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Mathematics
WAEC / WASSCE 1993
Statistics (Data Representation, Central Tendency & Dispersion)
Solution
Score
1
2
3
4
5
6
7
8
9
Frequency
2
3
6
7
9
6
2
2
3
The table above shows the scores of a group of 40 students in a physics test
What is the mean of the distribution?
A
4.2
B
4.5
C
4.8
D
5.0
E
5.2
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
x
1
2
3
4
5
6
7
8
9
Total
f
2
3
6
7
9
6
2
2
3
40
fx
2
6
18
28
45
36
14
16
27
192
Mean = \(\frac{\sum fx}{\sum f}\)
= \(\frac{192}{40}\)
= 4.8
Source: WAEC / JAMB / NECO Classroom Archive (Record #23225)
Mathematics
WAEC / WASSCE 1993
Sets, Logic & Venn Diagrams
Solution
S = {1, 2, 3, 4, 5, 6}, T = {2,4,5,7} and R = {1,4, 5}, and (S∩T) ∪ R
A
{1, 4, 5}
B
{2, 4, 5}
C
{1, 2, 4, 5}
D
{2, 3, 4, 5}
E
{1, 2, 3, 4, 5}
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
S = {1, 2, 3, 4, 5, 6}; T = {2, 4, 5, 7}; R = {1, 4, 5}
(S∩T) ∪ R = {2, 4, 5} ∪ {1, 4, 5}
= {1, 2, 4, 5}
Source: Myschool Past Questions Archive (Record #23187)
Mathematics
WAEC / WASSCE 1993
Plane Geometry, Polygons & Circle Theorems
Solution
Simplify: \(\frac{3}{4} \div 1\frac{1}{4} \times (1\frac{1}{2} - \frac{2}{3})\)
A
7/30
B
7/24
C
9/25
D
1/2
E
18/25
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\frac{3}{4} \div 1\frac{1}{4} \times (1\frac{1}{2} - \frac{2}{3})\)
\(\frac{3}{4} \div \frac{5}{4} \times (\frac{9 - 4}{6})\)
= \(\frac{3}{4} \times \frac{4}{5} \times \frac{5}{6}\)
= \(\frac{1}{2}\)
Source: Myschool Past Questions Archive (Record #23188)
Mathematics
WAEC / WASSCE 1993
Inequalities & Linear Programming
Solution
Solve the inequality: 3m + 3 > 9
A
m > 2
B
m > 3
C
m>4
D
m>6
E
m>12
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
3m + 3 > 9
3m > 9 - 3
3m > 6
m > 2
Source: Myschool Past Questions Archive (Record #23189)
Mathematics
WAEC / WASSCE 1993
Number Bases & Modular Arithmetic
Solution
Convert 89\(_{10}\) to a number in base two.
A
1101001
B
1011001
C
1001101
D
101101
E
11001
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(89_{10}\)
2
89
2
44 r 1
2
22 r 0
2
11 r 0
2
5 r 1
2
2 r 1
2
1 r 0
0 r 1
\(89_{10} = 1011001_{2}\)
Source: Myschool Past Questions Archive (Record #23190)
Mathematics
WAEC / WASSCE 1993
Fractions, Decimals, Percentages & Approximations
Solution
A stick of length 1.75m was measured by a boy as 1.80m. Find the percentage error in his measurement
A
27/9%
B
26/7%
C
5%
D
277/9%
E
284/7%.
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
% error = \(\frac{error value}{true value}\) x 100%
% error = \(\frac{1.80 - 1.75}{1.75}\) x 100% = \(\frac{0.05}{1.75}\) x 100% = \(\frac{20}{7}\)% = 2\(\frac{6}{7}\)%
Source: Myschool Past Questions Archive (Record #23191)
Mathematics
WAEC / WASSCE 1993
Indices, Logarithms & Surds
Solution
Simplify: \(\frac{4^{-\frac{1}{2}} \times 16^{\frac{3}{4}}}{4^{\frac{1}{2}}}\)
A
1/4
B
0
C
1
D
2
E
4
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\frac{4^{-\frac{1}{2}} \times 16^{\frac{3}{4}}}{4^{\frac{1}{2}}}\)
= \(\frac{16^{\frac{3}{4}}}{4^{\frac{1}{2}} \times 4^{\frac{1}{2}}}\)
= \(\frac{(2^4)^{\frac{3}{4}}}{4^{\frac{1}{2}} \times 4^{\frac{1}{2}}}\)
= \(\frac{2^3}{4}\)
= 2
Source: Myschool Past Questions Archive (Record #23193)
Mathematics
WAEC / WASSCE 1993
Indices, Logarithms & Surds
Solution
Simplify: \(\frac{\log \sqrt{27}}{\log {81}}\)
A
1/6
B
3/8
C
1/2
D
3/4
E
6
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(\frac{\log \sqrt{27}}{\log 81}\)
= \(\frac{\log \sqrt{3^3}}{\log 3^4}\)
= \(\frac{\log 3^{\frac{3}{2}}}{\log 3^4}\)
= \(\frac{\frac{3}{2} \log 3}{4 \log 3}\)
= \(\frac{\frac{3}{2}}{4}\)
= \(\frac{3}{8}\)
Source: Myschool Past Questions Archive (Record #23194)
Mathematics
WAEC / WASSCE 1993
Algebraic Expressions, Polynomials & Factorisation
Solution
Factorize the expression 2s\(^2\) - 3st - 2t\(^2\).
