4MA1 Mathematics A: Oct/Nov 2023 Paper 2HHigher Tier Paper 2

The table shows information about the lengths, in minutes, of 50 telephone calls.

10 < m 15

15 < m 20

20 < m 25

25 < m 30

(a)Write down the modal class.

[1]

(b)Work out an estimate for the total length, in minutes, of these telephone calls.

minutes[3]

The diagram shows triangle ABC and triangle ECD

ACD and EBC are straight lines.

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

w = [4]

(a)Reflect shape T in the line y = x[2]

(b)Describe fully the single transformation that maps triangle A onto triangle B

[3]

(a)Solve 2x  56  2x  5

Show clear algebraic working.

x = [3]

(b)Simplify h¹⁵ ÷ h³

[1]

(c)Simplify fully 2g³ k⁵

[2]

(d)Given that  yy₇  y

work out the value of n

n = [2]

Avril bakes a cake.

She uses flour, butter and sugar such that

Avril uses 120 grams of sugar.

Work out the weight of flour Avril uses.

grams[3]

Show that 3 37  2 23  1 27[3]

Hermione buys a boat for $26 800 The value of the boat depreciates by 8% each year.

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

$ [3]

The mean number of goals scored by a hockey team in 8 matches is 6 The team plays 2 more matches and scores k goals in each match. The mean number of goals scored by the hockey team in the 10 matches is 7

Work out the value of k

k = [3]

A straight line passes through the points with coordinates (0, –3) and (2, 0)

Find an equation of the line.

[2]

The diagram shows a hexagon ABCDEF

The area of hexagon ABCDEF is 258 cm²

Work out the value of x

x = [5]

Sid has 2 boxes of crayons, box X and box Y

5 of the 16 crayons in box X are red. 7 of the 20 crayons in box Y are red. Sid takes at random one crayon from box X and one crayon from box Y

(a)Complete the probability tree diagram.

[2]

(b)Work out the probability that Sid takes two crayons that are red or two crayons that are not red.

[3]

2⁷  4⁵  4^x

(a)Calculate the value of x

x = [2]

(b)Simplify fully 125 p⁶ y^242/3

[2]

Robert asked 11 people how many meetings they attended last week.

Here are the results in numerical order.

Find the interquartile range of the number of meetings.

[2]

Here is the graph of the equation 2 y  x  1 drawn on a grid.

By drawing another straight line on the grid, solve the simultaneous equations

x =

y = [3]

(a)Use algebra to show that 0.37 2  41110[2]

(b)Express in the form n where n is an integer.

Show your working clearly.

[3]

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

[3]

P  a(c  y)

a = 8.3 correct to 2 significant figures c = 2 correct to 1 significant figure y = 15 correct to the nearest 5

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

[3]

A particle is moving along a straight line that passes through the fixed point O The displacement, s metres, of the particle from O at time t seconds is given by

Find the value of t when the acceleration of the particle is 5 m/s²

t = [4]

The functions f and g are such that

(a)State which value of x cannot be included in any domain of g

[1]

(b)Find fg(4)

[2]

The function h is such that

(c)Express the inverse function h⁻¹ in the form h⁻¹:x  ...

h⁻¹:x  [4]

The diagram shows equilateral triangle ABC with sides of length 10 cm. A circle is drawn inside the triangle.

D, E and F are points on the circle.

ADB, BEC and CFA are tangents to the circle.

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

cm²[4]

The line with equation x  2 y  5 intersects the curve with equation x²  3y²  13 at the points A and B

Find the coordinates of A and the coordinates of B Show clear algebraic working.

( , )

( , )[5]

OACB is a quadrilateral.

(a)(i)Find the vector in terms of a and b Simplify your answer.

= [1]

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

= [1]

The point P lies on AB and on OC

(b)Using a vector method, find the ratio AP : PB Show your working clearly.

[3]

Here is a frustum of a cone. The frustum is made by removing a small cone from a similar large cone.

The height of the large cone is 15 cm.

The radius of the base of the large cone is 6 cm. The radius of the base of the small cone is x cm.

Given that the volume of the frustum is 421225 π cm³

work out the value of x Show clear algebraic working.

x =

³ 

[5]

Solve 45x3x₂  80x x  4  13x  4 1 x  4(x  2)5x  8

Show clear algebraic working.

x = [5]