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Mathematics
UTME / JAMB 2020
Algebra
Diagram
Solution
The equation of the line in the graph is
Attached Figure / Diagram
A
3y = 3x + 12
B
3y = 3x + 12
C
3y = -4x + 12
D
3y = -4x + 9
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Gradient of line = \(\frac{\text{Change in y}}{\text{Change in x}}\) = \(\frac{y_2 - Y}{x_2 - x}\)
y\(_2\) = 0\(_1\)
Y\(_1\) = 4
x\(_2\) = 3 and x\(_1\) = 0
\(\frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 4}{3 - 0} = \frac{-4}{3}\)
Equation of straight line y = mx + c
Where m = gradient and c = y
intercept = 4
y = -\(\frac{4}{3}\)x + 4 multiply through by 3
3y = -4x + 12
Source: Myschool Past Questions Archive (Record #56829)
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
Number and Numeration
Solution
Find the simple interest rate percent annum at which N1000 accumulates to N1240 in 3 years.
A
6%
B
8%
C
10%
D
12%
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
I = \(\frac{PRT}{100}\) = 1 = 1240 - 1000 = 240
R = \(\frac{240 \times 100}{100 \times 3}\) = 8%
Source: Myschool Past Questions Archive (Record #56834)
Mathematics
UTME / JAMB 2020
Number and Numeration
Diagram
Solution
The pie chart shows the income of a civil servant in month. If his monthly income is N6,000. Find his monthly basic salary.
Attached Figure / Diagram
A
N2,050
B
N2600
C
N3,100
D
N3,450
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
360\(^o\) - (60\(^o\) + 60\(^o\) + 67 + 50 = 237\(^o\))
360\(^o\) - 237 = 123\(^o\)
B. Salary = \(\frac{123}{360} X \frac{N6000}{1}\)
= N2,050
Source: Myschool Past Questions Archive (Record #56836)
Mathematics
UTME / JAMB 2020
Number and Numeration
Solution
If x is positive real number, find the range of values for which \(\frac{1}{3x}\) + \(\frac{1}{2}\) > \(\frac{1}{4x}\)
A
x > -\(\frac{1}{6}\)
B
x > 0
C
0 < x < 6
D
0 < x <\(\frac{1}{6}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(\frac{1}{3x}\) + \(\frac{1}{2}\)x = \(\frac{2 + 3x}{6x}\) > \(\frac{1}{4x}\)
= 4(2 + 3x) > 6x = 12x\(^2\) - 2x = 0
= 2x(6x - 1) > 0 = x(6x - 1) > 0
Case 1 (-, -) = x < 0, 6x - 1 > 0
= x < 0, x < \(\frac{1}{6}\) (solution)
Case 2 (+, +) = x > 0, 6x - 1 > 0 = x > 0
x > \(\frac{1}{6}\)
Combining solutions in cases (1) and (2)
= x > 0, x < \(\frac{1}{6}\) = 0 < x < \(\frac{1}{6}\)
Source: Myschool Past Questions Archive (Record #56838)
Mathematics
UTME / JAMB 2020
Number and Numeration
Solution
Find the value of x if \(\frac{\sqrt{2}}{x + \sqrt{2}}\) = \(\frac{1}{x - \sqrt{2}}\)
A
3\(\sqrt{2}\) + 4
B
3\(\sqrt{2}\) - 4
C
3 - 2\(\sqrt{2}\)
D
4 + 2\(\sqrt{2}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(\frac{\sqrt{2}}{x + 2}\) = x - \(\frac{1}{\sqrt{2}}\)
x\(\sqrt{2}\) (x - \(\sqrt{2}\)) = x + \(\sqrt{2}\) (cross multiply)
x\(\sqrt{2}\) - 2 = x + \(\sqrt{2}\)
= x\(\sqrt{2}\) - x
= 2 + \(\sqrt{2}\)
x (\(\sqrt{2}\) - 1) = 2 + \(\sqrt{2}\)
= \(\frac{2 + \sqrt{2}}{\sqrt{2} - 1} \times \frac{\sqrt{2} + 1}{\sqrt{2} + 1}\)
x = \(\frac{2 \sqrt{2} + 2 + 2 + \sqrt{2}}{2 - 1}\)
= 3\(\sqrt{2}\) + 4
Source: Myschool Past Questions Archive (Record #56842)
Mathematics
UTME / JAMB 2020
Number and Numeration
Solution
A binary operation x is defined by a x b = a\(^b\). If a x 2 = 2 - a, find the possible values of a?
A
1, -2
B
2, -1
C
2, -2
D
1, -1
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
a = b = a\(^2\)
a + 2 = a\(^2\).....(i)
a + 2 = 2 - a..............(ii)
a\(^2\) = 2 - a
a\(^2\)+ a - 2 = a\(^2\) + a - 2 = 0
= (a + 2)(a - 1) = 0
a = 1 or - 2
Source: Myschool Past Questions Archive (Record #56847)
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
Number and Numeration
Solution
A sector of circle of radius 7.2cm which substends an angle of 300\(^o\) at the centre is used to form a cone. What s the radius of the base of the cone?
A
8cm
B
9cm
C
6cm
D
7cm
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
r = radius of the cone's base, R = radius of the circle
r = \(\frac{R \theta}{360}\) = \(\frac{7.2 \times 300}{360}\) = 6cm
Source: Myschool Past Questions Archive (Record #56849)
Mathematics
UTME / JAMB 2020
Number and Numeration
Solution
A cylindrical tank has a capacity of 3080m\(^3\). What is the depth of the tank if the diameter of its base is 14m?
A
25m
B
23m
C
22m
D
20m
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
V = 2080cm\(^3\), h = ?
r = 7cm
V = V\(\pi r^2h\)
h = \(\frac{V}{\pi r^2} = \frac{3080}{\frac{22}{7} \times 49}\)
\(\frac{3080}{54}\) = 20cm
Source: Myschool Past Questions Archive (Record #56857)
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)
Mathematics
UTME / JAMB 2020
Number and Numeration
Solution
Three consecutive terms of a geometric progression are give as n - 2, n and n + 3. Find the common ratio
A
\(\frac{3}{2}\)
B
\(\frac{2}{3}\)
C
\(\frac{1}{2}\)
D
\(\frac{1}{4}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(\frac{h}{n - 2} = \frac{n + 3}{n}\)
n\(^2\) = (n + 3) (n - 2)
n\(^2\) = n\(^2\) + n - 6
n\(^2\) + n - 6 - n\(^2\) = 0
n - 6 = 0
n = 6
Common ratio: \(\frac{n}{n - 2} = \frac{6}{6 - 2} = \frac{6}{4}\) = \(\frac{3}{2}\)
Source: Myschool Past Questions Archive (Record #56859)
Mathematics
UTME / JAMB 2020
Number and Numeration
Solution
In a class of 40 students, 32 offer mathematics, 24 offer physics and 4 offer neither mathematics nor physics. How many offer both mathematics and physics?
A
4
B
8
C
16
D
20
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
40 = 32 - x + x + 24 + 4
40 = 60 - x
x = 60 - 40
x = 20
Source: Myschool Past Questions Archive (Record #56860)
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)