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.
If \(x^2+y^2+-2x-6y+5 =0\), evaluate dy/dx when x=3 and y=2.
2
-2
-4
4
Correct answer is A
\(x^2+y^2+-2x-6y+5 =0\)
When differentiated:
\(x^2+y^2+-2x-6y+5 =0\) → 2x + 2y - 2 - 6 = 0
where x=3 and y=2
2[3] + 2[2] - 8 = 0
6 + 4 - 8 = 2
Given that \(\frac{8x+m}{x^2-3x-4} ≡ \frac{5}{x+1} + \frac{3}{x-4}\)
23
17
-17
18
Correct answer is C
\(\frac{8x+m}{x^2-3x-4} ≡ \frac{5}{x+1} + \frac{3}{x-4}\)
\(\frac{8x+m}{x^2-3x-4}\) ≡ \(\frac{5(x-1)+ 3(x+4)}{x^2-3x-4}\)
multiplying both sides by x2-3x-4
8x+m ≡ 5(x-4)+3(x+1)
8x + m ≡ 5x - 20 + 3x + 3
8x - 5x - 3x + m = -20 + 3
m = -17
Differentiate \(\frac{5x^ 3+x^2}{x}\), x ≠ 0 with respect to x.
10x + 1
10x + 2
x(15x + 1)
x(15x + 2)
Correct answer is A
\(\frac{5x^ 3+x^2}{x}\) → \(\frac{5x^ 3}{x} + \frac{x^2}{x}\)
5x\(^2\) + x
Then dy/dx = 10x + 1
9/16
81/16
9
9 \(\frac{9}{16}\)
Correct answer is D
GP : 36, P, \(\frac{q}{4}\), q, ... p + q = ?
| Recall, | common | ratio, | r | = | Tn
Tn-1 |
= | T2
T1 |
= | T3
T2 |
= | T4
T3 |
| ∴ | P
36 |
= | 9
4 |
÷ | p | ; | p\(^2\) | = | 9
4 |
x | 36 | ; | p\(^2\) | = | 81 |
| p | = | 9 | ∴ | r | = | T2
T1 |
= | 9
36 |
= | 1
4 |
| Also | r | = | T4
T3 |
= | q | ÷ | 9
4 |
∴ \(\frac{1}{4}\) = q ÷ \(\frac{9}{4}\) ;
\(\frac{9}{4}\) = 4q
| 16q | = | 9 | , | q | = | 9
16 |
∴ | p | + | q | = | 9 | + | 9
16 |
= | 9 | 9
16 |
Evaluate \(∫^0_{-1}\) (x + 1)(x - 2) dx
7/6
5/6
-5/6
-7/6
Correct answer is D
\(∫^0_{-1}\) (x + 1)(x - 2) dx
= \(∫^0_{-1}\) \(x^2 - x - 2\) dx
Integrated \(x^2 - x - 2\) = \(\frac{x^3}{3} - \frac{x^2}{2} -2\)