid for the house. Give your answer correct to 3 significant figures.

_yuan[3]

Zhi bought a house on 1st January 2017 When she bought the house, its value was 120 000 yuan.

The value of the house increased by 1.8% per year.

(b)Work out the value of Zhi’s house on 1st January 2020 Give your answer correct to 3 significant figures.

_yuan[3]

The cumulative frequency table gives information about the distance, in kilometres, that each of 80 workers travel from home to work at Office A.

(a)On the grid below, draw a cumulative frequency graph for the information in the table.

[2]

(b)Use your graph to find an estimate for the median distance travelled.

_km[1]

(c)Use your graph to find an estimate for the interquartile range of the distances travelled.

_km[2]

For Office B, the median distance workers travel from home to work is 15 km and the interquartile range is 5 km.

(d)Use the information above to compare the distances that workers at Office A and workers at Office B travel from home to work. Write down two comparisons.

1

2 [2]

Emilie takes part in two races.

The probability that she wins the first race is 0.7 The probability that she wins the second race is 0.4 The outcomes of the two races are independent.

(a)Complete the probability tree diagram.

[2]

(b)Work out the probability that Emilie wins exactly one of the two races.

[3]

Emilie is going to take part in a third race.

If she wins both of the first two races, the probability that she will win the third race is 0.6

If she wins exactly one of the first two races, the probability that she will win the third race is 0.3

(c)Work out the probability that Emilie will win exactly two of the three races.

[3]

Simplify fully ₁₀ 

[3]

(a)Complete the table of values for y = 1x (x² + 4)

[2]

(b)On the grid, draw the graph of y = 1x (x² + 4) for 0.25 „ x „ 8

[2]

A = 5 when r = 0.3

(a)Find a formula for A in terms of r

[3]

(b)Find the value of A when r = 7.5A

A = [3]

The straight line L passes through the points (4, −1) and (6, 4)

The straight line M is perpendicular to L and intersects the y-axis at the point (0, 8)

Find the coordinates of the point where M intersects the x-axis.

( , )[4]

B Diagram NOT

ABCD is a quadrilateral where A, B, C and D are points on a circle.

AB = 8 cm BC = 7.5 cm Angle ABC = 98° Angle ACD = 35°

Work out the perimeter of quadrilateral ABCD. Give your answer correct to one decimal place.

_cm[6]

Solve the simultaneous equations

Show clear algebraic working.

[5]

Mathematically similar wooden blocks are made in a workshop.

There are small blocks and there are large blocks.

The volume of each small block is 300 cm³

Given that

work out the volume of each large block.

_cm³[3]

The point A is the only stationary point on the curve with equation y = kx² + 16x where k is a constant.

Given that the coordinates of A are  2 3, a

find the value of a. Show your working clearly.

a = [5]

The curve S has equation y = f(x) where f(x) = x² The curve T has equation y = g(x) where g(x) = 2x²– 12x + 13

By writing g(x) in the form a(x – b)²– c, where a, b and c are constants, describe fully a series of transformations that map the curve S onto the curve T.

[4]

Pippa has a box containing N pens.

There are only black pens and red pens in the box. The number of black pens in the box is 3 more than the number of red pens.

Pippa is going to take at random 2 pens from the box.

The probability that she will take a black pen followed by a red pen is 935

Find the possible values of N. Show clear algebraic working.

[5]