Mathematics 2005 Waec Past Questions and Answers

Question 56 :

• WAEC 2005

(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; \(\pi = \frac{22}{7}\)].

Question 57 :

• WAEC 2005

(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 \(\pi = \frac{22}{7}\)].

Question 58 :

• WAEC 2005

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.

Question 59 :

• WAEC 2005

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

Age (years)	10-14	15-19	20-24	25-29	30-34	35-39
Frequency	7	18	25	17	9	4

(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?

Question 60 :

• WAEC 2005

(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.