A
(2s - t)(s + 2t)
B
(2s + t)(s - 2t)
C
(s + t)(2s - 1)
D
(2s + t)(s -t)
E
(2s + t)(s + 2t)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
2s\(^2\) - 3st - 2t\(^2\)
= 2s\(^2\) - 4st + st - 2t\(^2\)
= 2s(s - 2t) + t(s - 2t)
= (2s + t)(s - 2t)
Source: Myschool Past Questions Archive (Record #23195)
Mathematics
WAEC / WASSCE 1993
Linear, Simultaneous & Quadratic Equations
Solution
Solve the equation x\(^2\) - 2x - 3 = 0
A
(-3, 1)
B
(-1, -3)
C
(3,1)
D
(43, 0)
E
(-1, 3).
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
x\(^2\) - 2x - 3 = 0
x\(^2\) - 3x + x - 3 = 0
x(x - 3) + 1(x - 3) = 0
(x + 1)(x - 3) = 0
x = (-1, 3)
Source: Myschool Past Questions Archive (Record #23196)
Mathematics
WAEC / WASSCE 1993
Plane Geometry, Polygons & Circle Theorems
Solution
Write as a single fraction: \(\frac{5}{6r} - \frac{3}{4r}\)
A
r/12
B
12/r
C
1/6r
D
r/6
E
1/12r
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
\(\frac{5}{6r} - \frac{3}{4r}\)
= \(\frac{10 - 9}{12r}\)
= \(\frac{1}{12r}\)
Source: Myschool Past Questions Archive (Record #23197)
Mathematics
WAEC / WASSCE 1993
Linear, Simultaneous & Quadratic Equations
Solution
Factorize 2x\(^2\) - 21x + 45
A
(2x - 9)(x - 5)
B
(2x-15)(x + 3)
C
(2x +15)(x - 3)
D
(2x -15(x - 3)
E
(2x - 9)(x + 5)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
2x\(^2\) - 21x + 45
= 2x\(^2\) - 15x - 6x + 45
= x(2x - 15) - 3(2x - 15)
= (x - 3)(2x - 15)
Source: Myschool Past Questions Archive (Record #23198)
Mathematics
WAEC / WASSCE 1993
Linear, Simultaneous & Quadratic Equations
Solution
Solve the simultaneous equations y = 3x; 4y - 5x =14
A
.-2,-6
B
2,6
C
2,-6
D
-2,6
E
-1,-3
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
y = 3x ... (i);
4y - 5x =14 ... (ii)
Put 3x for y in (ii).
4(3x) - 5x = 14
12x - 5x = 14
7x = 14 \(\implies\) x = 2.
y = 3x = 3(2) = 6
(x, y) = (2, 6)
Source: Myschool Past Questions Archive (Record #23199)
Mathematics
WAEC / WASSCE 1993
Mensuration (Areas, Perimeters & Volumes)
Solution
A sector of a circle of radius 9cm subtends angle 120^\circ at the centre of the circle. Find the area of the sector to the nearest cm\(^2\) [Take \pi = 22/7]
A
75cm2
B
84cm2
C
85cm2
D
86cm2
E
95cm2
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Area of a sector = \theta/360 x \pir\(^2\)
= 120/360 x 22/7 x 81/1
= 84.86 cm\(^2\)
\(\approxeq\) 85cm\(^2\) (to the nearest cm)
Source: Myschool Past Questions Archive (Record #23200)
Mathematics
WAEC / WASSCE 1993
Mensuration (Areas, Perimeters & Volumes)
Solution
Calculate the total surface area of a cone of height 12cm and base radius 5cm. [Take \pi = 22/7]
A
180\(\frac{5}{7}\)cm\(^2\)
B
240\(\frac{2}{7}\)cm\(^2\)
C
235\(\frac{5}{7}\)cm\(^2\)
D
282\(\frac{6}{7}\)cm\(^2\)
E
361\(\frac{3}{7}\)cm\(^2\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\pirl + \pir2 = \pir(l + r)
\(\frac{22}{7}\) x 5(13 + 5)
282\(\frac{6}{7}\)cm\(^2\)
Source: Myschool Past Questions Archive (Record #23201)