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Mathematics
WAEC / WASSCE 1990
Indices, Logarithms & Surds
Solution
Simplify \(\frac{\log \sqrt{8}}{\log 8}\)
A
1/3
B
1/2
C
1/3log√2
D
1/3log√8
E
1/2log√2
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(\frac{\log \sqrt{8}}{\log 8}\)
= \(\frac{\log 8^{\frac{1}{2}}}{log 8}\)
= \(\frac{\frac{1}{2} \log 8}{\log 8}\)
= \(\frac{1}{2}\)
Source: Myschool Past Questions Archive (Record #22603)
Mathematics
WAEC / WASSCE 1990
Indices, Logarithms & Surds
Solution
Evaluate using the logarithm table, log(0.65)2
A
1.6258
B
0.6272
C
0.6258
D
\(\overline{1}\).6258
E
1.6272
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
log(0.65)\(^2\) = 2log(0.65) but log0.65 = \(\overline{1}\).8129
∴2 x \(\overline{1}\).8129 = \(\overline{1}\).6258
Source: Myschool Past Questions Archive (Record #22604)
Mathematics
WAEC / WASSCE 1990
Indices, Logarithms & Surds
Solution
If log x = \(\bar{2}.3675\) and log y = 0.9750, what is the value of x + y? Correct to three significant figures
A
1.18
B
1.31
C
9.03
D
9.44
E
9.46
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
log x = \(\bar{2}.3675\) ; log y = 0.9750
\(x = 10^{\bar{2}.3675} = 0.02331 \)
\(y = 10^{0.9750} = 9.441 \)
\(x + y = 9.4641 \approxeq 9.46\)
Source: Myschool Past Questions Archive (Record #22605)
Mathematics
WAEC / WASSCE 1990
Fractions, Decimals, Percentages & Approximations
Solution
While doing his physics practical, Idowu recorded a reading as 1.12cm instead of 1.21cm. Calculate his percentage error
A
1.17%
B
6.38%
C
7.44%
D
8.035%
E
9.00%
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
%error = \(\frac{1.21 - 1.12}{1.21} \times 100%\)
= \(\frac{9}{121} \times 100%\)
= 7.44%
Source: Myschool Past Questions Archive (Record #22606)
Mathematics
WAEC / WASSCE 1990
Sequences & Series (AP & GP)
Solution
Find the 4th term of an A.P, whose first term is 2 and the common difference is 0.5
A
0.5
B
2.5
C
3.5
D
4
E
4.5
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(U_{n} = a + (n - 1)d\)
\(U_{4} = 2 + (4 - 1) \times 0.5\)
= \(2 + 1.5\)
= 3.5
Source: Myschool Past Questions Archive (Record #22607)
Mathematics
WAEC / WASSCE 1990
Linear, Simultaneous & Quadratic Equations
Diagram
Solution
From the graph determine the roots of the equation y = 2x\(^2\) + x - 6
Attached Figure / Diagram
A
-3, 4
B
-2, -6
C
-2, 1.5
D
-1, 1
E
2, 1.5
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Where the curve cut x-axis is the root of the equation i.e. x = -2.0 and x = 1.5
Source: Myschool Past Questions Archive (Record #22641)
Mathematics
WAEC / WASSCE 1990
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
Find the values of x for which y = 5
Attached Figure / Diagram
A
-2.5, 2.0
B
-2.6, 2.1
C
-2.0, 1.5
D
-2.0, 2.0
E
0, 0
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
from the graph, x = - 2.6 and 2.1
Source: Myschool Past Questions Archive (Record #22642)
Mathematics
WAEC / WASSCE 1990
Plane Geometry, Polygons & Circle Theorems
Solution
An arc of length 22cm subtends an angle of \theta at the center of the circle. What is the value of \theta if the radius of the circle is 15cm?[Take \pi = 22/7]
A
70o
B
84o
C
96o
D
156o
E
168o
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(2\pi r = 2 \times 3.142 \times 15 = 94.28cm\)
\(94.28cm = 360^\circ\)
\(1cm = \frac{360^\circ}{94.28}\)
\(\therefore 22cm = \frac{360^\circ}{94.28} \times 22\)
= 84^\circ
Source: Myschool Past Questions Archive (Record #22643)
Mathematics
WAEC / WASSCE 1990
Sequences & Series (AP & GP)
Solution
Find the sum of the first five terms of the G.P 2,6, 18 ....
