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Mathematics
WAEC / WASSCE 2020
Geometry and Trigonometry
Diagram
Solution
In the diagram, \(\overline{MN}\)//\(\overline{PQ}\), < MNP = 2x, and < NPQ = (3x - 50)°. Find the value of < NPQ
Attached Figure / Diagram
A
200\(^o\)
B
100\(^o\)
C
120\(^o\)
D
90\(^o\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
2x = 3x - 50 alternate angle
50\(^o\) = 3x - 2x
50\(^o\) = x
< NPQ = (3x - 50)\(^o\)
= 3(50)\(^o\) - 50
= 150 - 50 = 100\(^o\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #58325)
Mathematics
WAEC / WASSCE 2020
Geometry and Trigonometry
Diagram
Solution
In the diagram, PQR is a circle with center O. If ∠OPQ = 48°, find the value of M.
Attached Figure / Diagram
A
96\(^o\)
B
90\(^o\)
C
68\(^o\)
D
42\(^o\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
< O\(Q\)P = 48\(^o\) (base angles of isoceles \(\triangle\))
m = 48\(^o\) + 48\(^o\) = 96\(^o\) (exterior angle of a \(\triangle\))
Source: WAEC / JAMB / NECO Classroom Archive (Record #58333)
Mathematics
WAEC / WASSCE 2020
Geometry and Trigonometry
Diagram
Solution
In the diagram, PQ is a straight line. If m = \(\frac{1}{2}\) (x + y + z), find value of m.
Attached Figure / Diagram
A
45\(^o\)
B
60\(^o\)
C
90\(^o\)
D
100\(^o\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
x + y + m + z = 180º
but m = \(\frac{1}{2}\)(x + y + z)
2m = ( x + y + z )
Thus ( x + y + z) + m = 180º
(2m) + m = 180º
3m = 180º
m = \(\frac{180º}{3}\) = 60º
Source: WAEC / JAMB / NECO Classroom Archive (Record #58361)
Mathematics
WAEC / WASSCE 2020
Geometry and Trigonometry
Diagram
Solution
In the diagram, O is the center of the circle. \(\overline{PQ}\) and \(\overline{RS}\) are tangents to the circle. Find the value of (M + N).
Attached Figure / Diagram
A
120\(^o\)
B
90\(^o\)
C
75\(^o\)
D
60\(^o\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
m + n + 90\(^o\) + 180\(^o\) (sum of angle in a \(\triangle\))
m + n = 180\(^o\) - 90\(^o\)
m + n =90\(^o\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #58373)
Mathematics
UTME / JAMB 2020
Geometry and Trigonometry
Solution
What is the circumference of latitude 0\(^o\)S if R is the radius of the earth?
A
cos \(\theta\)
B
2\(\pi\)R cos \(\theta\)
C
R sin \(\theta\)
D
2 \(\pi\) r sin \(\theta\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Circumstances of latitude 0\(^o\)s where R is the radius of the earth 2\(\pi\)r cos \(\theta\)
Source: Myschool Past Questions Archive (Record #56750)
Mathematics
UTME / JAMB 2020
Geometry and Trigonometry
Solution
A room is 12m long, 9m wide and 8m high. Find the cosine of the angle which a diagonal of the room makes with the floor of the room
A
\(\frac{15}{17}\)
B
\(\frac{8}{17}\)
C
\(\frac{8}{15}\)
D
\(\frac{12}{17}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
ABCD is the floor. By pathagoras
AC\(^2\) = 144 + 81 = \(\sqrt{225}\)
AC = 15cm
Height of room 8m, diagonal of floor is 15m
Therefore, the cosine of the angle which a diagonal of the room makes with the floor is
EC\(^2\) = 15\(^2\) + 8\(^2\) cosine
\(\frac{adj}{Hyp} = \frac{15}{17}\)
EC\(^2\) = \(\sqrt{225 + 64}\)
EC = \(\sqrt{289}\)
= 17
Source: Myschool Past Questions Archive (Record #56751)
Mathematics
UTME / JAMB 2020
Geometry and Trigonometry
Solution
In a class of 150 students, the sector in a pie chart representing the students offering physics has angle 12\(^o\). How many students are offering physics?
A
18
B
15
C
10
D
5
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
No of students offering physics are
\(\frac{12}{360}\) x 150 = 5
Source: Myschool Past Questions Archive (Record #56758)
Mathematics
UTME / JAMB 2020
Geometry and Trigonometry
Solution
In preparing rice cutlets, a cook used 75g of rice, 40g of margarine, 105g of meat and 20g of bread crumbs. Find the angle of the sector which represent meat in a pie chart?
A
30\(^o\)
B
60\(^o\)
C
112.5\(^o\)
D
157.5\(^o\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Rice = 75g, Margarine = 40g, Meat = 105g
Bread = 20g
Total = 240
Angle of sector represented by meat
= \(\frac{105}{240} \times \frac{360^o}{1}\)
= 157.5
Source: Myschool Past Questions Archive (Record #56765)
Mathematics
UTME / JAMB 2020
Geometry and Trigonometry
Solution
The angle of a sector of a circle radius 10.5 cm is 48\(^o\). Calculate the perimeter of the sector.
