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Mathematics
UTME / JAMB 2017
Number and Numeration
Solution
If \(\frac{2 \sqrt{3} - \sqrt{2}}{\sqrt{3} + 2 \sqrt{2}}\) = m + n √ 6,
find the values of m and n respectively
A
1, − 2
B
− 2, n = 1
C
\(\frac{-2}{5}\), 1
D
\(\frac{2}{3}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(\frac{2 \sqrt{3} - \sqrt{2}}{\sqrt{3} + 2 \sqrt{2}}\)= m + n√6
\(\frac{2 \sqrt{3} - \sqrt{2}}{\sqrt{3} + 2 \sqrt{2}}\) x \(\frac{\sqrt{3} - 2 \sqrt{2}}{\sqrt{3} - \sqrt{2}}\)
\(\frac{2 \sqrt{3} (\sqrt{3} - 2 \sqrt{2}) - \sqrt{2}(\sqrt{3} - 2 \sqrt{2})}{\sqrt{3}(\sqrt{3} - 2 \sqrt{2}) + 2 \sqrt{2}(\sqrt{3} - 2 \sqrt{2})}\)
\(\frac{2 \times 3 - 4\sqrt{6} - 6 + 2 \times 2}{3 - 2 \sqrt{6} + 2 \sqrt{6} - 4 \times 2}\)
= \(\frac{6 - 4 \sqrt{6} - \sqrt{6} + 4}{3 - 8}\)
= \(\frac{0 - 4 \sqrt{6} - 6}{5}\)
= \(\frac{10 - 5 \sqrt{6}}{5}\)
= − 2 + √6
∴ m + n\(\sqrt{6}\) = − 2 + √6
m = − 2, n = 1
Source: Myschool Past Questions Archive (Record #46364)
Mathematics
UTME / JAMB 2017
Algebra
Solution
If \alpha and \beta are the roots of the equation 3x2 + 5x - 2 = 0, find the value of 1/\alpha + 1/\beta
A
\(\frac{-5}{3}\)
B
\(\frac{-2}{3}\)
C
\(\frac{1}{2}\)
D
\(\frac{5}{2}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
1/\alpha + 1/\beta = \beta+\alpha/\alpha\beta
3x2 + 5x - 2 = 0
x2 + 5x/3 - 2/3 = 0
\alpha\beta = -2/3
\beta+\alpha = -5/3
Thus; \beta+\alpha/\alpha\beta = -2/3 -2/3 = -5/2
Source: Myschool Past Questions Archive (Record #46365)
Mathematics
UTME / JAMB 2017
Number and Numeration
Solution
Find the range of the following set of numbers 0.4, −0.4, 0.3, 0.47, −0.53, 0.2 and −0.2
A
1.03
B
0.07
C
0.03
D
1.0
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
0.4, −0.4, 0.3, 0.47, −0.53, 0.2, −0.2
Range is the difference between the highest and lowest value
i.e Highest − Lowest
− 0.53, −0.4, −0.2, 0.2, 0.3, 0.4, 0.47
0.47 is the highest
− 0.53 is the lowest
∴ = 0.47 − (− 0.53)
∴0.47 + 0.53
= 1.0
Source: Myschool Past Questions Archive (Record #46366)
Mathematics
UTME / JAMB 2017
Number and Numeration
Solution
Evaluate 1 − (\(\frac{1}{5}\) x 1\(\frac{2}{3}\)) + (5 + 1\(\frac{2}{3}\))
A
4
B
3
C
\(\frac{22}{3}\)
D
3\(\frac{2}{3}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
1 − (\(\frac{1}{5}\) x 1\(\frac{2}{3}\)) + (5 + 1\(\frac{2}{3}\))
1 − (\(\frac{1}{5}\) x \(\frac{5}{3}\)) + (5 + \(\frac{5}{3}\))
1 − \(\frac{1}{3}\) + \(\frac{20}{3}\)
= \(\frac{22}{3}\)
Source: Myschool Past Questions Archive (Record #46367)
Mathematics
UTME / JAMB 2017
Number and Numeration
Solution
What is the product of 2x2 − x + 1 and 3 − 2x
A
4x3 − 8x2 + 5x + 3
B
−4x3 + 8x2 − 5x + 3
C
−4x3 − 8x2 + 5x + 3
D
4x3 + 8x2 − 5x + 3
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
(2x2 - x + 1) × (3 - 2x);
3(2x2 - x + 1) - 2x (2x2 - x + 1)
6x2 - 3x + 3 - 4x3 + 2x2 - 2x
-4x3 + 8x2 -5x + 3
Source: Myschool Past Questions Archive (Record #46368)
Mathematics
WAEC / WASSCE 2017
Number and Numeration
Solution
Express 0.0000407, correct to 2 significant figures
A
0.0
B
0.00004
C
0.000041
D
0.0000407
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
0.0000407 to 2 s.f
0.000041 (2 s.f)
Source: Myschool Past Questions Archive (Record #49905)
Mathematics
WAEC / WASSCE 2017
Geometry and Trigonometry
Solution
If x varies inversely as y and y varies directly as z, what is the relationship between x and z?
