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Mathematics
WAEC / WASSCE 1994
Geometry and Trigonometry
Solution
The sum of the angles of regular polygon is 2520o. How many sides does the polygon have?
A
20
B
18
C
17
D
16
E
15
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
2(n-2) x 90o = 2520; n = 16
Source: Myschool Past Questions Archive (Record #23571)
Mathematics
WAEC / WASSCE 1994
Geometry and Trigonometry
Which of the following is not a property of all parallelogram?
A
the diagonal bisects each other
B
Each diagonal bisects the area
C
the diagonal cut at right angles
D
The opposite sides are equal
E
The opposite angles are equal
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 #23572)
Mathematics
WAEC / WASSCE 1994
Geometry and Trigonometry
Diagram
Solution
In the diagram above, PQ is the tangent to the circle RST at T.|ST| = ST and ∠RTQ = 68o. Find ∠PTS
Attached Figure / Diagram
A
68o
B
62o
C
61o
D
56o
E
34o
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
∠TSR = 68o ∴ STR = 180-68/2 = 56o
PTS= 180-(68+56) = 56o
Source: Myschool Past Questions Archive (Record #23573)
Mathematics
WAEC / WASSCE 1994
Geometry and Trigonometry
Diagram
Solution
The diagram above shows a circle PQRS in which ∠PRQ = 54o and ∠SPQ = 97o. Find ∠PQS
Attached Figure / Diagram
A
61o
B
51o
C
43o
D
39o
E
29o
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
PSQ = 54o ∴PQS = 180o - (97 + 54)o = 29o
Source: Myschool Past Questions Archive (Record #23574)
Mathematics
WAEC / WASSCE 1994
Geometry and Trigonometry
Diagram
Solution
In the diagram, |PS| is a diameter of circle PQRS. |PQ| = |QR| and ∠RSP = 74º. Find ∠QPS
Attached Figure / Diagram
A
32o
B
37o
C
48o
D
53o
E
74o
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Join PR.
< PQR = 180º - 74º = 106º
Source: Myschool Past Questions Archive (Record #23575)
Mathematics
WAEC / WASSCE 1994
Geometry and Trigonometry
A ladder 6m long leans against a vertical wall so that it makes an angle of 60o with the wall. Calculate the distance of the foot of the ladder from the wall
A
3m
B
6m
C
2√3m
D
3√3m
E
6√3m
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 #23576)
Mathematics
WAEC / WASSCE 1994
Geometry and Trigonometry
The bearing of Q from P is 122o, what is the bearing of P from Q?
A
212o
B
238o
C
248o
D
292o
E
302o
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 #23577)
Mathematics
WAEC / WASSCE 1994
Geometry and Trigonometry
cos 57o has the same value as
A
sin 213o
B
-cos 303o
C
sin 147o
D
cos 123o
E
cos237o
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 #23578)
Mathematics
UTME / JAMB 1994
Geometry and Trigonometry
Solution
Given that \(\sqrt{2} = 1.414\), find without using tables, the value of \(\frac{1}{\sqrt{2}}\)
A
0.141
B
0.301
C
0.667
D
0.707
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\frac{1}{\sqrt{2}}\) = \(\frac{1}{\sqrt{2}}\) x \(\frac{\sqrt{2}}{\sqrt{2}}\)
= \(\frac{\sqrt{2}}{2}\)
= \(\frac{1.414}{2}\)
= 0.707
Source: Myschool Past Questions Archive (Record #30995)
Mathematics
UTME / JAMB 1994
Geometry and Trigonometry
Solution
If three angles of a quadrilateral are (3y - x - z)o, 3xo, (2z - 2y - x)o find the fourth angle in terms of x, y and z
A
(360 - x- y - z)o
B
(360 + x + y - z)o
C
(180 - x + y + z)o
D
(180 - x + y + z)o
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
The sum of angles of a quadrilateral is 360o
∴ (3y - x - z)o + 3xo + (2z - 2y - x)o + po = 360o
Where P is the fourth angle
3y - x - z + 3x + 2z - 2y - x + p = 360o
p = 360 - (x + y + z)
∴ p = (360 - x - y - z)o
Source: Myschool Past Questions Archive (Record #31021)
Mathematics
UTME / JAMB 1994
Geometry and Trigonometry
Solution
An open rectangular box is made of wood 2cm thick. If the internal dimensions of the box are 50cm long, 36cm wide and 20cm deep, the box volume of wood in the box is
A
11 520cm3
B
36 000cm3
C
38 200cm3
D
47 520cm3
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Internal dimension are 50cm, 36cm and 20cm
internal volume = 50 x 36 x 20cm3
1000 x 36cm3
= 36000cm3
External dimension are 54cm x 40cm x 22cm
= 2160cm2 x 22cm = 47520cm3
Volume of wood = Ext. volume - Int. volume
= 47,520cm3 - 36,000cm3
= 11,520cm3
Source: Myschool Past Questions Archive (Record #31024)
Mathematics
UTME / JAMB 1994
Geometry and Trigonometry
Solution
Calculate the perimeter, in cm, of a sector of a circle of radius 8cm and angle 45o
A
2\(\pi\)
B
8 + 2\(\pi\)
C
16 + 2\(\pi\)
D
16 + 16\(\pi\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Perimeter = OP + OQ + PQ
= 8 + 8 + PQ
length PQ = \(\frac{\theta}{360 \times 2\pi r}\)
= \(\frac{45}{360}\) x 2 x \(\pi\) x 8
= 2\(\pi\)
Perimeter of sector 2r + L
Where l = length of arc and r = radius
∴ P = 2(8) + 2\(\pi\)
= 16 + 2\(\pi\)
Source: Myschool Past Questions Archive (Record #31038)
Mathematics
UTME / JAMB 1994
Geometry and Trigonometry
Solution
What is the locus of a point P which moves on one side of a straight line XY, so that the angle XPY is always equal to 90o?
A
the perpendicular bisector of XY
B
a right-angled triangle
C
a circle
D
a semi circle
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Since XY is a fixed line and
XPY = 90o P is on one side of XY
P1P2P3......Pn are all possible cases where
XPY = 90o the only possible tendency is a semicircle because angles in semicircle equals 90o
Source: Myschool Past Questions Archive (Record #31040)
Mathematics
UTME / JAMB 1994
Geometry and Trigonometry
Solution
The angle of depression of a boat from the top of a cliff 10m high is 30. How far is the boat from the foot of the cliff?
A
\(\frac{5√3m}{3}\)
B
5√3m
C
10√3m
D
\(\frac{10√3m}{3}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
RQP = 90o
PQS = 30o but
RQS = 90o = \(\frac{RS}{10}\)
RS = 10 tan 60o
RS = 10 tan 60o
RS = 10√3m
Source: Myschool Past Questions Archive (Record #31042)
Mathematics
UTME / JAMB 1994
Geometry and Trigonometry
Solution
What is the value of sin(-690)?
A
\(\frac{\sqrt{3}}{2}\)
B
-\(\frac{\sqrt{3}}{2}\)
C
\(\frac{-1}{2}\)
D
\(\frac{1}{2}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Sin(-690o) = Sin(-360 -3300
sin - 360 = sin 0
∴ sin(-690o) = sin(330o)
Negative angles are measured in clockwise direction
The acute angle equivalent of sin(-330o) = sin(30o)
sin(-330o) = sin(30o)
= \(\frac{1}{2}\)
= 0.5
Source: Myschool Past Questions Archive (Record #31044)