A
25.8cm
B
25.4cm
C
25.6cm
D
29.8cm
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
The lenght of Arc AB = \(\frac{Q}{360}\) 2\(\pi\)r
= \(\frac{48}{360}\) x 2\(\frac{22}{7}\) x 10.5 = \(\frac{48}{360}\) x 2\(\frac{22}{7}\) x \(\frac{21}{2}\)
= \(\frac{4 \times 22 \times 3}{30} \times \frac{88}{10}\) = 8.8cm
Perimeter = 8.8 + 2r = 8.8 + 2r
= 8.8 + 2(10.5)
= 8.8 + 21
= 29.8cm
Source: Myschool Past Questions Archive (Record #56777)
Mathematics
UTME / JAMB 2020
Geometry and Trigonometry
Diagram
Solution
In this fiqure, PQ = PR = PS and SRT = 68\(^o\). Find QPS
Attached Figure / Diagram
A
136\(^o\)
B
124\(^o\)
C
112\(^o\)
D
68\(^o\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Since PQRS is quadrilateral
2y + 2x + QPS = 360\(^o\)
i.e. (y + x) + QPS = 360\(^o\)
QPS = 360\(^o\) - 2 (y + x)
But x + y + 68\(^o\) = 180\(^o\)
There; x + y = 180\(^o\) - 68\(^o\) = 112\(^o\)
QPS = 360 - 2(112\(^o\))
= 360\(^o\) - 224 = 136\(^o\)
Source: Myschool Past Questions Archive (Record #56799)
Mathematics
UTME / JAMB 2020
Geometry and Trigonometry
Solution
Calculate the standard deviation of the following data: 7, 8, 9, 10, 11, 12, 13
A
2
B
4
C
12
D
17
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
x
x - x
(x - x)\(^2\)
7
8
9
10
11
12
13
-3
-2
-1
0
1
2
3
9
4
1
1
0
4
9
--------------
28
S.D = \(\frac{\sqrt\sum (x - x)^2}{N} = \frac{\sum d^2}{N} = \frac{\sqrt{28}}{7}\)
= \(\sqrt{4}\)
= 2
Source: Myschool Past Questions Archive (Record #56826)
Mathematics
UTME / JAMB 2020
Geometry and Trigonometry
Solution
Express the product of 0.0014 and 0.011 in standard form
A
1.54 x 10\(^{-2}\)
B
1.54 x 10\(^{-3}\)
C
1.54 x 10\(^{-2}\)
D
1.54 x 10\(^{-5}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
0.0014 = 1.4 \times 10\(^{-3}\)
0.011 = 1.1 \times 10\(^{-2}\)
Product = (1.4 \times 1.1) \times 10\(^{-3}\) \times 10\(^{-2}\) = 1.54 \times 10\(^{-5}\)
Source: Myschool Past Questions Archive (Record #56830)
Mathematics
UTME / JAMB 2020
Geometry and Trigonometry
Solution
A school boy lying on the ground 30m away from the foot of a water tank towel observes that the angle of elevation of the top of the tank is 60\(^o\). Calculate the height of the tank.
A
60\(\sqrt{3m}\)
B
30\(\sqrt{3m}\)
C
20\(\sqrt{3m}\)
D
10\(\sqrt{3m}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
h = 30 tan 60
= 30\(\sqrt{3}\)
Source: Myschool Past Questions Archive (Record #56831)
Mathematics
UTME / JAMB 2020
Geometry and Trigonometry
Solution
The chord ST of a circle is equal to the radius r of the circle. Find the length of arc ST
A
\(\frac{\pi r}{3}\)
B
\(\frac{\pi r}{2}\)
C
\(\frac{\pi r}{12}\)
D
\(\frac{\pi r}{6}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(\frac{ \frac{r}{2}}{r}\) Sin \(\theta\) = \(\frac{1}{2}\)
\(\theta\) = sin\(^{-1}\) (\(\frac{1}{2}\)) = 30\(^o\) = 60\(^o\)
Length of arc (minor)
ST = \(\frac{\theta}{360}\) x 2\(\pi r\)
\(\frac{60}{360} \times 2 \pi \times r = \frac{\pi}{3}\)
Source: Myschool Past Questions Archive (Record #56848)
Mathematics
UTME / JAMB 2020
Geometry and Trigonometry
Solution
The acres for rice, pineapple, cassava, cocoa and palm oil in a certain district are given respectively as 2, 5, 3, 11 and 9. What is the angle of the sector of cassava in a pie chart?
A
180\(^o\)
B
36\(^o\)
C
60\(^o\)
D
108\(^o\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Total number of acres = 2 + 5 + 3 + 11 + 9 = 30
The angle of acres = 2 + 5 + 3 + 11 + 9 = 30
The angle of the sector for cassava in a pie chart = \(\frac{3}{30} \times 360^o = 36^o\)
Source: Myschool Past Questions Archive (Record #56858)