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Mathematics
UTME / JAMB 1998
Geometry and Trigonometry
Solution
When the expression pm\(^2\) + qm + 1 is divided by (m - 1), it has a remainder is 2, and when divided by (m + 1), the remainder is 4. Find p and q respectively
A
2, -1
B
-1, 2
C
3, -2
D
-2, 3
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
pm\(^2\) + qm + 1 = (m - 1) Q(x) + 2, where Q(x) = remainder.
p(1)\(^2\) + q(1) + 1 = 2
p + q + 1 = 2
p + q = 1.....(i)
pm\(^2\) + qm + 1 = (m - 1)Q(x) + 4
p(-1)\(^2\) + q(-1) + 1 = 4
p - q + 1 = 4
p - q = 3....(ii)
p + q = 1, p - q = 3
Using elimination method, add eqn i and ii
2p = 4, p = 2
from eqn ii
p - q = 3
2 - q = 3
-q = 3 - 2 = 1
q = - 1
Therefore, p = 2 and q = -1
q = 2
Source: WAEC / JAMB / NECO Classroom Archive (Record #30667)
Mathematics
WAEC / WASSCE 1998
Geometry and Trigonometry
Diagram
Solution
In the diagram O is the center of circle PRQ. The radius is 3.5cm and ∠POQ = 50o. Use the diagram to answer question below. (take π = 3.142)
Calculate, correct to three significant figures, the area of sector OPQ
Attached Figure / Diagram
A
3.403cm2
B
5.350cm2
C
10.99cm2
D
157.1cm2
E
175.0cm2
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Area of a sector = \(\frac{\theta}{360}\) x \(\pi\)r\(^2\)
Area of a sector = \(\frac{50}{360}\) x 3.142 x 3.5 x 3.5
= \(\frac{50 \times 3.142\times 3.5 \times 3.5}{360}\)
= \(\frac{1924.475}{360}\) ≈ 5.346cm\(^2\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #26359)
Mathematics
WAEC / WASSCE 1998
Geometry and Trigonometry
Solution
A ladder 5cm long long rest against a wall such that its foot makes an angle 30o with the horizontal. How far is the foot of the ladder from the wall?
A
\(\frac{5\sqrt{2}}{3}m\)
B
\(2\frac{1}{2}m\)
C
\(\frac{5\sqrt{3}}{2}m\)
D
\(\frac{10\sqrt{3}}{3}m\)
E
\(10\sqrt{3}m\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
cos 30 = \(\frac{adj}{hyp}\)
cross multiply:
adj = cos 30 X 5
= 5 \(\frac{\sqrt3}{2}\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #26352)
Mathematics
WAEC / WASSCE 1998
Geometry and Trigonometry
Diagram
Solution
The pie chart above show the distribution of how students travelled to a certain school on a particular day. Use this information to answer the question below
If a hundred students travelled by bus, find the total number of students in the school
Attached Figure / Diagram
A
300
B
400
C
500
D
600
E
750
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
If X represent the total number of students
where the bus holds a right angle; 90º
\(\frac{90}{360}\times X=100\)(students traveling by bus)
\(X=\frac{100\times 360}{90}=400\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #26362)
Mathematics
WAEC / WASSCE 1998
Geometry and Trigonometry
Solution
The radius of a geographical globe is 60cm. Find the length of the parallel of latitude 60oN
A
\(66\pi cm\)
B
\(60\pi cm\)
C
\(30\pi cm\)
D
\(15\pi cm\)
E
\(6\pi cm\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
The radius of the globe (sphere), R = 60 cm.
At latitude 60^\circN, the radius of the parallel of latitude is given by:
r = R \(\times \cos(60^\circ)\)
\(\cos(60^\circ) = \frac{1}{2}\)
r = 60 \(\times \frac{1}{2} = 30 \text{ cm}\)
The length of the parallel is the circumference of this circle:
\(\text{Length} = 2\pi r = 2\pi \times 30 = 60\pi \text{ cm}\)
This is the actual distance around the globe along the 60^\circN parallel.
