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Mathematics
WAEC / WASSCE 1996
Geometry and Trigonometry
Solution
If the hypotenuse of a right-angle isosceles triangle is 2, what is the length of each of the other side?
A
1/√2
B
√2 - 1
C
1
D
√2
E
√3
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
An Isosceles Right Triangle is a right triangle that consists of two equal length legs.
i.e opp = adj
hyp\(^2\) = adj\(^2\) + opp\(^2\)
2\(^2\) = x\(^2\) + x\(^2\)
4 = 2x\(^2\)
2 = x\(^2\)
\sqrt2 = x
Source: WAEC / JAMB / NECO Classroom Archive (Record #23810)
Mathematics
WAEC / WASSCE 1996
Geometry and Trigonometry
Diagram
Solution
In the diagram above, O is the center of the circle of radius 3.5cm, ∠POQ = 60°. What is the area of the minor sector POQ?
[Take π = 22/7].
Attached Figure / Diagram
A
1481/2cm2
B
77cm2
C
321/12cm2
D
65/12cm2
E
15/6cm2
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Area of sector = \(\frac{\theta}{360^\circ} \times \pi r^2\)
= \(\frac{60}{360} \times \frac{22}{7} \times 3.5 \times 3.5\)
= \(\frac{77}{12}\)
= \(6\frac{5}{12}\) cm\(^2\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #23809)
Mathematics
WAEC / WASSCE 1996
Geometry and Trigonometry
Diagram
In the diagram above, O is the center of the circle of radius 3.5cm, ∠POQ = 60o
Use the information to answer the question below [Take \pi = 22/7]
What is the length of the arc PXQ?
Attached Figure / Diagram
A
22cm
B
181/3cm
C
\(\frac{11}{3}\)cm
D
91/6cm
E
71/3cm
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 #23808)
Mathematics
WAEC / WASSCE 1996
Geometry and Trigonometry
Solution
One side of a rectangle is 8cm and the diagonal is 10cm. What is the area of the rectangle?
A
80cm2
B
48cm2
C
40cm2
D
36cm2
E
24cm2
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
From the diagram above, using Pythagoras' theorem
y = \(\sqrt{10^2 - 8^2}\) = \(\sqrt{36}\) = 6 cm
Area of Rectangle = length x breath = 6 x 8 = 48 cm\(^2\)
Source: Myschool Past Questions Archive (Record #23812)
Mathematics
WAEC / WASSCE 1996
Geometry and Trigonometry
two towns X and Y both on latitude 60oS have longitude 27oE and 33oW respectively. Find to the nearest kilometers, the distance between X and Y measured along the parallel of latitude. [Take 2πR = 4 x 104km, where R is the Radius of the earth]
A
28850km
B
16667km
C
8333km
D
6667km
E
3333km
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 #23813)
Mathematics
WAEC / WASSCE 1996
Geometry and Trigonometry
The angle of a sector of a circle of radius 35cm is 288o. Find the perimeter of the sector. [Take π = 22/7]
A
246cm
B
211cm
C
141cm
D
114cm
E
44cm
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 #23814)
Mathematics
WAEC / WASSCE 1996
Geometry and Trigonometry
How many sides has a polygon if the sum of its interior angle is 1440o?
A
6
B
7
C
8
D
9
E
10
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 #23815)
Mathematics
WAEC / WASSCE 1996
Geometry and Trigonometry
Each interior angle of a regular nonagon(nine sided polygon) is equal to
A
160o
B
144o
C
140o
D
132o
E
36o
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 #23816)
Mathematics
WAEC / WASSCE 1996
Geometry and Trigonometry
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
Geometry and Trigonometry
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
Geometry and Trigonometry
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
Geometry and Trigonometry
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
Geometry and Trigonometry
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
Geometry and Trigonometry
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
Geometry and Trigonometry
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)