The table below shows the mark distribution of candidates in an aptitude test for selection into the public service.Marks (in %)Freq44 - 46247 - 49550 - 521153 - 552056 - 614262 - 644665 - 673668 - 70971 - 733(a) Make a…
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1997
(a) PQRST is a circle with centre C. PCS is a straight line, RS // QT, |QR| = |RS| and < QTS = 56°. Find (i) SQT (ii) PQT.(b) In the diagram, points B and C are on a horizontal plane and |BC| = 30cm. A and D are po…
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1997
Above is the graph of the quadratic function \(y = ax^{2} + bx + c\) where a, b and c are constants. Using the graph, find :(a)(i) the scales on both axes ; (ii) the equation of the line of symmetry of the curve ; (iii)…
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1997
The solid is a cylinder surmounted by a hemispherical bowl. Calculate its(a) total surface area ;(b) volume (Take \(\pi = \frac{22}{7}\))
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1997
(a) Solve the simultaneous equation : \(\log_{10} x + \log_{10} y = 4\) \(\log_{10} x + 2\log_{10} y = 3\)(b) The time, t, taken to buy fuel at a petrol station varies directly as the number of vehicles V on queue and j…
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1997
(a) Using a ruler and a pair of compasses only, construst \(\Delta\) ABC in which |AB| = 7cm, |BC| = 5cm and < ABC = 75°. Measure |AC|.(b) In (a) above, locate by construction, a point D such that CD is parallel to A…
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1997
(a) Use logarithm tables to evaluate \(\frac{15.05 \times \sqrt{0.00695}}{6.95 \times 10^{2}}\).(b) The first 5 students to arrive in a school on a Monday morning were 2 boys and 3 girls. Of these, two were chosen at ra…
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1997
(a) Given that \(\frac{5y - x}{8y + 3x} = \frac{1}{5}\), find the value of \(\frac{x}{y}\) to two decimal places.(b) If 3 is a root of the quadratic equation \(x^{2} + bx - 15 = 0\), determine the value of b. Find the o…
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1997
The table below shows how a company's sales manager spent his 1995 annual salary.Food30%Rent18%Car Maintenance25%Savings12%Taxes5%Others 10%(a) Represent this information on a pie chart.(b) Find his savings at the end o…
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1997
(a) Given that \(\sin x = \frac{5}{13}, 0° \leq x \leq 90°\), find \(\frac{\cos x - 2 \sin x }{2\tan x}\).(b) The diagram represents the vertical cross-section of a mountain with height NQ standing on a horizontal grou…
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1997
(a) The 6th term of an A.P is 35 and the 13th term is 77. Find the 20th term.(b) The Venn diagram represents three subsets P, Q and R of the universal set U. Copy the Venn diagram. Shade and indicate the regions represe…
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1997
(a) Copy and complete the binary multiplication table:x10111001011010010001111011001001000010100(b) Convert \(11.011_{two}\) to a number in base ten.(c) Simplify \(\frac{9.6 \times 10^{18}}{0.24 \times 10^{5}}\) and exp…