4MA1 Mathematics A: January 2019 Paper 2HRHigher Tier Paper 2

The table gives information about the number of days that 100 cars were in an airport car park.

0 < d  4

4 < d  8

8 < d  12

12 < d  16

16 < d  20

(a)Write down the modal class.[1]

(b)Work out an estimate for the mean number of days.

[4]

The diagram shows two solid toy bricks, Brick A and Brick B.

6 cm 5 cm

Brick A is a triangular prism of length 5 cm. The cross section of Brick A is an isosceles right-angled triangle with equal sides of length 6 cm.

Brick B is half a cylinder of length 5 cm. The semicircular cross section of Brick B has diameter 6 cm.

The volume of Brick A is greater than the volume of Brick B.

How much greater? Give your answer correct to 1 decimal place.

[4]

Here are the first five terms of a number sequence S.

(a)Find an expression, in terms of n, for the nth term of this sequence.[2]

The nth term of a sequence T is given by n²− 3

There are numbers that are terms in both the sequence S and the sequence T.

(b)Find one of these numbers.[2]

On Saturday, Jacob walked 10 800 steps. On Sunday, he walked 7% more steps than on Saturday.

Work out how many steps Jacob walked on Sunday.[3]

The scale drawing shows the position of a hall and the position of a library.

A post box is 140 metres from the library on a bearing of 220°

(a)Show the position of the post box on the scale drawing. Mark the position with a cross ( ) and label it P.[2]

(b)Use your scale drawing to find

(i)the real distance, in metres, of the hall from the post box,

(ii)the bearing of the hall from the post box.

[2]

Pentagon ABCDE is drawn inside the regular octagon ABFGHIJK. The pentagon has exactly one line of symmetry.

Work out the value of x.

[4]

The diagram shows a trapezium.

Work out the value of y. Give your answer correct to 1 decimal place.

[4]

(a)Simplify fully

[2]

(b)Solve the inequality 7 < 4x − 1  17[3]

Omar invests 6000 dirham for 4 years in a savings account. He will get 1.5% per year compound interest.

Work out the total amount of interest Omar will have received by the end of 4 years. Give your answer correct to the nearest dirham.

[3]

(a)Simplify fully (16x⁸ y⁶ )^1/2[2]

(b)Solve 8 − 2x3 − 2x − 32 = 4

Show clear algebraic working.

[3]

(c)Make f the subject of m = 13 ef[2]

The straight line L₁ has equation x + 2y = 4 The straight line L₂ passes through the points (−1, −7) and (7, 9)

Michael says that the lines L₁ and L₂ are perpendicular.

Is Michael correct? You must show clearly how you get your answer.[3]

Freddie recorded the number of runs he scored in each of 11 cricket matches. Here are his results.

Find the interquartile range of his results.[3]

Carlos, Flavia and Tazia shared £861 between themselves.

The amount of money Flavia got is 65% of the amount of money Carlos got. The amount of money Tazia got is 22% more than the amount of money Carlos got.

Work out how much money Carlos got.

[3]

(a)Given that a = 3^x and b = 3^y

express in terms of a or b or a and b,

(i)3^2x

(ii)3^x+4y

(iii)3^y−1[3]

a = 3^x and b = 3^y

ab = 2187

a² b = 177 147

(b)Work out the value of x and the value of y. Show your working clearly.

[3]

Barney has a biased coin.

When the coin is thrown once, the probability that the coin will land heads is 0.3

Barney throws the coin 4 times.

(a)Work out the probability that the coin will land heads exactly 3 times.[3]

(b)Work out the probability that the coin will land heads at least once.[2]

120 people who visited a sports centre were asked if they went swimming (S), played basketball (B) or used the gym (G).

Their answers showed that

28 people went swimming 16 people played basketball 27 people used the gym 3 people went swimming and played basketball 5 people played basketball and used the gym 7 people went swimming and used the gym 2 people went swimming, played basketball and used the gym

(a)Using this information, complete the Venn diagram to show the number of people in each region of the Venn diagram.

[3]

One of the people who went swimming is chosen at random.

(b)Find the probability that this person also played basketball.[1]

P = ef

e = 4.8 correct to 2 significant figures. f = 0.26 correct to 2 significant figures.

(a)Work out the lower bound for the value of P. Show your working clearly. Give your answer correct to 3 significant figures. t Q = w t = 2.73 correct to 3 significant figures. w = 0.04 correct to 1 significant figure.[2]

(b)Work out the upper bound for the value of Q. Show your working clearly. Give your answer correct to 2 significant figures.[2]

ABCD is a quadrilateral.

Find the area of quadrilateral ABCD. Give your answer correct to 3 significant figures.

[5]

(a)Write 3x²− 12x + 7 in the form a(x + b)² + c[3]

The line L is the line of symmetry of the curve with equation y = 3x²− 12x + 7

(b)Using your answer to part (a) or otherwise, write down an equation of L.[1]

The curve with equation y = (10x − 3)(x + 1) and the line with equation y − 6x = 0 intersect at the points A and B.

Find the coordinates of the midpoint of AB. Show your working clearly.

[6]

OPQ is a sector of a circle, centre O OAB is a sector of a circle, centre O

A is the point on OP such that OA : AP = 3 : 2 B is the point on OQ such that OB : BQ = 3 : 2 Angle POQ = 45°

The area of the shaded region is 812 π cm²

Work out the perimeter of the shaded region. Give your answer in terms of π.

[6]

The 10th term of an arithmetic series, S, is 66 The sum of the first 20 terms of S is 1290

Find the 5th term of S. Show your working clearly.[4]