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Mathematics
WAEC / WASSCE 1988
Geometry and Trigonometry
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
Geometry and Trigonometry
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)
Mathematics
WAEC / WASSCE 1988
Geometry and Trigonometry
Diagram
Solution
In the diagram above, O is the center of the circle, BOC is a diameter and angle ADC is 37o
What is ACB?
Attached Figure / Diagram
A
147o
B
127o
C
65o
D
53o
E
37o
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
From the figure \(< ABC = < ADC = 37^\circ\) (angles on the same segment)
\(< BCA = 90^\circ\) (angle in semi-circle)
\(\therefore\) In \(\Delta ABC\), \(< ACB = 180^\circ - (37^\circ + 90^\circ)\)
= 53^\circ
Source: Myschool Past Questions Archive (Record #22148)
Mathematics
WAEC / WASSCE 1988
Geometry and Trigonometry
Diagram
Which of the following is a correct method for constructing an angle of 60o at Q?
Attached Figure / Diagram
A
I only
B
II only
C
III only
D
I and II only
E
II and III only
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 #22161)
Mathematics
WAEC / WASSCE 1988
Geometry and Trigonometry
Diagram
Solution
IN the diagram above, LK/PQ, reflex angle KLM = 241^\circ and ∠QPM = 89^\circ. What is the value of ∠LMP?
Attached Figure / Diagram
A
30o
B
61o
C
89o
D
119o
E
150o
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Produce ML to R.
From the figure < LRM = 89^\circ (corresponding angles)
In triangle LRM, < LMR = 180^\circ - (61^\circ + 89^\circ)
= 30^\circ
Source: Myschool Past Questions Archive (Record #22165)
Mathematics
WAEC / WASSCE 1988
Geometry and Trigonometry
Solution
Abidjan is 4o west of Accra and on the same circle of latitude. If the radius of this circle of latitude is 6370km, how far is Abidjan west of Accra, correct to the nearest kilometer? [Take π = 22/7]
A
222km
B
445km
C
890km
D
5005km
E
10010km
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
θ/360* 2πr = Rcos4o
4/360* 40041/1= 445km
Source: Myschool Past Questions Archive (Record #22182)
Mathematics
UTME / JAMB 1988
Geometry and Trigonometry
Solution
Tope bought X oranges at N5.00 each and some mangoes at N4.00 each. if she bought twice as many mangoes as oranges and spent at least N65.00 and at most N130.00, find the range of values of X.
A
4≤X≤5
B
5≤X≤8
C
5≤X≤10
D
8≤X≤10
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Number of oranges = X; Costing N5X.
Number of mangoes = 2X; Costing N8X.
\(\therefore 65 \leq 5X + 8X \leq 130\)
\(5 \leq X \leq 10\)
Source: Myschool Past Questions Archive (Record #21)
Mathematics
WAEC / WASSCE 1988
Geometry and Trigonometry
Diagram
Solution
In the diagram above, O is the centre of the circle through points L, M and N, if ∠MLN = 74o and ∠MNL = 39o, calculate ∠LON.
Attached Figure / Diagram
A
67o
B
100o
C
113o
D
126o
E
134o
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
From the diagram, < LMN = 180^\circ - (74^\circ + 39^\circ) (sum of angle in a triangle)
= 67^\circ
< LON = 2 x 67^\circ (angle subtended at the centre is twice the angle at the circumference)
= 134^\circ
Source: WAEC / JAMB / NECO Classroom Archive (Record #22196)
Mathematics
UTME / JAMB 1988
Geometry and Trigonometry
Solution
The thickness of an 800 pages of book is 18mm. Calculate the thickness of one leaf of the book giving your answer in meters and in standard form
A
2.25 x 10-4m
B
50 x 10-4m
C
2.25 x 10-5m
D
4.50 x 10-5m
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Thickness of an 800 pages book = 18mm to meter
18 x 103m = 1.8 x 10-2m
One leaf = \(\frac{1.8 \times 10^{-2}}{800}\)
= \(\frac{1.8 \times 10^{-2}}{8 \times 10^{2}}\)
= \(\frac{-1.8}{8}\) x 10-4
= 0.225 x 10-4
= 2.25 x 10-5m
one leaf contains 2 pages
: 2 * 2.25 x 10\(^{-5}\)m
= 4.5 * 10\(^{-5}\)m
Source: WAEC / JAMB / NECO Classroom Archive (Record #31708)
Mathematics
WAEC / WASSCE 1988
Geometry and Trigonometry
Solution
A cone is made from a sector of circle of radius 14cm and angle of 90o. What is the area of the curved surface of the cone? (Take x = 22/7)
A
22cm2
B
38.5cm2
C
77cm2
D
154cm2
E
308cm2
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Length of arc = θ/360 * 2πr
=> r = 90/360 * 14/4 = 3.5
slant height t = 14cm
curved surface area of cone = πrl
=> 3.142 x 3.5 x 14 = 153.95
Source: Myschool Past Questions Archive (Record #22192)
Mathematics
WAEC / WASSCE 1988
Geometry and Trigonometry
Solution
A rope of length 18m is used to form a sector of a circle of radius 3.5m on a school playing field. What is the size of the angle of the sector, correct to the nearest degree?
A
33o
B
40o
C
90o
D
180o
E
270o
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Circumference = 2\pir
2 x 22/7 x 3.5 ≅ 22m
22m = 360o
11m = 360/22 x 11 = 180o
Source: Myschool Past Questions Archive (Record #22199)
Mathematics
WAEC / WASSCE 1988
Geometry and Trigonometry
Diagram
Solution
In the diagram above, PR is perpendicular from P to QS, PQ = 2cm, QR = 1cm and PR = RS. what is the size of the angle QPS?
Attached Figure / Diagram
A
135o
B
105o
C
90o
D
75o
E
60o
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\Delta RPS\) = Isosceles triangle
\(\therefore < RPS = \frac{180^\circ - 90^\circ}{2}\) = 45^\circ
In \(\Delta QPR\),\(\sin < QPR = \frac{1}{2}\) = 30^\circ
\(\therefore < QPS = 30^\circ + 45^\circ = 75^\circ\)
Source: Myschool Past Questions Archive (Record #22208)
Mathematics
UTME / JAMB 1988
Geometry and Trigonometry
Diagram
For what values of x is the curve y = \(\frac{x^2 + 3}{x + 4}\) decreasing?
Attached Figure / Diagram
A
-3 < x \(\leq\) 0
B
-3 \(\geq\) x < 0
C
0 < x < 3
D
0 \(\leq\) x \(\leq\) 3
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option D.
Source: Myschool Past Questions Archive (Record #31638)
Mathematics
UTME / JAMB 1988
Geometry and Trigonometry
Solution
In a class of 150 students, the sector in a pie chart representing the students offering Physics has angle 12o. How many students are offering Physics?
A
18
B
15
C
10
D
5
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
No of students offering Physics are \(\frac{12}{360}\) x 150
= 5
Source: Myschool Past Questions Archive (Record #31646)
Mathematics
UTME / JAMB 1988
Geometry and Trigonometry
Solution
Four interior angles of a pentagon are 90o - xo, 90o + xo, 110o - 2xo, 110o + 2xo. Find the fifth interior angle
A
110o
B
120o
C
130o
D
140o
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Let the fifth interior angle be y: sum of interior angle of a pentagon
= (2 x 5 - 4) x 90o
= 6 x 90o
= 540o
(90 - x) + (90 + x) + (110 - 2x) + (110 + 2x) + y = 540o
400o + y = 540o
y = 540 - 400o
y = 140o
Source: Myschool Past Questions Archive (Record #31651)