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Mathematics
WAEC / WASSCE 1991
Indices, Logarithms & Surds
Solution
Simplify: log6 + log2 - log12
A
-4
B
-1
C
0
D
1
E
4
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
log 6 + log 2 - log 12
= \(\log (\frac{6 \times 2}{12})\)
= \(\log 1\)
= 0
Source: Myschool Past Questions Archive (Record #22866)
Mathematics
WAEC / WASSCE 1991
Indices, Logarithms & Surds
Solution
Find the number whose logarithm to base 10 is 2.6025
A
400.4
B
0.4004
C
0.04004
D
0.004004
E
0.0004004
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
For the log to be 2.6025, there must be three digits before the decimal point.
Source: Myschool Past Questions Archive (Record #22867)
Mathematics
WAEC / WASSCE 1991
Indices, Logarithms & Surds
Solution
Simplify: \((\frac{1}{4})^{-1\frac{1}{2}}\)
A
1/8
B
1/4
C
2
D
4
E
8
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
\((\frac{1}{4})^{-1\frac{1}{2}}\)
= \((\frac{1}{4})^{-\frac{3}{2}}\)
= \((\sqrt{\frac{1}{4}})^{-3}\)
= \((\frac{1}{2})^{-3}\)
= \(2^3\)
= 8
Source: Myschool Past Questions Archive (Record #22868)
Mathematics
WAEC / WASSCE 1991
Algebraic Expressions, Polynomials & Factorisation
Solution
For what value of y is the expression \(\frac{y + 2}{y^{2} - 3y - 10}\) undefined?
A
y = 0
B
y = 2
C
y = 3
D
y = 5
E
y = 10
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\frac{y + 2}{y^2 - 3y - 10}\)
\(y^2 - 3y - 10 = 0 \implies y^2 - 5y + 2y - 10 = 0\)
\(y(y - 5) + 2(y - 5) = 0\)
\((y - 5)(y + 2) = 0\)
\(\frac{y + 2}{(y - 5)(y + 2)} = \frac{1}{y - 5}\)
\(\therefore\) At y = 5, the expression \(\frac{y + 2}{y^2 - 3y - 10}\) is undefined.
Source: Myschool Past Questions Archive (Record #22869)
Mathematics
WAEC / WASSCE 1991
Algebraic Expressions, Polynomials & Factorisation
Solution
Factorize 3a\(^2\) - 11a + 6
A
(3a - 2)(a - 3)
B
(2a -2)(a - 3)
C
(3a - 2)(a + 3)
D
(3a + 2)(a - 3)
E
(2a-3)(a + 2)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
3a\(^2\) - 11a + 6
3a\(^2\) - 9a - 2a + 6
3a(a - 3) - 2(a - 3)
= (3a - 2)(a - 3)
Source: Myschool Past Questions Archive (Record #22870)
Mathematics
WAEC / WASSCE 1991
Linear, Simultaneous & Quadratic Equations
Solution
Solve the equation: 3a + 10 = a\(^2\)
A
a = 5 or a = 2
B
a = -5 or a = 2
C
a = 10 or a = 0
D
a = 5 or a = 0
E
a = 5 or a = -2
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
3a + 10 = a\(^2\)
a\(^2\) - 3a - 10 = 0
a\(^2\) - 5a + 2a - 10 = 0
a(a - 5) + 2(a - 5) = 0
(a - 5)(a + 2) = 0
a = 5 or a = -2.
Source: Myschool Past Questions Archive (Record #22871)
Mathematics
WAEC / WASSCE 1991
Plane Geometry, Polygons & Circle Theorems
Solution
Simplify \((\frac{3}{x} - \frac{15}{2y}) \div \frac{6}{xy}\)
A
\(\frac{2y - 5x}{4}\)
B
\(\frac{9(2x - 5x)}{x^2y^2}\)
C
\(\frac{5x - 2y}{2}\)
D
\(\frac{c^2y^2}{18y - 45x}\)
E
\(\frac{4}{2y - 5x}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\((\frac{3}{x} - \frac{15}{2y}) \div \frac{6}{xy}\)
= \((\frac{6y - 15x}{2xy}) \div \frac{6}{xy}\)
= \(\frac{6y - 15x}{2xy} \times \frac{xy}{6}\)
= \(\frac{3(2y - 5x)}{2xy} \times \frac{xy}{6}\)
= \(\frac{2y - 5x}{4}\)
Source: Myschool Past Questions Archive (Record #22872)
Mathematics
WAEC / WASSCE 1991
Indices, Logarithms & Surds
Solution
Simplify: \(\frac{1}{4}(2^n - 2^{n + 2}\))
A
\(2^{n - 2} - 2^n\)
B
\(2^{n-2}(1-2^n\))
C
\(2^n + 2^{2 + n}\)
D
\(2^{2n}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(\frac{1}{4}(2^n - 2^{n + 2}\)) = \(\frac{1}{4}(2^n - 2^n \times2^2\))
\(\frac{1}{4} \times2^n(1 - 2^2\)) = \(2^{-2}\times2^n(1 - 2^2\))
\(2^{n - 2}(2^0 - 2^2\)) = \(2^{n - 2} - 2^n\)
Source: Myschool Past Questions Archive (Record #22873)
Mathematics
WAEC / WASSCE 1991
Linear, Simultaneous & Quadratic Equations
Solution
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
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
x = \(-\frac{2}{3}\) and \(-\frac{1}{4}\)
\(\implies (x + \frac{2}{3}) = 0; (x + \frac{1}{4}) = 0\)
\((x + \frac{2}{3})(x + \frac{1}{4}) = 0\)
\(x^{2} + \frac{1}{4}x + \frac{2}{3}x + \frac{1}{6} = 0\)
\(x^2 + \frac{11}{12}x + \frac{1}{6} = 0\)
\(12x^2 + 11x + 2 = 0\)
Source: Myschool Past Questions Archive (Record #22874)
Mathematics
WAEC / WASSCE 1991
Plane Geometry, Polygons & Circle Theorems
Solution
Solve: 6(x - 4) + 3(x + 7) = 3
A
3/2
B
2/3
C
1/2
D
1/3
E
o
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
6(x - 4) + 3(x + 7) = 3
6x - 24 + 3x + 21 = 3
9x - 3 = 3
9x = 6
x = \(\frac{2}{3}\)
Source: Myschool Past Questions Archive (Record #22875)
Mathematics
WAEC / WASSCE 1991
Plane Geometry, Polygons & Circle Theorems
Solution
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
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical 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
Source: Myschool Past Questions Archive (Record #22876)
Mathematics
WAEC / WASSCE 1991
Mensuration (Areas, Perimeters & Volumes)
Solution
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
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical 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
Source: Myschool Past Questions Archive (Record #22877)
Mathematics
WAEC / WASSCE 1991
Fractions, Decimals, Percentages & Approximations
Solution
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
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical 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
Source: Myschool Past Questions Archive (Record #22878)
Mathematics
WAEC / WASSCE 1991
Linear, Simultaneous & Quadratic Equations
Solution
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
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical 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
Source: Myschool Past Questions Archive (Record #22879)
Mathematics
WAEC / WASSCE 1991
Fractions, Decimals, Percentages & Approximations
Solution
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%
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Error =12.75 - 7.50 = 5.25
Error % = \(\frac{5.25}{12.75}\) x 100% = 41.2%
Source: Myschool Past Questions Archive (Record #22880)