First Term Examination
Class : SSS 2
Subject : Mathematics
Time : 2 Hours.
Name : __________________________________
Section A : Objective Questions
Instruction : Read the question carefully and choose from the alternatives lettered a – d.
1. What is logarithm of 0.000197? (a) 42.945 (b) -4.2945 (c) 3.2945 (d) -3.2945
2. Use antilog table to write down the number whose logarithm is 3.8226 (a) 0.6646 (b) 0.06646 (c) 0.006646 (d) 66.46
3. Simplify log 8 – log 2 + log 4. (a) 0 (b) 3log 2 (c) 2og 2 (d) 4log 2
4. Given that log 2 = 0.3010, obtain the value of log 4 + log 16. (a) 0.6021 (b) 1.2041 (c) 1.3547 (d) 1.8060
5. Simplify : log 8 /(log 4 – log 2). (a) 2/3 (b) 1/2 log2 (c) 3/2 (d) log 3/2
6. A sales girl gave a girl a balance of #1. 15 to a customer instead of #1. 25, calculate the % error. (a) 10% (b) 7% (c) 8.0% (d) 2.4%
7. A man is 1.5m tall to the nearest cm, calculate his percentage error. (a) 0.05cm (b) 0.33% (c) 0.033% (d) 0.05cm
8. Find the 4th term of an A. P. whose first term is 2 and the common difference is 0.5. (a) 4 (b) 4.5 (c) 3.5 (d) 2.5
9. In an A. P. the difference the 8th and 4th term is 20 and the 8th term is 11/2 times the 4th term, find the common difference. (a) 5 (b) 7 (c) 3 (d) 10
10. The next term of the sequence: 18, 12, 60 is (a) 12 (b) 6 (c) – 6 (d) – 12
11. Find the common ratio of the G. P. : log 3, log 9, log 81. (a) – 1 (b) 3 (c) 2 (d) 6
12. Find the sum of the first five terms of the G. P : 2, 6, 18,… (a) 484 (b) 243 (c) 242 (d) 130
13. Find the nth Term of a sequence 5, 10, 20, 40, 80,…. (a) 5 × 2 ^n+1 (b) 2 × 5^n – 1 (c) 5 × 2 ^n-1 (d) 5 × 5^n-1
14. If the 2nd and 5th term of a G. P. are – 6 and 48 respectively, find the sum of the first four terms: (a) – 45 (b) -15 (c) 15 (d) 33
15. The 4th term of a G. P. is – 2/3 and it’s First term is 18. What is its common ratio? (a) 1/2 (b) 1/3 (c) – 1/3 (d) – 1/2
16. If the 2nd and 4th term of a G. P are 8 and 32 respectively, what is the sum of the first four terms? (a) 28 (b) 40 (c) 48 (d) 60
17. What is the nth term of the sequence 3, 8, 13,… (a) 5n + 3 (b) 5n – 2 (c) 5n – 3 (d) 5n – 5
18. Find the 8th term of the A. P -3, – 1, 1,… (a) 13 (b) 11 (c) – 8 (d) – 11
19. The 12th term of an A. P is – 41. If the first term is 3, find the 20th term. (a) – 77 (b) – 73 (c) 77 (d) 79
20. Find the number of terms of the sequence : 1/2, 3/4, 1, …, 5 1/2. (a) 21 (b) 43/4 (c) 1 (d) 22
21. What must be added to x² – 3x to make it a perfect square? (a) 9/4 (b) 9/2 (c) 6 (d) 9
22. If (x – 3) is a factor of the quadratic equation x² + kx – 21 = 0, where k is constant, find the value of k. (a) 5 (b) 4 (c) 3 (d) – 4
23. Factorize completely 3a² – 27b². (a) 3(a – 2b)(a + 3b) (b) 3(a – 3b)(a + 3b) (c) 3(a +3b)(a + 3b) (d) (a – 3b)(a + 3b)
24. Solve the equation: 5x² – 4x – 1 = 0. (a) – 1, 1/5 (b) – 1, – 1/5 (c) 1, 1/5 (d) 1, – 1/5
25. Find the equation whose roots are – 2/4 and – 1/4. (a) 12x² + 11x + 2 = 0 (b) 12x² – x + 2 = 0 (c) 12x² – x – 2 = 0 (d) 12x² – 11x – 2 = 0
26. Given that 2p – m = 6 and 2p + 4m = 1, find the value of (4p + 3m). (a) 5 (b) 9 (c) 7 (d) 3
27. A string is 4.8m. A boy measured it to be 4.95m. Find the percentage error. (a) 3 1/8% (b) 1 5/8% (c) 15% (d) 3 1/6%
28. The average of two numbers is 11. Their difference is 4. Find the numbers. (a) 12, 19 (b) 6 1/2, 9 1/2 (c) 13, 19 (d) 19, 14
29. Six books and three bags cost €234. Five books and two bags cost €184. How much does each cost? Let x represent cost of books and y represent cost of bags. (a) x = 22, y = 28 (b) x = 28, y = 22 (c) x = 28, y = 24 (d) x = 14, y = 48
