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Mathematics
WAEC / WASSCE 1993
Trigonometry, Elevation & Bearings
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
Trigonometry, Elevation & Bearings
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
Plane Geometry, Polygons & Circle Theorems
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
Trigonometry, Elevation & Bearings
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
Trigonometry, Elevation & Bearings
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
Trigonometry, Elevation & Bearings
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
Trigonometry, Elevation & Bearings
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
Trigonometry, Elevation & Bearings
Solution
At a point 500m from the base of a water tank the angle of elevation of the top of the tank is 45o. Find the height of the tank,
A
250m
B
353m
C
354m
D
433m
E
500m
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
\(\tan 45 = \frac{x}{500}\)
\(x = 500 \tan 45\)
= \(500 m\)
Source: Myschool Past Questions Archive (Record #23221)
Mathematics
WAEC / WASSCE 1993
Statistics (Data Representation, Central Tendency & Dispersion)
Solution
Find the median of the following set of numbers: 28, 29, 39, 38, 33, 37, 26, 20, 15, 25
A
33
B
29.5
C
29
D
28.5
E
28
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
15, 20, 25, 26, 28, 29, 33, 37, 38, 39
median = \(\frac{28 + 29}{2}\)
= 28.5
Source: Myschool Past Questions Archive (Record #23222)
Mathematics
WAEC / WASSCE 1993
Sets, Logic & Venn Diagrams
Diagram
What is A∩B in the diagram above?
Attached Figure / Diagram
A
(2,3)
B
(2,3,4)
C
(1,2,3)
D
(2,3,8)
E
(6,4,7)
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 #23223)
Mathematics
WAEC / WASSCE 1993
Statistics (Data Representation, Central Tendency & Dispersion)
Diagram
Solution
The table above shows the scores of a group of 40 students in a physics test.
If the mode is m and the median is n, then (m,n) is
Attached Figure / Diagram
A
(5,5)
B
(5,6)
C
(6,5)
D
(9,4)
E
(9,5)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Mode = 5
Median = 5
(m, n) = (5, 5)
Source: Myschool Past Questions Archive (Record #23224)
Mathematics
WAEC / WASSCE 1993
Statistics (Data Representation, Central Tendency & Dispersion)
Solution
Find the median of the set of numbers 12, 15, 13, 14, 12, 12.
A
12
B
12.5
C
13
D
13.5
E
14
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
12, 12, 12, 13, 14, 15
Median = \(\frac{12 + 13}{2}\)
= 12.5
Source: Myschool Past Questions Archive (Record #23226)
Mathematics
WAEC / WASSCE 1993
Statistics (Data Representation, Central Tendency & Dispersion)
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
Statistics (Data Representation, Central Tendency & Dispersion)
Diagram
Solution
How many student took the examination
Attached Figure / Diagram
A
18
B
20
C
21
D
23
E
24
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
= 2 + 4 + 3 + 6 + 6 + 2 + 1
= 24 students
Source: Myschool Past Questions Archive (Record #23228)
Mathematics
WAEC / WASSCE 1993
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
How many students scored less than 7 marks?
Attached Figure / Diagram
A
9
B
15
C
18
D
21
E
25
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
= 2 + 4 + 3 + 6
= 15 students scored less than 7 marks.
Source: Myschool Past Questions Archive (Record #23229)