A chord of a circle of a diameter 42cm subtends an angle of 60o at the centre of the circle. Find the length of the mirror arc
- A. 22cm
- B. 44cm
- C. 110cm
- D. 220cm
Each of the base angles of a isosceles triangle is 58° and the verticles of the triangle lie on a circle. Determine the angle which the base of the triangle subtends at the centre of the circle.
- A. 128o
- B. 16o
- C. 64o
- D. 58o
Find the non-zero positive value of x which satisfies the equation \(\begin{vmatrix} x & 1 & 0 \\ 1 & x & 1 \\ 0 & 1 & x\end{vmatrix}\) = 0
- A. 2
- B. 4
- C. √3
- D. √2
- E. 1
Determine x + y if \(\begin{pmatrix} 2 & -3 \\ -1 & 4 \end{pmatrix}\) \(\begin{pmatrix} x \\ y \end{pmatrix}\) = \(\begin{pmatrix}-1 \\ 8 \end{pmatrix}\)
- A. 3
- B. 4
- C. 7
- D. 12
If X \(\ast\) Y = X + Y – XY, find x when (x \(\ast\) 2) + (x \(\ast\) 3) = 68
- A. 24
- B. 22
- C. -12
- D. -21
Two binary operations \(\ast\) and \(\oplus\) are defines as m \(\ast\) n = mn – n – 1 and m \(\oplus\) n = mn + n – 2 for all real numbers m, n.
Find the value of 3 \(\oplus\) (4 \(\ast\) 5)
- A. 60
- B. 57
- C. 54
- D. 42
The nth term of a sequence is given \(3^{1 – n}\), find the sum of the first three terms of the sequence.
- A. \(\frac{13}{9}\)
- B. 1
- C. \(\frac{1}{3}\)
- D. \(\frac{1}{9}\)
Sn is the sum of the first n terms of a series given by Sn = n\(^2\) – 1. Find the nth term
- A. 4n + 1
- B. 4n - 1
- C. 2n + 1
- D. 2n - 1
Find the range of values of x which satisfies the inequality 12x2 < x + 1
- A. -\(\frac{1}{4}\) < x < \(\frac{1}{3}\)
- B. \(\frac{1}{4}\) < x < -\(\frac{1}{3}\)
- C. -\(\frac{1}{3}\) < x < \(\frac{1}{4}\)
- D. -\(\frac{1}{4}\) < x < - \(\frac{1}{3}\)
Let f(x) = 2x + 4 and g(x) = 6x + 7 here g(x) > 0. Solve the inequality \(\frac{f(x)}{g(x)}\) < 1
- A. x < - \(\frac{3}{4}\)
- B. x > - \(\frac{4}{3}\)
- C. x > - \(\frac{3}{4}\)
- D. x > - 12
Find the value of k if \(\frac{5 + 2r}{(r + 1)(r – 2)}\) expressed in partial fraction is \(\frac{k}{r – 2}\) + \(\frac{L}{r + 1}\) where K and L are constants
- A. 3
- B. 2
- C. 1
- D. -1
What value of g will make the expression 4x2 – 18xy + g a perfect square?
- A. 9
- B. \(\frac{9y^2}{4}\)
- C. 81y^2
- D. \(\frac{18y^2}{4}\)
Make F the subject of the formula t = \(\sqrt{\frac{v}{\frac{1}{f} + \frac{1}{g}}}\)
- A. \(\frac{gv-t^2}{gt^2}\)
- B. \(\frac{gt^2}{gv-t^2}\)
- C. \(\frac{v}{\frac{1}{t^2} - \frac{1}{g}}\)
- D. \(\frac{gv}{t^2 - g}\)
Find the minimum value of X2 – 3x + 2 for all real values of x
- A. -\(\frac{1}{4}\)
- B. -\(\frac{1}{2}\)
- C. \(\frac{1}{4}\)
- D. \(\frac{1}{2}\)
Solve the simultaneous equations \(\frac{2}{x} – {\frac{3}{y}}\) = 2, \(\frac{4}{x} + {\frac{3}{y}}\) = 10
- A. x = \(\frac{3}{2}\), y = \(\frac{3}{2}\)
- B. x = \(\frac{1}{2}\), y = \(\frac{3}{2}\)
- C. x = \(\frac{-1}{2}\), y = \(\frac{-3}{2}\)
- D. x = \(\frac{1}{3}\), y = \(\frac{3}{2}\)
If the function f(fx) = x3 + 2x2 + qx – 6 is divisible by x + 1, find q
- A. -5
- B. -2
- C. 2
- D. 5
A survey of 100 students in an institution shows that 80 students speak Hausa and 20 students speak Igbo, while only 9 students speak both language. How many students speak neither Hausa nor Igbo?
- A. 0
- B. 9
- C. 11
- D. 20
If U = (s, p, i, e, n, d, o, u, r), X = (s, p, e, n, d) Y = (s, e, n, o, u), Z = (p, n, o, u, r) find X ∩( Y ∪ Z)
- A. (p, o, u, r)
- B. (s, p, d, r)
- C. (s, p, n, e)
- D. (n, d, u)
Find the simple interest rate percent per annum at which N1,000 accumulates to N1,240 in 3 years
- A. 6%
- B. 8%
- C. 10%
- D. 12%
Simplify \(\frac{2\sqrt{3} + 3\sqrt{5}}{3\sqrt{5} – 2\sqrt{3}}\)
- A. \(\frac{19 + 4\sqrt{25}}{11}\)
- B. \(\frac{19 + 4\sqrt{15}}{11}\)
- C. \(\frac{19 + 2\sqrt{15}}{11}\)
- D. \(\frac{19 + 2\sqrt{15}}{19}\)
If \(8^{\frac{x}{2}} = (2^{\frac{3}{8}})(4^{\frac{3}{4}}\)), find x
- A. \(\frac{3}{8}\)
- B. \(\frac{3}{4}\)
- C. \(\frac{4}{5}\)
- D. \(\frac{5}{4}\)