A
x \(\alpha\) z
B
x \(\alpha\) \(\frac{1}{z}\)
C
a \(\alpha\) z\(^2\)
D
x \(\alpha\) \(\frac{1}{z^2}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(x \propto \frac{1}{y}\), y \(\propto\) z
x = \(\frac{k}{y}\)
y = mz
Since y = mz,
x = \(\frac{k}{mz}\), where k and m are constants. Hence,
x \(\propto\) \(\frac{1}{z}\)
Source: Myschool Past Questions Archive (Record #49907)
Mathematics
WAEC / WASSCE 2017
Number and Numeration
Solution
Evaluate \(\frac{3\frac{1}{4} \times 1\frac{3}{5}}{11\frac{1}{3} - 5 \frac{1}{3}}\)
A
\(\frac{14}{15}\)
B
\(\frac{13}{15}\)
C
\(\frac{4}{5}\)
D
\(\frac{11}{15}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(\frac{3\frac{1}{4} \times 1\frac{3}{5}}{11\frac{1}{3} - 5 \frac{1}{3}}\) = \(\frac{\frac{26}{5}}{\frac{18}{3}}\) = \(\frac{26}{5} \div \frac{18}{3}\) = \(\frac{26}{5} \times \frac{3}{18}\)
= \(\frac{13}{15}\)
Source: Myschool Past Questions Archive (Record #49929)
Mathematics
WAEC / WASSCE 2017
Number and Numeration
Solution
The ages of Tunde and Ola are in the ratio 1:2. If the ratio of Ola's age to Musa's age is 4:5, what is the ratio of Tunde's age to Musa's age?
A
1 : 4
B
1 : 5
C
2 : 5
D
5 : 2
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Tunde: Ola \(\to\) 1 : 2 ; Ola; Musa \(\to\) 4 : 5
\(\frac{1}{2}\) x \(\frac{4}{5}\)
= \(\frac{2}{5}\)
Source: Myschool Past Questions Archive (Record #49931)
Mathematics
WAEC / WASSCE 2017
Number and Numeration
Solution
If M = {x : 3 \(\leq\) x < 8} and N = {x : 8 < x \(\leq\) 12}, which of the following is true?
i. 8 \(\in\) M \(\cap\) N
ii. 8 \(\in\) M \(\cup\) N
iii. M \(\cap\) N = \(\varnothing\)
A
iii only
B
i and ii
C
ii and iii only
D
i, ii and iii
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
M = {3, 4, 5, 6, 7,}, N = {9, 10, 11, 12}
Source: Myschool Past Questions Archive (Record #49938)
Mathematics
WAEC / WASSCE 2017
Number and Numeration
Solution
Given that a = log 7 and b = \(\log\) 2, express log 35 in terms of a and b.
A
a + b + 1
B
ab - 1
C
a - b + 1
D
b - a + 1
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\frac{\log 7 \times \log 10}{\log 2}\)
log 7 x log 10 \(\div\) log 2
a + 1 - b
a - b + 1
Source: Myschool Past Questions Archive (Record #49948)
Mathematics
WAEC / WASSCE 2017
Number and Numeration
Solution
If x = \(\frac{2}{3}\) and y = - 6, evaluate xy - \(\frac{y}{x}\)
A
0
B
5
C
8
D
9
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
x = \(\frac{2}{3}\) and y = - 6
xy - \(\frac{y}{x}\)
\(\frac{2}{3} - (6)^2 - (-6) \div \frac{2}{3}\)
= -4 - (6) x \(\frac{3}{2}\)
= -4 - (-6) x \(\frac{3}{2}\)
= -4 - (-9)
= -4 + 9
= 5
Source: Myschool Past Questions Archive (Record #49951)
Mathematics
WAEC / WASSCE 2017
Algebra
Solution
Solve the equation: \(\frac{1}{5x} + \frac{1}{x}\)= 3
A
\(\frac{1}{5}\)
B
\(\frac{2}{5}\)
C
\(\frac{3}{5}\)
D
\(\frac{4}{5}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(\frac{1}{5x} + \frac{1}{x}\)= 3
\(\frac{1 + 5}{5x}\) = 3
6 = 15x
x = \(\frac{6}{15}\)
= \(\frac{2}{5}\)
Source: Myschool Past Questions Archive (Record #49954)
Mathematics
WAEC / WASSCE 2017
Number and Numeration
Solution
A sum of N18,100 was shared among 5 boys and 4 girls with each boy taking N20.00 more than each girl. Find a boy's share.
A
N1,820.00
B
2,000.00
C
N2,020.00
D
N2,040.00
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Let a girl's share = x + 20
4x + 5(x + 20) = 18,100
4x + 5x + 100 = 18,100
9x + 100 = 18,100
9x = 18,000
x = \(\frac{18,000}{9}\)
x = 2,000
\(\therefore\) Each boy gets N(2,000 + 20)
= N2,020.
Source: Myschool Past Questions Archive (Record #49957)
Mathematics
WAEC / WASSCE 2017
Number and Numeration
Solution
One factor of \(7x^2 + 33x - 10\) is
A
7x + 5
B
x - 2
C
7x - 2
D
x - 5
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(7x^2 + 33x - 10\)
\(7x^2 + 35x - 2x - 10\)
7x (x + 5) - 2 (x + 5)
(7x - 2) (x + 5)
Source: Myschool Past Questions Archive (Record #49963)