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Mathematics
WAEC / WASSCE 1993
Geometry and Trigonometry
Solution
Two chords PQ and RS of a circle when produced meet at K. If ∠KPS = 31o and ∠PKR = 42o, find ∠KQR
A
11o
B
73o
C
107o
D
138o
E
149o
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
QPS - QRK = 31o
QRK + RKQ + KQR = 180
31 + 42 + KQR = 180o
KQR = 180 - 73 = 107o
Source: Myschool Past Questions Archive (Record #23209)
Mathematics
WAEC / WASSCE 1993
Geometry and Trigonometry
Diagram
Solution
In the diagram above, QRS is a straight line, QP//RT, PRQ = 56^\circ, ∠QPR =84^\circ and ∠TRS = x^\circ. Find x
Attached Figure / Diagram
A
28°
B
40°
C
44°
D
84°
E
124°
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
< PQR = 180^\circ - (84^\circ + 56^\circ)
= 40^\circ
\(\therefore\) x = 40^\circ (corresponding angles QP// RT)
Source: Myschool Past Questions Archive (Record #23210)
Mathematics
WAEC / WASSCE 1993
Geometry and Trigonometry
Solution
Simplify \(\frac{2.25}{0.015}\) leaving your answer in standard form
A
1.5 x 10-4
B
1.5 x 10-2
C
1.5 x 10-3
D
1.5 x 101
E
1.5 x 102
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
\(\frac{2.25}{0.015}\)
= \(\frac{2250}{15}\)
= \(150\)
= \(1.5 \times 10^{2}\)
Source: Myschool Past Questions Archive (Record #23211)
Mathematics
WAEC / WASSCE 1993
Geometry and Trigonometry
Solution
A plane tiles 90km on a bearing 030° and then flies 150km due east. How far east of the starting point is the plane?
A
120km
B
165km
C
195km
D
(150 + 45√3)km
E
240km
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
complete x as in the diagram. x/90 = sin30o
x = 90 x sin30 = 45o
∴Dist = 150 + 45 = 195km
Source: Myschool Past Questions Archive (Record #23214)
Mathematics
WAEC / WASSCE 1993
Geometry and Trigonometry
If sin x = cos 50o, then x equals
A
40o
B
45o
C
50o
D
90o
E
130o
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option A.
Source: Myschool Past Questions Archive (Record #23215)
Mathematics
WAEC / WASSCE 1993
Geometry and Trigonometry
Solution
From a point on the edge of the sea, one ship is 24km away on a bearing S 50oE and another ship is 7km away on a bearing S40oW. How far apart are the ships?
A
20km
B
24km
C
25km
D
31km
E
84km
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
x2 = 242 + 72 = 576 + 49
x2 = 625
x = √625 = 25
Source: Myschool Past Questions Archive (Record #23216)
Mathematics
WAEC / WASSCE 1993
Geometry and Trigonometry
Solution
Given that tan x = 5/12, what is the value of sin x + cos x ?
A
5/13
B
7/13
C
12/13
D
17/13
E
5/12
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\tan x = \frac{opp}{adj} = \frac{5}{12}\)
\(Hyp^2 = opp^2 + adj^2\)
\(Hyp^2 = 5^2 + 12^2\)
= \(25 + 144 = 169\)
\(Hyp = \sqrt{169} = 13\)
\(\sin x = \frac{5}{13}; \cos x = \frac{12}{13}\)
\(\sin x + \cos x = \frac{5}{13} + \frac{12}{13}\)
= \(\frac{17}{13}\)
Source: Myschool Past Questions Archive (Record #23217)
Mathematics
WAEC / WASSCE 1993
Geometry and Trigonometry
Cos 75o has the same value as
A
cos 115o
B
cos 255o
C
cos 285o
D
-sin165o
E
-sin 255o
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 #23218)
Mathematics
WAEC / WASSCE 1993
Geometry and Trigonometry
Solution
If sin x = 12/13, where 0^\circ < x < 90^\circ, find the value of 1 - cos\(^2\)x
A
25/169
B
64/169
C
105/169
D
144/169
E
8/13
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\sin x = \frac{12}{13}\)
\(\cos x = \frac{5}{13}\)
\(\cos^{2} x = (\frac{5}{13})^2 = \frac{25}{169}\)
\(1 - \cos^{2} x = 1 - \frac{25}{169}\)
= \(\frac{144}{169}\)
Source: Myschool Past Questions Archive (Record #23219)
Mathematics
WAEC / WASSCE 1993
Geometry and Trigonometry
Solution
The angle of elevation of the top of a tower from a point on the horizontal ground, 40m away from the foot of the tower is 30o. Find the height of the tower.
A
20m
B
40√3m /3
C
20√3m
D
40√3m
E
60cm
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(\tan 30 = \frac{x}{40}\)
\(x = 40 \tan 30 = \frac{40}{\sqrt{3}}\)
= \(\frac{40\sqrt{3}}{3} m\)
Source: Myschool Past Questions Archive (Record #23220)
Mathematics
WAEC / WASSCE 1993
Geometry and Trigonometry
Solution
The distribution by state of 840 students in the Faculty of Science of a Nigerian University in a certain session is as follows:
Bendel
45
kwara
410
Ogun
105
Ondo
126
Oyo
154
In a pie chart drawn to represent this distribution, the angle subtended by Ondo is
A
36o
B
42o
C
45o
D
48o
E
54o
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
Ondo = \(\frac{126}{840} \times 360^\circ\)
= \(54^\circ\)
Source: Myschool Past Questions Archive (Record #23227)
Mathematics
WAEC / WASSCE 1993
Geometry and Trigonometry
Solution
What is the probability of having an even 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
Prob(even number in single toss) = \(\frac{3}{6}\)
= \(\frac{1}{2}\)
Source: Myschool Past Questions Archive (Record #23232)
Mathematics
UTME / JAMB 1993
Geometry and Trigonometry
Solution
Solve without using tables log5(62.5) - log5(\(\frac{1}{2}\))
A
3
B
4
C
5
D
8
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
log5(62.5) - log5(\(\frac{1}{2}\))
= log5\(\frac{(62.5)}{\frac{1}{2}}\) - log5(2 x 62.5)
= log5(125)
= log553 - 3log55
= 3
Source: Myschool Past Questions Archive (Record #31147)
Mathematics
UTME / JAMB 1993
Geometry and Trigonometry
Solution
Which of the following is a factor of 15 + 7x - 2x2
A
x + 3
B
x - 3
C
x - 5
D
x + 5
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Factorize 15 + 7x - 2x2
(5 - x)(3 + 2x); suppose 15 + 7x = 2x2 = 0
∴ (5 - x)(3 + 2x) = 0
x = 5 or x = -\(\frac{3}{2}\)
Since 5 is a root, then (x - 5) is a factor
Source: Myschool Past Questions Archive (Record #31166)
Mathematics
UTME / JAMB 1993
Geometry and Trigonometry
Solution
A rectangular polygon has 150o as the size of each interior angle. How many sides has the polygon?
A
12
B
10
C
9
D
8
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
A rectangular polygon has each interior angle to be 150o
let the polygon has n-sides
therefore, Total interior angle 150 x n = 150n
hence 150n = (2n - 4)90
150n = 180n - 360
360 = (180 - 150)n
30n = 360
n = 12
Source: Myschool Past Questions Archive (Record #31206)