Mathematics Past Questions and Answers

Tunde and Shola can do a piece of work in 18 days. Tunde can do it alone in x days, whilst Shola takes 15 days longer to do it alone. Which of the following equations is satisfied by x?

A X² - 5x - 10 = 0
B X² - 20x + 360 = 0
C X² - 21x - 270 = 0
D 3x² - 65x + 362 = 0

Question 22:

If f(x) = 2(x - 3)\(^2\) + 3(x - 3) + 4 and g(y) = \(\sqrt{5 + y}\), find g [f(3)] and f[g(4)].

A 3 and 4
B -3 and 4
C -3 and -4
D 3 and -4
E 0 and 5

Question 23:

The quadratic equation whose roots are 1 - \(\sqrt{13}\) and 1 + \(\sqrt{13}\) is

A X² + (1 - \(\sqrt{13}\)x + 1 + \(\sqrt{13}\) = 0
B X² - 2x - 12 = 0
C X² - 2x + 12 = 0
D X² + 12 + 2x² = 0

Question 24:

Find a factor which is common to all three binomial expressions 4a2 - 9b2, 8a3 + 27b3, (4a + 6b)2

A 4a + 6b
B 4a - 6b
C 2a + 3b
D 2a - 3b
E None

Question 25:

If (x - 2) and (x + 1) are factors of the expression x³ + px² + qx + 1, what is the sum of p and q

A 9
B -3
C 3
D \(\frac{17}{3}\)
E \(\frac{2}{3}\)