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SENIOR FOUR ENTRY MATHEMATICS EXAM SENIOR FOUR 2012 ENTRY MATHS EXERCISE TWO 1. The velocity of water flowing through a pipe is inversely proportional to the square of the radius of the pipe. If the velocity of the water is 30cm/s when the radius of the pipe is 2cm. Find the velocity of water when the radius of the pipe is 4cm. 2. Solve the inequality below hence illustrate your answer on a number line. x>x 3. A sales woman earns a basic salary of Ush. 10,000 per month plus commission of 4% of all the sales above Ush.50,000. Find her gross income for a month in which she sold goods of value Ushs.90,000. 4. In the figure below, it is given that AD and BC are perpendicular to AB. If AB=10cm, ACD = 150 and CAB = 60. Find the perpendicular height AD leaving your answer in surd form. 5. Find the volume of a regular Hexagonal nut of side 4cm and height 2cm. 6. In the rectangle ABCD, AB=15cm and AD = 9cm the arcs DX, XY and YZ are all quadrants of a circle. i) Determine the radii of the three quadrants. (ii) Find the curved length DXYZ giving your answer in terms of . 7. A two digit number is 36 less than the number formed by reversing the digits. If the sum of the digits is 8 find the number. Senior four entry 2012 Page 1 SENIOR FOUR ENTRY MATHEMATICS EXAM 8. Two metal spheres of diameter 2.3cm and 3.86cm are melted down and recast as one sphere. Determine the diameter of the new sphere if 5% of the metal is lost during recasting. 9. Two grades of coffee grade A and grade B costing shs.30 per kg and shs. 24 per kg respectively were mixed to produce a mixture costing shs. 26.40 per kg. Determine the ratio in which grade A and B were mixed. 2 3 3 10. Given that a b c Find the values of a, b and c. 1 3 1 3 11. In the figure below AB is an arc of a circle of radius 5cm, centre C. D is a point in the sector ABC such that CD is 2cm and AD=BD, ACB=720. Determine the area of the shaded region. 12. Solve the simultaneous equation below 4 2 a 3b 11 ~ ~ 3 b a ~ ~ 2 13. Solve the equation 64 3x – 1 ÷ 16 x + 2 = 256 x x 4 2x. 14. a) Using a ruler and a pair of compasses only construct a rhombus ABCD such that AB = 6cm and ABC = 1350. b) Drop a perpendicular from C to AB extended meeting AB extended at N. Measure BN and CN. c) Bisect ABC and DAB, let the two bisectors meet at M. Measure MA d) Determine the area of ABM. Senior four entry 2012 Page 2 SENIOR FOUR ENTRY MATHEMATICS EXAM 15. A lampshade is in the form of a frustum of a cone. Its bottom and top diameters are 12cm and 8cm respectively. Its height is 6cm. a) Find the area of the curved surface of the lamp shade. b) The material used for making the lampshade is sold at Ush.800 per square metre. Find the cost of ten lampshades if a lampshade is sold at twice the cost of the material. (Take = 3.142) 16. A circular lawn is surrounded by a path of uniform width of 7m. The area of the path is 21% of the area of the lawn. (a) Calculate the radius of the lawn. (b) Given further that the path surrounding the lawn is fenced on both sides by a barbed wire on posts at intervals of 10m and 11m on the inner and outer sides respectively. Calculate the total number of posts required for the fencing. c) Hence calculate the total cost of the posts given that each post costs shs. 10500. Senior four entry 2012 Page 3

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