S 4 TEST Express as single logarithms: ii) Express as single logarithms: log24

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1 S 4 TEST 08 Express as single logarithms: i) log log log6 log4 ii) log6 log8 log log Express as single logarithms: log4 log9 log Without using tables or calculators, evaluate log0 log6 log 7 4 Rationalise Given that p is inversely proportional to the cube root of x and p when x 7, find the value of p when x PREPARED BY SSEKYEWA EDWARD GHS 08 seds04@yahoocom Page

2 6 Simplify: log0 log0 log06 7 y y Solve for y : Factorise completely; x xy 9 Given x x x x f, find the value(s) of x for which x f is not defined 0 Find the equation of a line passing through the point, x 4y 0 and is parallel to the line PREPARED BY SSEKYEWA EDWARD GHS 08 seds04@yahoocom Page

3 S 4 TEST 08 Given that log , log and log , evaluate: (i) log 0 0 (ii) log 0 Evaluate: Given n 7ten, find n 4 Given that f x x and g x x 6, find gf Make p the subject of the formula, T p, hence find p, given T 4, g 0 g PREPARED BY SSEKYEWA EDWARD GHS 08 seds04@yahoocom Page

4 6 Given that f x x and hx x, find the value of x for which x hf 7 Two similar jugs have heights of cm and 4cm The smaller jug has an area of the area of the big jug cm Find 8 Solve the simultaneous equations; x y 0 x y 7 9 Find the equation of the line passing through the point, and 4, 9 0 Solve for y in the given equation: y y 7 4 PREPARED BY SSEKYEWA EDWARD GHS 08 seds04@yahoocom Page 4

5 S 4 TEST 08 x Solve for x : 4 0 Form an equation whose roots are, 6 Given 8 7 P and 6 Q, find PQ det 4 Simplify: Simplify: PREPARED BY SSEKYEWA EDWARD GHS 08 seds04@yahoocom Page

6 PREPARED BY SSEKYEWA EDWARD GHS Page 6 6 Solve using matrices y x y x 7 Evaluate: of 8 Make b the subject given d b bd a 9 Find the area of the figure below 0 Given 4 4 r, find the coordinates of the point R

7 S 4 TEST 4 08 Calculate the simple interest on shs 0,000 for years at 4% per annum The angle of a sector of a circle radius cm is o 6 Calculate the area of the sector Convert to hour system 000hours 70hours Convert to 4 hour system :0pm : 00 am 4 Evaluate: 4 log log log 7 4 Use tables to evaluate: PREPARED BY SSEKYEWA EDWARD GHS 08 seds04@yahoocom Page 7

8 6 Express in the form p r q 7 The sum of interior angles of a polygon is o 080, find the number of sides of the polygon 8 The point, P is given a translation, find the coordinates of its image R 4 9 Find the values of m and n 0 Show that the points P,, Q, and, R are collinear PREPARED BY SSEKYEWA EDWARD GHS 08 seds04@yahoocom Page 8

9 Solve using matrices x y 0 x 6y S 4 TEST 08 Solve the equation x 4 x x x Without using tables or calculator, evaluate Given the point 6, 4 P and =, determine the coordinates of Q A rectangle with area 70cm is the image of the rectangle with area 0cm If the object triangle measures 8cm by 7cm, find the dimensions of the larger (image) rectangle PREPARED BY SSEKYEWA EDWARD GHS 08 seds04@yahoocom Page 9

10 6 Solve the equation: 0 0 log x 4 log0 x 0 7 Given that tan, without using tables or a calculator, determine the value of cos sin 8 The cost of shirts and a pair of trousers is shs,000 and the cost of shirts and 4 pairs of trousers is shs 7,000 Find the cost of each item 9 Make t the subject in the formular n F P m k t 0 Solve for x in the equation; x x 4 PREPARED BY SSEKYEWA EDWARD GHS 08 seds04@yahoocom Page 0

11 Given that S 4 TEST A and B Find the inverse of matrix (AB) 0 4 Given that 4tan and that is an obtuse angle, find the value of cos sin Solve the inequality: x x x 4 Given that loga 0 98 and logb 0, find the values of: i) logab ii) a log b Express 4as an improper fraction in its simplest form PREPARED BY SSEKYEWA EDWARD GHS 08 seds04@yahoocom Page

12 6 Without using tables or calculators, simplify (0) Given that f x x and g x x 4, find the values of x for which x 0 gf 8 Evaluate 7 9 At a certain company, three bells A, B and C are always rang on Tuesday at exactly 08:00 am They are rand at intervals of 7, 00 and minutes respectively When will all the bells be rang again? 0 A map has a scale of :,000 The area of a farm on the map is 6cm What is the actual area of the farm in km? PREPARED BY SSEKYEWA EDWARD GHS 08 seds04@yahoocom Page

