SIXTH FORM 2020

MATHEMATICS 1 hour 30 minutes

Name: …………………………………………..……….……

School: …………………………….……………….….………

Date: …………………………………..………….…………

Instructions • Use black ink or ball-point pen.

• If pencil is used for diagrams/sketches/graphs it must be dark (HB or B). Coloured pencils and highlighter

pens must not be used.

• Calculators and geometrical instruments are allowed in this examination.

• At the top of this page write your name and your current school.

• Answer all questions and ensure that your answers to parts of questions are clearly labelled.

• Answer the questions in the spaces provided – there may be more space than you need.

• You should show sufficient working to make your methods clear. Answers without working may not gain full

credit.

• When a calculator is used, the answer should be given to an appropriate degree of accuracy. Information.

• There are 30 questions in this examination and the total mark for this paper is 100.

• The marks for each question are shown in brackets – use this as a guide as to how much time to spend on each question.

• Check your answers if you have time at the end.

For examiner’s use only

1.

(a) Write 640 000 000 in standard form.

...........................................................

(1)

(b) Work out (3 × 107) ÷ (6 × 104)

Give your answer in standard form.

...........................................................

(2)

(Total for question = 3 marks)

2.

Claire is making a loaf of bread.

A loaf of bread loses 12% of its weight when it is baked.

Claire wants the baked loaf of bread to weigh 1.1 kg.

Work out the weight of the loaf of bread before it is baked.

........................................................... kg

(Total for question = 3 marks)

Q3. x = 0.7

Work out the value of

Write down all the figures on your calculator display.

...........................................................

(Total for question is 2 marks)

4.

Identical pairs of boots are sold in London, in Geneva and in Paris. These

boots have a price of

£115 in London

189 Swiss francs in Geneva

174 euros in Paris

The exchange rates are

£1 = 1.39 Swiss francs

£1 = 1.27 euros

Are the boots the best value for money in London or in Geneva or in Paris? You

must show how you get your answer.

...........................................................

(Total for question = 4 marks)

5.

30% of the people at a concert are female. 1295

of the people at the concert are male.

Work out the number of people at the concert who are female.

...........................................................

(Total for question = 3 marks)

6.

Sandra has a piece of string 153 cm long.

She cuts the string into three lengths in the ratio 4 :2:3

Work out the length, in centimetres, of each piece of string.

........................................................... cm

........................................................... cm

........................................................... cm

(Total for question = 3 marks)

7.

Jack is building a wall.

He uses 300 bricks to build part of the wall.

This part of the wall is 5 metres long and 1.5 metres high.

The complete wall will be 8 metres long and 1.5 metres high.

How many more bricks does Jack need to complete the wall?

...........................................................

(Total for question = 3 marks)

8.

(a) Work out the value of 25−3

...........................................................

(1)

(b) Work out the value of 3503

Give your answer in standard form.

...........................................................

(2)

(Total for question = 3 marks)

9.

Use your calculator to work out

Write down all the figures on your calculator display. You

must give your answer as a decimal.

...........................................................

(Total for question = 2 marks)

10.

The body mass index, B, for a person of mass m kg and height h metres is given by the formula

Usman has a mass of 50 kg. He

has a height of 1.57 m.

(a) Work out Usman's body mass index.

Give your answer correct to one decimal place.

...........................................................

(2)

Tom's height is 1.80 m.

He wants his body mass index to be 21

(b) Work out the mass that will give Tom a body mass index of 21

........................................................... kg (2) Tom is a ski jumper.

The maximum length of skis he can use is 145% of his height. Tom's

height is 1.80 m.

(c) Work out the maximum length of skis Tom can use.

........................................................... m

(3)

(Total for question = 7 marks)

11.

T is inversely proportional to d2 T

= 12 when d = 8

Find the value of T when d = 0.5

...........................................................

(Total for question = 3 marks)

12.

Make t the subject of the formula 2(d – t) = 4t + 7

t = ...........................................................

(Total for question is 2 marks)

13.

Gemma has the same number of sweets as Betty.

Gemma gives 24 of her sweets to Betty.

Betty now has 5 times as many sweets as Gemma.

Work out the total number of sweets that Gemma and Betty have.

...........................................................

(Total for question = 4 marks)

14.

