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Mathematics
NECO SSCE 2004
Geometry and Trigonometry
Solution
A man is 40m from the foot of a cliff of height 23m. Calculate the angle of elevation of the top of the cliff from the man
A
50° 54′
B
35° 06′
C
30° 00′
D
290 90′
E
29° 54′
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
From the diagram above,
Tan \(\alpha\) = \(\frac{\text{opp}}{\text{Adj}}\)
Tan \(\alpha\) = \(\frac{23}{40}\) = 0.575
\(\alpha\) = Tan\(^{-1}\) 0.575 ≈ 29.899
In degrees per minute = 29 + 0.89 x 60 = 29^\circ 54¹
Source: WAEC / JAMB / NECO Classroom Archive (Record #42332)
Mathematics
UTME / JAMB 2004
Geometry and Trigonometry
Solution
The shadow of a pole 5√3m high is 5m. Find the angle of elevation of the sun.
A
45o
B
75o
C
30o
D
60o
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Tan θ = 5√3/5
Tan θ = √3
θ = 60o
Source: Myschool Past Questions Archive (Record #11100)
Mathematics
UTME / JAMB 2004
Geometry and Trigonometry
Solution
PQRSTV is a regular polygon of side 7 cm inscribed in a circle. Find the circumference of the circle PQRSTV.
A
56 cm
B
22 cm
C
42 cm
D
44 cm
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Each interior Angle of the polygon = (n-2)180_n
= (6-2)180_6
= 4 x 30
= 120o
i.e ∠PQR = 120o ∴ RQD = 120/2 = 60o also
∴ Δ QOR is equilateral Δ ∴ QO = 7cm
∴ PO = QO = RO ...... = 7cm radius of the circumference of the circle = 2πr
= 2 x 22/7 x 7/1
= 44 cm
Source: Myschool Past Questions Archive (Record #11111)
Mathematics
WAEC / WASSCE 2004
Geometry and Trigonometry
Solution
Given that sin (5x - 28)o = cos (3x - 50)o,0 o, find the value of x
A
14o
B
21o
C
32o
D
39o
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Sin (5x – 28)o = cos (3x - 50)o
Since by the trigonometry relation
Sin(5x – 28)o = cos[90 – (5x – 28)]o
Hence cos(3x – 50)o = cos[90 – (5x – 28)]o
3x – 50 = 90 - (5x-28)
3x – 50 = 90 – 5x + 28
3x + 5x = 90 + 28 + 50
8x = 168
\(x = \frac{168}{8}=21^{\circ}\)
Source: Myschool Past Questions Archive (Record #26619)
Mathematics
WAEC / WASSCE 2004
Geometry and Trigonometry
Solution
The angle of elevation of the top of a tower from a point on the ground which is 36m away from the foot of the tower is 30o. Calculate the height of the tower.
A
62.35m
B
20.78m
C
18.00m
D
10.39m
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Where H is the height of the tower H = ?
\(Tan 30^{\circ} = \frac{H}{36} \Rightarrow H = 36 \times tan30^{\circ}\\
H = 36 \times 0.5774 = 20.79\)
Source: Myschool Past Questions Archive (Record #26626)
Mathematics
WAEC / WASSCE 2004
Geometry and Trigonometry
Diagram
Solution
In the diagram, POQ is the diameter of the circle centre O. Calculate ∠QRS
Attached Figure / Diagram
A
35o
B
70o
C
100o
D
125o
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
∠PSQ = 90^\circ (angle in a semi-circle)
(when SR is joined to SP)
∠SPQ = 180 – (90+35) = 180 – 125 = 55^\circ
∠QRS + ∠SPQ = 180^\circ (opposite angles in a cyclic quad is supplementary)
∠QRS = 180^\circ - 55^\circ
= 125^\circ
Source: Myschool Past Questions Archive (Record #26629)
Mathematics
WAEC / WASSCE 2004
Geometry and Trigonometry
Solution
Each interior angle of a regular polygon is 108^\circ. How many sides has it?
A
5
B
7
C
9
D
14
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
The exterior angle of the polygon = 180 – 108 = 72^\circ. The sum of exterior angle of the regular polygon = 360^\circ
The number of sides \(=\frac{360}{72}=5\)
Source: Myschool Past Questions Archive (Record #26637)
Mathematics
WAEC / WASSCE 2004
Geometry and Trigonometry
Solution
A point X is on the bearing 342o from a point Y. What is the bearing of Y from X?
