Year : 
2006
Title : 
Mathematics (Core)
Exam : 
WASSCE/WAEC MAY/JUNE

Paper 1 | Objectives

21 - 30 of 46 Questions

# Question Ans
21.

Which of these equations best describes the points of intersection of the curve and the line?

A. \(x^2 + 5x - 6 = 0\)

B. x2 - 5x - 6 = 0

C. x2 + x - 6 = 0

D. x2 - x - 6 = 0

Detailed Solution

The roots are -3 and 1

x = -3 and x = 1

y = (x + 3)(x - 1)

= x2 - x + 3x - 3

y = x2 + x - 6 = 0
22.

If loga270 - loga10 + loga \(\frac{1}{3}\) = 2, what is the value of a?

A. 3

B. 4

C. 5

D. 6

Detailed Solution

loga270 - loga10 + loga\(\frac{1}{3}\) = 2

loga270 + loga\(\frac{1}{3}\) - loga10 = 2

loga(270\(\frac{\frac{1}{3}}{10}\)) = 2

loga9 = 2

aa = 9

a = \(\sqrt{9}\) = 3
23.

A conical water-jug is 7cm in diameter and 6cm deep. find the volume of water it can hold. [Take \(\pi = \frac{22}{7}\)]

A. 22cm2

B. 44cm3

C. 77cm3

D. 3082

Detailed Solution

Volume = \(\frac{1}{3} \pi r^2h = \frac{1}{3} \times \frac{22}{7} \times \frac{7}{2} \times \frac{7}{2} \times \frac{6}{1}\)

V = \(\frac{6468}{84}\)

= 77cm3
24.

If p = [\(\frac{Q(R - T)}{15}\)]\(^ \frac{1}{3}\), make T the subject of the relation

A. T = R + \(\frac{P^3}{15Q}\)

B. T = R - \(\frac{15P^3}{Q}\)

C. T = R + \(\frac{P^3}{15Q}\)

D. T = 15R - \(\frac{Q}{P^3}\)

Detailed Solution

Cubic both sides; P3 = \(\frac{Q(R - T)}{15}\)

(cross multiplication) Q(R - T) = 15P3

(divide both sides by Q); R - T = 15\(\frac{1}{Q}\)

(subtract r from both sides) - T = \(\frac{15P^3}{Q - R}\)

T = R - \(\frac{15P^3}{Q}\)
25.

A seller allows 20% discount for cash payment on the marked price of his goods. What is the ratio of the cash payment to the marked price

A. 1:4

B. 1:5

C. 3:4

D. 4:5

Detailed Solution

(1 - \(\frac{20}{100}\)) = cash payment fraction= \(\frac{4}{5}\)

The ratio of the cash payment to the marked price = 4:5
26.

The wheel of a tractor has a diameter 1.4m. What distance does it cover in 100 complete revolutions? [Take \(\pi = \frac{22}{7}\)]

A. 140m

B. 220m

C. 280m

D. 440m

Detailed Solution

radius = \(\frac{diameter}{2}\) = \(\frac{1.4}{2}\)

= 0.7m

circumference = 2\(\pi r = 2 \times \frac{22}{7} \times 0.7m = 4.4m\)

distance covered = 4.4m x 100 = 440m
27.

If p = {1, 3, 5, 7, 9} and Q = {2, 4, 6, 8, 10} are subsets of a universal set. U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. What are the elements of P1 \(\cap\) Q1?

A. {1, 3, 5, 7, 9}

B. [2, 4, 6, 8, 10}

C. \(\varnothing\)

D. {1, 2, 6, 8, 10}

Detailed Solution

P1 = {2, 4, 6, 8, 10}; {1, 3, 5, 7, 9}

P1 \(\cap\) q1 = {} or \(\varnothing\)
28.

The values of three angles at a point are 3y - 45o, y + 25o and yo . Find the value of y.

A. 40o

B. 58o

C. 68o

D. 76o

Detailed Solution

(3y - 450 + (y + 25) + t = 360o(angles at a point)

3y - 45 + y + 25 + y = 360

5y = 360 + 20

5y = 380

y = \(\frac{380}{5}\)

= 76o
29.

A rectangular carpet 2.5m long and 2.4m wide covers 5% of a rectangular floor. Calculate the area of the floor

A. 30m2

B. 57m2

C. 120m2

D. 225m2

Detailed Solution

Area of carpet = 2.5 x 2.4 = 6

Let F represent the floor

6 = 5% of F

6 = \(\frac{5}{100}\) x F

5F = 6 x 100

F = 6 x \(\frac{100}{5}\)

= 120m2
30.

