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.
Solve \(3^{2x} - 3^{x+2} = 3^{x+1} - 27\)
1 or 0
1 or 2
1 or -2
-1 or 2
Correct answer is B
\(3^{2x} - 3^{x+2} = 3^{x+1} - 27\)
= \((3^{x})^{2} - (3^{x}).(3^{2}) = (3^{x}).(3^{1}) - 27\)
Let \(3^{x}\) be B; we have
= \(B^{2} - 9B - 3B + 27 = B^{2} - 12B + 27 = 0\).
Solving the equation, we have B = 3 or 9.
\(3^{x} = 3\) or \(3^{x} = 9\)
\(3^{x} = 3^{1}\) or \(3^{x} = 3^{2}\)
Equating, we have x = 1 or 2.
A force (10i + 4j)N acts on a body of mass 2kg which is at rest. Find the velocity after 3 seconds.
\((\frac{5i}{3} + \frac{2j}{3})ms^{-1}\)
\((\frac{10i}{3} + \frac{4j}{3})ms^{-1}\)
\((5i + 2j)ms^{-1}\)
\((15i + 6j)ms^{-1}\)
Correct answer is D
Recall, \(F = mass \times acceleration \implies acceleration = \frac{force}{mass}\)
= \(\frac{10i + 4j}{2} = (5i + 2j) ms^{-2}\)
= \(v = u + at \implies v \text{at 3 seconds} = 0 + (5i + 2j \times 3)\)
= \((15i + 6j) ms^{-1}\)
Given that a = 5i + 4j and b = 3i + 7j, evaluate (3a - 8b).
9i + 44j
-9i + 44j
-9i - 44j
9i - 44j
Correct answer is C
= \(3(5i+4j) - 8(3i+7j) = 15i + 12j - 24i -56j\)
= \(-9i - 44j\)
| Face | 1 | 2 | 3 | 4 | 5 | 6 |
| Frequency | 12 | 18 | y | 30 | 2y | 45 |
Given the table above as the result of tossing a fair die 150 times, find the mode.
3
4
5
6
Correct answer is D
The mode is the occurrence with the highest frequency which, from the table, is 45 (the occurrence of obtaining a 6).
| Face | 1 | 2 | 3 | 4 | 5 | 6 |
| Frequency | 12 | 18 | y | 30 | 2y | 45 |
Given the table above as the results of tossing a fair die 150 times. Find the probability of obtaining a 5.
\(\frac{1}{10}\)
\(\frac{1}{6}\)
\(\frac{1}{5}\)
\(\frac{3}{10}\)
Correct answer is C
Probability of obtaining a 5 = \(\frac{\text{frequency of 5}}{\text{total frequency}}\)
\(12+18+y+30+2y+45 = 150 \implies 105+3y = 150\)
\(3y = 45; y = 15\)
Probability of 5 = \(\frac{2\times 15}{150} = \frac{1}{5}\)