30. The sum of two numbers is 19. Their difference is 5, find the two numbers. (a) 12, 7 (b) 12, 5 (c) 5, 7 (d) 14, 7
31. Solve the pairs of equations simultaneously: xy = -12 ; x – y = 7. (a) (3, – 4) (4, – 3) (b) (-2, 4) (-3, 4) (c) ( – 4, 5) (- 2, 3) (d) (3, – 3) (4, – 4)
32. What value of x in the equation : 3x² – 8x – 3 = 0? (a) 1/3, – 3 (b) – 1/3, – 3. (c) – 1/3, 3 (d) 1/3, 3
33. The roots of Quadratic equation in x, are – m and 2n. Find the equation. (a) x² + (m – 2n)x – 2mn = 0 (b) x² – (m – 2n)x – 2mn = 0 (c) x² – (2n – m)x + 2mn = 0 (d) x² – (m – 2n)x + 2mn = 0
If α and λ are the roots of the equation 2x² + 9x + 9 = 0. Use the equation to answer questions 34 – 37.
34. Find the product of their roots. (a) 4 (b) 4.5 (c) 5.5 (d) – 4.5
35. Find the sum of their roots. (a) 4 (b) 4.5 (c) 5.5 (d) – 4.5
36. Find α² + λ². (a) 11.5 (b) – 11. 25 (c) 11.25 (d) – 11.5
37. Find αλ / (α + λ). (a) 1 (b) – 1 (c) 1.5 (d) 4
38. Given that x + 7y = 7 and 3x – y = 5, evaluate y/2 – 3. (a) – 1 (b) 1 (c) 3 (d) 4
39. Find the x coordinate of the point of intersection of y = x² and y = x + 2. (a) x = -1 or – 2 (b) x = 1 or 2 (c) x = -1 or 2 (d) x = -2 or 1
40. A student bought 3 notebooks and 2 pens for #35. After misplacing these items, she again bought 2 notebooks and 2 pens, all of the same type of #30. What is the cost of a pen? (a) #5 (b) #7.50 (c) #10.00 (d) #15.00
Section B : Theory
Instructions : Answer five questions from this section. Each questions carry equal marks.
1a. Evaluate using logarithm table : (23.97 x √0.7124) / (3.877 x 52.18)
1b. If α and λ are the roots of the equation : 3x² – 4x – 1 = 0, find the value of : i.) α/λ + λ/α ii.) (α² + λ²) / αλ.
2a. In ten years time, a father will be twice as old as his son. Ten years ago, he was six times as old as his son. How old are they now?
2b. Solve the simultaneous equation : 3x.- 2y = 8; and 2x – 3y = 14.
3a. The length of a field is measured as 500m; find the percentage error of the length if the room is measured to :
i.) nearest metre ii.) nearest 10m
iii.) One Significant figure.
3b. If (m + 1) and (m – 3) are factor of m² – km + C, find the value of k and c.
4a. Given that log 2 = 0.3010, log 5 = 0.6990, and log 7 = 0.8451. Evaluate without using logarithm tables :
i.) Log 35 ii.) Log 2.8
4b. Given that 2 and – 3 are the roots of the equation ax² + bz + C = 0, find the values of a, b and c.
5a. 1, 5,…, 69 are the 1st, 2nd, and last term of the sequence; find the common difference between them and the number of terms in the sequence.
5b. The sum of a G. P is 100. Find its first term, if the common ratio is 0.8n.
6ai. Using a scale of 2cm to 1 unit on both axes, on the same graph sheet, draw the graphs of y. – 3x /4 = 3 and y + 2x = 6.
ii.) From your graph, find the coordinates of the point of intersection of the two graphs.
7a. A trader bought 30 baskets of pawpaw and 100 baskets of mangoes for #2, 450.00. She sold the pawpaw at a profit of 40% and the mangoes at a profit of 30%. If her profit on the entire transaction was #855.00, find the : (i.) cost price of a basket of pawpaw ; (ii.) selling price of the 100 baskets of mangoes.
7b. Evaluate: (2 log 8 + log 4 – log 16) / log 32
8a. The graph of y = 2px² – p²x – 14 passes through the point (3, 10). Find the value of p.
8b. The third term of a geometric progression (G. P) is 360 and the sixth term is 1215. Find the : (a) common ratio; (b) first term; (c) sum of the first four terms.