Mathematics 2013 Waec Past Questions and Answers

Question 56 :

• WAEC 2013

(a) Copy and complete the table of values for the relation \(y = 3x^{2} - 5x - 7\).

x	-3	-2	-1	0	1	2	3	4
y	35			-7	-9		5

(b) Using scales of 2 cm to 1 unit on the x- axis and 2 cm to 5 units on the y- axis, draw the graph of \(y = 3x^{2} - 5x - 7, -3 \leq x \leq 4\).
(c) From the graph : (i) find the roots of the equation \(3x^{2} - 5x - 7 = 0\) ; (ii) estimate the minimum value of y ; (iii) calculate the gradient of the curve at the point x = 2.

Question 57 :

• WAEC 2013

(a) If (3 - x), 6, (7 - 5x) are consecutive terms of a geometric progression (GP) with constant ratio r > 0, find the :
(i) values of x ; (ii) constant ratio.
(b) In the diagram, |AB| = 3 cm, |BC| = 4 cm, |CD| = 6 cm and |DA| = 7 cm. Calculate <ADC, correct to the nearest degree.

Question 58 :

• WAEC 2013

(a) Using ruler and a pair of compasses only, construct : (i) a trapezium WXYZ such that |WX| = 10.2 cm, |XY| = 5.6 cm, |YZ| = 5.8 cm, < WXY = 60° and WX is parallel to YZ (ii) a perpendicular from Z to meet \(\overline{WX}\) at N.
(b) Measure : (i) |WZ| ; (ii) |ZN| .

Question 59 :

• WAEC 2013

(a)
A segment of a circle is cut off from a rectangular board as shown in the diagram. If the radius of the circle is \(1\frac{1}{2}\) times the length of the chord; calculate, correct to 2 decimal places, the perimeter of the remaining portion. [Take \(\pi = \frac{22}{7}\)]
(b) Evaluate without using calculators or tables, \(\frac{3}{\sqrt{3}}(\frac{2}{\sqrt{3}} - \frac{\sqrt{12}}{6})\).

Question 60 :

• WAEC 2013

The frequency distribution table shows the marks obtained by 100 students in a Mathematics test.

Marks (%)	1-10	11-20	21-30	31-40	41-50	51-60	61-70	71-80	81-90	91-100
Frequency	2	3	5	13	19	31	13	9	4	1

(a) Draw the cumulative curve for the distribution.
(b) Use the graph to find the : (i) 60th percentile ; (ii) probability that a student passed the test if the pass mark was fixed at 35%.