If y = 8x\(^3\) – 3x\(^2\) + 7x – 1, find \(\frac{\mathrm d^2 y}{\mathrm d x^2}\).
- A. 48x - 6
- B. 11x\(^2\) + 6x - 7
- C. 32x + 7
- D. 24x\(^2\) - 6x + 7
Given the matrix \(A = \begin{vmatrix} 3 & -2 \\ 1 & 6 \end{vmatrix}\). Find the inverse of matrix A.
- A. \(\begin{vmatrix} 6 & 2 \\ 1 & 6 \end{vmatrix}\)
- B. \(\begin{vmatrix} \frac{2}{11} & \frac{1}{12}\\ \frac{3}{20} & \frac{1}{10} \end{vmatrix}\)
- C. \(\begin{vmatrix} -3 & 2 \\ -1 & -6 \end{vmatrix}\)
- D. \(\begin{vmatrix} \frac{3}{10} & \frac{1}{10} \\ \frac{-1}{20} & \frac{3}{20}\end{vmatrix}\)
If \(\begin{vmatrix} 2 & -5 & 3 \\ x & 1 & 4 \\ 0 & 3 & 2 \end{vmatrix} = 132\), find the value of x.
- A. 5
- B. 8
- C. 6
- D. 3
If 2x\(^2\) + x – 3 divides x – 2, find the remainder.
- A. 7
- B. 3
- C. 5
- D. 6
Find the polynomial if given q(x) = x\(^2\) – x – 5, d(x) = 3x – 1 and r(x) = 7.
- A. 3x\(^3\) - 4x\(^2\) - 14x + 12
- B. 3x\(^2\) + 3x - 7
- C. 3x\(^3\) + 4x\(^2\) + 14x - 12
- D. 3x\(^2\) - 3x + 4
Determine the values for which \(x^2 – 7x + 10 \leq 0\)
- A. 2 \(\leq\) x \(\geq\) 5
- B. -2 \(\leq\) x \(\leq\) 3
- C. -2 \(\leq\) x \(\geq\) 3
- D. 2 \(\leq\) x \(\leq\) 5
Find the value of x for \(\frac{2 + 2x}{3} – 2 \geq \frac{4x – 6}{5}\)
- A. x \(\geq\) -5
- B. x \(\geq\) -1
- C. x \(\leq\) -1
- D. x \(\leq\) 3
Evaluate \(\frac{2\log_{3} 9 \times \log_{3} 81^{-2}}{\log_{5} 625}\)
- A. 4
- B. -32
- C. -8
- D. 16
Find the value of k in the equation: \(\sqrt{28} + \sqrt{112} – \sqrt{k} = \sqrt{175}\)
- A. \(\sqrt{28}\)
- B. 7
- C. 28
- D. \(\sqrt{7}\)
In a committee of 5, which must be selected from 4 males and 3 females. In how many ways can the members be chosen if it were to include 2 females?
- A. 144 ways
- B. 15 ways
- C. 185 ways
- D. 12 ways
If the universal set μ = {x : 1 ≤ x ≤ 20} and
A = {y : multiple of 3}
B = |z : odd numbers}
Find A ∩ B
- A. {1, 3, 6}
- B. {3, 5, 9, 12}
- C. {3, 9, 15}
- D. {2, 3, 9}
If the 3rd and 7th terms of a G.P are 9 and 1/9 respectively. Find the common ratio.
- A. \(\frac{1}{3}\)
- B. \(\frac{1}{9}\)
- C. \(\frac{2}{3}\)
- D. \(\frac{2}{9}\)
Find the probability that a number selected at random from 21 to 34 is a multiple of 3
- A. \(\frac{3}{11}\)
- B. \(\frac{2}{9}\)
- C. \(\frac{5}{14}\)
- D. \(\frac{5}{13}\)
Integrate \(\int (4x^{-3} – 7x^2 + 5x – 6) \mathrm d x\).
- A. \(-2x^{-2} - \frac{7}{3}x^3 + \frac{5}{2} x^2 - 6x\)
- B. \(2x^2 + \frac{7}{3} x^3 - 5x + 6\)
- C. \(12x^2 + 14x - 5\)
- D. \(-12x^{-4} - 14x + 5\)
This table below gives the scores of a group of students in a Further Mathematics Test.
| Score | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| Frequency | 4 | 6 | 8 | 4 | 10 | 6 | 2 |
Calculate the mean deviation for the distribution
- A. 4.32
- B. 2.81
- C. 1.51
- D. 3.90
This table below gives the scores of a group of students in a Further Mathematics Test.
| Score | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| Frequency | 4 | 6 | 8 | 4 | 10 | 6 | 2 |
Find the mode of the distribution.
- A. 7
- B. 10
- C. 5
- D. 4
If M varies directly as N and inversely as the root of P. Given that M = 3, N = 5 and P = 25. Find the value of P when M = 2 and N = 6.
- A. 36
- B. 63
- C. 47
- D. 81
A binary operation Δ is defined by a Δ b = a + 3b + 2.
Find (3 Δ 2) Δ 5
- A. 35
- B. 59
- C. 28
- D. 87
A factory worker earns ₦50,000 per month out of which he spends 15% on his children’s education, ₦13,600 on Food, 3% on electricity and uses the rest for his personal purpose. How much does he have left?
- A. N21,850
- B. N18,780
- C. N27,400
- D. N32,500
Find the equation of the locus of a point A(x, y) which is equidistant from B(0, 2) and C(2, 1)
- A. 4x + 2y = 3
- B. 4x - 3y = 1
- C. 4x - 2y = 1
- D. 4x + 2y = -1
A bricklayer charges ₦1,500 per day for himself and ₦500 per day for his assistant. If a two bedroom flat was built for ₦95,000 and the bricklayer worked 10 days more than his assistant, how much did the assistant receive?
- A. N20,000
- B. N28,000
- C. N31,200
- D. N41,000