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.

216.

The equation of the line of best fit for variables x and y is \(y = 19.33 + 0.42x\), where x is the independent variable. Estimate the value of y when x = 15.

A.

18.91

B.

19.75

C.

25.63

D.

38.23

Correct answer is C

\(y = 19.33 + 0.42x\)

\(\text{The value of y when x = 15} = 19.33 + (0.42 \times 15)\)

= \(19.33 + 6.30\)

= 25.63

217.

In a firing contest, the probabilities that Kojo and Kwame hit the target are \(\frac{2}{5}\) and \(\frac{1}{3}\) respectively. What is the probability that none of them hit the target?

A.

\(\frac{1}{5}\)

B.

\(\frac{2}{5}\)

C.

\(\frac{3}{5}\)

D.

\(\frac{4}{5}\)

Correct answer is B

No explanation has been provided for this answer.

218.

Age(in years) 1 - 5 6 - 10 11 - 15
Frequency 3 5 2

Calculate the standard deviation of the distribution.

A.

1.10

B.

2.36

C.

3.50

D.

7.50

Correct answer is C

Age

(years)

Freq

(f)

Mid-value

(x)

fx \(d = (x - \bar{x})\) \(d^{2}\) \(fd^{2}\)
1 - 5 3 3 9 - 4.5 20.25 60.75
6 - 10 5 8 40 0.5 0.25 1.25
11 - 15 2 13 26 5.5 30.25 60.5
\(\sum =\) 10   75     122.5

\(Mean (\bar {x}) = \frac{\sum fx}{\sum f} = \frac{75}{10} = 7.5\)

\(SD = \sqrt{\frac{\sum fd^{2}}{\sum f}}\)

= \(\sqrt{\frac{122.5}{10}}\)

= \(\sqrt{12.25} = 3.50\)

219.

A particle of mass 2.5 kg is moving at a speed of 12 m/s. If a force of magnitude 10 N acts against it, find how long it takes to come to rest.

A.

1.5 s

B.

3.0 s

C.

4.0 s

D.

6.0 s

Correct answer is B

\(F = ma \)

\(10 = 2.5a \implies a = 4 ms^{-2}\)

Since it is a retarding movement, then \(a = -4 ms^{-2}\).

\(v = u + at; v = 0 ms^{-1}, u = 12 ms^{-1}\)

\(0 = 12 + (-4t) \implies 0 = 12 - 4t\)

\(4t = 12 \implies t = 3 s\)

220.

The area of a sector of a circle is 3\(cm^{2}\). If the sector subtends an angle of 1.5 radians at the centre, calculate the radius of the circle

A.

1 cm

B.

\(\sqrt{2}\) cm

C.

2 cm

D.

4 cm

Correct answer is C

The area of sector in radians = \(\frac{r^{2} \theta}{2}\)

\(3 cm^{2} = \frac{1.5 \times r^{2}}{2}\)

\(r^{2} = \frac{3 \times 2}{1.5} = 4\)

\(r = 2 cm\)