4MA1 Mathematics A: May/June 2018 Paper 2HRHigher Tier Paper 2

x, 10 and y are three integers written in order of size, starting with the smallest integer.

The mean of x, 10 and y is 11 The range of x, 10 and y is 7

Work out the value of x and the value of y.

x =

y =

[2]

A box is put on a table.

The face of the box in contact with the table is in the shape of a rectangle, 2 m by 1.25 m. The pressure on the table due to the box is 42 newtons/m²

Work out the force exerted by the box on the table.

_newtons[3]

Behnaz makes candles.

She has 6.3 kilograms of wax and uses it all to make candles. Each candle Behnaz makes uses 210 grams of wax.

Behnaz sells 25 of the candles for $13 each.

She then reduces this price by 20% and sells the rest of the candles.

Work out the total amount of money Behnaz gets by selling all the candles she made.

$ [4]

(a)Expand and simplify 3(c – 7) + 2(3c + 4)

[2]

(b)Expand and simplify (x + 7)(x – 2)

[2]

(c)Factorise fully 28y²– 21y

[2]

(d)Solve 7x − 24 = 3x + 1

Show clear algebraic working.

x = [3]

Abelie flew by plane from Dubai to Rome.

The flight time was 6 hours 42 minutes. The average speed of the plane was 650 kilometres per hour.

Work out the distance the plane flew.

kilometres[3]

Hiran invests 20 000 rupees in an account for 3 years at 1.5% per year compound interest.

Work out the total amount of money in the account at the end of 3 years. Give your answer to the nearest rupee.

rupees[3]

(a)Simplify fully 20x y4x y₂₂

[2]

(b)Make e the subject of the formula h = 3e + f

[2]

From point A, Stanley walks 200 m due east to point B. From B, he then walks 160 m due south to point C.

Work out the length of AC. Give your answer correct to 3 significant figures.

metres[3]

The diagram shows a regular pentagon, ABCDE, a regular octagon, ABFGHIJK, and an isosceles triangle, BCF.

Work out the size of angle x.

[4]

ABCD is a trapezium.

Work out the size of angle x. Give your answer correct to 1 decimal place.

[4]

The table shows information about the amount of money spent on holiday by each of 120 families.

(a)Write down the modal class.

[1]

(b)Complete the cumulative frequency table for the information in the table.

[1]

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

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

£ [2]

(e)Use your graph to find an estimate for the number of families that spent more than £450 on holiday.

[2]

A, C and D are points on a circle, centre O. AB and CB are tangents to the circle.

Angle ABC = 74°

Work out the size of angle ADC. Show your working clearly.

[3]

The straight line L₁ has equation y = 6 – 2x The straight line L₂ is perpendicular to L₁ and passes through the point (4, 7)

Find the coordinates of the point where the line L₂ crosses the x-axis.

( , )[4]

128 = 4^2x q 2^x

Work out the value of x.

x = [3]

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

7, 3, 8, 1, 4 and 9 represent the numbers of elements.

Find

(i)n(A ‰ B )

(ii)n($үˆ
C )

(iii)n($ү ‰%ү )

[3]

There are 8 counters in a bag. There is a number on each counter.

Fiona takes at random three of the counters. She adds the numbers on the three counters to get her total.

Work out the probability that her total is an odd number.

[4]

(a)Use algebra to show that 0. 436 = 2455[2]

(b)Show that 20 +3 can be expressed in the form a where a is an integer.

Show your working clearly.[3]

Solve the simultaneous equations

Show clear algebraic working.

[5]

a =

p = 8.4 correct to 2 significant figures. q = 6.3 correct to 2 significant figures. t = 0.27 correct to 2 significant figures.

Work out the upper bound for the value of a. Show your working clearly. Give your answer correct to 1 decimal place.

[3]

Solve the inequality 4x²– 5x – 6  0

[4]

Here is the graph of y = f(x)

(a)On the grid above, draw the graph of y = 2f(x)[2]

Here is the graph of y = f(x)

(b)On the grid above, draw the graph of y = f(–x)[2]

Express 4x5x− 25+ 2x − 7 × ⎛⎝ x − 3 − 32x − 5⎠ as a single fraction in its simplest form. ₂ ⎜ ⎟

[4]

OAB is a triangle. → → OA = a OB = b

C is the midpoint of OA. D is the point on AB such that AD : DB = 3 : 1

E is the point such that OB = 2BE

Using a vector method, prove that the points C, D and E lie on the same straight line.[5]

(a)Express 7 – 4x – x² in the form p – (x + q)² where p and q are constants.

[2]

(b)Use your answer to part (a) to solve the equation 7 – 4( y + 3) – ( y + 3)²= 0

Give your solutions in the form e ± f where e and f are integers.

[3]

The curve C has equation y = 3 – 5(x + 1)² The point A is the maximum point on C.

(c)Write down the coordinates of A.

( , )[1]