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Mathematics
UTME / JAMB 2020
Number and Numeration
Solution
A number is selected at random between 20 and 30, both numbers inclusive. Find the probability that the number is a prime.
A
\(\frac{2}{11}\)
B
\(\frac{5}{11}\)
C
\(\frac{6}{11}\)
D
\(\frac{8}{11}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Possible outcomes are 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30. Prime numbers have only two factors, itself and 1. The prime numbers among the group are 23, 29.
The probability of choosing a prime number
= \(\frac{\text{Number of Prime}}{\text{No. of Total Possible Outcome}}\)
= \(\frac{2}{11}\)
Source: Myschool Past Questions Archive (Record #56827)
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
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
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
WAEC / WASSCE 2020
Number and Numeration
Solution
If X = {x : x < 7} and Y = {y:y is a factor of 24} are subsets of \(\mu\) = {1, 2, 3...10} find X \(\cap\) Y.
A
{2, 3, 4, 6}
B
{1, 2, 3, 4, 6}
C
{2, 3, 4, 6, 8}
D
{1, 2, 3, 4, 6, 8}
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(\mu\) = {1, 2, 3, 4..., 10}
X = {1, 2, 3, 4, 5, 6}
Y = {1, 2, 3, 4, 6, 8}
Therefore;
X \(\cap\) Y = {1, 2, 3, 4, 6}
Source: Myschool Past Questions Archive (Record #58215)
Mathematics
WAEC / WASSCE 2020
Number and Numeration
Solution
Simplify; [(\(\frac{16}{9}\))\(^{\frac{-3}{2}}\) x 16\(^{\frac{-3}{4}}\)]\(^{\frac{1}{3}}\)
A
\(\frac{3}{4}\)
B
\(\frac{9}{16}\)
C
\(\frac{3}{8}\)
D
\(\frac{1}{4}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
[(\(\frac{16}{9}\))\(^{\frac{-3}{2}}\) x 16\(^{\frac{-3}{4}}\)]\(^{\frac{1}{3}}\)
= [(\(\frac{9}{16}\))]\(^{\frac{3}{2}}\) x [(\(\frac{1}{16}\))\(^{\frac{3}{4}}\)]\(^{\frac{1}{3}}\)
= [(\(\sqrt{\frac{9}{16}}\))\(^3\) x (4\(\sqrt{\frac{1}{16}})^3\)]\(^{\frac{1}{3}}\)
= [(\(\frac{3}{4})^3 \times (\frac{1}{2})^3\)]\(^\frac{1}{3}\)
(\(\frac{27}{64} \times \frac{1}{8}\))\(^\frac{1}{3}\) = \({3}\sqrt{\frac{27}{64} \times \frac{1}{8}}\)
= \(\frac{3}{4} \times \frac{1}{2}\) = \(\frac{3}{8}\)
Source: Myschool Past Questions Archive (Record #58218)
Mathematics
WAEC / WASSCE 2020
Number and Numeration
Solution
Express 1 + 2 log10\(^3\) in the form log10\(^9\)
A
log10\(^{90}\)
B
log10\(^{19}\)
C
log10\(^{9}\)
D
log10\(^{6}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
1 + 2log\(_{10}^3\)
= log\(_{10}^{10} + log_{10}^{3^2}\)
= log\(_{10}^{10} + log_{10}^{9}\)
= log\(_{10}^{10 \times 90}\) = log\(_{10}^{90}\)
Source: Myschool Past Questions Archive (Record #58223)
Mathematics
WAEC / WASSCE 2020
Number and Numeration
Solution
If 101\(_{\text{two}}\) + 12\(_y\) = 23\(_{\text{five}}\). Find the value of y
A
8
B
7
C
6
D
5
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
012 + 01 = 01
101\(_2\) + 12\(_y\) = 23\(_5\)
1 x 2\(^o\) + 0 x 2\(^o\) + 1 x2\(^2\) + 1 x y\(^o\) + 2 x y\(^1\) = 3 x 5\(^o\) + 3 x 5\(^1\)
1 + 4 + 1 + 2y = 3 + 15
6 + 2y = 18
2y = 18 - 6
\(\frac{2y}{2} = \frac{12}{2}\)
y = 6
Source: Myschool Past Questions Archive (Record #58247)
Mathematics
WAEC / WASSCE 2020
Number and Numeration
Solution
An amount of N550,000.00 was realized when a principal, x was saved at 2% simple interest for 5 years. Find the value of x
A
N470,000.00
B
N480,000.00
C
N490,000.00
D
N500,000.00
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
S.I = \(\frac{x \times 2 \times 5}{100}\) = 0.1x
A = P + S.I
550,000 = x + 0.1x
\(\frac{550,000}{1.1} = \frac{1.1x}{1.1}\)
x = N500,000
Source: Myschool Past Questions Archive (Record #58249)