(a) How many numbers between 75 and 500 are divisible by 7?(b) The 8th term of an Arithmetic Progression (A.P) is 5 times the 3rd term while the 7th term is 9 greater than the 4th term. Write the first 5 terms of the A.…
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2009
(a) Copy and complete the table of values for \(y = \sin x + 2 \cos x\), correct to one decimal place.x0°30°60°90°120°150°180°210°240°y2.2-1.2-2.0-1.9(b) Using a scale of 2 cm to 30° on the x- axis and 2 cm to 0.5 units…
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2009
(a) A circle is inscribed in a square. If the sum of the perimeter of the square and the circumference of the circle is 100 cm, calculate the radius of the circle. [Take \(\pi = \frac{22}{7}\)].(b) A rope 60cm long is m…
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2009
(a) Using ruler and a pair of compasses only, construct : (i) quadrilateral PQRS such that /PQ/ = 10 cm, /QR/ = 8 cm, /PS/ = 6 cm, < PQR = 60° and < QPS = 75° ;(ii) the locus \(l_{1}\) of points equidistant from Q…
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2009
(a) Simplify \(\frac{x + 2}{x - 2} - \frac{x + 3}{x - 1}\)(b) The graph of the equation \(y = Ax^{2} + Bx + C\) passes through the point (0, 0), (1, 4) and (2, 10). Find the : (i) value of C ; (ii) values of A and B ; (…
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2009
The marks scored by 50 students in a Geography examination are as follows :60 54 40 67 53 73 37 55 62 43 44 69 39 32 45 58 48 67 39 51 46 59 40 52 61 48 23 60 59 47 65 58 74 47 40 59 68 51 50 50 71 51 26 36 38 70 46 40…
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2009
(a) A woman looking out from the window of a building at a height of 30m, observed that the angle of depression of the top of a flag pole was 44°. If the foot of the pole is 25m from the foot of the building and on the…
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2009
(a) If \(\log 5 = 0.6990, \log 7 = 0.8451\) and \(\log 8 = 0.9031\), evaluate \(\log (\frac{35 \times 49}{40 \div 56})\).(b) For a musical show, x children were present. There were 60 more adults than children. An adult…
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2009
In the diagram, ABCDEF is a triangular prism. < ABC = < DEF = 90°, /AB/ = 24 cm, /BC/ = 7 cm and /CD/ = 40 cm. Calculate : (a) /AC/ ; (b) the total surface area of the prism.
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2009
(a) Out of 30 candidates applying for a post, 17 have degrees, 15 have diplomas and 4 neither degree nor diploma. How many of them have both?(b) In triangle PQR, M and N are points on the side PQ and PR respectively suc…
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2009
The table shows the number of children per family in a community.No of children012345No of families357432(a) Find the : (i) mode ; (ii) third quartile ; (iii) probability that a family has at least 2 children.(b) If a p…
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2009
(a) If \(9 \cos x - 7 = 1\) and \(0° \leq x \leq 90°\), find x.(b) Given that x is an integer, find the three greatest values of x which satisfy the inequality \(7x < 2x - 13\).
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2009
(a) Given that \((\sqrt{3} - 5\sqrt{2})(\sqrt{3} + \sqrt{2}) = a + b\sqrt{6}\), find a and b.(b) If \(\frac{2^{1 - y} \times 2^{y - 1}}{2^{y + 2}} = 8^{2 - 3y}\), find y.