On the grid, draw the graph of y = 2x − 3 for values of x from −2 to 3

Space

for working

(Total for question = 3 marks)

15.

(a) Factorise 4x2 − 9

...........................................................

(1)

(b) Solve the equation

2x2 − 5x − 3 = 0

...........................................................

(3)

(Total for question is 4 marks)

16. m is an integer such that –2 < m

≤ 3

(a) Write down all the possible values of m.

.............................................................................................................................................. (2) (b) Solve 7x – 9 < 3x + 4

.............................................................................................................................................. (2)

(Total for question is 4 marks)

17.

L1 and L2 are parallel lines.

The equation of L1 is y = 3x + 2 L2

passes through the point (3, 4).

Find an equation for L2.

...........................................................

(Total for question = 3 marks)

18.

Here are the first five terms of an arithmetic sequence.

2 6 10 14 18

(a) Write down an expression, in terms of n, for the nth term of this sequence.

...........................................................

(2)

(b) Is 86 a term in the sequence?

You must give a reason for your answer.

(1)

(Total for question = 3 marks)

19.

(a) Simplify (p3)2

...........................................................

(1)

(b) Simplify

...........................................................

(1)

23 × 2n = 29

(c) Work out the value of n.

...........................................................

(1)

2x3 = 128

(d) Work out the value of x.

...........................................................

(1)

(Total for question is 4 marks)

20.

A and B are straight lines.

Line A has equation 2y = 3x + 8

Line B goes through the points (−1, 2) and (2, 8)

Do lines A and B intersect?

You must show all your working.

(Total for question is 3 marks)

21.

The diagram shows a rectangular framework.

The framework is made from 5 metal rods.

The metal rods have a weight of 0.9 kg per metre.

Work out the total weight of the framework.

Give your answer, in kg, correct to 3 significant figures.

........................................................... kg

(Total for question = 4 marks)

22.

A, B, C and D are points on the circumference of a circle, centre O.

BOD is a straight line. Angle ACD = 62°

Find the size of angle ADB.

Give a reason for each stage in your working.

(Total for question = 3 marks)

23.

Fred is making two rectangular flower beds.

The dimensions of the larger rectangle will be three times the dimensions of the smaller rectangle.

There is going to be the same depth of soil in each flower bed. Fred

needs 180 kg of soil for the smaller flower bed.

Work out how much soil Fred needs for the larger flower bed.

........................................................... kg

(Total for question = 2 marks)

24.

ABC is a straight line.

AB: BC = 2 : 5

in terms of a and b.

Give your answer in its simplest form.

...........................................................

(Total for question = 4 marks)

25.

Peter goes for a walk.

He walks 15 miles in 6 hours.

(a) Work out Peter's average speed. Give

your answer in miles per hour.

..................................................... mph

(2)

5 miles = 8 km.

Sunita says that Peter walked more than 20 km.

(b) Is Sunita right?

You must show all your working.

(2)

(Total for question is 4 marks)

Express

26.

A circle has a diameter of 140 cm.

Work out the circumference of the circle.

Give your answer correct to 3 significant figures.

........................................................... cm

(Total for question is 2 marks)

27.

Describe fully the single transformation that maps triangle A onto triangle B.

.............................................................................................................................................

.............................................................................................................................................

.............................................................................................................................................

.............................................................................................................................................

(Total for question = 3 marks)

28.

Louise makes a spinner.

The spinner can land on green or on red.

The probability that the spinner will land on green is 0.7 Louise

spins the spinner twice.

(a) Complete the probability tree diagram.

(2) (b) Work out the probability that the spinner lands on two different colours.

...........................................................

(3)

(Total for question = 5 marks)

29.

25 students in class A did a science exam.

30 students in class B did the same science exam.

The mean mark for the 25 students in class A is 67.8 The

mean mark for all the 55 students is 72.0

Work out the mean mark for the students in class B.

...........................................................

(Total for question is 3 marks)

30.

The frequency table gives information about the numbers of emails sent by 51 teachers on Monday.

(a) On the grid below, draw a frequency polygon for this information.

(2) (b) Nalini says that at least a quarter of these teachers sent more than 30 emails.

Is Nalini correct?

You must explain your answer.

.............................................................................................................................................

.............................................................................................................................................

.............................................................................................................................................

.............................................................................................................................................

(2)

(Total for question = 4 marks)

END OF EXAMINATION