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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
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
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)
Mathematics
WAEC / WASSCE 2017
Number and Numeration
Solution
Solve: - \(\frac{1}{4}\) < \(\frac{3}{4}\) (3x - 2) < \(\frac{1}{2}\)
A
-\(\frac{5}{9}\) < x <\(\frac{8}{9}\)
B
-\(\frac{8}{9}\) < x <\(\frac{7}{9}\)
C
-\(\frac{8}{9}\) < x <\(\frac{5}{9}\)
D
-\(\frac{7}{9}\) < x <\(\frac{8}{9}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(\frac{3}{4}\) (3x - 2) < \(\frac{1}{2}\); \(\frac{3}{4}\) (3x - 2) > - \(\frac{1}{4}\)
3(3x - 2) < 2; 3(3x - 2) > -1
9x - 6 < 2; 9x - 6 > -1
9x < 8; 9x > 5
x < \(\frac{5}{9}\); x > \(\frac{8}{9}\)
Source: Myschool Past Questions Archive (Record #49984)
Mathematics
WAEC / WASSCE 2017
Number and Numeration
Solution
Simplify; 3x - (p - x) - (r - p)
A
2x - r
B
2x + r
C
4x - r
D
2x - 2p - r
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
3x - (p - x) - ( r - p)
= 3x - p + x - r + p
= 4x - r
Source: Myschool Past Questions Archive (Record #49987)
Mathematics
WAEC / WASSCE 2017
Number and Numeration
Solution
Water flows out of a pipe at a rate of 40\(\pi cm^2\) per seconds into an empty cylinder container of base radius 4cm. Find the height of water in the container after 4 seconds.
A
10 cm
B
14 cm
C
16 cm
D
20 cm
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Volume of a cylinder = \(\pi r^2h\)
40\(\pi cm^3\) = \(\pi. 4^2h\)
40\(cm^3\) = 16h
h = 2.5cm/sec
In 4 seconds, 2.5cm x 4
= 10cm
Source: Myschool Past Questions Archive (Record #49992)
Mathematics
WAEC / WASSCE 2017
Number and Numeration
Solution
If the total surface area of a solid hemisphere is equal to its volume, find the radius
A
3.0cm
B
4.5cm
C
5.0cm
D
9.0cm
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
T.S.A of hemisphere = 3\(\pi r^2\)
vol of hemisphere = \(\frac{2}{3} \pi r^3\)
3\(\pi r^2\) = \(\frac{2}{3} \pi r^3\)
3 = \(\frac{2}{3}r\)
9 = 2r
r = \(\frac{9}{2}\)
r = 4.5cm
Source: Myschool Past Questions Archive (Record #49998)