Year : 
1991
Title : 
Mathematics (Core)
Exam : 
WASSCE/WAEC MAY/JUNE

Paper 1 | Objectives

11 - 20 of 50 Questions

# Question Ans
11.

Find the equation whose roots are -2/3 and -1/4

A. 12x2 + 11x + 2 = 0

B. 12x2 - 11x + 2 = 0

C. x2 - 11/12x + 2 = 0

D. 12x2 - 11x - 2 = 0

E. x2 - 11/12x - 2 = 0

Detailed Solution

x = \(-\frac{2}{3}\) and \(-\frac{1}{4}\)
\(\implies (x + \frac{2}{3}) = 0; (x + \frac{1}{4}) = 0\)
\((x + \frac{2}{3})(x + \frac{1}{4}) = 0\)
\(x^{2} + \frac{1}{4}x + \frac{2}{3}x + \frac{1}{6} = 0\)
\(x^2 + \frac{11}{12}x + \frac{1}{6} = 0\)
\(12x^2 + 11x + 2 = 0\)
12.

Solve: 6(x - 4) + 3(x + 7) = 3

A. 3/2

B. 2/3

C. 1/2

D. 1/3

E. o

Detailed Solution

6(x - 4) + 3(x + 7) = 3
6x - 24 + 3x + 21 = 3
9x - 3 = 3
9x = 6
x = \(\frac{2}{3}\)
13.

If 2x + y = 7 and 3x - 2y = 3, by how much is 7x greater than 10?

A. 1

B. 3

C. 7

D. 10

E. 17

Detailed Solution

2x + y = 7 = i
3x - 2y = 3 = ii
i x 2 + ii = 4x + 2y = 14

\(\frac {3x - 2y = 3}{7x = 17}\)

x = \(\frac {17}{7}\) = 7x = 17 x 1/7 x 7
17 - 10 = 7
14.

A cylinder of base radius 4cm is open at one end . If the ratio of the area of its base to that of its curved surface is 1:4, calculate the height of the cylinder

A. 1cm

B. 2cm

C. 4cm

D. 8cm

E. 16cm

Detailed Solution

r= 4cm; base area = \(\pi\)r2; Curve S.A = 2\(\pi\)rh

\(\frac{base area}{curved area}\) = 1/4; \(\pi\)/2\(\pi\)rh

=h = \(\frac{4 x 4cm}{2}\)

h= 8cm
15.

A headmaster contributes 7% of his income into a fund and his wife contributes 4% of her income. If the husband earns N5,500 per annum (p.a) and the wife earns N4,000 (P.a), find the sum of their annual contribution to the fund

A. N1045

B. N605

C. N545

D. N490

E. N440

Detailed Solution

Husband contributions = \(\frac{7}{100}\) x N5,500 = N385

Wife contribution = \(\frac{4}{100}\) x N4,000 = N160

Sum of their Annual contribution = N385 + N160 = N545
16.

A car is travelling at an average speed of 80km/hr. Its speed in meters per second (m/s) is

A. 13.3m/s

B. 22.2m/s

C. 133.3m/s

D. 222.2m/s

E. 1333.3m/s

Detailed Solution

80km/h = \(\frac{80}{60}\) x \(\frac{1000}{60}\) = 3 x 3= \(\frac{40 x 5}{9}\)

= \(\frac{200m/s}{9}\) = 22.22m/s
17.

Mrs. Kofi sold an article for C7.50 instead of C12.75. Calculate her percentage of error, correct to one decimal place.

A. 41.2%

B. 18.3%

C. 5.3%

D. 1.7%

E. 1.4%

Detailed Solution

Error =12.75 - 7.50 = 5.25

Error % = \(\frac{5.25}{12.75}\) x 100% = 41.2%
18.

Find the area of the enclosed region, PXROY correct to the nearest whole number

A. 96cm2

B. 116cm2

C. 154cm2

D. 192cm2

E. 385cm2

Detailed Solution

Area of the bigger semi circle P x RO =
πr2/2
=
22/7
x
49/2
= 77cm2
19.

Find the perimeter of the region

A. 22cm

B. 33cm

C. 40cm

D. 47cm

E. 66cm

Detailed Solution

P = \(\pi\)r + \(\pi\)r + R = \(\frac{22}{7}\) x 7 + \(\frac{22}{7}\) x \(\frac{7}{2}\) + 7

P = 22 + 11 + 7 = 40cm
20.

The shaded portion shows the outer boundary
of the half plane defined by the inequality

A. 4x + 3y \(\geq\) 6

B. 4x + 3y = 6

C. 4x + 3y < 6

D. 3y >6

E. 4x < 6

Detailed Solution

The region is denoted by 4x + 3y \(\geq\) 6
11.

