\(\begin{array}{c|c} Score & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ \hline Frequency & 1 & 0 & 7 & 5 & 2 & 3 & 1 & 1 \end{array}\)
The table above shows the scores of 20 students in further mathematics test. What is the range of the distribution?
- A. 7
- B. 6
- C. 3
- D. 10
If the variance of 3+x, 6, 4, x and 7-x is 4 and the mean is 5, find the standard deviation
- A. \(\sqrt{3}\)
- B. 2
- C. 3
- D. \(\sqrt{2}\)
\(\begin{array}{c|c}Age & 20 & 25 & 30 & 35 & 40 & 45 \\
\hline \text{No. of people} & 3 & 5 & 1 & 1 & 2 & 3 \end{array}\)
Calculate the median age of the frequency distribution in the table above
- A. 25
- B. 30
- C. 35
- D. 20
The mean of seven numbers is 10. If six of the numbers are 2, 4, 8, 14, 16 and 18, find the mode.
- A. 6
- B. 8
- C. 14
- D. 2
Find the mean of t + 2, 2t – 4, 3t + 2 and 2t.
- A. t + 1
- B. 2t
- C. 2t + 1
- D. t
The radius of a circle is increasing at the rate of 0.02cms-1. Find the rate at which the area is increasing when the radius of the circle is 7cm.
- A. 0.75cm2S-1
- B. 0.53cm2S-1
- C. 0.35cm2S-1
- D. 0.88cm2S-1
If y = (2x + 2)\(^3\), find \(\frac{\delta y}{\delta x}\)
- A. 3(2x +2)2
- B. 6(2x +2)
- C. 3(2x +2)
- D. 6(2x +2)2
If y = x sin x, find \(\frac{\delta y}{\delta x}\)
- A. sin x - cos x
- B. cos x - x sin x
- C. cos x + x sin x
- D. sin x + x cos x
Find the inverse \(\begin{pmatrix} 5 & 3 \\ 6 & 4 \end{pmatrix}\)
- A. \(\begin{vmatrix} 2 & -\frac{3}{2} \\ -3 & -\frac{5}{2} \end{vmatrix}\)
- B. \(\begin{vmatrix} 2 & -\frac{3}{2} \\ -3 & \frac{5}{2} \end{vmatrix}\)
- C. \(\begin{vmatrix} 2 & \frac{3}{2} \\ -3 & \frac{5}{2} \end{vmatrix}\)
- D. \(\begin{vmatrix} 2 & \frac{3}{2} \\ -3 & \frac{5}{2} \end{vmatrix}\)
If P = \(\begin{pmatrix} 5 & 3 \\ 2 & 1 \end{pmatrix}\) and Q = \(\begin{pmatrix} 4 & 2 \\ 3 & 5 \end{pmatrix}\), find 2P + Q
- A. \(\begin{vmatrix} 7 & 7 \\ 14 & 8 \end{vmatrix}\)
- B. \(\begin{vmatrix} 14 & 8 \\ 7 & 7 \end{vmatrix}\)
- C. \(\begin{vmatrix} 7 & 7 \\ 8 & 14 \end{vmatrix}\)
- D. \(\begin{vmatrix} 8 & 14 \\ 7 & 7 \end{vmatrix}\)
If a binary operation * is defined by x * y = x + 2y, find 2 * (3 * 4)
- A. 24
- B. 16
- C. 14
- D. 26
The nth term of the progression \(\frac{4}{2}\), \(\frac{7}{3}\), \(\frac{10}{4}\), \(\frac{13}{5}\) is …
- A. \(\frac{1 - 3n}{n + 1}\)
- B. \(\frac{3n + 1}{n + 1}\)
- C. \(\frac{3n + 1}{n - 1}\)
- D. \(\frac{3n - 1}{n + 1}\)
Solve for x: |x – 2| < 3
- A. x < 5
- B. -2 < x < 3
- C. -1 < x < 5
- D. x < 1
If r varies inversely as the square root of s and t, how does s vary with r and t?
- A. s varies inversely as r and t2
- B. s varies inverely as r2 and t
- C. s varies directly as r2 and t2
- D. s varies directly as r and t
P varies jointly as m and u, and varies inversely as q. Given that p = 4, m = 3 and u = 2 and q = 1, find the value of p when m = 6, u = 4 and q =\(\frac{8}{5}\)
- A. 12\(\frac{8}{5}\)
- B. 15
- C. 10
- D. 28\(\frac{8}{5}\)
The remainder when 6p3 – p2 – 47p + 30 is divided by p – 3 is
- A. 21
- B. 42
- C. 63
- D. 18
If S = \(\sqrt{t^2 – 4t + 4}\), find t in terms of S
- A. S2 - 2
- B. S + 2
- C. S - 2
- D. S2 + 2
if P = {x:x is odd, \(-1 < x \leq 20\)} and Q is {y:y is prime, \(-2 < y \leq 25\), find P \(\cap\) Q
- A. {3,5,7,11,17,19}
- B. {3,5,11,13,17,19}
- C. {3,5,7,11,13,17,19}
- D. {2,3,5,7,11,13,17,19}
Simplify \(\frac{\sqrt{5}(\sqrt{147} – \sqrt{12}}{\sqrt{15}}\)
- A. 5
- B. \(\frac{1}{5}\)
- C. \(\frac{1}{9}\)
- D. 9