Which of the following is not a measure of centre tendency?

A. mean

B. mode

C. range

D. median

C
21.

Which of these equations best describes the points of intersection of the curve and the line?

A. \(x^2 + 5x - 6 = 0\)

B. x2 - 5x - 6 = 0

C. x2 + x - 6 = 0

D. x2 - x - 6 = 0

Detailed Solution

The roots are -3 and 1

x = -3 and x = 1

y = (x + 3)(x - 1)

= x2 - x + 3x - 3

y = x2 + x - 6 = 0
22.

If loga270 - loga10 + loga \(\frac{1}{3}\) = 2, what is the value of a?

A. 3

B. 4

C. 5

D. 6

Detailed Solution

loga270 - loga10 + loga\(\frac{1}{3}\) = 2

loga270 + loga\(\frac{1}{3}\) - loga10 = 2

loga(270\(\frac{\frac{1}{3}}{10}\)) = 2

loga9 = 2

aa = 9

a = \(\sqrt{9}\) = 3
23.

A conical water-jug is 7cm in diameter and 6cm deep. find the volume of water it can hold. [Take \(\pi = \frac{22}{7}\)]

A. 22cm2

B. 44cm3

C. 77cm3

D. 3082

Detailed Solution

Volume = \(\frac{1}{3} \pi r^2h = \frac{1}{3} \times \frac{22}{7} \times \frac{7}{2} \times \frac{7}{2} \times \frac{6}{1}\)

V = \(\frac{6468}{84}\)

= 77cm3
24.

If p = [\(\frac{Q(R - T)}{15}\)]\(^ \frac{1}{3}\), make T the subject of the relation

A. T = R + \(\frac{P^3}{15Q}\)

B. T = R - \(\frac{15P^3}{Q}\)

C. T = R + \(\frac{P^3}{15Q}\)

D. T = 15R - \(\frac{Q}{P^3}\)

Detailed Solution

Cubic both sides; P3 = \(\frac{Q(R - T)}{15}\)

(cross multiplication) Q(R - T) = 15P3

(divide both sides by Q); R - T = 15\(\frac{1}{Q}\)

(subtract r from both sides) - T = \(\frac{15P^3}{Q - R}\)

T = R - \(\frac{15P^3}{Q}\)
25.

A seller allows 20% discount for cash payment on the marked price of his goods. What is the ratio of the cash payment to the marked price

A. 1:4

B. 1:5

C. 3:4

D. 4:5

Detailed Solution

(1 - \(\frac{20}{100}\)) = cash payment fraction= \(\frac{4}{5}\)

The ratio of the cash payment to the marked price = 4:5
26.

The wheel of a tractor has a diameter 1.4m. What distance does it cover in 100 complete revolutions? [Take \(\pi = \frac{22}{7}\)]

A. 140m

B. 220m

C. 280m

D. 440m

Detailed Solution

radius = \(\frac{diameter}{2}\) = \(\frac{1.4}{2}\)

= 0.7m

circumference = 2\(\pi r = 2 \times \frac{22}{7} \times 0.7m = 4.4m\)

distance covered = 4.4m x 100 = 440m
27.

If p = {1, 3, 5, 7, 9} and Q = {2, 4, 6, 8, 10} are subsets of a universal set. U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. What are the elements of P1 \(\cap\) Q1?

A. {1, 3, 5, 7, 9}

B. [2, 4, 6, 8, 10}

C. \(\varnothing\)

D. {1, 2, 6, 8, 10}

Detailed Solution

P1 = {2, 4, 6, 8, 10}; {1, 3, 5, 7, 9}

P1 \(\cap\) q1 = {} or \(\varnothing\)
28.

The values of three angles at a point are 3y - 45o, y + 25o and yo . Find the value of y.

A. 40o

B. 58o

C. 68o

D. 76o

Detailed Solution

(3y - 450 + (y + 25) + t = 360o(angles at a point)

3y - 45 + y + 25 + y = 360

5y = 360 + 20

5y = 380

y = \(\frac{380}{5}\)

= 76o
29.

A rectangular carpet 2.5m long and 2.4m wide covers 5% of a rectangular floor. Calculate the area of the floor

A. 30m2

B. 57m2

C. 120m2

D. 225m2

Detailed Solution

Area of carpet = 2.5 x 2.4 = 6

Let F represent the floor

6 = 5% of F

6 = \(\frac{5}{100}\) x F

5F = 6 x 100

F = 6 x \(\frac{100}{5}\)

= 120m2
30.

Which of the following is not a measure of centre tendency?

A. mean

B. mode

C. range

D. median

C