How good are you with figures and formulas? Find out with these Mathematics past questions and answers. This Test is useful for both job aptitude test candidates and students preparing for JAMB, WAEC, NECO or Post UTME.
Which of the following binary operations is cumulative on the set of integers?
a \(\ast\) b = a + 2b
a \(\ast\) b = a + b - ab
a \(\ast\) b = a2 + b
a \(\ast\) b = \(\frac{a(b + 1)}{2}\)
Correct answer is B
\(a \ast b = a + b - ab\)
\(b \ast a = b + a - ba\)
On the set of integers, the two above are cumulative as multiplication and addition are cumulative on the set of integers.
Express \(\frac{5x - 12}{(x - 2)(x - 3)}\) in partial fractions
\(\frac{2}{x + 2} - \frac{3}{x - 3}\)
\(\frac{2}{x - 2} + \frac{3}{x - 3}\)
\(\frac{2}{x - 3} - \frac{3}{x - 2}\)
\(\frac{5}{x - 3} - \frac{4}{x - 2}\)
Correct answer is B
\(\frac{5x - 12}{(x - 2)(x - 3)} = \frac{A}{x - 2} + \frac{B}{x - 3}\)
= \(\frac{A(x - 3) + B(x - 2)}{(x - 2)(x - 3)}\)
\(\implies 5x - 12 = Ax - 3A + Bx - 2B\)
\(A + B = 5 ... (i)\)
\(-(3A + 2B) = -12 \implies 3A + 2B = 12 ... (ii)\)
From (i), \(A = 5 - B\)
\(3(5 - B) + 2B = 12\)
\(15 - 3B + 2B = 12 \implies B = 3\)
\(A + 3 = 5 \implies A = 2\)
\(\frac{5x - 12}{(x - 2)(x - 3)} = \frac{2}{x - 2} + \frac{3}{x - 3}\)
Simplify \(\frac{x^2 - 1}{x^3 + 2x^2 - x - 2}\)
\(\frac{1}{x + 2}\)
\(\frac{x - 1}{x + 1}\)
\(\frac{x - 1}{x + 2}\)
\(\frac{1}{x - 2}\)
Correct answer is A
\(\frac{x^2 - 1}{(x - 1)(x + 2)(x + 1)}\) = \(\frac{(x -
1)(x + 1)}{(x - 1)(x + 2)(x + 1)}\)
= \(\frac{1}{x + 2}\)
The 4th term of an A.P. is 13 while the 10th term is 31. Find the 21st term.
175
85
64
45
Correct answer is C
a + 3d = 13
a + 9d = 31
6d = 18
= d = 3
a = 13 - 9
= 4
a + 20d = 4 + (20 x 3)
= 64
Solve the inequality (x - 3)(x - 4) \(\leq\) 0
3 \(\leq\) x \(\leq\) 4
3 < x < 4
3 \(\leq\) x < 4
3 < x \(\leq\) 4
Correct answer is A
(x - 3)(x - 4) \(\leq\) 0
Case 1 (+, -) = x - 3 \(\geq\) 0, X - 4 \(\geq\) 0
= X \(\leq\) 3, x \(\geq\) 4
= 3 < x \(\geq\) 4 (solution)
Case 2 = (-, +) = x - 3 \(\leq\) 0, x - 4 \(\geq\) 0
= x \(\leq\) 3, x \(\geq\) 4
therefore = 3 \(\leq\) x \(\leq\) 4