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.
Which of the following quadratic curves will not intersect with the x- axis?
\(y = 2 - 4x - x^{2}\)
\(y = x^{2} - 5x -1\)
\(y = 2x^{2} - x - 1\)
\(y = 3x^{2} - 2x + 4\)
Correct answer is D
The criterion for the quadratic curve to intersect the x- axis is \(b^{2} > 4ac\).
If \(2\log_{4} 2 = x + 1\), find the value of x.
-2
-1
0
1
Correct answer is C
\(2\log_{4} 2 = x + 1\)
\(\log_{4} 2^{2} = \log_{4} 4 = 1\)
\(x + 1 = 1 \implies x = 0\)
8
6
-6
-8
Correct answer is B
Remainder for f(2) = 20.
\(f(2) = 2(2^{3}) + 2^{2} - 3(2) + p = 20\)
\(16 + 4 - 6 + p = 20\)
\(14 + p = 20\)
\(p = 6\)
If \(f(x) = 2x^{2} - 3x - 1\), find the value of x for which f(x) is minimum.
\(\frac{3}{2}\)
\(\frac{4}{3}\)
\(\frac{3}{4}\)
\(\frac{2}{3}\)
Correct answer is C
\(y = 2x^{2} - 3x - 1\)
\(\frac{\mathrm d y}{\mathrm d x} = 4x - 3 = 0\) (At turning point)
\(4x = 3 \implies x = \frac{3}{4}\)
n + 1
2n + 1
3n + 1
4n + 1
Correct answer is B
\(S_{n} = \frac{n}{2}(2a + (n - 1) d = n^{2} + 2n\)
\(n(2a + (n - 1) d = 2n^{2} + 4n\)
\(2an + n^{2}d - nd = 2n^{2} + 4n\)
\(n^{2}d = 2n^{2}\)
\(d = 2\)
\((2a - d) n = 4n\)
\(2a - d = 4 \implies 2a = 4 + d = 4 + 2 = 6\)
\(a = 3\)
\(T_{n} = a + (n - 1)d\)
= \(3 + (n - 1)2 = 3 + 2n - 2 = 2n + 1\)