WAEC Further Mathematics Past Questions & Answers - Page 116

576.

Each of the 90 students in a class speak at least Igbo or Hausa. If 56 students speak Igbo and 50 speak Hausa, find the probability that a student selected at random from the class speaks Igbo only.

A.

\(\frac{28}{45}\)

B.

\(\frac{4}{9}\)

C.

\(\frac{8}{45}\)

D.

\(\frac{1}{9}\)

Correct answer is B

Let the number of candidates that speak both Igbo and Hausa = x

The number that speaks Igbo only = 56 - x

The number that speaks Hausa only = 50 - x

56 - x + x + 50 - x = 90

106 - x = 90

x = 16

P(Igbo only) = \(\frac{56 - 16}{90} = \frac{4}{9}\)

577.

A mass of 75kg is placed on a lift. Find the force exerted by the floor of the lift on the mass when the lift is moving up with constant velocity. \([g = 9.8ms^{-2}]\)

A.

750N

B.

745N

C.

735N

D.

98N

Correct answer is C

Net force = Upward force - weight

\(ma = F - mg\)

With constant velocity, acceleration = 0, therefore, ma = 0

\(\therefore F = mg = 75 \times 9.8 = 735N\).

578.

Marks 0 1 2 3 4 5
Number of candidates 6 4 8 10 9

3

The table above shows the distribution of marks scored by students in a test. Find the interquartile range of the distribution.

A.

4

B.

3

C.

2

D.

1

Correct answer is B

No explanation has been provided for this answer.

579.

Marks 0 1 2 3 4 5
Number of candidates 6 4 8 10 9 3

The table above shows the distribution of marks scored by students in a test. How many candidates scored above the median score?

A.

3

B.

12

C.

22

D.

30

Correct answer is B

The total number of candidates = 40, therefore, the median occurs as the average between the 20th and 21st candidates. = \(\frac{3+3}{2} = 3\)

Number of candidates that scored above 3 : 9 + 3 = 12.

580.

Given that \(r = 2i - j\), \(s = 3i + 5j\) and \(t = 6i - 2j\), find the magnitude of \(2r + s - t\).

A.

\(\sqrt{15}\)

B.

4

C.

\(\sqrt{24}\)

D.

\(\sqrt{26}\)

Correct answer is D

\(r = 2i - j , s = 3i + 5j , t = 6i - 2j\)

\(2r + s - t = 2(2i - j) + (3i + 5j) - (6i - 2j) = i + 5j\)

\(|2r + s - t| = \sqrt{1^{2} + 5^{2}} = \sqrt{26}\)