A
484
B
243
C
242
D
130
E
121
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(S_{n} = \frac{a(r^n - 1)}{r - 1}\)
a = 2; r = 6/2 = 3.
\(S_{5} = \frac{2(3^5 - 1)}{3 - 1}\)
= \(243 - 1 = 242\)
Source: Myschool Past Questions Archive (Record #22644)
Mathematics
WAEC / WASSCE 1990
Sets, Logic & Venn Diagrams
Solution
Let J be the set of positive integers, If H = {x: x∈J, x\(^2\) < 3 and x ≠ 0}, then
A
H = {1}
B
H is an infinite set
C
H = {0, 1, 2}
D
H = {}
E
J ≤ H
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
H = {x: x is a positive integer, x\(^2\) < 3 and x \(\neq\) 0}
H = {1}
Source: Myschool Past Questions Archive (Record #22645)
Mathematics
WAEC / WASSCE 1990
Sets, Logic & Venn Diagrams
Solution
In a class of 80 students, every students had to study economics or geography, or both economics and geography, if 65 students studied economics and 50 studied geography, how many studied both subjects?
A
15
B
30
C
35
D
45
E
50
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
∩(E∩G) = ∩(E) + ∩(G) - ∩(E∩G)
80 = 65 + 50 - ∩(F∩G)
∴∩(E∩G) = 115 - 80 = 35
Source: Myschool Past Questions Archive (Record #22646)
Mathematics
WAEC / WASSCE 1990
Inequalities & Linear Programming
Diagram
The area shaded with horizontal lines is the solution set of the inequalities;
Attached Figure / Diagram
A
y ≥ x, y + 3 ≥ 2x, x ≤ 3
B
y ≤ x, y + 2x ≥ -3, x ≤ 3
C
y ≤ -x, y + 2x ≤ 3, x ≥ -3
D
y ≥ -x, y + 3 ≤ 2x, x ≥ -3
E
y ≤ x, y ≤ 2x - 3, x ≥ 3
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option B.
Source: Myschool Past Questions Archive (Record #22647)
Mathematics
WAEC / WASSCE 1990
Inequalities & Linear Programming
Diagram
Solution
the area shaded with vertical lines is the solution set of the inequalities;
Attached Figure / Diagram
A
y ≤ x, y + 2x ≤ -3
B
y ≥ x, y + 2x ≥ - 3
C
y ≤ x, y ≤ 2x - 3, x ≤ 3
D
y ≤ -x, y ≤ 2x - 3, x ≤ 3
E
y ≥ x, y + 2x ≥ 3, x ≤ 3
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Vertical Line x = 3:
This line indicates a constraint on x, specifically that
x \le 3.(behind is shaded)
The line y + 2x = -3 or y = - 2x - 3
This line has a negative slope of -2 and intersects the y-axis at -3. The region below this line corresponds to
y \le − 2x − 3.
Line y = x:
.This line has a slope of 1 and passes through the origin. The region below this line corresponds to y \le x
The lines are all thick = strict inequalities.
Source: Myschool Past Questions Archive (Record #22649)
Mathematics
WAEC / WASSCE 1990
Fractions, Decimals, Percentages & Approximations
Diagram
Solution
In the diagram above, O is the center of the circle with radius 10cm, and ∠ABC = 30^\circ. Calculate, correct to 1 decimal place, the length of arc AC [Take \pi = 22/7]
Attached Figure / Diagram
A
5.2cm
B
10.5cm
C
13.2cm
D
20.6cm
E
31.4cm
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
In the figure, < AOC = 2 x < ABC = 60^\circ (angle subtended at the centre)
\(\therefore\) Arc AC = \(\frac{60}{360} \times 2 \times 10 \times \frac{22}{7}\)
= \(\frac{31.4}{3}\)
= 10.466 cm \(\approxeq\) 10.5 cm
Source: Myschool Past Questions Archive (Record #22650)
Mathematics
WAEC / WASSCE 1990
Linear, Simultaneous & Quadratic Equations
Solution
Factorize x\(^2\) + 4x - 192
A
(x-4) (x+48)
B
(x-48) (x+4)
C
(x-12) (x+16)
D
(x-12) (x-16)
E
(x+12) (x+16)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
x\(^2\) + 4x - 192
x\(^2\) + 16x - 12x - 192
x(x + 16) - 12(x + 16)
(x + 16)(x - 12)
Source: Myschool Past Questions Archive (Record #22652)