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.
If (x+2) and (3x−1) are factors of 6x3+x2−19x+6, find the third factor.
2x−3
3x+1
x−2
3x+2
Correct answer is A
To get the third factor, take the product of the other 2 factors and then divide the main equation by their product.
64.245
61.255
60.255
60.245
Correct answer is C
(1.98)6=(1+0.98)6=1+6(0.98)+15(0.98)2+20(0.98)3+15(0.98)4+6(0.98)5+(0.98)6
≊
= 60.255
Simplify \frac{1 + \sqrt{8}}{3 - \sqrt{2}}
7 + \sqrt{2}
7 + 7\sqrt{2}
1 - 7\sqrt{2}
1 + \sqrt{2}
Correct answer is D
\frac{1 + \sqrt{8}}{3 - \sqrt{2}}
Rationalizing by multiplying through with 3 + \sqrt{2},
(\frac{1 + \sqrt{8}}{3 - \sqrt{2}})(\frac{3 + \sqrt{2}}{3 + \sqrt{2}}) = \frac{3 + \sqrt{2} + 3\sqrt{8} + 4}{9 - 2}
= \frac{3 + \sqrt{2} + 3\sqrt{4 \times 2} + 4}{7}
= \frac{7 + 7\sqrt{2}}{7} = 1 + \sqrt{2}
If 8^{x} ÷ (\frac{1}{4})^{y} = 1 and \log_{2}(x - 2y) = 1, find the value of (x - y)
\frac{5}{4}
\frac{3}{5}
1
\frac{2}{3}
Correct answer is A
8^{x} ÷ (\frac{1}{4})^{y} = 1
(2^{3})^{x} ÷ (2^{-2})^{y} = 2^{0}
2^{3x - (-2y)} = 2^{0}
\implies 3x + 2y = 0 .... (1)
\log_{2}(x - 2y) = 1
x - 2y = 2^{1} = 2 ..... (2)
Solving equations 1 and 2,
x = \frac{1}{2}, y = \frac{-3}{4}
(x - y) = \frac{1}{2} - \frac{-3}{4} = \frac{5}{4}
If f(x) = 3x^{3} + 8x^{2} + 6x + k and f(2) = 1, find the value of k.
-67
-61
61
67
Correct answer is A
f(x) = 3x^{3} + 8x^{2} + 6x + k
f(2) = 3(2^{3}) + 8(2^{2}) + 6(2) + k = 1
\implies 24 + 32 + 12 + k = 1
68 + k = 1 \therefore k = 1 - 68 = -67