If the 3rd and 7th terms of a G.P are 9 and 1/9 respectively. Find the common ratio.
\(\frac{1}{3}\)
\(\frac{1}{9}\)
\(\frac{2}{3}\)
\(\frac{2}{9}\)
Correct answer is A
\(T_n = ar^{n - 1}\) (terms of a G.P)
\(T_3 = ar^2 = 9\) ... (i)
\(T_7 = ar^6 = \frac{1}{9}\) ... (ii)
Divide (i) by (ii);
\(\frac{ar^6}{ar^2} = \frac{\frac{1}{9}}{9}\)
\(r^4 = \frac{1}{81}\)
\(r^4 = (\frac{1}{3})^4\)
\(r = \frac{1}{3}\)
Find the probability that a number selected at random from 21 to 34 is a multiple of 3
\(\frac{3}{11}\)
\(\frac{2}{9}\)
\(\frac{5}{14}\)
\(\frac{5}{13}\)
Correct answer is C
S = {21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34}
n(S) = 14
multiples of 3 = {21, 24, 27, 30, 33}
n(multiples of 3) = 5
Prob( picking a multiple of 3) = 5/14
Integrate \(\int (4x^{-3} - 7x^2 + 5x - 6) \mathrm d x\).
\(-2x^{-2} - \frac{7}{3}x^3 + \frac{5}{2} x^2 - 6x\)
\(2x^2 + \frac{7}{3} x^3 - 5x + 6\)
\(12x^2 + 14x - 5\)
\(-12x^{-4} - 14x + 5\)
Correct answer is A
\(\int (4x^{-3} - 7x^2 + 5x - 6) \mathrm d x\)
= \(\frac{4x^{-3 + 1}}{-3 + 1} - \frac{7x^{2 + 1}}{2 + 1} + \frac{5x^{1 + 1}}{1 + 1} - 6x\)
= \(-2x^{-2} - \frac{7}{3} x^3 + \frac{5}{2} x^2 - 6x\)
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
4.32
2.81
1.51
3.90
Correct answer is C
Mean = \(\frac{\sum fx}{\sum f}\)
= \(\frac{156}{40}\)
= 3.9
M.D = \(\frac{\sum f|x - \bar{x}|}{\sum f}\)
= \(\frac{60.4}{40}\)
= 1.51
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.
7
10
5
4
Correct answer is C
Mode = Score with the highest frequency
= 5