1991 - WAEC Mathematics Past Questions and Answers - page 2
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
correct option: a
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
correct option: b
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
correct option: c
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
Users' Answers & Comments3x - 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
correct option: d
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
Users' Answers & Comments\(\frac{base area}{curved area}\) = 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
correct option: c
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
Users' Answers & CommentsWife 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
correct option: b
80km/h = \(\frac{80}{60}\) x \(\frac{1000}{60}\) = 3 x 3= \(\frac{40 x 5}{9}\)
= \(\frac{200m/s}{9}\) = 22.22m/s
Users' Answers & Comments= \(\frac{200m/s}{9}\) = 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%
correct option: a
Error =12.75 - 7.50 = 5.25
Error % = \(\frac{5.25}{12.75}\) x 100% = 41.2%
Users' Answers & CommentsError % = \(\frac{5.25}{12.75}\) 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
correct option: a
Area of the bigger semi circle P x RO =
Users' Answers & Commentsπr2/2 =
22/7 x
49/2 = 77cm2
2nd Area of the smaller circle DYO =
2nd Area of the smaller circle DYO =
22/7 x
3.52/2 = 19.25
Total Area = 77 + 19.25 = 96.25 = 96.00
Total Area = 77 + 19.25 = 96.25 = 96.00
19
Find the perimeter of the region
A
22cm
B
33cm
C
40cm
D
47cm
correct option: c
P = \(\pi\)r + \(\pi\)r + R = \(\frac{22}{7}\) x 7 + \(\frac{22}{7}\) x \(\frac{7}{2}\) + 7
P = 22 + 11 + 7 = 40cm
Users' Answers & CommentsP = 22 + 11 + 7 = 40cm
20
The shaded portion shows the outer boundary
of the half plane defined by the inequality
of the half plane defined by the inequality
A
4x + 3y \(\geq\) 6
B
4x + 3y = 6
C
4x + 3y < 6
D
3y >6