WAEC Mathematics 1997 Past Questions

(a) Copy and complete the binary multiplication table:

(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 express your answer in the form \(P \times 10^{m}\) where 1 < P < 10 and m is an integer.

(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 represented by (i) \(P \cap Q' \cap R\) ; (ii) \(P' \cap Q \cap R'\).

(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 ground PRN. If the angles of elevation of the top of the mountain from P and R are 30° and 70° respectively and PR = 500m, calculate, correct to 3 significant figures :

(i) |QP| ; (ii) the height of the mountain.

The table below shows how a company's sales manager spent his 1995 annual salary.

(a) Represent this information on a pie chart.

(b) Find his savings at the end of the year if his annual salary was N60,000.00.

(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 other root.

(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 random for an assignment. Find the probability that :

(i) both were boys ; (ii) the two were of different sexes.

(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 AB and D is equidistant from points A and C. Measure < BAD.

(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 jointly varies inversely as the number of pumps P available in the station. In a station with 5 pumps, it took 10 minutes to fuel 20 vehicles. Find :

(i) the relationship between t, P and V ; (ii) the time it will take to fuel 50 vehicles in the station with 2 pumps ; (iii) the number of pumps required to fuel 40 vehicles in 20 minutes.

  The solid is a cylinder surmounted by a hemispherical bowl. Calculate its

(a) total surface area ;

(b) volume (Take \(\pi = \frac{22}{7}\))

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) the roots of the quadratic equation \(ax^{2} + bx + c = 0\)

(b) Use the coordinates of D, E and G to find the values of the constants a, b and c hence write down the quadratic function illustrated in the graph.

(c) Find the greatest value of y within the range \(-3 \leq x \leq 5\).

(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 points vertically above B and C respectively. |DC| = 40 cm and |AB| = 26 cm. Calculate the angles of depression of : (i) B from D ; (ii) A from D ; correct to the nearest degree.

The table below shows the mark distribution of candidates in an aptitude test for selection into the public service.

(a) Make a cumulative frequency for the distribution

(b) Draw the cumulative frequency curve.

(c) From your graph, estimate the median mark.

(d) The cut-off mark was 63%. What percentage of the candidates was selected?