Further Mathematics questions and answers

Further Mathematics Questions and Answers

Test your knowledge of advanced level mathematics with this aptitude test. This test comprises Further Maths questions and answers from past JAMB and WAEC examinations.

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

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

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

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