Source: Myschool Past Questions Archive (Record #26339)
Mathematics
WAEC / WASSCE 1998
Geometry and Trigonometry
Diagram
Solution
In the diagram above, O is the center if the two concentric circle of radii 13cm and 10cm respectively. Find the area of the shaded portion in the sector with angle 120^\circ at the center
Attached Figure / Diagram
A
\(\frac{1}{3}\pi cm^2\)
B
\(\pi cm^2\)
C
\(3\pi cm^2\)
D
\(23\pi cm^2\)
E
\(46\pi cm^2\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\frac{120\pi}{360}(R^2 - r^2)\)
= \(\frac{1}{3}\times \pi (13^2 - 10^2)\)
= \(\frac{1}{3}\times \pi \times 69\) = 23\(\pi cm^2\)
Source: Myschool Past Questions Archive (Record #26340)
Mathematics
WAEC / WASSCE 1998
Geometry and Trigonometry
Diagram
Solution
In the diagram above, the area of triangle ABC is 35cm\(^2\). Find the value of y
Attached Figure / Diagram
A
5cm
B
10cm
C
17.5cm
D
28cm
E
70cm
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Area of triangle ABC = 35cm\(^2\).
Area of triangle ABC = \(\frac{1}{2}\) x B x H
= 0.5 x y x 7 = 35
= 3.5y = 35
y = \(\frac{35}{3.5}\) = 10 cm.
Source: Myschool Past Questions Archive (Record #26344)
Mathematics
WAEC / WASSCE 1998
Geometry and Trigonometry
Diagram
Solution
In ∆PQR. ∠PQR is a right angle. |QR| = 2cm and ∠PRQ = 60o. Find |PR|
Attached Figure / Diagram
A
4√3cm
B
4cm
C
2√3cm
D
\(\frac{4}{3}cm\)
E
1cm
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
cos60 = \(\frac{adj}{hyp}\)
cos60 = \(\frac{2}{x}\)
x = \(\frac{2}{cs60}\) = 2 x \(\frac{2}{1}\) = 4cm
Source: Myschool Past Questions Archive (Record #26348)
Mathematics
WAEC / WASSCE 1998
Geometry and Trigonometry
Diagram
Solution
In the diagram, PQ||SR. Find the value of Z
Attached Figure / Diagram
A
30o
B
40o
C
45o
D
90o
E
120o
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
In the diagram above:
x = x\(_1\) alternate angles
y = y\(_1\) same reason
(x\(_1\) + y\(_1\)) + x + y = 180º
(x + y) + x + y = 2 x 90º
2(x + y) = 2 x 90º
⇒ x + y = 90º
but Z = (x\(_1\) + y\(_1\)) = 90º
Source: Myschool Past Questions Archive (Record #26349)
Mathematics
WAEC / WASSCE 1998
Geometry and Trigonometry
Solution
In \(sin(X+30)^o=cos40^o\),find X
A
10o
B
20o
C
50o
D
60o
E
90o
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Using Sin \theta = Cos(90 - \theta)
Given that Sin(x - 30)º = Cos 40º
Cos 40º = Cos(90 - (x + 30º)
Cos cancels out Cos
40º = 90º - 30º - x
40º = 60º - x
40º - 60º = - x
-20º = - x
Therefore, x = 20º
Source: Myschool Past Questions Archive (Record #26350)
Mathematics
WAEC / WASSCE 1998
Geometry and Trigonometry
Find the value of X if \(cos x = \frac{5}{8}\) for \(0^o\le X\le 180^o\)
A
141.3o
B
128.7o
C
51.3o
D
48.7o
E
38.7o
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 #26351)
Mathematics
WAEC / WASSCE 1998
Geometry and Trigonometry
A chord of circle of radius 26cm is 10cm from the center of the circle. calculate the length of the chord
A
16cm
B
27.86cm
C
32cm
D
48cm
E
55.72cm
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 #26353)
Mathematics
WAEC / WASSCE 1998
Geometry and Trigonometry
Two chords PQ and RS of a circle intersected at right angles at a point inside the circle. If ∠QPR = 35o,find ∠PQS
A
35o
B
45o
C
55o
D
70o
E
90o
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 #26354)
Mathematics
WAEC / WASSCE 1998
Geometry and Trigonometry
Diagram
In the diagram, O is the center of the circle and the reflex angle ROS is 264o. Find ∠RTS
Attached Figure / Diagram
A
48o
B
53o
C
66o
D
132o
E
192o
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 #26355)
Mathematics
WAEC / WASSCE 1998
Geometry and Trigonometry
If the exterior angles of quadrilateral are yo, (y + 5)o, (y + 10)o and (y + 25)o, find y
A
10o
B
20o
C
40o
D
60o
E
80o
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 #26356)