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.
5
4
3
2
Correct answer is D
Sn=n2(2a+(n−1)d
n2(2a+(n−1)d=n2+2n
n(2a+(n−1)d=2n2+4n
2an+n2d−nd=2n2+4n
Comparing the equations, d = 2 (coefficient of n2).
A function f is defined on R, the set of real numbers, by: f:x→x+3x−2,x≠2, find f−1.
f−1:x→2x+3x−1,x≠1
f−1:x→x+3x+2,x≠−2
f−1:x→x−12x+3,x≠−32
f−1:x→x−2x+3,x≠−3
Correct answer is A
f(x)=x+3x−2
f(y)=y+3y−2
Let f(y) = x,
x=y+3y−2
x(y−2)=y+3
xy−y=2x+3⟹y(x−1)=2x+3
y=2x+3x−1
Find the range of values of x for which 2x2+7x−15>0.
x<−32 or x>5
x<−5 or x>32
−32<x<5
−5<x<32
Correct answer is B
2x2+7x−15>0⟹2x2−3x+10x−15>0
x(2x−3)+5(2x−3)>0
(x+5)(2x−3)>0
For their product to be positive, they are either both +ve or -ve.
x+5>0⟹x>−5
2x−3>0⟹2x>3
x>32
Check:
x>−5:x=−3
2(−3)2+7(−3)−15=18−21−15=−18<0 (Not satisfied)
∴
x > \frac{3}{2}: x = 2
2(2^{2}) + 7(2) - 15 = 8 + 14 - 15 = 7 > 0 (Satisfied)
Simplify \frac{\sqrt{3} + \sqrt{48}}{\sqrt{6}}
3\sqrt{2}
5\sqrt{2}
\frac{5\sqrt{2}}{2}
\frac{3\sqrt{2}}{2}
Correct answer is C
\frac{\sqrt{3} + \sqrt{48}}{\sqrt{6}} = \frac{\sqrt{3} + 4\sqrt{3}}{\sqrt{6}}
\frac{5\sqrt{3}}{\sqrt{6} = \frac{5\sqrt{3} \times \sqrt{6}}{\sqrt{6} \times \sqrt{6}}
\frac{5\sqrt{18}{6} = \frac{15\sqrt{2}}{6}
= \frac{5\sqrt{2}}{2}