13 Given that S 4 TEST 7 08 b a, hence, state the values of a, b and c c Given that the matrix m m A is singular Find the value of m For tan and is obtuse Find the value of sin 4cos 4 If OA 4 and OB, Evaluate for AB 6 Given that a b = a + b Find the value of y if y 0 74 PREPARED BY SSEKYEWA EDWARD GHS 08 seds04@yahoocom Page

14 6 Simplify Given that f ( z) and g( z) z Find the value of z for which fg( z) gf ( z) z 8 Use logarithms to evaluate A certain amount of money was shared between ratios: Tom: James and John in the ratio: ::6 respectively If John got shs 8,000 more than tom How much did James get? 0 It s given that y varies inversely as the square root of x and that when value of y when x y, x 00 Find the PREPARED BY SSEKYEWA EDWARD GHS 08 seds04@yahoocom Page 4

15 S 4 TEST 8 08 Use logarithms to evaluate, Given 6 A 4 7 A B B, Find Use matrix method to solve the equations: x y 9 y x 6 4 Evaluate without using tables or calculator 4 The function is defined as Find h(-) and the values of x for which h(x) is meaningless PREPARED BY SSEKYEWA EDWARD GHS 08 seds04@yahoocom Page

16 6 Given that a * b b a, evaluate 7 * * 7 P varies as Q and inversely proportional to the square of R, given that P when R and Q 6, find the value of Q when P and R 8 The line through the points A, and,, 4 Q Determine the equation of the line through Q B is perpendicular to the line through 9 Edward wanted to exchange Kenyan shillings Ksh 40, 000 to Tanzanian shillings (TZsh ) It is given that Ug sh 8 TZsh and Ksh Ugsh Calculate how much (TZsh ) Edward got 0 Given that x 4x f x, find f x and hence f PREPARED BY SSEKYEWA EDWARD GHS 08 seds04@yahoocom Page 6

17 S 4 TEST 9 08 If hx nx m, and h 4 9 and h, find n and m given PQ 8 cm In the figure above, angle o OQP 40, find the length OQ and OP Without using tables or calculator, find the value of log log given that log 0 0 and 4 Given that P varies directly as fourth root of Q and P = 4 when Q = 6 Find the value of Q when P = The domain,,, is mapped on to the function gx 8x state the type of mapping, determine the range and PREPARED BY SSEKYEWA EDWARD GHS 08 seds04@yahoocom Page 7

18 6 Solve: 4x x x 4 7 Given that x 8 x 8 f x, find the values of x for which x f is not defined 8 The points P,, Q k, and 4, 8 R lie on a straight line, find k 9 Solve for x : x x x 0 Form an equation whose roots are, 4 PREPARED BY SSEKYEWA EDWARD GHS 08 seds04@yahoocom Page 8

19 S 4 TEST 0 08 Simplify: x x Factorise completely: x y painters can finish a job in 48 days Given that all the painters work at the same rate, find the number of additional painters needed to finish the job 8 days earlier 4 7x 6 Solve the inequality and show the solution on a number line x x 6 4 Solve the simultaneous equations: x y 4x y 8 PREPARED BY SSEKYEWA EDWARD GHS 08 seds04@yahoocom Page 9

20 6 If the simple interest on shs,00,000 for 6 months is shs 40,800, find the interest rate per annum 7 Given that 8 tan and is acute, find the value of sin 4cos 8 The perimeter of a rectangular swimming pool is 84 m If the width is of the length, find the 4 dimensions of the pool and hence the area 9 At Dan s automobile shop, 0 cars were inspected, of the cars needed new brakes, 4 needed new exhaust system and 6 needed neither repair How many needed both? 0 x x Solve: 8 PREPARED BY SSEKYEWA EDWARD GHS 08 seds04@yahoocom Page 0

21 S 4 TEST 08 Given that p * q p q, evaluate: 7 * * Use matrix method to solve: x 9 y y x 6 Factorise completely, x x, hence solve x x 0 4 Given 4 P, Q find the matrix R, such that Q P R Given that y: x y 8 : x, find the ratio of x : y PREPARED BY SSEKYEWA EDWARD GHS 08 seds04@yahoocom Page

22 6 A man pays no income tax on the first shs 0,000 of his monthly salary On each of shs 0,000 above this, he pays shs,00 If he pays shs 0,000 tax, what is the montly salary? 7 Find the equation of a line whose x intercept is 4 and y intercept is 8 In a school of 40 students, the ratio of girls to boys is : 4 Find the number of boys If 0 more girls join the school, what is the new ratio of boys to girls? 9 Solve: 0n 40six 0 The two sides of a square are x m and 4x 9m, find the value of x hence, the area of the square PREPARED BY SSEKYEWA EDWARD GHS 08 seds04@yahoocom Page

For examiners use only Section total

For examiners use only Section total NAME ADM NO - 121/2 FORM III TERM 3 MATHEMATICS PAPER 2 2½ HOURS INSTRUCTIONS TO CANDIDATES a) Write your name and admission number in the spaces provided. b) This paper consists of TWO sections. Section