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Mathematics
WAEC / WASSCE 1988
Trigonometry, Elevation & Bearings
Solution
If cos 60^\circ = 1/2, which of the following angle has cosine of -1/2?
A
30o
B
120o
C
150o
D
210o
E
300o
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
cos 60^\circ = 1/2, cos(180^\circ - 60^\circ) = -1/2
cos120^\circ = -1/2
Source: Myschool Past Questions Archive (Record #22025)
Mathematics
WAEC / WASSCE 1988
Fractions, Decimals, Percentages & Approximations
Diagram
Solution
In the diagram above, find the ratio |PQ|/|PR|
Attached Figure / Diagram
A
2 : 5
B
3 : 5
C
2 : 3
D
3 : 2
E
5 : 3
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
From the diagram: PQ = 3 ; PR = 3+2 → 5
PQ: PR = \(\frac{3}{5}\)
Source: Myschool Past Questions Archive (Record #22026)
Mathematics
WAEC / WASSCE 1988
Trigonometry, Elevation & Bearings
Solution
A ladder 9m long leans against a vertical wall, making an angle of 64^\circ with the horizontal ground. calculate correct to one decimal place, how far the foot of the ladder is from the wall.
A
4.0m
B
5.8m
C
7.1m
D
8.1m
E
18.5m
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
cos 64^\circ = x/9
x = 9 cos 64^\circ
=3.94 ≅ 4.0m
Source: Myschool Past Questions Archive (Record #22030)
Mathematics
WAEC / WASSCE 1988
Mensuration (Areas, Perimeters & Volumes)
Solution
What is the difference in longitude between P (lat. 50^\circN. long. 50^\circW) and Q (lat.50^\circN, long. 150^\circW)?
A
300o
B
200o
C
130o
D
100o
E
30o
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Let \(\theta\) be the angular difference between P (50^\circN. 50^\circW), and Q (50^\circN, 150^\circW),
\(\theta\) = 150^\circ - 50^\circ =100^\circ
Source: Myschool Past Questions Archive (Record #22035)
Mathematics
WAEC / WASSCE 1988
Fractions, Decimals, Percentages & Approximations
The number 186,470 was corrected to 186,000. Which of the following describe the degree of approximation made?
I. to the nearest hundred II. to the nearest thousand III. to 3 significant figures IV. to 4 significant figures
A
I & III only
B
I & IV only
C
II & III only
D
II & IV only
E
All of the above
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option C.
Source: Myschool Past Questions Archive (Record #22040)
Mathematics
WAEC / WASSCE 1988
Indices, Logarithms & Surds
Solution
Points P and Q respectively 24m north and 7m east point R. Calculate |PQ| in meters
A
20
B
24
C
25
D
31
E
84
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
PQ\(^2\) = 24\(^2\) + 7\(^2\)
PQ\(^2\) = 625
PQ = 25
Source: Myschool Past Questions Archive (Record #22043)
Mathematics
WAEC / WASSCE 1988
Trigonometry, Elevation & Bearings
Solution
Points P and Q are respectively 24m north and 7m east of point R. What is the bearing of Q from P to the nearest whole degree?
A
16o
B
17o
C
73o
D
106o
E
164o
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
Using Pythagoras' theorem:
Hyp\(^2\) = Adj\(^2\) + Opp\(^2\) → 24\(^2\) + 7\(^2\)
Hyp = \(\sqrt{625}\) → 25
\(\tan P = \frac{7}{24}\)
tan P = 0.2917
P = tan\(^{-1}\) (0.2917)
= 16.26^\circ
Bearing of Q from P = 180^\circ - 16.26^\circ
= 163.74^\circ \(\approxeq\) 164^\circ
Source: Myschool Past Questions Archive (Record #22046)
Mathematics
WAEC / WASSCE 1988
Trigonometry, Elevation & Bearings
Solution
If sinθ = 3/5 find tanθ for 0 o
A
4\5
B
3\4
C
5\8
D
1\2
E
3\8
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
sinθ = 3/5
tanθ = 3/4
Source: Myschool Past Questions Archive (Record #22048)
Mathematics
WAEC / WASSCE 1988
Plane Geometry, Polygons & Circle Theorems
Solution
Simplify (271/3)2
A
41/2
B
6
C
9
D
18
E
81
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
(271/3)2
= (33 x 1/3)2 = 32 = 9
Source: Myschool Past Questions Archive (Record #22049)
Mathematics
WAEC / WASSCE 1988
Plane Geometry, Polygons & Circle Theorems
Solution
A student told to draw the graph of y = x2 + 4x - 6. He is then told to draw a liner graph on the same axis such that the intersection of the two graphs will give the solutions to the equation x2 + 4x - 7 = 0, What is the equation of the linear graph he needs to draw?
A
x = 1
B
x = -1
C
y = 1
D
y = -1
E
x + y = 1
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
The linear equation will be the difference between the equation.
y=x2 + 4x - 6 and x2 + 4x - 7 = 0
y=x2 + 4x - 6, ( 0 = x2 + 4x - 7)
y = -(-1) y = 1
Source: Myschool Past Questions Archive (Record #22050)
Mathematics
WAEC / WASSCE 1988
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
Calculate the value of x in the diagram above
Attached Figure / Diagram
A
18o
B
30o
C
40o
D
60o
E
15°
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
vertically opposite angles are equal, hence
3x + 6x + 3x = 180^\circ
12x = 180^\circ
x = 15^\circ
Source: Myschool Past Questions Archive (Record #22051)
Mathematics
WAEC / WASSCE 1988
Linear, Simultaneous & Quadratic Equations
Solution
Find the quadratic equation whose roots are x = -2 or x = 7
A
x2 + 2x - 7 = 0
B
x2 - 2x + 7 = 0
C
x2 + 5 +14 = 0
D
x2 - 5x - 14 = 0
E
x2 + 5x - 14 = 0
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
x + 2 and x - 7 are factors
(x+2)(x+7) = 0
x(x-7) + 2(x-7) = 0
x2 - 7x + 2x - 14 = 0
x2 - 5x - 14 = 0
Source: Myschool Past Questions Archive (Record #22052)
Mathematics
WAEC / WASSCE 1988
Fractions, Decimals, Percentages & Approximations
Solution
A sales girl gave a change of N1.15 to a customer instead of N1.25. Calculate her percentage error
A
10%
B
7%
C
8.0%
D
2.4%
E
10%
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Error = 1.25 - 1.15 = 0.10
0.10/1.25* 100 = 8.0%
Source: Myschool Past Questions Archive (Record #22054)
Mathematics
WAEC / WASSCE 1988
Permutations, Combinations & Probability
Solution
What is the probability of having an odd number in a single toss of a fair die?
A
1/6
B
1/3
C
1/2
D
2/3
E
5/6
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
n(S) = 6(odd) = {1, 3, 5}
n(odd) = 3
pr(odd) = \(\frac{n(odd)}{n(S)}\) 3/6 =1/2
Source: Myschool Past Questions Archive (Record #22057)
Mathematics
WAEC / WASSCE 1988
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
A water tank is made with a right-angled trapezium - shaped vertical cross-section so that when it is placed on sloping ground the top of the tank is level. The dimension are given in the diagram above
If the tank is completely filled with water, how many cubic metres can it hold?
Attached Figure / Diagram
A
66m3
B
84m3
C
132m3
D
168m3
E
264m3
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Area of trapezium = 1/2(a+b)h
= 1/2(4 + 7)x4 = 22m2
volume = 22 x 6 = 132m3
Source: Myschool Past Questions Archive (Record #22061)