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.
What is the coordinate of the centre of the circle \(5x^{2} + 5y^{2} - 15x + 25y - 3 = 0\)?
\((\frac{15}{2}, -\frac{25}{2})\)
\((\frac{3}{2}, -\frac{5}{2})\)
\((-\frac{3}{2}, \frac{5}{2})\)
\((-\frac{15}{2}, \frac{25}{2})\)
Correct answer is B
Equation for a circle: \((x - a)^{2} + (y - b)^{2} = r^{2}\)
Expanding, we have:
\(x^{2} - 2ax + a^{2} + y^{2} - 2by + b^{2} = r^{2}\)
Given: \(5x^{2} + 5y^{2} - 15x + 25y - 3 = 0\)
Divide through by 5,
\(= x^{2} + y^{2} - 3x + 5y - \frac{3}{5} = 0\)
Comparing, we have
\(- 2a = -3; a = \frac{3}{2}\)
\(-2b = 5; b = -\frac{5}{2}\)
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)
\(4x = 3 \implies x = \frac{3}{4}\)