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.
\(\frac{3}{5}\)
\(\frac{1}{3}\)
\(\frac{1}{6}\)
\(\frac{2}{15}\)
Correct answer is C
For independent events A and B, \(P(A \cap B) = P(A) \times P(B)\)
\(\frac{1}{15} = \frac{2}{5} \times P(B)\)
\(P(B) = \frac{1}{15} \div \frac{2}{5}\)
\(P(B) = \frac{1}{6}\)
Find the coordinates of the centre of the circle \(4x^{2} + 4y^{2} - 5x + 3y - 2 = 0\).
\((\frac{-5}{4}, \frac{3}{4})\)
\((\frac{3}{8}, -\frac{5}{8})\)
\((\frac{5}{8}, -\frac{3}{8})\)
\((\frac{5}{4}, -\frac{3}{4})\)
Correct answer is C
Equation : \((x - a)^{2} + (y - b)^{2} = r^{2}\)
Expanding : \(x^{2} + y^{2} - 2ax - 2by + a^{2} + b^{2} = r^{2}\)
Given, \(4x^{2} + 4y^{2} - 5x + 3y - 2 = 0\)
Divide through by 4 to make the coefficient of \(x^{2}\) and \(y^{2}\) to be 1.
\(x^{2} + y^{2} - \frac{5}{4}x + \frac{3}{4}y - \frac{1}{2} = 0\)
Comparing, \(2a = \frac{5}{4} \implies a = \frac{5}{8}\)
\(2b = -\frac{3}{4} \implies b = -\frac{3}{8}\)
\((a, b) = (\frac{5}{8}, -\frac{5}{8})\)
-8
-5
4
-3
Correct answer is D
\(\begin{pmatrix} 1 & -3 \\ 1 & 4 \end{pmatrix} \begin{pmatrix} -6 \\ P \end{pmatrix} = \begin{pmatrix} 3 \\ -26 \end{pmatrix}\)
\(\implies (1 \times -6) + (-3 \times P) = 3\)
\(-6 - 3P = 3 \implies -3P = 9\)
\(P = -3\)
12
16
6
4
Correct answer is D
\(F = ma\)
\(32 = 8m \implies m = 4 kg\)
Find the least value of the function \(f(x) = 3x^{2} + 18x + 32\)
5
4
-3
-2
Correct answer is A
\(f(x) = 3x^{2} + 18x + 32\)
\(\frac{\mathrm d y}{\mathrm d x} = 6x + 18 = 0\)
\(6x = -18 \implies x = -3\)
\(f(-3) = 3(-3^{2}) + 18(-3) + 32 = 27 - 54 + 32 = 5\)