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.
A polynomial is defined by \(f(x + 1) = x^{3} + px^{2} - 4x + 2\), find f(2)
-8
-2
2
8
Correct answer is C
Given: \(f(x + 1) = x^{3} + 3x^{2} - 4x + 2\).
\(f(2) = f(x + 1) \implies x + 1 = 2; x = 1\)
\(f(2) = 1^{3} + 3(1)^{2} - 4(1) + 2 = 1 + 3 - 4 + 2 = 2\)
If (x + 1) is a factor of the polynomial \(x^{3} + px^{2} + x + 6\). Find the value of p.
-8
-4
4
8
Correct answer is B
If (x + 1) is a factor, then f(-1) = 0.
\((-1)^{3} + p(-1)^{2} + (-1) + 6 = 0\)
\(-1 + p - 1 + 6 = 0 \implies p + 4 = 0\)
\(p = -4\)
8i + j
2i - j
-2i - 3j
-8i - j
Correct answer is A
\(\overrightarrow{SQ} = \overrightarrow{SR} + \overrightarrow{RQ}\)
\(\overrightarrow{RQ} = -\overrightarrow{QR} = - (3i + 2j) = -3i - 2j\)
\(\overrightarrow{SQ} = (-5i + 3j) - 3i - 2j = -8i + j\)
Evaluate \(\log_{10}(\frac{1}{3} + \frac{1}{4}) + 2\log_{10} 2 + \log_{10} (\frac{3}{7})\)
-3
0
\(\frac{5}{6}\)
1
Correct answer is B
\(\log_{10} (\frac{1}{3} + \frac{1}{4}) + 2\log_{10} 2 + \log_{10} (\frac{3}{7})\)
\(\frac{1}{3} + \frac{1}{4} = \frac{7}{12}\)
= \(\log_{10} (\frac{7}{12} \times 2^{2} \times \frac{3}{7})\)
= \(\log_{10} 1 = 0\)
Given that \(\sin x = \frac{-\sqrt{3}}{2}\) and \(\cos x > 0\), find x
300°
240°
120°
60°
Correct answer is A
In order to do this, simply find the option in the range where only the cos is +ve. This occurs in the range \(270° \leq x \leq 360°\).
Check: \(\sin 300 = - \sin 60 = \frac{-\sqrt{3}}{2}\)
\(\cos 300 = \cos 60 = \frac{1}{2}\)