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Mathematics
WAEC / WASSCE 2017
Fractions, Decimals, Percentages & Approximations
Solution
The average age of a group of 25 girls is 10year. If one girl, aged 12 years and 4 months joins the group, find the new average age of the group
A
10.1 years
B
9.3 years
C
8.7 years
D
8 . 3 years
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
x = 10 ; 10 = \(\frac{x}{25}\)
x = 250
x = \(\frac{250 + 12.4}{26}\)
x = 10.09
x = 10.1 years
Source: WAEC / JAMB / NECO Classroom Archive (Record #50023)
Mathematics
WAEC / WASSCE 2017
Fractions, Decimals, Percentages & Approximations
Solution
Make x the subject of the relation d = \(\sqrt{\frac{6}{x} - \frac{y}{2}}\)
A
x = \(\frac{6 + 12}{d^2 + y}\)
B
x = \(\frac{12}{d^2 - y}\)
C
x = \(\frac{12}{y} - 2d^2\)
D
x = \(\frac{12}{2d^2 + y}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
d = \(\sqrt{\frac{6}{x} - \frac{y}{2}}\)
\(d^2 = \frac{6}{x} - \frac{y}{2}\)
\(2xd^2 = 12 - xy\)
\(2xd^2 + xy = 12\)
x = \(\frac{12}{2d^2 + y}\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #50125)
Physics
WAEC / WASSCE 2017
Magnetism, Electromagnetism & AC Circuits
Solution
A transformer connected to a 240\(V_{r.m.s}\) has 3000 turns in its primary coil and 500 turns in its secondary coil. Calculate the output voltage.
A
4000V
B
400V
C
40V
D
4V
medium Difficulty
Verified Correct Answer: Option C
Physical Principles & Numerical Solution
\(N_{p} = 3000 turns\)
\(N_{s} = 500 turns\)
\(E_{p} = 240V_{r.m.s}\)
\(E_{s} = ?\)
\(\frac{N_{s}}{N_{p}} = \frac{E_{s}}{E_{p}}\)
\(\frac{500}{3000} = \frac{E_{s}}{240}\)
\(\implies E_{s} = \frac{240\times500}{3000} = 40V\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #50080)
Physics
WAEC / WASSCE 2017
Electrostatics & Capacitors
Diagram
Solution
The diagram above illustrates two charged bodies, X and Y separated by a distance r. Each body has charge q and mass m. Which of the following statements about the electrostatic force \(F_{e}\) and gravitational force \(F_{g}\) acting between the bodies is correct?
Attached Figure / Diagram
A
\(F_{e}\) is attraction while \(F_{g}\) is repulsion
B
Both \(F_{e}\) and \(F_{g}\) are that of repulsion
C
Both \(F_{e}\) and \(F_{g}\) is that of attraction
D
\(F_{e}\) is repulsion while \(F_{g}\) is attraction
medium Difficulty
Verified Correct Answer: Option D
Physical Principles & Numerical Solution
electrostatic force can be repulsive or attractive and gravitational force is only attractive.
Source: WAEC / JAMB / NECO Classroom Archive (Record #50092)
Physics
WAEC / WASSCE 2017
Units, Measurements & Dimensional Analysis
Diagram
Solution
The diagram above is a micrometer screw gauge. Determine its reading.
Attached Figure / Diagram
A
2.44mm
B
2.46mm
C
2.86mm
D
2.96mm
medium Difficulty
Verified Correct Answer: Option B
Physical Principles & Numerical Solution
- Main scale: 2 mm
- Thimble scale: 46 divisions \times 0.01 mm = 0.46 mm
Total reading = 2 + 0.46 = 2.46 mm
Source: WAEC / JAMB / NECO Classroom Archive (Record #49910)
Mathematics
WAEC / WASSCE 2017
Fractions, Decimals, Percentages & Approximations
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
Variations
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
Plane Geometry, Polygons & Circle Theorems
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
Fractions, Decimals, Percentages & Approximations
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
Sets, Logic & Venn Diagrams
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
Indices, Logarithms & Surds
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
Plane Geometry, Polygons & Circle Theorems
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
Linear, Simultaneous & Quadratic Equations
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
Fractions, Decimals, Percentages & Approximations
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
Linear, Simultaneous & Quadratic Equations
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)