WAEC Mathematics 2005 Past Questions

(a) Evaluate without using the mathematical table or calculator, \(\log_{10} \sqrt{30} - \log_{10} \sqrt{6} + \log_{10} \sqrt{2}\).

(b) \(U = {1, 2, 3, ..., 10} ; A = {1, 2, 3, 4, 5} ; B = {2, 3, 5}\) and \(C = {6, 8, 10}\). (i) Given that the Venn diagram represents the sets above, copy and fill in the elements.

(ii) Find \(A \cap C\) ; (iii) Find \(A \cap B'\).

(a) Evaluate : \(2 \div (\frac{64}{125})^{-\frac{2}{3}}\)

(b) The lines \(y = 3x + 5\) and \(y = - 4x - 1\) intersect at a point k. Find the coordinates of k.

(a) Simplify : \(\frac{5}{8} of 2\frac{1}{2} - \frac{3}{4} \div \frac{3}{5}\).

(b) A cone and a right pyramid have equal heights and volumes. If the area of the base of the pyramid is \(154 cm^{2}\), find the base radius of the cone. [Take \(\pi = \frac{22}{7}\)].

(a) Two fair die are thrown once. Find the probabitlity of getting : (i) the same digit ; (ii) a total score greater than 5.

(b) Given that \(x = \cos 30°\) and \(y = \sin 30°\), evaluate without using a mathematical table or calculator : \(\frac{x^{2} + y^{2}}{y^{2} - x^{2}}\).

(a) In the diagram, A, B, C and D are points on the circumference of a circle. XY is a tangent at A. Find : (i) < CAX ; (ii) < ABY.

(b) If (m + 1) and (m - 3) are factors of \(m^{2} - km + c\), find the values of k and c.

(a) Without using mathematical table or calculator, evaluate : \(\sqrt{\frac{0.18 \times 12.5}{0.05 \times 0.2}}\).

(b) Simplify : \(\frac{8 - 4\sqrt{18}}{\sqrt{50}}\).

(c) x, y and z are related such that x varies directly as the cube of y and inversely as the square of z. If x = 108 when y = 3 and z = 4, find z when x = 4000 and y = 10.

(a) A regular polygon of n sides is such that each interior angle is 120° greater than the exterior angle. Find :

(i) the value of n ; (ii) the sum of all the interior angles.

(b) A boy walks 6km from a point P to a point Q on a bearing of 065°. He then walks to a point R, a distance of 13km, on a bearing of 146°. 

(i) Sketch the diagram of his movement. (ii) Calculate, correct to the nearest kilometre, the distance PR.

(a) A plane flies due East from A(lat. 53°N, long. 25°E) to a point B(lat. 53°N, long. 85°E) at an average speed of 400 km/h. The plane then flies South from B to a point C 2000km away. Calculate, correct to the nearest whole number : 

(a) the distance between A and B.

(b) the time the plane takes to reach point B ;

(c) the latitude of C. 

[Take radius of the earth = 6400km; \(\pi = \frac{22}{7}\)].

(a) Find the smallest integer that satisfies the inequality \(x + 8 < 4x - 15\).

(b) A sales girl is paid a monthly salary of N2,500 in addition to a commission of 5 kobo in the naira on all sales made by her during the month. If her sales for a month amounts to N200,000.00, calculate her income for that month.

(c)   The diagram shows a window consisting of a rectangular and semi- circular parts. The radius of the semi- circular part is 35 cm and the height of the rectangular part is 50 cm. Find the area of the window. [Take \(\pi = \frac{22}{7}\)].

The sketch shows a plot of land . 

(a) Using a scale of 1 cm to 10m, draw an accurate diagram of the plot ;

(b) Construct : (i) The locus \(l_{1}\) of points equidistant from AC and BC ; (ii) the locus \(l_{2}\) of points 60m from A.

(c) A tree T inside the plot is on both \(l_{1}\) and \(l_{2}\). Locate T and find |TC| in metres.

(d) A flagpole, P is to be placed such that it it is nearer AC than BC and more than 60m from A. Shade the regions where P can be located.

The table shows the age distributions of the members of a club.

(a) Calculate, correct to one decimal place, the mean age.

(b) (i) Draw a histogram to illustrate the information.

(ii) Use the histogram to estimate the modal age .

(c) If a member is selected at random, what is the probability that he/she is in the modal class?

(a)   In the diagram, \(\Delta\) ABD is right-angled at B. |AB| = 3 cm, |AD| = 5 cm, \(\stackrel\frown{ACB}\) = 61° and \(\stackrel\frown{DAC}\) = x°. Calculate, correct to one decimal place, the value of x.

(b)   In the diagram, OABCD is a pyramid with a square base of side 2cm and a slant height of 4 cm. Calculate, correct to three significant figures : (i) the vertical height of the pyramid ; (ii) the volume of the pyramid.

(a) Copy and complete the table. 

\(y = x^{2} - 2x - 2\) for \(-4 \leq x \leq 4\)

(b) Using a scale of 2 cm to 1 unit on the x- axis and 2 cm to 5 units on the y- axis, draw the graph of \(y = x^{2} - 2x - 2\).

(c) Use your graph to find : (i) the roots of the equation \(x^{2} - 2x - 2 = 0\) ; (ii) the values of x for which \(x^{2} - 2x - 4\frac{1}{2} = 0\) ; (iii) the equation of the line of symmetry of the curve.