Further Mathematics Questions and Answers
Test your knowledge of advanced level mathematics with this aptitude test. This test comprises Further Maths questions and answers from past JAMB and WAEC examinations.
Test your knowledge of advanced level mathematics with this aptitude test. This test comprises Further Maths questions and answers from past JAMB and WAEC examinations.
83
73
53
2
Correct answer is A
∫1−1(x+1)2dx≡∫1−1(x2+2x+1)dx
= x33+x2+x|1−1
= (133+12+1)−((−1)33+(−1)2+(−1))=73+13=83
Calculate the standard deviation of 30, 29, 25, 28, 32 and 24.
2.0
2.8
3.0
3.2
Correct answer is B
| x | x−μ | (x−μ)2 |
| 24 | -4 | 16 |
| 25 | -3 | 9 |
| 28 | 0 | 0 |
| 29 | 1 | 1 |
| 30 | 2 | 4 |
| 32 | 4 | 16 |
| ∑ = 168 | 46 |
μ=24+25+28+29+30+326=1688=28
S.D=√∑(x−μ)2n=√466
= √7.67≊
Evaluate \int_{\frac{1}{2}}^{1} \frac{x^{3} - 4}{x^{3}} \mathrm {d} x.
-5.5
-2.0
2.0
5.5
Correct answer is A
\int_{\frac{1}{2}}^{1} \frac{x^{3} - 4}{x^{3}} \mathrm {d} x \equiv \int_{\frac{1}{2}}^{1} 1 - \frac{4}{x^{3}} \mathrm {d} x.
= \int_{\frac{1}{2}}^{1} 1 - 4x^{-3} \mathrm {d} x.
= \left. x - \frac{4x^{-2}}{-2}\right |_{\frac{1}{2}}^{1} = \left. x + \frac{2}{x^{2}}\right |_{\frac{1}{2}}^{1}
= (1 + 2) - (\frac{1}{2} + 8) = 3 - 8.5 = -5.5
Find the stationary point of the curve y = 3x^{2} - 2x^{3}.
(1, 0)
(-1, 0)
(1, 1)
(-1, -1)
Correct answer is A
y = 3x^{2} - 2x^{3}
\frac{\mathrm d y}{\mathrm d x} = 6x - 6x^{2} = 0 \implies 6x(1 - x) = 0
x = 0, 1, when x = 1, y = 0.
when x = 1, y = 0.
The stationary point is (1, 0)
The midpoint of M(4, -1) and N(x, y) is P(3, -4). Find the coordinates of N.
(2, -3)
(2, -7)
(-1, -3)
(-10, -7)
Correct answer is B
Given M(4, -1) and N(x, y) with midpoint P(3, -4).
\implies \frac{4 + x}{2} = 3; \frac{-1 + y}{2} = -4
\therefore x = 2; y = -7
N = (2, -7)