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Mathematics
WAEC / WASSCE 1997
Plane Geometry, Polygons & Circle Theorems
Which of the following statements is/are true when two straight lines intersect?
I. Adjacent angles are equal II. Vertically opposite angles are equal III. Adjacent angles are supplementary
A
II only
B
I and III only
C
II and III only
D
I, II and III
E
I and II
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 #23874)
Mathematics
WAEC / WASSCE 1997
Plane Geometry, Polygons & Circle Theorems
Diagram
PQRS and GHRS are parallelograms on the same base SR and between the same parallel straight line PH and SR. Which of the following is true?
Attached Figure / Diagram
A
Δ PGS = Δ QHR
B
Parallelogram PQRS = Δ QHR
C
Trapezium PQXS = Δ QHR
D
Δ PGS = Parallelogram GHRS
E
Parallelogram PQRS = Parallelogram GHRS
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 #23875)
Mathematics
WAEC / WASSCE 1997
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
From the diagram above, which of the following is true?
Attached Figure / Diagram
A
a +b + x =180
B
a = b + x
C
a – b = 180 - x
D
a + b = x + 180
E
a – b = x - 180.
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
From the diagram, the angles in the triangle are:
(180 - a)^\circ, (180 - b)^\circ and x^\circ.
\(\therefore\) (180 - a) + (180 - b) + x = 180^\circ
360 + x - a - b = 180^\circ
360 - 180 + x = a + b
180 + x = a + b.
Source: Myschool Past Questions Archive (Record #23876)
Mathematics
WAEC / WASSCE 1997
Plane Geometry, Polygons & Circle Theorems
Solution
The interior angles of a pentagon are 126o, 114o, y, 92o and 83o. Find the value of y.
A
85o
B
95o
C
105o
D
115o
E
125o
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
Sum of the angle of a pentagon
= (2 x 5 - 4) x 90
= 540o
126 + 114 + y + 92 + 83 = 540
y = 540 - 415 = 125o
Source: Myschool Past Questions Archive (Record #23877)
Mathematics
WAEC / WASSCE 1997
Inequalities & Linear Programming
Solution
Solve the inequality 3x - 8 ≥ 5x
A
x ≤ 4
B
x ≥ 1
C
x ≤ -4
D
x ≤ -1
E
x < 2
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
3x - 8 ≥ 5x
3x - 5x ≥ 8
-2x ≥ 8
x ≤ -4
Source: Myschool Past Questions Archive (Record #23878)
Mathematics
WAEC / WASSCE 1997
Plane Geometry, Polygons & Circle Theorems
Solution
Divide 3.6721 by 4
A
0.9180
B
1.4180
C
1.1680
D
1.9180
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(\frac{3.6721}{4} = 0.918025\)
\(\approxeq\) 0.9180
Source: Myschool Past Questions Archive (Record #23879)
Mathematics
WAEC / WASSCE 1997
Sequences & Series (AP & GP)
Solution
The eleventh term of an AP, is 25 and its first term is -3. Find its common difference.
A
19/10
B
21/5
C
23/11
D
21/2
E
24/5
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
a + 10d = 25
-3 + 10d = 25
d = 28/10 = 24/5
Source: Myschool Past Questions Archive (Record #23880)
Mathematics
WAEC / WASSCE 1997
Indices, Logarithms & Surds
Solution
Find the common ratio in the GP: log 3, log 9, log 81 ..........
A
1
B
2
C
3
D
6
E
9
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
r = log9/log3 = 2log3/log3 = 2
Source: Myschool Past Questions Archive (Record #23881)
Mathematics
WAEC / WASSCE 1997
Plane Geometry, Polygons & Circle Theorems
Solution
Find the value of t for which \(\frac{64}{27} = (\frac{3}{4})^{t - 1}\)
A
-4
B
-2
C
11/3
D
2
E
4
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(\frac{64}{27} = (\frac{3}{4})^{t-1}\)
\((\frac{3}{4})^t = \frac{64}{27} \times \frac{3}{4} = \frac{16}{9}\)
\((\frac{3}{4})^t = (\frac{9}{16})^{-1}\)
\((\frac{3}{4})^t = (\frac{3}{4})^{-2}\)
t = -2
Source: Myschool Past Questions Archive (Record #23882)
Mathematics
WAEC / WASSCE 1997
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
O is the centre of the circle PQRS. PR and QS intersect at T POR is a diameter, ∠PQT = 42o and ∠QTR = 64o; Find ∠QRT
Attached Figure / Diagram
A
68o
B
64o
C
42o
D
32o
E
22o.
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
TQR = 90 - 42 = 48o
QRT = 180 - (64 - 48)
= 180 - 112
= 68o
Source: Myschool Past Questions Archive (Record #23883)
Mathematics
WAEC / WASSCE 1997
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
TR is the tangent to the circle PQR with centre O. Find the size of ∠PRT
Attached Figure / Diagram
A
44o
B
46o
C
60o
D
74o
E
118o
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Reflex < POQ = 360^\circ - 148^\circ = 212^\circ
< PRO = 360^\circ - 330^\circ = 30^\circ
But < ORT = 90^\circ \(\implies\) < PRT = 90^\circ - 30^\circ = 60^\circ
Source: Myschool Past Questions Archive (Record #23884)
Mathematics
WAEC / WASSCE 1997
Indices, Logarithms & Surds
Solution
Given that \(\frac{1}{2} \log_{10} P = 1\), find the value of P.
A
104
B
103
C
102
D
101
E
10-1
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\frac{1}{2} \log_{10} P = 1\)
\(\log_{10} P^{\frac{1}{2}} = 1\)
\(P^{\frac{1}{2}} = 10^{1}\)
\(\implies P = 10^{2}\)
Source: Myschool Past Questions Archive (Record #23885)
Mathematics
WAEC / WASSCE 1997
Plane Geometry, Polygons & Circle Theorems
If two triangles are similar, which of the following is true? Their
A
corresponding sides are equal
B
corresponding angles are equal
C
corresponding altitudes are equal
D
areas are equal
E
perimeters are equal
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 #23886)
Mathematics
WAEC / WASSCE 1997
Plane Geometry, Polygons & Circle Theorems
Which of the following is not necessarily true of a rectangle?
A
The diagonals are equal
B
The diagonals bisect each other
C
The diagonals are perpendicular
D
Each diagonal divides the area of the rectangle equally
E
Each diagonal divides the rectangle into two congruent triangles
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 #23887)
Mathematics
WAEC / WASSCE 1997
Plane Geometry, Polygons & Circle Theorems
Solution
A chord is 5cm from the centre of a circle of diameter 26cm. Find the length of the chord
A
16cm
B
18cm
C
24cm
D
25.51cm
E
51.1cm
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
BC = \sqrt132 - 52 = 12cm
Source: Myschool Past Questions Archive (Record #23896)