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 coefficient of x4 in the binomial expansion of (1−2x)6.
320
240
-320
-240
Correct answer is B
(1−2x)6=6C0(16)+6C1(15)(−2x1)+6C2(14)(−2x2)+6C3(13)(−2x3)+6C4(12)(−2x4)+...
The coefficient ofx4=15×16=240
If f(x)=12−x,x≠2, find f−1(−12).
4
0
-2
-4
Correct answer is A
f(x)=12−x,x≠2
f(y)=12−y
x=12−y (Let x = f(y))
2x−xy=1⟹y=2x−1x
∴
f^{-1}(-\frac{1}{2}) = \frac{2(-\frac{1}{2}) - 1}{-\frac{1}{2}}
= -2 \times -2 = 4
Given that (\sqrt{3} - 5\sqrt{2})(\sqrt{3} + \sqrt{2}) = p + q\sqrt{6}, find q.
4
-4
-5
-7
Correct answer is B
(\sqrt{3} - 5\sqrt{2})(\sqrt{3} + \sqrt{2}) = 3 + \sqrt{6} - 5\sqrt{6} - 10
= -7 - 4\sqrt{6} = p + q\sqrt{6}
\therefore q = -4
Given that \frac{1}{8^{2y - 3y}} = 2^{y + 2}.
\frac{1}{5}
\frac{7}{8}
1
1\frac{1}{5}
Correct answer is C
\frac{1}{8^{2y - 3y}} = \frac{1}{8^{-y}} = 8^{y}
8^{y} = 2^{y + 2} \implies (2^{3})^{y} = 2^{y + 2}
3y = y + 2 \implies 2y = 2
y = 1
Two functions f and g are defined by f : x \to 3x - 1 and g : x \to 2x^{3}, evaluate fg(-2)
-49
-47
-10
-9
Correct answer is A
g : x \to 2x^{3}
g(-2) = 2(-2^{3}) = 2(-8) = -16
f : x \to 3x - 1
f(-16) = 3(-16) -1 = -48 - 1 = - 49