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Mathematics
WAEC / WASSCE 2019
Geometry and Trigonometry
Diagram
Solution
In the diagram, PQ is parallel to RS, < QFG = 105\(^o\) and < FEG = 50\(^o\). Find the value of n
Attached Figure / Diagram
A
40\(^o\)
B
55\(^o\)
C
75\(^o\)
D
130\(^o\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
E\(G\)R = 50\(^o\) (Alternative angles)
n + 55\(^o\) + 50\(^o\) = 180\(^o\) (Sum of angles on a straight line)
n = 180\(^o\) - 105\(^o\)
n = 75\(^o\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #57384)
Mathematics
WAEC / WASSCE 2019
Fractions, Decimals, Percentages & Approximation
Solution
Evaluate: \(\frac{0.42 \div 2.5}{0.5 \times 2.05}\), leaving the answer in the standard form.
A
1.639 x 10\(^2\)
B
1.639 x 10\(^1\)
C
1.639 x 10\(^{-1}\)
D
1.639 x 10\(^{-2}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\frac{0.42 \div 2.5}{0.5 \times 2.05} = \frac{0.168}{1.025}\)
= 1.639 x 10\(^{-1}\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #57686)
Mathematics
WAEC / WASSCE 2019
Sets & Set Operations
Solution
If T = {prime numbers} and M = {odd numbers} are subsets of \(\mu\) = {x : 0 < x ≤ 10} and x is an integer, find (T\(^{\prime}\) n M\(^{\prime}\)).
A
{4, 6, 8, 10}
B
{1. 4, 6, 8, 10}
C
{1, 2, 4, 6, 8, 10}
D
{1, 2, 3, 5, 7, 8, 9}
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
T = {2, 3, 5, 7}
M = {1, 3, 5, 7, 9}
\(\mu\) = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
T\(^{\prime}\) = = {1, 4, 6, 8, 9, 10}
M\(^{\prime}\) = {2, 4, 6, 8, 10}
(T\(^{\prime}\) \(\cap\) M\(^{\prime}\)) = {4, 6, 8, 10}
Source: WAEC / JAMB / NECO Classroom Archive (Record #57122)
Mathematics
WAEC / WASSCE 2019
Triangles and Polygons
Diagram
Solution
In XYZ, |YZ| = 32cm, < YXZ 53\(^o\) and XZY = 90\(^o\). Find, correct to the nearest centimetre, |XZ|
Attached Figure / Diagram
A
31 cm
B
25 cm
C
20 cm
D
13 cm
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Tan 52\(^o\) = \(\frac{32}{\text{|XZ|}}\)
|XZ| = \(\frac{32}{Tan 52^o}\)
= 25cm
Source: WAEC / JAMB / NECO Classroom Archive (Record #57253)
Mathematics
WAEC / WASSCE 2019
Measures of Location (Mean, Median, Mode)
Solution
8, 18, 10,14, 18, 11, 13, 14, 13, 17, 15, 8, 16, and 13
The following are scores obtained by some students in a test. How many students scored above the mean score?
A
10
B
9
C
8
D
7
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Mean = \(\frac{8 + 18 + 10 + 14 + 18 + 11 + 13 + 14 + 13 + 17 + 15 + 8 + 16 + 13}{14}\)
Mean = \(\frac{188}{14}\)
Mean = 13.4
Number above the mean is 7
Source: WAEC / JAMB / NECO Classroom Archive (Record #57395)
Mathematics
WAEC / WASSCE 2019
Probability
Solution
A box contains 2 white and 3 blue identical balls. If two balls are picked at random from the box, one after the other with replacement, what is the probability that they are of different colours?
A
\(\frac{2}{3}\)
B
\(\frac{3}{5}\)
C
\(\frac{7}{20}\)
D
\(\frac{12}{25}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
(\(\frac{2}{5} \times \frac {3}{5}) + (\frac{3}{5} \times \frac{2}{5})\)
\(\frac{6}{25} + \frac{6}{25} = \frac{12}{25}\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #57331)
Physics
WAEC / WASSCE 2019
Heat Energy & Temperature
Solution
Which of the following thermometers is used to measure the temperature of the human body?
A
Thermocouple
B
Alcohol-in-glass thermometer
C
Gas thermometer
D
Platinum resistance thermometer
medium Difficulty
Verified Correct Answer: Option B
Physical Principles & Numerical Solution
The range of usefulness of the thermometer is set by the boiling point of the liquid used. In the case of the ethanol-filled thermometer, the upper limit for measurement is 78 ^\circC (172.4 ^\circF), which makes it useful for measuring daytime, nighttime and body temperatures, although not for anything much hotter than these.
