HALF YEARLY EXAMINATIONS 2015/2016

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1 FORM 4 SECONDARY SCHOOLS HALF YEARLY EXAMINATIONS 2015/2016 MATHS NON-CALCULATOR PAPER Track 3 Time: 20 min Name: Non-Calculator Paper Class: Answer all questions. Each question carries 1 mark. Question Answer 1. Find the value of Simplify: k2 x k 3 k 7 3. Which of the following is the graph of y = 4 x? Diagram A Diagram B Diagram C 4. Which of the following statements is true? a b c Diagram is not drawn to scale. (A) c = b Sin x (B) a = b Cos x (C) a = b Tan x (D) c = a Tan x HY MATHS FORM 4 - TRACK 3 Page 1 of 4 NON CALCULATOR PAPER

2 2.01 x Estimate the value of: A bank pays an annual interest of 1% on a savings account. What is the interest paid in 2 years on 5000? 7. Work out the value of 1 2 of ( ). 8. B(4, 5) Find the gradient of the line AB. A(2, 1) Diagram is not drawn to scale. 9. Find the value of x, given that 81 = 1 3 x. 10. Solve: x 2 5x 6 = 0 HY MATHS FORM 4 - TRACK 3 Page 2 of 4 NON CALCULATOR PAPER

3 11. Expand and simplify: (2x + 3)(x 1) 12. The price of an article is increased from 30 to 33. What is the percentage increase? 13. Luke goes to sleep at 22:45 on Saturday. At what time does he wake up on Sunday if he sleeps for exactly 5 hours and 30 minutes? 14. The area of a circle is 100π cm 2. Calculate the radius of the circle. 15. Change m 3 to cm 3. HY MATHS FORM 4 - TRACK 3 Page 3 of 4 NON CALCULATOR PAPER

4 cm h The parallelogram shown in the diagram has base 11 cm and its area is 33 cm 2. Find its perpendicular height h. Diagram is not drawn to scale. 17. Factorise: x 2 + 2x Simplify: 16p2 q 8 25r Simplify: x 3 + x If x = 1 2, find the value of (1 + x)2. End of Paper HY MATHS FORM 4 - TRACK 3 Page 4 of 4 NON CALCULATOR PAPER

5 FORM 4 SECONDARY SCHOOLS HALF YEARLY EXAMINATIONS 2015/2016 MATHS Track 3 TTime: 1hr 40 min Name: Class: Main NC Total Answer all questions. 1. (a) The number 84 can be written in the form 2 n m p, where n, m and p are prime numbers. Find the values of n, m and p. (b) Sally said that when two prime numbers are multiplied by each other the result obtained is always odd. Is Sally correct? Give a reason for your answer. 2. Work out the value of p 2 2q 2 + r 2, when p = 2, q = 3 and r = 5. Ans: HY MATHS FORM 4 - TRACK 3 Page 1 of 8

6 3. (a) Simplify: 6x3 2x 4 4x 2 (b) (i) Factorise: p 2 q 2 (i) (ii) Hence, without using a calculator, find the value of (ii) 4. (a) Rearrange the formula p = 5 + q r to make q the subject of the formula. (b) Solve the equation: 3x 2 + (x 3) 3 = 10 (4 marks) 5. (a) The price of a printer is reduced by 15% during a sale. The original price of the printer was 200. What is the sale price? HY MATHS FORM 4 - TRACK 3 Page 2 of 8

7 Name: Class: (b) A house is bought for 60,000 and its value appreciates by 8% each year. What will it be worth in 2 years time? 6. (a) What is the value of y where the line y = 3x 2 cuts the y-axis? (b) A(3, a) and B(b, 1) are points on the line y = 4x + 2. Find the values of a and b. (5 marks) 7. A swimming pool has a cross-sectional area in the shape of a trapezium, as shown in the diagram. Water is pumped into the pool at the rate of 2 m 3 per minute. Using the dimensions shown in the diagram, calculate: 1 m 10 m 25 m 3 m (a) The volume of the pool. (b) How long it takes to fill the pool with water, giving your answer in hours, correct to 1 decimal place. Diagram is not drawn to scale. HY MATHS FORM 4 - TRACK 3 Page 3 of 8

8 8. The length of a rectangular wall is 5 m longer than the height of the same wall. (a) If x metres is the height of the wall, write down an expression in terms of x for the length of the wall. x (1 marks) (b) If the area of the wall is 24 m 2, form an equation in x and solve it to find the length of the wall. (5 marks) 9. In ABC, AC = CB = 10 cm and A = 64 o. D is the midpoint of AB. Find: (a) The height CD of the triangle, giving your answer correct to 3 significant figures. 10 cm C Diagram is not drawn to scale 10 cm 64 o A D B HY MATHS FORM 4 - TRACK 3 Page 4 of 8

9 (b) The length of AB, giving your answer correct to 2 decimal places. (c) The area of ABC, giving your answer correct to the nearest cm 2. Ans: (c) 10. Martin goes to a discount supermarket and buys 10 trays of drinks. Each tray costs 9.50 and holds 24 cans of cola. (a) (i) How much did Martin pay for the 10 trays? (i) (1 mark) (ii) How many cans of cola were there in all the 10 trays? (ii) (1 mark) (b) Martin sells 150 cans at a fair, for 55c each and the rest of the cans at a car boot sale, for 35c each. How much did he earn from the sale of all the cans? HY MATHS FORM 4 - TRACK 3 Page 5 of 8

10 (c) Work out the percentage profit made by Martin. Ans: (c) 11. The figure shown in the diagram is made up of a semicircle, with centre O and radius 16 cm, and a sector of a circle with centre A, angle at centre 60 o and radius AB. Hence the diameter of the semi-circle is the radius of the sector and AB=AC. Find: A Semi-circle 16 cm O 60 o B (a) (i) The length of the arc AB, correct to 1 decimal place. Sector C Diagram not drawn to scale (i) (ii) The length of the arc BC, correct to 3 significant figures. (ii) (iii) The perimeter of the shape, correct to the nearest cm. (iii) HY MATHS FORM 4 - TRACK 3 Page 6 of 8

11 (b) The area of the sector ABC, correct to 2 significant figures. 12. The diagram shows a rectangle. All measurements are in centimetres and the perimeter of this rectangle is 24 cm. 2x (a) Show that 2x + y = 12. y Diagram not drawn to scale (b) (i) Use the equation 2x + y = 12 to fill in the table below for the given values of x. x y (ii) On the graph paper provided, draw the graph of 2x + y = 12, using the values obtained in the above table. Take 2 cm to represent 1 unit on the x-axis and 1 cm to represent 1 unit on the y-axis. (4 marks) (c) Use your graph to find the value of x for which the rectangle becomes a square. Ans: (c) (d) Work out the gradient of the graph. Ans: (d) (1 mark) HY MATHS FORM 4 - TRACK 3 Page 7 of 8

12 END OF PAPER HY MATHS FORM 4 - TRACK 3 Page 8 of 8

1. Peter cuts a square out of a rectangular piece of metal. accurately drawn. x + 2. x + 4. x + 2

1. Peter cuts a square out of a rectangular piece of metal. 2 x + 3 Diagram NOT accurately drawn x + 2 x + 4 x + 2 The length of the rectangle is 2x + 3. The width of the rectangle is x + 4. The length