Further Mathematics Questions & Answers - Free Online Practice

461.

A stone is dropped from a height of 45m. Find the time it takes to hit the ground. $[g = 10 ms^{-2}]$

3.0 seconds

4.5 seconds

5.0 seconds

9.0 seconds

View answer & explanation

Correct answer is A

$s = ut + \frac{1}{2}gt^{2}$

$u = 0; s = 45m; g = 10ms^{-2}$

$45 = 0 + \frac{1}{2}(10)t^{2} = 5t^{2}$

$t^{2} = \frac{45}{5} = 9$

$t = 3.0s$

462.

If r denotes the correlation coefficient between two variables, which of the following is always true?

$0 < r \leq 1$

$-1 \leq r < 1$

$-1 < r \leq 0$

$-1 \leq r \leq 1$

View answer & explanation

Correct answer is D

No explanation has been provided for this answer.

463.

The marks obtained by 10 students in a test are as follows: 3, 7, 6, 2, 8, 5, 9, 1, 4 and 10. Find the variance.

8.25

8.50

9.00

9.17

View answer & explanation

Correct answer is A

Mean $\bar{x}$ = $\frac{3 + 7 + 6 + 2 + 8 + 5 + 9 + 1 + 4 + 10}{10}$

= $\frac{55}{10} = 5.50$

$x$	3	7	6	2	8	5	9	1	4	10	Total
$x - \bar{x}$	-2.5	1.5	0.5	-3.5	2.5	-0.5	3.5	-4.5	-1.5	4.5
$(x - \bar{x})^{2}$	6.25	2.25	0.25	12.25	6.25	0.25	12.25	20.25	2.25	20.25	82.5

Variance = $\frac{\sum (x - \bar{x})^{2}}{n}$

= $\frac{82.5}{10}$

= 8.25

464.

The marks obtained by 10 students in a test are as follows: 3, 7, 6, 2, 8, 5, 9, 1, 4 and 10. Find the mean mark.

4.50

5.50

6.50

6.75

View answer & explanation

Correct answer is B

Mean $\bar{x}$ = $\frac{3 + 7 + 6 + 2 + 8 + 5 + 9 + 1 + 4 + 10}{10}$

= $\frac{55}{10} = 5.50$

465.

A binary operation, $\Delta$ , is defined on the set of real numbers by $a \Delta b = a + b + 4$ . Find the identity element.

$\frac{1}{4}$

-4

View answer & explanation

Correct answer is D

$a \Delta b = a + b + 4$

$a \Delta e = a + e + 4 = a$

$e = a - a - 4 = -4$

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