Source: WAEC / JAMB / NECO Classroom Archive (Record #59023)
Physics
WAEC / WASSCE 2019
Motion Force Circular Motion
Solution
An electron of mass 9.1 x 10\(^{-31}\) kg moves with a speed of 2.0 x 10\(^6\) ms\(^{-1}\) round the nucleus of an atom in a Circular path of radius 6.1 x 10(^{11}\) m. Determine the angular speed of the electron.
A
3.28 x 10\(^{16}\) rad s\(^{-1}\)
B
8.55 x 10\(^{3}\) rad s\(^{-1}\)
C
9.11 x 10\(^{13}\) rad s\(^{-1}\)
D
5.22 x 10\(^{15}\) rad s\(^{-1}\)
medium Difficulty
Verified Correct Answer: Option A
Physical Principles & Numerical Solution
Angular speed of the electron (W)
w = \(\frac{Velocity}{Radius} = \frac{V}{R}\)
= \(\frac{2.0 \times 10^6}{6.1 \times 10^{11}}\)
= 3.28 x 10\(^{16}\) rads\(^{-1}\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #58963)
Physics
WAEC / WASSCE 2019
Momentum Impulse Newtons Law of Motion
Solution
In an elastic collision, momentum is conserved as well as well as?
A
velocity
B
kinetic energy
C
potential energy
D
speed
medium Difficulty
Verified Correct Answer: Option B
Physical Principles & Numerical Solution
An elastic collision is an encounter (collision) between two bodies in which the total kinetic energy of the two bodies remains the same.
Source: WAEC / JAMB / NECO Classroom Archive (Record #58783)
Physics
WAEC / WASSCE 2019
Density and Relative Density
Solution
An instrument used to measure relative humidity is the?
A
hygrometer
B
hydrometer
C
pyrometer
D
manometer
medium Difficulty
Verified Correct Answer: Option A
Physical Principles & Numerical Solution
A hydrometer is an instrument used for measuring the relative density of liquids based on the concept of buoyancy.
A hygrometer measures humidity, the amount of water vapor in air
Source: WAEC / JAMB / NECO Classroom Archive (Record #59028)
Physics
WAEC / WASSCE 2019
Structure of the Nucleus
Solution
Which of the following statements about a neutral atom is correct? The
A
core is composed of electrons and protons
B
number of electrons is equal to that of neutron
C
number of neutrons is equal to that of protons
D
number of protons is equal to that of electrons.
medium Difficulty
Verified Correct Answer: Option D
Physical Principles & Numerical Solution
Atoms are neutral; they contain the same number of protons as electrons.
Source: WAEC / JAMB / NECO Classroom Archive (Record #59031)
Physics
WAEC / WASSCE 2019
Reflection of Light
Diagram
Solution
The diagram above represents an experimental set-up for verifying?
Attached Figure / Diagram
A
lens formula
B
refraction laws
C
reflection laws
D
mirror formula
medium Difficulty
Verified Correct Answer: Option A
Physical Principles & Numerical Solution
the diagram above is an experimental set up for verifying lens formula
Source: WAEC / JAMB / NECO Classroom Archive (Record #58810)
Physics
WAEC / WASSCE 2019
Refraction of Light
Solution
A ray of light traveling from a rectangular glass block of refractive index 1.5 into air strikes the block at an angle of incidence of 30. Calculate its angle of refraction.
A
48.6°
B
19.5°
C
20.0
D
45.0
medium Difficulty
Verified Correct Answer: Option A
Physical Principles & Numerical Solution
Given that refractive index = 1.5, angle of incidence = 30^\circ, angle of refraction =?
using snell's law = refractive index = \(\frac{sini}{sinr}\)
=\(\frac{1}{n } = \frac{sin30}{sinr}\)
= \(sinr = 1.5\times sin 30\)
r = \(sin^10.75\)
= 48.6^\circ
this is because ray is traveling from a more denser medium to a less dense medium
Source: WAEC / JAMB / NECO Classroom Archive (Record #59015)
Physics
WAEC / WASSCE 2019
Waves
Solution
Which of the following characteristics of waves can a ripple tank be used to demonstrate?
I. Reflection
II. Refraction
III. Diffraction
A
I, II and Ill
B
ll and ll only
C
l and lII only
D
I and II only
medium Difficulty
Verified Correct Answer: Option A
Physical Principles & Numerical Solution
ripple tank experiment can be used to demonstrate the following properties of waves:
Reflection
Refraction
Diffraction
Source: WAEC / JAMB / NECO Classroom Archive (Record #58888)
Physics
WAEC / WASSCE 2019
Waves
Solution
Which property of a wave remains constant when the wave travels from one medium into another?
A
Amplitude
B
Wavelength
C
Velocity
D
Frequency
medium Difficulty
Verified Correct Answer: Option D
Physical Principles & Numerical Solution
Frequency remains unchanged as waves travel from one medium to another because it is characterized by the source of the wave.
Source: WAEC / JAMB / NECO Classroom Archive (Record #59012)