A
342o
B
252o
C
198o
D
162o
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
If x is the bearing 342ofrom a point y
= 360o - 342o = 18o;
The bearing of y from x = 180o - 18o = 162o
Source: Myschool Past Questions Archive (Record #26647)
Mathematics
WAEC / WASSCE 2004
Geometry and Trigonometry
Diagram
Solution
In the diagram, PQRW is a circle. Line PW and QR are produced to meet at M, where ∠WMR = 30o and |WM| = |MR| Find the value of x
Attached Figure / Diagram
A
10o
B
25o
C
35o
D
60o
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
MPQ = PQM = 3x; ∆MPQ
MPQ + PQM + PMQ = 180o; 3x + 3x + 30o = 180o
6x \times 30o = 180o; 6x + 180o - 30o; 6x + 150o
\(x = \frac{150}{6} = 25^{\circ}\)
Source: Myschool Past Questions Archive (Record #26651)
Mathematics
WAEC / WASSCE 2004
Geometry and Trigonometry
Solution
A boy walks 800m in 20 minutes. Calculate his average speed in km per hour
A
2.4
B
4
C
16
D
24
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(Average \hspace{1mm}speed = \frac{Distance}{Time\hspace{1mm} taken}\)
Distance = 800m = \(\frac{800}{1000}\)km = 0.8km
Time\(\hspace{1mm}taken = 20\hspace{1mm}minutes = \frac{20}{60}\)hr
= \(\frac{1}{3}hr\\Average \hspace{1mm} speed = \left(0.8\div \frac{1}{3}\right)\)km/hr
= (0.8\(\times\)3)km/hr =2.4km/hr
Source: Myschool Past Questions Archive (Record #26656)
Mathematics
WAEC / WASSCE 2004
Geometry and Trigonometry
Diagram
Solution
The diagram is a circle centre O. Find the value of x
Attached Figure / Diagram
A
30o
B
50o
C
61o
D
78o
E
65.5\(^{\circ}\)
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
∠PQR (Reflex) = 360^\circ – 68^\circ = 292^\circ
∠PQR = 2∠PQR
292^\circ = 4x + 30^\circ
4x = 292 – 30 = 262
\(x = \frac{262}{4}=65.5^\circ\)
Source: Myschool Past Questions Archive (Record #26658)
Mathematics
WAEC / WASSCE 2004
Geometry and Trigonometry
The locus of a point which moves in a plane such that it is equidistant from two fixed points X and Y is
A
the perpendicular bisector of the line segment X Y
B
a line parallel to the line segment XY
C
a circle with XY as diameter
D
the line perpendicular to the line segment XY
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 #26662)
Mathematics
WAEC / WASSCE 2004
Geometry and Trigonometry
Which of the following is/are true? In a plane, the locus of points I. Equidistant from a straight line is a circle radius d where d is the distance between the point and the straight line.
II Equidistant from two given points P and Q is a circle of radius |PQ|. III Equidistant from two points is the perpendicular bisector of the line joining the two points.
A
I only
B
II only
C
III only
D
I, II and III
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 #26664)
Mathematics
WAEC / WASSCE 2004
Geometry and Trigonometry
Solution
A point on the ground is 5m away from the foot of a vertical wall 7 m high, Calculate, correct to the nearest degree, the angle of depression of the point from the top of the wall
A
36o
B
44o
C
46o
D
54o
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
θ= angle of depression of the point from the top of the wall
\(tan\theta = \frac{7}{5}=1.4; \theta = tan^{-1}(1.400)\
\theta = 54.4^{\circ}; \theta = 54^{\circ}\) to the nearest degree
Source: Myschool Past Questions Archive (Record #26669)
Mathematics
NECO SSCE 2004
Geometry and Trigonometry
Solution
Two angles of a triangle are 45º each and its longest side is 12cm. Find the length of one of the other sides
A
12cm
B
9\(\sqrt{2}\)cm
C
6\(\sqrt{2}\)cm
D
6cm
E
3\(\sqrt{2}\)cm
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Two angles of a triangle are 45º each and its longest side is 12cm, this simply describes an isosceles triangle
two equal angles and two equal sides
using Pythagoras theorem,
\(x^2 + x^2 = 12^2\)
\(2x^2\) = 144
\(x^2\) = 72( after dividing b/sides by 2)
x = \(\sqrt{72} = 6\sqrt{2}\)cm.
Source: Myschool Past Questions Archive (Record #42248)