WAEC - Mathematics (1988)

1
Evaluate (101.5)² - (100.5)²
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(D)
202
2
Express the product of 0.06 and 0.09 in standard form
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(C)
5.4*10^-3
3
Simplify 36\(^\frac{1}{2}\) x 64\(-^\frac{1}{3}\) x 5\(^0\)
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(D)
1¹/₂
4
Find the 8th term of the A.P -3, -1, 1 ......
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(B)
11
5
A group of students took a test and the following frequency table shows the scores above
Find the mode
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(C)
4
6

A group of students took a test and the following frequency table shows the scores above

The mean score is
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(D)
2.75
7

A group of students took a test and the following frequency table shows the scores above

The median score is
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(C)
3
8
If cos 60° = 1/2, which of the following angle has cosine of -1/2?
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(B)
120^o
9

In the diagram above, find the ratio |PQ|/|PR|
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(B)
3 : 5
10
A ladder 9m long leans against a vertical wall, making an angle of 64° with the horizontal ground. calculate correct to one decimal place, how far the foot of the ladder is from the wall.
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(A)
4.0m
11
What is the difference in longitude between P (lat. 50°N. long. 50°W) and Q (lat.50°N, long. 150°W)?
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(D)
100^o
12
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
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(C)
II & III only
13
Points P and Q respectively 24m north and 7m east point R. Calculate |PQ| in meters
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(C)
25
14
Points P and Q respectively 24m north and 7m east point R. What is the bearing of Q from P to the nearest whole degree?
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(E)
164^o
15
If sinθ = 3/5 find tanθ for 0 < θ < 90^o
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(B)
3\4
16
Simplify (27^1/3)²
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(C)
9
17
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?
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(C)
y = 1
18

Calculate the value of x in the diagram above
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(E)
15°
19
Find the quadratic equation whose roots are x = -2 or x = 7
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(D)
x² - 5x - 14 = 0
20
A sales girl gave a change of N1.15 to a customer instead of N1.25. Calculate her percentage error
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(C)
8.0%
21
What is the probability of having an odd number in a single toss of a fair die?
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(C)
1/2
22
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?
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(C)
132m³
23

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
By what number will you multiply your answer in 22 above to determine the capacity of the tank in liters?
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(E)
1000
24
Evaluate log₁₀6 + log₁₀45 - log₁₀27 without using logarithm tables
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(B)
1
25
Find the product xy if, x, 3/2, 6/7, y are in G.P
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(C)
9/7
26

In the diagram above, O is the center of the circle, BOC is a diameter and angle ADC is 37o
What is ACB?
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(D)
53^o
27
Factorize 5y\(^2\) + 2ay - 3a\(^2\)
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(E)
(y + a) (5y - 3a)
28
Which of the following is a correct method for constructing an angle of 60^o at Q?
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(B)
II only
29

IN the diagram above, LK/PQ, reflex angle KLM = 241° and ∠QPM = 89°. What is the value of ∠LMP?
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(A)
30^o
30
Abidjan is 4^o 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]
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(B)
445km
31
Which of the regions P, Q, R, S and T satisfies the following 0 < y < 1, y < x + 2, x < 0
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(E)
T
32
A cone is made from a sector of circle of radius 14cm and angle of 90^o. What is the area of the curved surface of the cone? (Take x = 22/7)
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(D)
154cm²
33

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.
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(E)
134^o
34
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?
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(D)
180^o
35

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?
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(D)
75^o
36
Cotonou and Niamey are on the same line of longitude and Niamey is 7^o north of Cotonou. If the radius of the earth is 6400km, how far is Niamey north of Cotonou along the line of longitude, correct to the nearest kilometer? [Take π = 22/7]
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(C)
782km
37
If Q = (all perfect squares less than 30) and P = (all odd numbers from 1 to 10). Find Q ∩ P.
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(D)
(1, 9)
38

The histogram below shows the number of candidates, in thousands, obtaining given ranges of marks in a State examination. Find the total number of candidates that sat for the examination
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(E)
270,000
39

The histogram below shows the number of candidates, in thousands, obtaining given ranges of marks in a State examination. How many candidates scored at most 30%?
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(D)
35,000
40
The surnames of 40 children in a class arranged in alphabetical order. 16 of the surnames begins with O and 9 of the surname begins with A, 14, of the letters of the alphabet do not appear as the first letter of a surname

What is the probability that the surname of a child picked at random from the class begins with either O or A?
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(A)
5/8