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

Last season, the number of goals scored by Arjun, by Simon and by Kath for their football team were in the ratios 2 : 5 : 8

Simon scored 12 more goals than Arjun.

Work out the number of goals scored by Kath.

[3]

The table gives information about the number of minutes that Abby spent walking each day in September.

120 < M  150

Work out an estimate for the total number of minutes that Abby spent walking in September.

_minutes[3]

Nanette buys 60 notebooks for a total cost of 780 dirhams.

Nanette sells 70% of the notebooks for 22 dirhams each. She sells the remaining notebooks for 19 dirhams each.

Work out Nanette’s percentage profit. Give your answer correct to 3 significant figures.

%[4]

The diagram shows a sketch of triangle A and triangle B on a coordinate grid.

(a)Given that triangle A has been translated to give triangle B, work out the value of d, the value of e and the value of f

d =

e =

f = [3]

The diagram shows shape P and shape Q drawn on a grid.

y 12

11

10

(b)Describe fully the single transformation that maps shape P onto shape Q

[3]

(c)On the grid above, rotate shape P 90° clockwise about (3, 5) Label your shape R[2]

The diagram shows a shaded shape AEBCD made by removing triangle AEB from rectangle ABCD

Work out the perimeter of the shaded shape.

_cm[4]

(a)Simplify (2c⁴ d⁷)³

[2]

(b)Find the value of 5y⁰ where y > 0

[1]

(c)Factorise fully 16a² b³+ 20a³ b

[2]

(d)(i)Factorise x²+ 9x – 22

[2]

(ii)Hence solve x²+ 9x – 22 = 0

[1]

The region R, shown shaded in the diagram, is bounded by three straight lines.

Find the inequalities that define R

[4]

(a)Write 300 as a product of its prime factors. Show your working clearly.

[2]

A = 2 × 2 × 2 × 3 × 3 × 5

B = 2 × 2 × 3 × 3 × 3 × 5

(b)Find the lowest common multiple (LCM) of 5A and 7B Show your working clearly.

[2]

Solve the simultaneous equations

Show clear algebraic working.

x =

y = [3]

Here are the test marks of 15 students.

Find the interquartile range of these marks.

[2]

The curve C has equation y = 4x³+ x²– 20x

(a)Find dydx

dydx = [2]

(b)Find the x coordinates of the points on C where the gradient is 4 Show clear algebraic working.

[4]

The cumulative frequency graph shows information about the heights, in centimetres, of 50 plants in a flowerbed.

(a)Use the graph to find an estimate for the median height of these plants.

_centimetres[1]

(b)Use the graph to find the frequency for the class interval 30 < Height  40

[1]

(c)Use the graph to find an estimate for the number of plants with a height greater than 35 centimetres.

[2]

A is the point with coordinates (–5, 12)

B is the point with coordinates (19, –48)

Find an equation of the straight line that passes through the points A and B

[3]

Factorise fully 50g²– 18

8³_n[3]

(a)2   2 16^3/2

Work out the value of n Show your working clearly.

n = [3]

(b)Find 4% of 4.5 × 10¹⁵⁷ Give your answer in standard form.

[3]

The Venn diagram shows a universal set ℰ and sets A, B and C

The numbers and the letter x represent numbers of elements.

Given that n(A ∪ B) = 42

(a)find the value of x

x = [1]

(b)Find n(Aʹ)

[1]

(c)Find n(Bʹ ∩ C )

[1]

The functions g and h are such that

(a)What value of x must be excluded from any domain of g?

[1]

(b)Solve gh(x) = 1

[3]

The incomplete table and incomplete histogram give information about the times, in minutes, that 140 people waited at a station for a train.

0 < t  5

5 < t  15

Complete the table and the histogram.[4]

OMA, ONB, MPB and NPA are straight lines.

M is the midpoint of OA

ON : NB = 1 : 5

OM = a ON = b

(a)Find in terms of a and b the vector AN

[1]

(b)Use a vector method to find the ratio AP : PN

AP : PN = [4]

The sum of the first 80 terms of an arithmetic series, S, is 470

The 75th term of S is 14.5

The sum of the first X terms of S is 171

Work out the value of X Show your working clearly.

X = [6]

A curve has equation y = f(x)

There is only one turning point on the curve. The coordinates of this turning point are (6, 5)

Write down the coordinates of the turning point on the curve with equation

(a)y = f(x – 4)

( , )[1]

(b)y = f(3x)

( , )[1]

The diagram shows two circles with centre O and a regular pentagon ABCDE

A, B, C, D and E are points on the larger circle. The pentagon has sides of length 8 cm.

The diagram is shaded such that

Work out the radius of the smaller circle. Give your answer correct to 3 significant figures.

_cm[6]

A frustum is made by removing a small square-based pyramid from a similar large squared-based pyramid as shown in the diagram.

The height of the small pyramid is 15 cm. The height of the large pyramid is 45 cm. The square base of the large pyramid has side length 39 cm.

Work out the total surface area of the frustum. Give your answer correct to the nearest whole number.

_cm²[5]