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Mathematics
UTME / JAMB 2020
Statistics and Probability
Solution
The mean age group of some students is 15years. When the age of a teacher, 45 years old, is added to the ages of the students, the mean of their ages become 18 years. Find the number of students in the group.
A
7
B
9
C
15
D
42
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
x \(\frac{\sum x}{N}\)
15 = \(\frac{\sum x }{N}\)
\(\sum x\) = 15N........(i)
y = \(\frac{\sum y}{Ny} = \frac{\sum x + 45}{N + 1}\)
\(\frac{18}{1} = \frac{15N + 45}{N + 1}\)
18(N + 1) = 15N + 45
18N + 18 = 15N + 45
18N - 15N = 45 - 18
3N = 27
N = \(\frac{27}{3}\)
= 9
Source: Myschool Past Questions Archive (Record #56862)
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
UTME / JAMB 2020
Algebra
Solution
Find the non-zero positive value of x which satisfies the equation
\(\begin{bmatrix} x & 1 & 0 \\ 1 & x & 1 \\ 0 & 1 & x \end{bmatrix}\) = 0
A
2
B
\(\sqrt{3}\)
C
\(\sqrt{2}\)
D
1
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\begin{bmatrix} x & 1 & 0 \\ 1 & x & 1 \\ 0 & 1 & x \end{bmatrix}\) = 0
To find the value of x, we will have to calculate for the determined of the given matrix and equate it to 0
x[x\(^2\) - 1] - 1[x - 0] + 0[0 - 1] = 0
x\(^3\) - x] - x + 0 = 0
x\(^3\) - x - x = 0
x\(^3\) - 2x = 0
x\(^3\) = 2x
x\(^2\) = 2
take the square root of both sides
x = \(\sqrt{2}\)
Source: Myschool Past Questions Archive (Record #56864)
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)
Mathematics
WAEC / WASSCE 2020
Number and Numeration
Solution
Given that \(\frac{\sqrt{3} + \sqrt{5}}{\sqrt{5}}\)
= x + y\(\sqrt{15}\), find the value of (x + y)
A
1\(\frac{3}{5}\)
B
1\(\frac{2}{5}\)
C
1\(\frac{1}{5}\)
D
\(\frac{1}{5}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\frac{\sqrt{3} + \sqrt{5}}{\sqrt{5}}\) = x + y\(\sqrt{15}\)
cross multiply to have: \(\sqrt{3}\) + \(\sqrt{5}\) = x\(\sqrt{5}\) + 5y\(\sqrt{3}\)
Collect like roots : x\(\sqrt{5}\) = \(\sqrt{5}\) → x = 1
5y\(\sqrt{3}\) = \(\sqrt{3}\) → y = \(\frac{1}{5}\)
∴ ( x + y ) = 1 + \(\frac{1}{5}\)
= 1\(\frac{1}{5}\)
Source: Myschool Past Questions Archive (Record #58254)
Mathematics
WAEC / WASSCE 2020
Number and Numeration
Solution
If x = 3 and y = -1, evaluate 2(x\(^2\) - y\(^3\))
A
24
B
22
C
20
D
16
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
2(\(x^2 - y^3\))
= 2(\(3^2 - (-1)^3\))
= 2(9 - (-1))
= 2 x 10 = 20
Source: Myschool Past Questions Archive (Record #58265)
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
Number and Numeration
Solution
The first term of a geometric progression (G.P) is 3 and the 5th term is 48. Find the common ratio.
A
2
B
4
C
8
D
16
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
T\(_5\) = ar\(^4\)
\(\frac{48}{3} = \frac{3r^4}{3}\)
16 = r\(^4\)
r = \(4\sqrt{16}\)
= 2
Source: Myschool Past Questions Archive (Record #58292)
Mathematics
WAEC / WASSCE 2020
Number and Numeration
Solution
Make m the subject of the relation k = \(\sqrt{\frac{m - y}{m + 1}}\)
A
m = \(\frac{y + k^2}{k^2 + 1}\)
B
m = \(\frac{y + k^2}{1 - k^2}\)
C
m = \(\frac{y - k^2}{k^2 + 1}\)
D
m = \(\frac{y - k^2}{1 - k^2}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
k = \(\sqrt{\frac{m - y}{m + 1}}\)
k\(^2\) = \(\frac{m - y}{m + 1}\)
k\(^2\)m + k\(^2\) = m - y
k\(^2\) + y = m - k\(^2\)m
\(\frac{k^2 + y}{1 - k^2}\) = m\(\frac{(1 - k^2)}{1 - k^2}\)
m = \(\frac{y + k^2}{1 - k^2}\)
Source: Myschool Past Questions Archive (Record #58298)
Mathematics
WAEC / WASSCE 2020
Algebra
Solution
Find the quadratic equation whose roots are \(\frac{1}{2}\) and -\(\frac{1}{3}\)
A
3x\(^2\) + x + 1 = 0
B
6x\(^2\) + x - 1 = 0
C
3x\(^2\) + x - 1 = 0
D
6x\(^2\) - x - 1 = 0
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
x = \(\frac{1}{2}\) and x = \(\frac{-1}{3}\)
(2x - 1) = 0 and (3x + 1) = 0
(2x - 1) (3x + 1) = 0
6x\(^2\) - x - 1 = 0
Source: Myschool Past Questions Archive (Record #58300)
Mathematics
WAEC / WASSCE 2020
Algebra
Solution
Given that x is directly proportional to y and inversely proportional to Z, x = 15 when y = 10 and Z = 4, find the equation connecting x, y and z
A
x = \(\frac{6y}{z}\)
B
x = \(\frac{12y}{z}\)
C
x = \(\frac{3y}{z}\)
D
x = \(\frac{3y}{2z}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(x\) x \(\frac{y}{z}\)
x = \(\frac{ky}{z}\)
15 = \(\frac{10k}{4}\)
\(\frac{60}{10}\) = k = 6
Therefore; x = \(\frac{6y}{z}\)
Source: Myschool Past Questions Archive (Record #58302)