SPECIMEN PAPERS INSTRUCTIONS TO CANDIDATES INFORMATION FOR CANDIDATES Centre Number Rewarding Learning Candidate Number General Certificate of Secondary Education 2020 Mathematics Unit M4 (With calculator) HigherTier SPECIMEN PAPER TIME 2 hours Write your Centre Number and Candidate Number in the spaces provided at the top of this page. Write your answers in the spaces provided in the question paper. Complete in blue or black ink only. Do not write in pencil or with a gel pen. Answer all twenty-five questions. Any working should be clearly shown in the spaces provided since marks may be awarded for partially correct solutions. You can use a calculator for this paper. The total mark for this paper is 100 Figures in brackets printed down the right-hand side of pages indicate the marks awarded to each question or part question. You should have a ruler, compasses and protractor. The Formula Sheet is on page 2.
Transcript
SPECIMEN PAPERS
INSTRUCTIONS TO CANDIDATES
INFORMATION FOR CANDIDATES
Centre Number
Rewarding Learning Candidate Number
General Certificate of Secondary Education 2020
Mathematics
Unit M4
(With calculator)
HigherTier
SPECIMEN PAPER TIME
2 hours
Write your Centre Number and Candidate Number in the spaces provided at the top of this page. Write your answers in the spaces provided in the question paper. Complete in blue or black ink only. Do not write in pencil or with a gel pen. Answer all twenty-five questions. Any working should be clearly shown in the spaces provided since marks may be awarded for partially correct solutions. You can use a calculator for this paper.
The total mark for this paper is 100 Figures in brackets printed down the right-hand side of pages indicate the marks awarded to each question or part question. You should have a ruler, compasses and protractor. The Formula Sheet is on page 2.
1 Two points P(–4, –1) and Q(–8, 5) are joined by a straight line.
Work out the coordinates of the midpoint of the line PQ.
Answer ( , ) [2]
2 The volume of oil in a tank decreases by 5% every hour.
At 11am there are 9000 litres of oil in the tank.
What will the volume of oil be at 2pm?
Answer litres [3]
3 During a Science experiment the growth of plants was recorded. The results are shown in the table below.
(a) Calculate an estimate of the mean growth of the plants.
Answer cm [4]
(b) Explain why your answer is only an estimate of the mean growth.
[1]
4
A trawler T has sailed 26 km from a harbour H. It is now 10 km west of the harbour.
Calculate how far south it is from the harbour.
Answer km [3]
5 Sarah has a salary of £26,520 per year.
Her personal allowance free of tax is £11,500.
She pays basic rate income tax at 20%
How much of her monthly salary is left after income tax has been deducted?
Round your answer to the nearest penny.
Answer £ [5]
6 Five times a number is the same as adding 24 to the number.
What is the number?
Answer [3]
7 Ten models of car were tested to find how long it took each car to travel
500 metres.
The times and engine sizes are plotted below.
Estimate the time for a car with engine size 1700 cc to travel 500 metres.
You must show your method clearly.
Answer seconds [2]
8
The diagram above is a parallelogram.
The sizes of the angles in degrees are 3x, 4x – 23, 3x and 2x + 35
Work out the value of x.
Answer x = [3]
9 Tony opened a savings account with the Western Bank.
After one year, the bank paid 6% per annum interest into his account.
The total amount in his account was then £710.20
Work out the amount of money with which Tony opened the account.
Answer £ [3]
10
11 A solid is formed by attaching a cylinder to a cone.
The cylinder has a base radius of 3 cm and a height of 7.2 cm.
The height of the cone is 4.2 cm.
Find the total volume of the solid.
Give your answer correct to 2 significant figures.
Answer cm3 [3]
12 (a) Expand and simplify (5x + 2) (4x – 3)
Answer [2]
(b) Factorise x2 – 16
Answer [2]
(c) Simplify x + 4
x2 – 16
Answer [2]
13 (a) Given that 1001 = 7 × 11 × 13, write 9009 as a product of primes.
Answer [2]
(b) Given that 945 = 33 × 5 × 7, use (a) to find the HCF of 945 and 9009
Answer [2]
14 A parallelogram has sides of length 3 cm and 5 cm, with an angle of 50˚ between the sides.
Calculate the area of the parallelogram.
5
5
Answer _ cm2 [4]
3 3
50o
15
The straight line above passes through the points (0, 1) and (1, 4) and (2, 7).
(a) Find the equation of the line which is parallel to the line shown and which passes through the point (0, –1).
Answer [3]
(b) Find the equation of the line which is perpendicular to the line shown and passes through the point (6, 4)
Answer [3]
16
17
18 The table shows information about 250 workers in a factory.
The manager decides to carry out a survey about the workers’ views on a new logo for the company.
The manager decides to use a stratified sample of 60 workers.
Work out the number of women that should be in the sample.
Answer [2]
19
Diagram A above represents the cross section of a solid sculpture (B).
The lower section is a rectangle measuring 1.5 metres by 2.2 metres.
The upper section is a sector of a circle containing an angle of 120°
The sculpture is 3.6 metres long.
Work out the volume of the sculpture.
Answer m3 [4]
20 Solve 5t 2 − 8t − 11 = 0
No marks will be awarded for using trial and improvement.
Give your answers correct to two decimal places.
Answer [3]
21
The histogram illustrates how much time drivers took on a particular journey.
(a) Calculate an estimate for the mean time.
Answer minutes [4]
(b) Two-thirds of the drivers took more than M minutes.
Calculate an estimate for the value of M.
Answer minutes [3]
22 There are 30 pupils in a class.
All 30 pupils completed a test and the mean mark was 68.4%
There are 16 girls and 14 boys in the class.
The mean mark for the girls was 74%
What was the mean mark for the boys?
Answer [4]
23 PQRS is a rhombus.
Q has co-ordinates (5, 2) and S has co-ordinates (11, 4)
Find the equation of the line that passes through the points R and P.
Answer [5]
24 (a) Answer ________________ [3]
(b) Prove that
14 (2n + 1)(n + 4) – 1
4 n (2n + 1) ≡ 2n + 1
[3]
25
The width of rectangle P is (x − 3) cm and the width of Q is (2x − 5) cm.
The area of rectangle P is 2 cm2 and the area of rectangle Q is 3 cm2
The sum of the lengths of the two rectangles is 3 cm.
By forming and solving an equation find the lengths of both rectangles. Length of rectangle P cm
