Calculate the perimeter, in cm, of a sector of a circle of radius 8cm and angle 45o
- A. 2\(\pi\)
- B. 8 + 2\(\pi\)
- C. 16 + 2\(\pi\)
- D. 16 + 16\(\pi\)
An open rectangular box is made of wood 2cm thick. If the internal dimensions of the box are 50cm long, 36cm wide and 20cm deep, the box volume of wood in the box is
- A. 11 520cm3
- B. 36 000cm3
- C. 38 200cm3
- D. 47 520cm3
If three angles of a quadrilateral are (3y – x – z)o, 3xo, (2z – 2y – x)o find the fourth angle in terms of x, y and z
- A. (360 - x- y - z)o
- B. (360 + x + y - z)o
- C. (180 - x + y + z)o
- D. (180 - x + y + z)o
\(\begin{array}{c|c} \text{Age in years} & 10 & 11 & 12 \\ \hline \text{Number of pupils} & 6 & 27 & 7\end{array}\)
The table above shows the number of pupils in each age group in a class. What is the probability that a pupil chosen at random is at least 11 years old?
- A. \(\frac{27}{40}\)
- B. \(\frac{17}{20}\)
- C. \(\frac{33}{40}\)
- D. \(\frac{3}{20}\)
The determination of the matrix \(\begin{pmatrix} 1 & 3 & 3 \\ 4 & 5 & 6\\ 2 & 0 & 1 \end{pmatrix}\) is
- A. -67
- B. -57
- C. -1
- D. 3
Solve for x and y \(\begin{pmatrix} 1 & 1 \\ 3 & y \end{pmatrix}\)\(\begin{pmatrix} x \\ 1 \end{pmatrix}\) = \(\begin{pmatrix} 4 \\ 1\end{pmatrix}\)
- A. x = 3, y = 8
- B. x = 3, y = -8
- C. x = -8, y = 3
- D. x = 8, y = -3
\(\begin{array}{c|c} \oplus mod 10 & 2 & 4 & 6 & 8 \\ \hline 2 & 4 & 8 & 2 & 6 \\4 & 8 & 6 & 4 & 2\\ 4 & 8 & 6 & 4 & 2\\ 6 & 2 & 4 & 6 & 8\\ 8 & 6 & 2 & 8 & 4\end{array}\)
The multiplication table above has modulo 10 on the set S = (2, 4, 6, 8). Find the inverse of 2
- A. 2
- B. 4
- C. 6
- D. 8
A binary operation \(\oplus\) is defines on the set of all positive integers by a \(\oplus\) b = ab for all positive integers a, b. Which of the following properties does NOT hold?
- A. closure
- B. identity
- C. positive
- D. inverse
Find the nth term of the sequence 3, 6, 10, 15, 21…..
- A. \(\frac{n(n - 1)}{2}\)
- B. \(\frac{n(n + 1)}{2}\)
- C. \(\frac{(n + 1)(n + 2)}{2}\)
- D. n(2n + 1)
Find the value of log10 r + log10 r2 + log10 r4 + log10 r8 + log10 r16 + log10 r32 = 63
- A. 10-1
- B. 10o
- C. 10
- D. 102
If the 6th term of an arithmetic progression is 11 and the first term is 1, find the common difference.
- A. \(\frac{12}{5}\)
- B. \(\frac{5}{3}\)
- C. -2
- D. 2
Find the range of values of x for which \(\frac{1}{x}\) > 2 is true
- A. x < \(\frac{1}{2}\)
- B. x < 0 or x < \(\frac{1}{2}\)
- C. 0 < x < \(\frac{1}{2}\)
- D. 1 < x < 2
Find P if \(\frac{x – 3}{(1 – x)(x + 2)}\) = \(\frac{p}{1 – x}\) + \(\frac{Q}{x + 2}\)
- A. \(\frac{-2}{3}\)
- B. \(\frac{-5}{3}\)
- C. \(\frac{5}{3}\)
- D. \(\frac{2}{3}\)
Solve for r in the following equation \(\frac{1}{r – 1}\) + \(\frac{2}{r + 1}\) = \(\frac{3}{r}\)
- A. 3
- B. 4
- C. 5
- D. 6
If a = 1, b = 3, solve for x in the equation \(\frac{a}{a – x}\) = \(\frac{b}{x – b}\)
- A. \(\frac{4}{3}\)
- B. \(\frac{2}{3}\)
- C. \(\frac{3}{2}\)
- D. \(\frac{3}{4}\)
Find the values of p and q such that (x – 1)and (x – 3) are factors of px3 + qx2 + 11x – 6
- A. -1, -6
- B. 1, -6
- C. 1, 6
- D. 6, -1
Factorize a2x – b2y – b2x + a2y
- A. (a - b)(x + y)
- B. (y - x)(a - b)(a + b)
- C. (x - y)(a - b)(a + b)
- D. (x + y)(a - b)(a + b)
Simplify \(\frac{(2m – u)^2 – (m – 2u)^2}{5m^2 – 5u^2}\)
- A. \(\frac{3}{5}\)
- B. \(\frac{2}{5}\)
- C. \(\frac{2m - u}{5m + u}\)
- D. \(\frac{m - 2u}{m + 5u}\)
Given that for sets A and B, in a universal set E, A \(\subseteq\) B then A \(\cap\)(A \(\cap\) B)’ is
- A. A
- B. \(\phi\)
- C. B
- D. E
Given that \(\sqrt{2} = 1.414\), find without using tables, the value of \(\frac{1}{\sqrt{2}}\)
- A. 0.141
- B. 0.301
- C. 0.667
- D. 0.707
Simplify \(\sqrt{48}\) – \(\frac{9}{\sqrt{3}}\) + \(\sqrt{75}\)
- A. 5√3
- B. 6√3
- C. 8√3
- D. 18√3