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Mathematics
WAEC / WASSCE 1992
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the diagram above, O is the center of the circle QOR is a diameter and ∠PSR is 37^\circ. Find ∠PRQ
Attached Figure / Diagram
A
37o
B
53o
C
65o
D
127o
E
147o
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Construction: Join PQ.
Then < RSP = 37^\circ = < RQP (angles on the same segment)
But < RPQ = 90^\circ (angle in a semi-circle)
\(\therefore\) < PRQ = 180^\circ - (90^\circ + 37^\circ)
= 53^\circ
Source: Myschool Past Questions Archive (Record #23161)
Mathematics
WAEC / WASSCE 1992
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the diagram above, ML//PQ and NP//QR, if ∠LMN = 40^\circ and ∠MNP = 55^\circ. Find ∠QPR
Attached Figure / Diagram
A
15o
B
25o
C
35o
D
40o
E
55o
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Draw line ANB// ML
< MNA = 40^\circ (alternate angle AB/ ML)
< ANP = 55^\circ - 40^\circ = 15^\circ
< PQR = 15^\circ = < ANP (corresponding angles, PN // RQ)
Source: Myschool Past Questions Archive (Record #23162)
Mathematics
WAEC / WASSCE 1992
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
The angles marked in the diagram above are measured in degrees. Find x
Attached Figure / Diagram
A
15o
B
24o
C
30o
D
36o
E
48o
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Sum of exterior angles = 360^\circ
2x + 3x + 2x + 3x + 5x = 360^\circ
15x = 360^\circ
x = 360^\circ/15 = 24^\circ
Source: Myschool Past Questions Archive (Record #23163)
Mathematics
WAEC / WASSCE 1992
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
Find the value of t in the diagram above
Attached Figure / Diagram
A
5.6cm
B
6.5cm
C
6.6cm
D
6.8cm
E
7.0cm
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(\frac{\text{t}}{t + 4}\) = \(\frac{7}{7 + 5}\)
\(\frac{\text{t}}{t + 4}\) = \(\frac{7}{12}\)
12t = 7t + 28
12t - 7t = 28
5t = 28
t = \(\frac{28}{5}\) = 5.6cm
Source: Myschool Past Questions Archive (Record #23164)
Mathematics
WAEC / WASSCE 1992
Plane Geometry, Polygons & Circle Theorems
Solution
A regular polygon has each of its exterior angles as 18o. How many sides has the polygon
A
10
B
11
C
12
D
20
E
24
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
360/18 = 20
Source: Myschool Past Questions Archive (Record #23165)
Mathematics
WAEC / WASSCE 1992
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the diagram above, PQT is an isosceles triangle.|PQ| = |QT|, ∠SRQ = 75^\circ, ∠QPT = 25^\circ and PQR is straight line. Find ∠RST
Attached Figure / Diagram
A
20o
B
50o
C
55o
D
70o
E
75o
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
< PTQ = 25^\circ (base angles of an isos. triangle)
\(\therefore\) < PQT = 180^\circ - (25^\circ + 25^\circ) = 130^\circ (sum of angles in triangle PQT)
\(\therefore\) < RST = 130^\circ - 75^\circ = 55^\circ (exterior angle = sum of 2 opp. interior angles)
Source: Myschool Past Questions Archive (Record #23166)
Mathematics
WAEC / WASSCE 1992
Trigonometry, Elevation & Bearings
Solution
Sin 60^\circ has the same value as I. Sin 120^\circ II. cos 240^\circ III. -sin 150^\circ IV. cos 210^\circ V. sin 240^\circ
A
I only
B
II only
C
IV only
D
III only
E
IV and V only
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
In the second quadrant, \(\sin 120 = \sin (180 - 120)\)
= \(\sin 60\)
Source: Myschool Past Questions Archive (Record #23167)
Mathematics
WAEC / WASSCE 1992
Trigonometry, Elevation & Bearings
If cos \theta = 5/13, what is the value of tan \(\theta\) for 0 < \theta < 90^\circ ?
A
13
B
5
C
13/5
D
12/5
E
5/12
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 #23168)
Mathematics
WAEC / WASSCE 1992
Trigonometry, Elevation & Bearings
Solution
The value of tan 315^\circ
A
1
B
√2/2
C
o
D
-1
E
-√2/2
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
tan 315^\circ = - tan (360 - 315) = - tan 45
= -1
Source: Myschool Past Questions Archive (Record #23169)
Mathematics
WAEC / WASSCE 1992
Trigonometry, Elevation & Bearings
Solution
The value of sin 210^\circ is
A
\(-\frac{1}{2}\)
B
\(-\frac{\sqrt{3}}{2}\)
C
\(\frac{1}{2}\)
D
\(\frac{\sqrt{2}}{2}\)
E
\(\frac{\sqrt{3}}{2}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
sin 210 = - sin (210 - 180) = - sin 30
= \(-\frac{1}{2}\)
Source: Myschool Past Questions Archive (Record #23170)
Mathematics
WAEC / WASSCE 1992
Plane Geometry, Polygons & Circle Theorems
Town P is on bearing 315o from town Q while town R is south of town P and west of town Q. lf town R is 60km away from Q, how far is R from P?
A
30km
B
42km
C
45km
D
60km
E
120km
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 #23171)
Mathematics
WAEC / WASSCE 1992
Trigonometry, Elevation & Bearings
Solution
A ladder leans against a vertical wall at an angle
60^\circ to the wall, if the foot of the ladder is 5 metres
away from the wall, calculate the length of the
ladder.
A
\(\frac{5\sqrt3}{3}\)m
B
5m
C
\(\frac{10\sqrt3}{3}\)m
D
5√3m
E
10m
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
The ladder makes 60^\circ inclination with the wall and its foot is 5m away from the wall.
Sketching the diagram, you will see that we have
\(sin 60 = \frac{5}{x}\) (where x is the length of the ladder)
⇒ \(x = \frac{5}{sin60}\)
\(x = \frac{10\sqrt{3}}{3}m\)
Source: Myschool Past Questions Archive (Record #23172)
Mathematics
WAEC / WASSCE 1992
Trigonometry, Elevation & Bearings
A cliff on the bank of a river is 300 metres
high. if the angle of depression of a point on the
opposite side of the river is 60° find the width of
the river.
A
100m
B
75√3m
C
100√3m
D
200√3m
E
300m
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 #23173)
Mathematics
WAEC / WASSCE 1992
Statistics (Data Representation, Central Tendency & Dispersion)
Find the median of the following set of scores:
65, 72, 55, 48, 78
A
55
B
60
C
63.5
D
65
E
72
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 #23175)
Mathematics
WAEC / WASSCE 1992
Statistics (Data Representation, Central Tendency & Dispersion)
Diagram
The data above shows the frequency distribution
of marks scored by a group of students in a class
test.
How many students took the test?
Attached Figure / Diagram
A
13
B
14
C
15
D
18
E
20
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 #23176)