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Mathematics
UTME / JAMB 2020
Geometry and Trigonometry
Solution
The sum of the interior angle of pentagon is 6x + 6y. Find y in terms of x.
A
y = 6 - x
B
y = 90 - x
C
y = 120 - x
D
y = 150 - x
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Sum of interior angles = (2n - 4) 90\(^o\)
For perntagon, n = 5
Sum of interior angles = 6 x 90\(^o\) = 540\(^o\)
6x + 6y = 540\(^o\)
6(x + y) = 540\(^o\)
x + y = \(\frac{540^o}{6}\) = 90\(^o\)
y = 90\(^o\)
y = 90 - x
Source: Myschool Past Questions Archive (Record #56861)
Mathematics
UTME / JAMB 2020
Geometry and Trigonometry
Solution
A surveyor walks 500m up a hill which slopes at an angle of 30\(^o\). Calculate the vertical height through which he rises
A
252m
B
500m
C
250m
D
255m
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\frac{h}{500}\) = sin 30\(^o\)
= 500 sin 30\(^o\)
= 500 x \(\frac{1}{2}\)
= 250m
Source: Myschool Past Questions Archive (Record #56863)
Mathematics
WAEC / WASSCE 2020
Geometry and Trigonometry
Solution
Solve 3x - 2y = 10 and x + 3y = 7 simultaneously
A
x = -4 and y = 1
B
x = -1 and y = -4
C
x = 1 and y = 4
D
x = 4 and y = 1
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
3x - 2y = 10 - - x 3
x + 3y = 7 ---x 2
------------------------
9x - 6y = 30
2x + 6y = 14
-------------------------
\(\frac{11x}{11} \frac{44}{11}\)
x = 4
From x + 3y = 7
3y = 7 - 4
\(\frac{3y}{3}\) = \(\frac{3}{3}\)
y = 1
Source: Myschool Past Questions Archive (Record #58273)
Mathematics
WAEC / WASSCE 2020
Geometry and Trigonometry
Solution
In the diagram, XYZ is an equilateral triangle of side 6cm and Y is the midpoint of \(\overline{XY}\). Find tan (< XZT)
A
\(\frac{1}{\sqrt{3}}\)
B
\(\frac{\sqrt{3}}{2}\)
C
\(\sqrt{3}\)
D
\(\frac{1}{2}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
ZT = \(\sqrt{6^2 - 3^2}\)
ZT = \(\sqrt{27}\) = \(3\sqrt{3}\)
tan (< XZT) = \(\frac{3}{3\sqrt{3}}\)
= - \(\frac{1}{\sqrt{3}}\)
Source: Myschool Past Questions Archive (Record #58311)
Mathematics
WAEC / WASSCE 2020
Geometry and Trigonometry
Solution
A fence 2.4 m tall, is 10m away from a tree of height 16m. Calculate the angle of elevation of the top of the tree from the top of the fence.
A
76.11\(^o\)
B
53.67\(^o\)
C
52.40\(^o\)
D
51.32\(^o\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Tan \(\theta\) = \(\frac{13.6}{10}\)
= tan\(^{-1}\)(1.36)
\(\theta\) = 53.67\(^o\)
Source: Myschool Past Questions Archive (Record #58312)
Mathematics
WAEC / WASSCE 2020
Geometry and Trigonometry
If tan y is positive and sin y is negative, in which quadrant would y lie?
A
First and third only
B
First and second only
C
Third only
D
Second only
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 #58315)
Mathematics
WAEC / WASSCE 2020
Geometry and Trigonometry
Solution
Each interior angle of a regular polygon is 168\(^o\). Find the number of sides of the polygon
A
30
B
36
C
24
D
18
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Exterior angle = 180\(^o\) - 168\(^o\)
Number of sides = \(\frac{360^o}{12}\)
= 30\(^o\)
Source: Myschool Past Questions Archive (Record #58317)
Mathematics
WAEC / WASSCE 2020
Geometry and Trigonometry
Solution
The length of an arc of a circle of radius 3.5 cm is 1\(\frac{19}{36}\) cm. Calculate, correct to the nearest degree , the angle substended by the centre of the circle. [Take \(\pi = \frac{22}{7}\)]
A
55\(^o\)
B
36\(^o\)
C
25\(^o\)
D
22\(^o\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
L = \(\frac{\theta}{360^o}\) = 2\(\pi\)
\(\frac{55}{36} = \frac{\theta}{360^o} \times 2 \times \frac{22}{7} \times 3.5\)
\(\theta = \frac{360 \times 55 \times 44 \times 0.5}{3 \times 44 \times 0.5}\)
= \(\theta = 25^o\)
Source: Myschool Past Questions Archive (Record #58330)
Mathematics
WAEC / WASSCE 2020
Geometry and Trigonometry
Diagram
Solution
The pie chart shows the population of men, women, and children in a city. If the population of the city is 1,800,000, how many men are in the city?
