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Mathematics
WAEC / WASSCE 1996
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the diagram above, find x correct to the nearest degree
Attached Figure / Diagram
A
15o
B
25o
C
26o
D
36o
E
72o
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
4x + 3x + 5x + 2x = 360 ( sum of angles of a quadrilateral )
14x = 360
x = \(\frac{ 360}{14}\)
= 25. 7142^\circ..
\(therefore = x = 26^0\) to the nearest degrees.
Note; opposite angles are equal.
Source: Myschool Past Questions Archive (Record #23817)
Mathematics
WAEC / WASSCE 1996
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the diagram above, TRQ is a straight line. Find p, if p = \(\frac{1}{3}\)(a + b + c)
Attached Figure / Diagram
A
45o
B
60o
C
90o
D
120sup>o
E
150o
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
a + b + c + p = 180 (sum of angles on a straight line)
But p = \(\frac{1}{3}\)(a + b + c), Then, (a + b + c) = 3p
3p + p = 180
4p = 180
p = \(\frac{180}{4}\) = 45º
Source: Myschool Past Questions Archive (Record #23818)
Mathematics
WAEC / WASSCE 1996
Plane Geometry, Polygons & Circle Theorems
Which of the following is not true? You may construct a
A
triangle given all the three sides
B
triangle given one side and two angles
C
triangle given two sides and the included angle
D
quatrilateral given all the four sides
E
parallelogram given two adjacent sides and the diagonal joining them
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 #23819)
Mathematics
WAEC / WASSCE 1996
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the diagram above, PQ is parallel to RST. /RS/ = /SQ/ = /TQ/ and ∠PQR = 35o.Calculate ∠SQT
Attached Figure / Diagram
A
30o
B
35o
C
40o
D
70o
E
110o
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
< QRS = 35º alt
< PQS = 35º ( base
therefore, RSQ = 180º - ( 35º+ 35º) = 110º
therefore < QST = 180º- 110º = 70º
< SQT = 180º - ( 70º + 70º ) = 40º
Source: Myschool Past Questions Archive (Record #23820)
Mathematics
WAEC / WASSCE 1996
Plane Geometry, Polygons & Circle Theorems
Diagram
In the diagram above, /PQ/ = /PS/ and /QR/ = /SR/. Which of the following is/are true? i. the line PR bisects ∠QRS ii. The line PR is the perpendicular bisector of the line segment QS iii. Every point on PR is equidistant from SP and QP
Attached Figure / Diagram
A
I only
B
III only
C
I and II only
D
I and III only
E
I, II and III
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option E.
Source: Myschool Past Questions Archive (Record #23821)
Mathematics
WAEC / WASSCE 1996
Plane Geometry, Polygons & Circle Theorems
Diagram
In the diagram above, PQ is a tangent to the circle MTN at T. What is the size of ∠MTN?
Attached Figure / Diagram
A
52o
B
54o
C
66o
D
72o
E
128o
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 #23823)
Mathematics
WAEC / WASSCE 1996
Plane Geometry, Polygons & Circle Theorems
Diagram
In the diagram above, KLMN is a cyclic quadrilateral. /KL/ = /KN/, ∠NKM = 55o and ∠KML = 40o. Find ∠LKM
Attached Figure / Diagram
A
35o
B
40o
C
45o
D
50o
E
55o
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 #23824)
Mathematics
WAEC / WASSCE 1996
Plane Geometry, Polygons & Circle Theorems
Diagram
In the diagram above, ∠SPQ = 79o. Find ∠SRQ
Attached Figure / Diagram
A
11o
B
391/2
C
79o
D
90o
E
101o
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option E.
Source: Myschool Past Questions Archive (Record #23825)
Mathematics
WAEC / WASSCE 1996
Plane Geometry, Polygons & Circle Theorems
Solution
Two angles (a + 31) and (b - 49o) are adjacent angles on a straight line. Which of the following is true
A
a + b = 198o
B
a + b = 180o
C
a + b = 162o
D
a + b = 100o
E
a + b = 80o
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
a + 31 + b - 49 = 180o(sum of angles on str line)
a + b - 18 = 180o
a + b = 180 + 18
a + b = 198o
Source: Myschool Past Questions Archive (Record #23826)
Mathematics
WAEC / WASSCE 1996
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
The trapezium PQRS parallel to SR,∠PQS = 34o and ∠SPQ = 2 ∠SRQ. Find the size of, SQR
Attached Figure / Diagram
A
58o
B
68o
C
78o
D
90o
E
112o
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
considering SPQ
S = 34o (base ∠s of Isos. Δ)
P = 180o - 68o = 112o
R = 122/2 = 56o
a = 34o (alt ∠s)
SQR = 180o - (56 + 34)
180o - 90o = 90o
Source: Myschool Past Questions Archive (Record #23827)
Mathematics
WAEC / WASSCE 1996
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the diagram above, AB, CD and XY are straight lines intersecting at W. Find ∠CWX
Attached Figure / Diagram
A
20o
B
80o
C
100o
D
120o
E
140o
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
a = 40o (vertical opp. ∠s are equal) b = 60o
a + b + c = 180o (sum of ∠s on a str line)
40o + 60o + c = 180o
C = 180o - 100o
C = 80o
Source: Myschool Past Questions Archive (Record #23828)
Mathematics
WAEC / WASSCE 1996
Inequalities & Linear Programming
If sin\(\theta\) cos\(\theta\), for 0o \(\leq\) θ \(\leq\) 360o, find the value of \(\theta\)
A
45o, 225o
B
135o, 315o
C
45o, 315o
D
135o, 225o
E
45o, 135o
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 #23829)
Mathematics
WAEC / WASSCE 1996
Inequalities & Linear Programming
Solution
If tan x = \(2\frac{2}{5}\), find the value of sin x; 0 \(\leq\) x \(\leq\) 90o
A
5/13
B
5/12
C
144/169
D
12/13
E
13/12
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Tan x = 22/5 = 12/5
sin x = 12/13
Source: Myschool Past Questions Archive (Record #23830)
Mathematics
WAEC / WASSCE 1996
Trigonometry, Elevation & Bearings
Solution
A town P is 150km from a town Q in the direction 050o. What is the bearing of Q from P?
A
050o
B
130o
C
230o
D
270o
E
310o
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
a = 50o (Alt. ∠s)
Bearing of Q from P = 180o + a
= 180o + 50o = 230o
Source: Myschool Past Questions Archive (Record #23831)
Mathematics
WAEC / WASSCE 1996
Trigonometry, Elevation & Bearings
Solution
The angle of elevation of the top X of a vertical pole from a point P on a level ground is 60o. The distance from P to the foot of the pole is 55m. Without using tables, find the height of the pole.
A
50/3m
B
50m
C
55√3m
D
60m
E
65m
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Tan60o = h/55
h = 55Tan60o
h 55 x √3 ; h = 55√3m
Source: Myschool Past Questions Archive (Record #23832)