4MA1 Mathematics A: May/June 2023 Paper 1HRHigher Tier Paper 1

Write 2250 as a product of powers of its prime factors. Show your working clearly.

[3]

Here is a Venn diagram.

E

(a)Write down the numbers that are in the set

(i)A

[1]

(ii)B ∪ C

[1]

Dominic writes down 9 ∉ C

(b)Explain why Dominic is correct.

[1]

ABCD and EFGH are similar quadrilaterals.

(a)Work out the length of GH

_cm[2]

(b)Work out the length of BC

_cm[2]

The diagram shows a shape made up of three semicircles, enclosing a right‑angled triangle.

AB, BC and CA are each the diameter of a semicircle.

BC = CA = 6 cm.

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

_cm[5]

Each time Evie plays a game against her computer, she will win or lose.

For each game, the probability that Evie will win is 0.74 Evie is going to play 300 games against her computer.

Work out an estimate for the number of games that Evie will lose.

[2]

(a)Simplify m¹⁰÷ m³

[1]

k ⁿ × k⁴= k¹²

(b)Write down the value of n

n = [1]

(c)Simplify (3x⁶ y⁸)²

[2]

(a)Expand 4x(x – 5)

[1]

(b)Factorise y²– 9y + 20

[2]

(a)Write 5.6 × 10^–3 as an ordinary number.

[1]

(b)Work out 6  102.1  10_45

Give your answer in standard form.

[2]

Kazi buys a car for 700 000 taka. The value of the car depreciates by 12% each year.

Work out the value of the car at the end of 3 years. Give your answer correct to the nearest taka.

_taka[3]

On the grid, enlarge the shaded shape with scale factor 13 and centre (1, 7)[2]

The diagram shows a block of iron in the shape of a cuboid.

The block has length w cm, width 5 cm and height 4 cm

The density of iron is 7.8 g / cm³ The mass of the block is 1950 g

Work out the value of w

w = [3]

Moeen has a biased 6‑sided dice.

The table gives information about the probability that, when the dice is thrown, it will land on each number.

(a)Show that x + y = 0.19[2]

Given that 3x – y = 0.09

and x + y = 0.19

(b)work out the value of x and the value of y Show clear algebraic working.

x =

y = [3]

Novak is going to play two games of tennis.

The probability that he wins the first game is 0.7

If he wins the first game, the probability that he wins the second game is 0.9 If he loses the first game, the probability that he wins the second game is 0.4

(a)Complete the probability tree diagram.

[1]

(b)Work out the probability that Novak wins both games of tennis.

[2]

The table gives information about the times taken by 80 people to run a race.

Time taken (t minutes) Frequency

(a)Complete the cumulative frequency table.

Time taken (t minutes) Cumulative frequency

[1]

(b)On the grid below, draw a cumulative frequency graph for your table.

[2]

(c)Use your graph to find an estimate for the median time taken.

_minutes[1]

(d)Use your graph to find an estimate for the interquartile range of the times taken.

_minutes[2]

BCDEFG is a hexagon. AB, BC and CD are three sides of a regular n‑sided polygon.

Calculate the value of n Show your working clearly.

n =

[4]

Use algebra to show that 00.17. 1766 == 35198[2]

F is inversely proportional to the square of r

F = 36 when r = 4

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

[3]

(b)Work out the value of F when r = 48

[1]

Diego builds a fence using fence panels.

The total length of the fence is 50 metres, correct to the nearest 5 metres. The length of each fence panel is 1.3 metres, correct to the nearest 10 cm.

The cost of each fence panel is £8.65

Diego may only buy complete fence panels. Diego only pays for the number of panels he needs to build the fence.

Work out the greatest difference in the possible amounts that Diego could pay to build the fence. Show your working clearly.

£ [4]

The diagram shows a triangle ABC where A, B and C represent the positions of three towns.

C

Pru travels directly from A to B and then directly from B to C

Yang travels directly from A to C

Given that the values for AB and BC are in kilometres,

work out how much further Pru travels than Yang travels. Give your answer in km, correct to one decimal place.

_km[5]

Curve C has equation y = f (x) The graph of curve C has one maximum point. The coordinates of this maximum point are (3, 5)

(a)Write down the coordinates of the maximum point on the curve with equation

(i)y = 2f (x)

( , )[1]

(ii)y = f (x) – 7

( , )[1]

(iii)y = f (–x)

( , )[1]

Curve L has equation y = x²+ 7x + 20

 2  Curve L is transformed to curve S under the translation   0  

(b)Find an equation for S Give your answer in the form y = ax²+ bx + c

y = [4]

The curve T has equation y = x³– 2x²– 9x + 15

(a)Find dydx

dydx = [2]

(b)Find the range of values of x for which T has a positive gradient. Give your values correct to 3 significant figures. Show your working clearly.

[4]

Some people attend a concert. The histogram shows information about the ages of these people.

Work out an estimate for the percentage of these people who are aged more than 55 years. Give your answer correct to one decimal place.

%[4]

Simplify  x²  4   4x  7x  2 x  2x

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

[4]

Given that

find an expression for x in terms of n State any restrictions on n

[5]

Here is a triangle ABC

(2x + 1) cm

The area of the triangle is (x²+ x – 3.75) cm²

Find the size of the largest angle in triangle ABC Give your answer correct to the nearest degree.

[6]