Attached Figure / Diagram
A
845,000
B
600,000
C
355,000
D
250,000
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Angle of Men = 360\(^o\) - (120 + 169)
= 360\(^o\) - 289\(^o\) = 71\(^o\)
No. of men \(\frac{71}{360}\) x 1800,000
= 355,000
Source: Myschool Past Questions Archive (Record #58335)
Mathematics
WAEC / WASSCE 2020
Geometry and Trigonometry
Solution
The mean of the numbers 15, 21, 17, 26, 18, and 29 is 21. Calculate the standard deviation
A
9
B
6
C
5
D
0
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
x
x - \(\overline{x}\))\(^2\)
(x - \(\overline{x}\))\(^2\)
15
21
17
26
18
29
-6
0
-4
5
-3
-8
36
0
16
25
9
64
\(\sum (x - \overline{x})^2\) = 150
Standard deviation = \(\sqrt{\frac{ \sum (x - \overline{x})^2}{n} }\)
= \(\frac{150}{6}\)
= \(\sqrt{25}\)
= 5
Source: Myschool Past Questions Archive (Record #58337)
Mathematics
WAEC / WASSCE 2020
Geometry and Trigonometry
Solution
Find the sum of the interior angle of a pentagon.
A
340\(^o\)
B
350\(^o\)
C
540\(^o\)
D
550\(^o\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Sum = (5 - ) 180\(^o\)
= (5 - 2) 180\(^o\) = 3 x 180\(^o\)
= 540\(^o\)
Source: Myschool Past Questions Archive (Record #58344)
Mathematics
WAEC / WASSCE 2020
Geometry and Trigonometry
Solution
x
6.20
6.85
7.50
y
3.90
5.20
6.50
The points on a linear graph are as shown in the table. Find the gradient (slope) of the line.
A
2\(\frac{1}{2}\)
B
2
C
1
D
\(\frac{1}{2}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Gradient = \(\frac{y_2 - y_ 1}{x_2 - x_1}\)
= \(\frac{5.20 - 3.90}{6.85 - 6.20}\)
= \(\frac{1.3}{0.5}\)
= 2
Source: Myschool Past Questions Archive (Record #58365)
Mathematics
WAEC / WASSCE 2020
Geometry and Trigonometry
Which of the following is not a sufficient condition for two triangles to be congruent?
A
AAS
B
SSS
C
SAS
D
SSA
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 #58381)
Mathematics
WAEC / WASSCE 2020
Geometry and Trigonometry
Diagram
Solution
In the diagram, O is the centre of the circle. If < NLM = 74\(^o\), < LMN = 39\(^o\) and < LOM = x, find the value of x.
Attached Figure / Diagram
A
134\(^o\)
B
126\(^o\)
C
113\(^o\)
D
106\(^o\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
L\(N\)M = 180\(^o\) - (74\(^o\) + 39\(^o\))
180\(^o\) - 113\(^o\)
= 67\(^o\)
L\(^O\)
M = x = 2 x 67\(^o\)
= 134\(^o\)
Source: Myschool Past Questions Archive (Record #58465)
Mathematics
WAEC / WASSCE 2020
Geometry and Trigonometry
Diagram
Solution
(a} In the diagram, O is the centre of the circle ABCDE, = I\(\overline{BC}\)I = |\(\overline{CD}\)| and < BCD = 108^\circ. Find < CDE.
(b) Given that tan x = \(\sqrt{3}\), 0\(^o\) \(\geq\) x \(\geq\) 90\(^o\), evaluate
\(\frac{(cos x)^2 - sin x}{(sin x)^2 + cos x}\)
Attached Figure / Diagram
medium Difficulty
Verified Correct Answer: Option
Step-by-Step Mathematical Solution
(a)
C\(B\)D = C\(D\)B = \(\frac{180^o - 108^o}{2}\)
= \(\frac{72^o}{2}\) = 36\(^o\)
< CDE = < BDE + 36\(^o\)
< CDE = 90\(^o\) + 36 = 126\(^o\)
(b) tan x = \(\sqrt{3}\)
y\(^2\) (\(\sqrt{3}\))\(^2\) - (l)\(^2\)
y\(^2\) 3 + 1, Cos x = \(\frac{1}{2}\)
y = \(\sqrt{4}\) = 2
sin x = \(\frac{\sqrt{3}}{2}\)
\(\frac{(cos x)^2 - sin x}{(sin x)^2 + cos x}\)
= \(\frac{(\frac{1}{2})^2 - \frac{\sqrt{3}}{2}} {(\frac{\sqrt{3}}{2})^2 + \frac{1}{2}}\)
= \(\frac{\frac{1}{4} - \frac{\sqrt{3}}{2}}{\frac{3}{4} + \frac{1}{2}}\)
= \(\frac{1 - 2\sqrt{3}}{4}\) \(\div\) \(\frac{5}{4}\)
= \(\frac{1 - 2 \sqrt{3}}{4}\) x \(\frac{4}{5}\)
= \(\frac{1 - 2\sqrt{3}}{5}\)
Source: Myschool Past Questions Archive (Record #58708)