Find the equation whose roots are -2/3 and -1/4

A. 12x2 + 11x + 2 = 0

B. 12x2 - 11x + 2 = 0

C. x2 - 11/12x + 2 = 0

D. 12x2 - 11x - 2 = 0

E. x2 - 11/12x - 2 = 0

Detailed Solution

x = \(-\frac{2}{3}\) and \(-\frac{1}{4}\)
\(\implies (x + \frac{2}{3}) = 0; (x + \frac{1}{4}) = 0\)
\((x + \frac{2}{3})(x + \frac{1}{4}) = 0\)
\(x^{2} + \frac{1}{4}x + \frac{2}{3}x + \frac{1}{6} = 0\)
\(x^2 + \frac{11}{12}x + \frac{1}{6} = 0\)
\(12x^2 + 11x + 2 = 0\)
12.

Solve: 6(x - 4) + 3(x + 7) = 3

A. 3/2

B. 2/3

C. 1/2

D. 1/3

E. o

Detailed Solution

6(x - 4) + 3(x + 7) = 3
6x - 24 + 3x + 21 = 3
9x - 3 = 3
9x = 6
x = \(\frac{2}{3}\)
13.

If 2x + y = 7 and 3x - 2y = 3, by how much is 7x greater than 10?

A. 1

B. 3

C. 7

D. 10

E. 17

Detailed Solution

2x + y = 7 = i
3x - 2y = 3 = ii
i x 2 + ii = 4x + 2y = 14

\(\frac {3x - 2y = 3}{7x = 17}\)

x = \(\frac {17}{7}\) = 7x = 17 x 1/7 x 7
17 - 10 = 7
14.

A cylinder of base radius 4cm is open at one end . If the ratio of the area of its base to that of its curved surface is 1:4, calculate the height of the cylinder

A. 1cm

B. 2cm

C. 4cm

D. 8cm

E. 16cm

Detailed Solution

r= 4cm; base area = \(\pi\)r2; Curve S.A = 2\(\pi\)rh

\(\frac{base area}{curved area}\) = 1/4; \(\pi\)/2\(\pi\)rh

=h = \(\frac{4 x 4cm}{2}\)

h= 8cm
15.

A headmaster contributes 7% of his income into a fund and his wife contributes 4% of her income. If the husband earns N5,500 per annum (p.a) and the wife earns N4,000 (P.a), find the sum of their annual contribution to the fund

A. N1045

B. N605

C. N545

D. N490

E. N440

Detailed Solution

Husband contributions = \(\frac{7}{100}\) x N5,500 = N385

Wife contribution = \(\frac{4}{100}\) x N4,000 = N160

Sum of their Annual contribution = N385 + N160 = N545
16.

A car is travelling at an average speed of 80km/hr. Its speed in meters per second (m/s) is

A. 13.3m/s

B. 22.2m/s

C. 133.3m/s

D. 222.2m/s

E. 1333.3m/s

Detailed Solution

80km/h = \(\frac{80}{60}\) x \(\frac{1000}{60}\) = 3 x 3= \(\frac{40 x 5}{9}\)

= \(\frac{200m/s}{9}\) = 22.22m/s
17.

Mrs. Kofi sold an article for C7.50 instead of C12.75. Calculate her percentage of error, correct to one decimal place.

A. 41.2%

B. 18.3%

C. 5.3%

D. 1.7%

E. 1.4%

Detailed Solution

Error =12.75 - 7.50 = 5.25

Error % = \(\frac{5.25}{12.75}\) x 100% = 41.2%
18.

Find the area of the enclosed region, PXROY correct to the nearest whole number

A. 96cm2

B. 116cm2

C. 154cm2

D. 192cm2

E. 385cm2

Detailed Solution

Area of the bigger semi circle P x RO =
πr2/2
=
22/7
x
49/2
= 77cm2
19.

Find the perimeter of the region

A. 22cm

B. 33cm

C. 40cm

D. 47cm

E. 66cm

Detailed Solution

P = \(\pi\)r + \(\pi\)r + R = \(\frac{22}{7}\) x 7 + \(\frac{22}{7}\) x \(\frac{7}{2}\) + 7

P = 22 + 11 + 7 = 40cm
20.

The shaded portion shows the outer boundary
of the half plane defined by the inequality

A. 4x + 3y \(\geq\) 6

B. 4x + 3y = 6

C. 4x + 3y < 6

D. 3y >6

E. 4x < 6

Detailed Solution

The region is denoted by 4x + 3y \(\geq\) 6