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.
Find the equation of the tangent to the curve \(y = 4x^{2} - 12x + 7\) at point (2, -1).
y + 4x - 9 = 0
y - 4x - 9 = 0
y - 4x + 9 = 0
y + 4x + 9 = 0
Correct answer is C
\(y = 4x^{2} - 12x + 7\)
\(\frac{\mathrm d y}{\mathrm d x} = 8x - 12\)
At x = 2, y = 8(2) - 12 = 4
Equation of the tangent to the curve: \(y - (-1) = 4(x - 2)\)
\(y + 1 = 4x - 8 \implies y - 4x + 1 + 8 = y - 4x + 9 = 0\)
Find the axis of symmetry of the curve \(y = x^{2} - 4x - 12\).
x = -2
y = -2
x = 2
y = 2
Correct answer is C
The vertical line \(x = \frac{-b}{2a}\) is the axis of symmetry of the curve.
\(y = x^{2} - 4x - 12\)
\(\text{Axis of symmetry} = x = \frac{-(-4)}{2(1)} = \frac{4}{2} = 2\)
The third of geometric progression (G.P) is 10 and the sixth term is 80. Find the common ratio.
2
3
4
8
Correct answer is A
\(T_{n} = ar^{n - 1}\) ( Geometric Progression)
\(T_{3} = ar^{3 - 1} = ar^{2} = 10 .... (1)\)
\(T_{6} = ar^{6 - 1} = ar^{5} = 80 .....(2)\)
Divide (2) by (1)
\(r^{5 - 2} = r^{3} = 8 \)
\(r = \sqrt[3]{8} = 2\)
{-1, 5, 13}
{5, 13, 49}
{1, 2, 3, 6}
{-1, 5, 13, 49}
Correct answer is D
\(P = {x : \text{x is a factor of 6}} \implies P = {1, 2, 3, 6}\)
\(g(x) = x^{2} + 3x - 5\)
\(g(1) = 1^{2} + 3(1) - 5 = 1 + 3 - 5 = -1\)
\(g(2) = 2^{2} + 3(2) - 5 = 4 + 6 - 5 = 5\)
\(g(3) = 3^{2} + 3(3) - 5 = 9 + 9 - 5 = 13\)
\(g(6) = 6^{2} + 3(6) - 5 = 36 + 18 - 5 = 49\)
\(\therefore Range(g(x)) = {-1, 5, 13, 49}\)
If \(\begin{vmatrix} 3 & x \\ 2 & x - 2 \end{vmatrix} = -2\), find the value of x.
-8
4
-4
8
Correct answer is A
\(\begin{vmatrix} 3 & x \\ 2 & x - 2 \end{vmatrix} = 3(x - 2) - 2x = -2\)
\(3x - 6 - 2x = -2 \implies x - 6 = -2\)
\(x = -2 + 6 = 4\)