Mathematics Past Paper - Ogun State - SSS 3

**OGUN STATE MINISTRY OF EDUCATION, SCIENCE AND TECHNOLOGY** **GOVERNMENT SCIENCE AND TECHNICAL COLLEGE, IDI-ABA ABEOKUTA,** **OGUN STATE.** **MOCK EXAMINATION** **SUBJECT: MATHEMATICS CLASS: SSS 3 TIME: 2HOURS 30MINS** **SECTION A: Objective Test Questions** **INSTRUCTION: Answer all question...

**OGUN STATE MINISTRY OF EDUCATION, SCIENCE AND TECHNOLOGY** **GOVERNMENT SCIENCE AND TECHNICAL COLLEGE, IDI-ABA ABEOKUTA,** **OGUN STATE.** **MOCK EXAMINATION** **SUBJECT: MATHEMATICS CLASS: SSS 3 TIME: 2HOURS 30MINS** **SECTION A: Objective Test Questions** **INSTRUCTION: Answer all questions in this section** 1. Simplify 2^o^ x 3^2/3^ (a) 1 (b) 2 (c) 3 (d) 4 2. The sum of two numbers is 43 and their difference is 7. What is the smallest number? a. 18 (b) 17 (c) 16 (d) 15 3. Find the area of a triangle with base 6cn and height 4cn (a) 10cm^2^ (b) 6cm^2^ \(c) 24cm^2^ (d) 12cm^2^ 4. Express 3.195 correct to 2 decimal places (a) 3.10 (b) 3.190 (c) 3.2 (d) 3.20 5. Given 37^2^ -- 33^2^ = 8x, find the value of x (a) 33 (b) 35 (c) 37 (d) 70 6. If the angles of a quadrilateral are 5x, 4x, 3x, and 6x, what is the value of x? \(a) 180^o^ (b) 20^o^ (c) 90^o^ (d) 180^o^ 7. Express 110111~two~ to base ten (a) 55 (b) 56 (c) 65 (d) 555 8. Find the positive difference between 3 ¾ and 2 ^2^/~3~ (a) ^13^/~12~ (b) ^12^/~13~ (c) ^13^/~15~ \(d) ^15^/~13~ 9. Solve the equation h = 18 + 5h 10. How many sides has a regular polygon whose sum of the interior angles is 540^o^ \(a) 4 (b) 5 (c) 6 (d) 7 11. Find the angle whose tangent is 0.9325 (a) 43^o^ (b) 34^o^ (c) 13^o^ (d) 31^o^ 12. Give that 7 ; y = 21; 6, find the value of y (a) 2 (b) 16 (c) 6 (d) 24 13. If a number is chosen at random from the number 2,3,4,5,6,7,8,9,10. What is the probability that, it is a multiple of 3 (a) ^1^/~5~ (b) ^3^/~10~ (c) ^1^/~3~ (d) ^5^/~9~ 14. A house bought for N100,000 was later auctioned for N80,000. Find the loss percent \(a) 20% (b) 30% (c) 40% (d) 50% 15. Simplify 2^o^ x 8^2/3^ (a) 1 (b) 2 (c) 3 (d) 4 16. A ladder 6m long leans against a vertical wall so that it makes angle 60^o^ with the wall. Calculate the distance of the foot of the ladder from the wall. \(a) 3m (b) 6m (c) 2 3m (d) 3 3m 17. If the hypotenuse of a right angled isosceles triangle is 2, what is the length of each of the other side. (a) 1 (b) 2 -- 1 (c) 1 (d) 2 18. Three of the angles of a hexagon are each X^o^, the others are each 3X^o^. Find X \(a) 30^o^ (b) 40^o^ (c) 60^o^ (d) 80^o^ 19. Evaluate (3^o^ -- 9^-1/2^)^-3^ (a) ^3^/~2~ (b) ^27^/~8~ (d) ^2^/~3~ (d) ^1^/~9~ 20. If a = X^1/n^ , log~a~X^n^ is (a) n^2^ (b) n (c) n^-1^ (d) n^2^ 21. Find X if log~2~X = log^3^~9~ (b) ^2^/~3~ (b) ½ (c) 2 (d) 4 22. The population of a village is 5846. Express this number to three significant figures \(a) 5850 (b) 5846 (c) 5840 (d) 585 23. Bola saves N10,000 at 10% per annum compound interest. How much will she collect after 2 years? (a) N1,100.00 (b) N21,100.00 (c) N12,100.00 (d) N1,000.00 **The following are scores obtained by students in a physics test 2,2,5,2,6,3,8,7,9,4. Use the information to answer 18-21.** 24. Find the range of the set of scores (a) 4 (b) 5 (c) 6 (d) 7 25. Calculate the means score (a) 3.6 (b) 5.5 (c) 4.8 (d) 8.4 26. What is the median score? (a) 6.5 (b) 5.5 (c) 4.8 (d) 8.4 27. Find the mode (a) 7 (b) 2 (c) 4 (d) 5 28. Three lines meet at a point, if the sum of the two angles formed is 163^o^. the other angle is (a) 17^o^ (b) 197^o^ (c) 243^o^ (d) 73^o^ 29. Give that 6x -- y = 2, find the value of x (a) ^3^/~8~ (b) ^5^/~8~ (c) ^4^/~5~ (d) ^5^/~4~ 30. The expression "a" is at least 5 means (a) 1=5 (b) a\ 2. Evaluate log0.04 + log 0.25 ^10^ ^10^ log100 -- log4 3. Points X, Y and Z are located in the same horizontal plane such that Y is 12km north of X and Z is on a bearing of 270^o^ from X. If /XZ/ = 6km, calculate, correct to one decimal place, /YZ/. 4. The ratio of the number of men to the number of women in a 20 member committee is 3:1. How many women must be added to the 20 member committee so as to make the ratio of men to women 3:2? 5. Simplify 3 - 2 2 **Part B: Attempt any four (4) questions from this part B** 6. The sides of a rectangle are as given in the diagram below. Find the values of x any y. 7. The probability that a man will live for twenty more years is ^1^/~3~ and the probability that his wife will live twenty more years is ¼, find the probability that: i. Both will be alive in 20 years time ii. At least one will be alive in 20 years time iii. Neither will be alive in 20 years time. 8. 2 solve the following inequalities. Sketch a number line graph for each solution. i. 3x -- 1 \< 2 ii. 5x -- 1 - 1 -- 2x 9. In the figure /EF/ is a chord of the circle passing through, E, C, and F. /CD/ bisects /EF/ perpendicularly at D. a. If /EF/ = 12cm and /CD/ = 2cm, calculate the length of the radius of the circle whose segment is shown. b. If O is the centre of the completed circle, calculate the area of the sector OEC correct to three significant figures. (Take II = ^22^/~7~) 10. Two points M and N on the surface of the Earth are given by their latitudes and longitudes as M(5O^o^S, 15^o^E) and N (5O^o^S, 75^o^E). Calculate. a. The radius of the parallel of latitude on which M and N lie. b. The distance MN measured along the parallel of latitude. (Take the radius of the Earth to be 6,400km). 11. The table below shows the frequency distributions of the marks of 800 candidates in an examination. ----------- ----- ------- ------- ------- ------- ------- ------- ------- ------- ------- Marks % 0-9 10-19 20-29 30-39 40-49 50-59 60-69 70-79 80-89 90-99 Frequency 10 40 80 140 170 130 100 70 40 20 ----------- ----- ------- ------- ------- ------- ------- ------- ------- ------- ------- i. Construct a cumulative frequency table ii. Draw the cumulative frequency curve iii. Use your Ogive to determine the 50^th^ percentile.