WAEC Further Mathematics Past Questions & Answers - Page 93

461.

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

A.

3.0 seconds

B.

4.5 seconds

C.

5.0 seconds

D.

9.0 seconds

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?

A.

\(0 < r \leq 1\)

B.

\(-1 \leq r < 1\)

C.

\(-1 < r \leq 0\)

D.

\(-1 \leq r \leq 1\)

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.

A.

8.25

B.

8.50

C.

9.00

D.

9.17

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.

A.

4.50

B.

5.50

C.

6.50

D.

6.75

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.

A.

4

B.

2

C.

\(\frac{1}{4}\)

D.

-4

Correct answer is D

\(a \Delta b = a + b + 4\)

\(a \Delta e = a + e + 4 = a\)

\(e = a - a - 4 = -4\)