Mathematics 2003 Waec Past Questions and Answers

Question 56 :

• WAEC 2003

The marks obtained by 40 students in an examination are as follows :
85 77 87 74 77 78 79 89 95 90 78 73 86 83 91 74 84 81 83 75 77 70 81 69 75 63 76 87 61 78 69 96 65 80 84 80 77 74 88 72.
(a) Copy and complete the table for the distribution using the above data.

Class Boundaries	Tally	Frequency
59.5 - 64.5
64.5 - 69.5
69.5 - 74.5
74.5 - 79.5
79.5 - 84.5
84.5 - 89.5
89.5 - 94.5
94.5 - 99.5

(b) Draw a histogram to represent the distribution.
(c) Using your histogram, estimate the modal mark.
(d) If a student is chosen at random, find the probability that the student obtains a mark greater than 79.

Question 57 :

• WAEC 2003

In the diagram, PQT is a straight line and SQ // RT.

(a) Join QR and show that : (i) < RPS = < QRT ; (ii) < PRS = < QTR.
(b) ABC is a triangle. The sides AB and AC are produced to D and E respectively such that < DBC = 132° and < ECD = 96°. Show that \(\Delta\) ABC is isosceles.

Question 58 :

• WAEC 2003

An aeroplane flies due west for 3 hours from P (lat. 50°N, long. 60°W) to a point Q at an average speed of 600km/h. The aeroplane then flies due south from Q to a point Y 500km away. Calculate, correct to 3 significant figures,
(a) the longitude of Q ;
(b) the latitude of Y . [Take the radius of the earth = 6400km and \(\pi = \frac{22}{7}\)].

Question 59 :

• WAEC 2003

Using ruler and a pair of compasses only,
(a) construct a quadrilateral PXYQ such that /PX/ = 9.9 cm, /QX/ = 10.2 cm, < QPZ = 75°, /QY/ = 10.4 cm and PQ // XY.
(b) Construct the (i) locus \(l_{1}\) of points equidistant from X and Y ; (ii) locus \(l_{2}\) of points equidistant from QY and YX.
(c) Locate M, the point of intersection of \(l_{1}\) and \(l_{2}\).
(d) Measure /PM/.