1. (a) Factorise 20x – 35y

MATHEMATICSHIGHER TIER

MOCK EXAM – DECEMBER 5TH 2016

Name:___________________________________________________________

Mathematics Group:_____________________________________________

Mathematics Teacher:____________________________________________

Time Allowed: 1 hour 30 minutes

Question Mark

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TotalGrade

(1)(b) Factorise x2 – 8x + 12

(2)[3 marks]

2. Make m the subject of the formular = 5m + 7

[2 marks]3. Ann, Barry and Chris share money in the ratio 4 : 6 : 9.

Chris receives £75 more than Ann.How much money do they receive altogether?

[3 marks]

4. ABC is a right angled triangle. Work out the angle marked x.Give your answer to 1 decimal place.

[3 marks]5. The first 4 terms of an arithmetic sequence are 4, 11, 18, 25

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

18cm

11cmx

C

B

A

(2)(b) The nth term of a different sequence is 6n – 2.

Is 200 a term in this sequence? Show how you came by your answer.

(2)[4 marks]

6. Paul and Edna are driving along a motorway. Because of roadworks, the speed limit on the motorway is 50 miles per hour.A sign on the motorway says that Sheffield is 15 miles away and that the average time it takes a motorist to drive this distance is 16 minutes.Paul says “we will have to go faster than the speed limit to reach Sheffield in that time”.Is Paul correct? Show how you came by your answer.

[3 marks]

7. The time taken by a group of 45 students to complete a times tables test in seconds is shown in the table…Time taken (t secs) Number of

Students30 ≤ t < 40 5

40 ≤ t < 50 1150 ≤ t < 60 1860 ≤ t < 70 670 ≤ t < 80 5

(a) Write down the modal class interval

(1)(b) Calculate an estimate for the mean time taken to complete the

test.

(3)[4 marks]

8. In a bag there are red counters, white counters and black counters.There are four times as many red counters than white counters and twice as many white counters as black counters.Write down the ratio of red counters to white counters to black counters.

[2 marks]9. Triangles ABC and BCD are right angled triangles.

x cm16cm

10cm26cm

CB

A

(a) Find the length BC

(2)(b) Using your answer to part (a), find the length marked x. Give your answer correct to 2 decimal places.

(2)

[4 marks]

10. y is directly proportional to the square of x.When x is 11, y is 605.Find the value of y when x is 0.5.

[3 marks]11. The graph of y = f(x) is shown on the drawn on the grid below.

y8

6

4

2

(a) Estimate the coordinates of the turning point of the graph.

(1)(b) Write down the roots of f(x) = -4.

(1)(c) Write down the value of f(2.5)

(1)[3 marks]

12. ABCD is a rectangle and EFG is an isosceles triangle.The perimeter of the two shapes is the same.Work out the area of rectangle ABCD.

x

2x

4x + 3

D C

BA

3x

6x – 6

[5 marks]13. Wayne invests £5000 in a savings account for 4 years.

The account pays compound interest at an annual rate of…3% for the first yearx% for the second yearx% for the third yearx% for the fourth year.

At the end of four years there is £5465.22 in the savings account.(a) Work out the rate of interest in the second year.

Give your answer correct to 2 decimal places.

(4)Wayne travels to work by train. He buys a monthly railcard. The cost of his monthly railcard rises by 15% to £82.80.(b) What was the cost of the railcard BEFORE the increase?

(2)[6 marks]

14. B and C are points on the circumference of a circle with centre O.AB is a tangent to the circle.AOC is a straight line.Angle BCO is 28°.Work out the size of angle x.You must give a reason for eachstage of your working. 28

°

x

OC

BA

[4 marks]

15. (a) Expand and fully simplify (3x + 2)2

(2)

(b) Using your answer to (a) prove algebraically that (3x + 2)2 + (3x + 2) is divisible by 3 for all positive values of x.

(2)[3 marks]

16. Sheffield United are playing two games over the Christmas period.The probability they win their first game is 0.8.If they win their first game, the probability they don’t win their second game is 0.1.If they don’t win their first game, the probability they don’t win their second game is 0.4.

(a) Compete the tree diagram…

FIRST GAME SECOND GAME

Doesn’t

Doesn’t Win

Doesn’t Win

Win

Win

Win

(2)(b) What is the probability that they only win exactly one of their

games over the Christmas period?

(3)[5 marks]

17. Prove algebraically that the recurring decimal 0.6 4̇ has the value 2945 .

[3 marks]18. (a) Factorise 25x2 – 4

(2)(b) Show that 1

5x2+3 x−2÷ 125x2−4

simplifies to ax+bcx+d where a, b, c and d are integers.

(3)[5 marks]

19. The diagram shows the sector of a circle with a radius of 11cm.Work out the length of the arc AB.

Doesn’t

Give your answer correct to 3 significant figures.

[2 marks]

20. r=mt2

m = 21.2 correct to 3 significant figurest = 8.1 correct to 1 decimal place.

By considering the bounds of m and t, work out the smallest possible value for r.

[3 marks]21. Solve algebraically the simultaneous equations

x2 + y2 = 29

B

A

11cm

11cm

75°

y – x = 3

[5 marks]

22. This shape is made of a cone on top of a hemisphere.

The shape is made of a material with a density of 4.2g/cm3.Work out the mass of the object.Give your answer to an appropriate degree of accuracy.

21cm

8.1cm

[5 marks]