Further Mathematics 2009 Waec Past Questions and Answers

Question 51 :

• WAEC 2009

(a) Using the same axes, sketch the curves \(y = 6 - x - x^{2}\) and \(y = 3x^{2} - 2x + 3\).
(b) Find the x- coordinates of the points of intersection of the two curves in (a).
(c) Calculatethe area of the finite region bounded by the two curves in (a).

Question 52 :

• WAEC 2009

(a) Evaluate \(\int_{1} ^{2} \frac{x}{\sqrt{5 - x^{2}}} \mathrm {d} x\)
(b)(i) Evaluate: \(\begin{vmatrix} 2 & -3 & 1 \\ 0 & 1 & -2 \\ 1 & 2 & -3 \end{vmatrix}\)
(ii) Using your answer in b(i), solve the simultaneous equations :
\(2x - 3y + z = 10\)
\(y - 2z = -7\)
\(x + 2y - 3z = -9\)

Question 53 :

• WAEC 2009

(a) Use the trapezium rule with five ordinates to evaluate \(\int_{0} ^{1} \frac{3}{1 + x^{2}} \mathrm {d} x\), correct to four significant figures.
(b) If \(A = \begin{pmatrix} 2 & 1 \\ 3 & 2 \end{pmatrix}\), find the image of the point (1, 2) under the linear transformation \(A^{2} + A + 2I\), where I is the \(2 \times 2\) unit matrix.

Question 54 :

• WAEC 2009

(a) Simplify \(^{n + 1}C_{3} - ^{n - 1}C_{3}\)
(b) A fair die is thrown five times. Calculate, correct to three decimal places, the probability of obtaining (i) at most two sixes ; (ii) exactly three sixes.

Question 55 :

• WAEC 2009

(a) The distribution of the lives (in days) of 40 transitor batteries is shown in the table:

Battery life(in days)	26-30	31-35	36-40	41-45	46-50	51-55
Frequency	4	7	13	8	6	2

(a) Draw a histogram for the distribution.
(b) Use your graph in (a) to determine the mode for the distribution.
(c) Using an assumed mean of 43 days, calculate the mean of the distribution.
(d) What percentage number of batteries will live for less than 31 days or more than 45 days?