Mathematics Past Questions And Answers
For what values of m is \(9y^{2} + my + 4\) a perfect square?
- A. \(\pm {2}\)
- B. \(\pm {3}\)
- C. \(\pm {6}\)
- D. \(+12\)
Correct Answer: D. \(+12\)
Find the least value of the function \(f(x) = 3x^{2} + 18x + 32\).
- A. 5
- B. 4
- C. -3
- D. -2
Correct Answer: A. 5
Explanation
\(f(x) = 3x^{2} + 18x + 32\)
\(\frac{\mathrm d y}{\mathrm d x} = 6x + 18 = 0\)
\(6x = -18 \implies x = -3\)
\(f(-3) = 3(-3^{2}) + 18(-3) + 32 = 27 - 54 + 32 = 5\)
(a) Copy and complete the table.
\(y = x^{2} - 2x - 2\) for \(-4 \leq x \leq 4\)
| x | -4 | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 |
| \(x^{2}\) | 16 | 9 | 4 | 1 | 0 | 1 | 4 | 9 | 16 |
| \(-2x\) | 8 | 6 | 4 | 2 | 0 | -2 | -4 | -6 | -8 |
| \(-2\) | -2 | -2 | -2 | -2 | -2 | -2 | -2 | -2 | -2 |
| \(y\) | 22 | 13 | 6 | 1 | -2 | -3 | -2 | 1 | 6 |
(b).jpg)
(c)(i) \(x^{2} - 2x - 2 = 0\)
\(\therefore y = 0 ; x = \text{-0.7 or 2.7}\)
(ii) \(x^{2} - 2x - 4\frac{1}{2} = 0\)
\(x^{2} - 2x - 4\frac{1}{2} + 2\frac{1}{2} = 0 + 2\frac{1}{2}\)
\(x^{2} - 2x - 2 = 2.5\)
When y = 2.5, \(x = \text{-1.3 or 3.3}\).
(iii) Line of symmetry at x = 1.
View Discussion (0)WAEC 2005 THEORYAt what value of x is the function y = x2 - 2x - 3 minimum?
- A. 1
- B. -1
- C. -4
- D. 4
Correct Answer: A. 1
(a) Find the number N such that when \(\frac{1}{3}\) of it is added to 8, the result is the same as when \(\frac{1}{2}\) of it is subtracted from 18.
(b) Using a ruler and a pair of compasses only, construct a trapezium ABCD, in which the parallel sides AB and DC are 4 cm apart. < DAB = 60°, /AB/ = 8 cm and /BC/ = 5 cm. Measure /DC/.
Explanation
(a) Let the number be N.
\(\frac{N}{3} + 8 = 18 - \frac{N}{2}\)
\(\frac{N}{3} + \frac{N}{2} = 18 - 8 = 10\)
\(\frac{5N}{6} = 10 \implies 5N = 60\)
\(N = 12\)
(b).jpg)
Find the quadratic equation whose roots are c and -c
- A. x2 - c2 = 0
- B. x2 + 2cx = 0
- C. x2 + 2cx + c2 = 0
- D. x2 - 2cx + c2 = 0
Correct Answer: A. x2 - c2 = 0
Explanation
Roots; x and -c
sum of roots = c + (-c) = 0
product of roots = c x -c = -c2
Equation; x2 - (sum of roots) x = product of roots = 0
x2 - (0)x + (-c2) = 0
x2 - c2 = 0
If \(\frac{3}{2x} - \frac{2}{3x} = 4\), solve for x
- A. \(\frac{4}{5}\)
- B. \(\frac{4}{13}\)
- C. \(\frac{5}{24}\)
- D. \(\frac{13}{24}\)
Correct Answer: C. \(\frac{5}{24}\)
Explanation
\(\frac{3}{2x} - \frac{2}{3x} = 4\)
\(\frac{9 - 4}{6x}\); \(\frac{5}{6x}\) = 4
5 = 24x ; x = \(\frac{5}{24}\)
If \(f ' '(x) = 2\), \(f ' (1) = 0\) and \(f(0) = - 8\), find f(x).
Explanation
\(f ' ' (x) = \frac{\mathrm d ^{2} y}{\mathrm d ^{2} x} = 2\)
\(f ' (x) = \int 2 \mathrm {d} x\)
= \(2x + c\)
When x = 1, f'(x) = 0.
\(2(1) + c = 0 \implies c = -2\)
\(\therefore f ' (x) = 2x - 2\)
\(f(x) = \int (2x - 2) \mathrm {d} x\)
= \(x^{2} - 2x + c\)
When x = 0, f(x) = -8
\(0^{2} - 2(0) + c = -8\)
\(c = -8\)
\(\therefore f(x) = x^{2} - 2x - 8\)
Evaluate (2√3 - 4) (2√3 + 4)
- A. -4
- B. -2
- C. 2
- D. 4
Correct Answer: A. -4
Make s the subject of the relation: P = S + \(\frac{sm^2}{nr}\)
- A. s = \(\frac{mrp}{nr + m^2}\)
- B. s = \(\frac{nr + m^2}{mrp}\)
- C. s = \(\frac{nrp}{mr + m^2}\)
- D. s = \(\frac{nrp}{nr + m^2}\)
Correct Answer: D. s = \(\frac{nrp}{nr + m^2}\)
Explanation
P = S + \(\frac{sm^2}{nr}\)
P = S(1 + \(\frac{m^2}{nr}\))
P = S(1 + \(\frac{nr + m^2}{nr}\))
nrp = S(nr + m2)
S = \(\frac{nrp}{nr + m^2}\)