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.
The coordinates of the centre of a circle is (-2, 3). If its area is 25πcm2, find its equation.
x2+y2−4x−6y−12=0
x2+y2−4x+6y−12=0
x2+y2+4x+6y−12=0
x2+y2+4x−6y−12=0
Correct answer is D
Equation of a circle with centre coordinates (a, b) : (x−a)2+(y−b)2=r2
Area of circle = πr2=25πcm2⟹r2=25
∴
(a, b) = (-2, 3)
Equation: (x - (-2))^{2} + (y - 3)^{2} = 5^{2}
x^{2} + 4x + 4 + y^{2} - 6y + 9 = 25 \implies x^{2} + y^{2} + 4x - 6y + 13 - 25 = 0
= x^{2} + y^{2} + 4x - 6y - 12 = 0
-4
-1
3
4
Correct answer is C
y = 1 - 3x + 2x^{3}
\frac{\mathrm d y}{\mathrm d x} = -3 + 6x^{2}
At (1, 0), \frac{\mathrm d y}{\mathrm d x} = -3 + 6(1^{2}) = -3 + 6 = 3
y = mx - 3 \implies \frac{\mathrm d y}{\mathrm d x} = m = 3 (Tangent with equal gradient)
-1
-2
-3
-4
Correct answer is D
x + 3 = 0 \implies x = -3
Using remainder theorem, if x + 3 is a factor, f(-3) = 0.
f(-3) = (-3)^{3} + 3(-3)^{2} + n(-3) - 12 = 0
-27 + 27 - 3n - 12 = 0 \implies -3n = 12
n = -4
x < -4 or x > 2
x < -2 or x > 4
-2 < x < 4
-4 < x < 2
Correct answer is B
No explanation has been provided for this answer.
What is the angle between a = (3i - 4j) and b = (6i + 4j)?
13°
87°
100°
110°
Correct answer is B
a . b = |a||b| \cos \theta
a = 3i - 4j; b = 6i + 4j
18 - 16 = (\sqrt{3^{2} + (-4)^{2}})(\sqrt{6^{2} + 4^{2}}) \cos \theta
2 = 5\sqrt{52} \cos \theta
\cos \theta = \frac{2}{5\sqrt{52}} = 0.0555
\theta = 86.8° \approxeq 87°