Scalars and Vectors Practice Questions
WAEC (West Africa) · WAEC Physics · 147 free MCQs with instant results and detailed explanations.
147
Total
45
Easy
79
Medium
23
Hard
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Sample Questions from Scalars and Vectors
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Q1
Easy
Which of the following quantities is a scalar?
A.
Temperature
B.
Velocity
C.
Force
D.
Acceleration
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Correct Answer: A
Temperature is a scalar quantity because it has magnitude but no direction. Unlike velocity, force, and acceleration, which have both magnitude and direction, temperature is measured without any directional component.
Q2
Easy
If a vector has a magnitude of 5 units and is directed towards the east, which of the following represents this vector?
A.
5 units East
B.
5 units
C.
East
D.
5 units West
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Correct Answer: A
The vector must include both its magnitude and direction. '5 units East' correctly describes a vector with both a magnitude of 5 and a direction towards the east. The other options lack one of these essential components.
Q3
Easy
Which of the following statements is true regarding scalar and vector quantities?
A.
All vector quantities can be added algebraically.
B.
Scalar quantities have direction.
C.
Vector quantities are represented by arrows.
D.
Scalars can be negative.
Show Answer & Explanation
Correct Answer: C
Vector quantities are indeed represented by arrows, where the length represents the magnitude and the arrowhead indicates the direction. Option A is incorrect because vectors follow specific rules for addition; option B is false as scalars do not have direction; option D is misleading since scalars are usually non-negative quantities in many physical contexts.
Q4
Medium
Which of the following quantities is a scalar?
A.
Velocity
B.
Force
C.
Mass
D.
Displacement
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Correct Answer: C
Mass is a scalar quantity because it has only magnitude and no direction, unlike velocity, force, and displacement which are vector quantities.
Q5
Medium
A car travels 50 km north and then 30 km east. What is the magnitude of the resultant displacement?
A.
80 km
B.
70 km
C.
58.31 km
D.
100 km
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Correct Answer: C
The resultant displacement can be calculated using the Pythagorean theorem: R = โ(50ยฒ + 30ยฒ) = โ(2500 + 900) = โ3400 โ 58.31 km.
Q6
Medium
If vector A = 3i + 4j and vector B = 1i - 2j, what is the resultant vector A + B?
A.
4i + 2j
B.
2i + 6j
C.
2i + 2j
D.
4i + 6j
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Correct Answer: A
To find the resultant vector, add the corresponding components: (3 + 1)i + (4 - 2)j = 4i + 2j.
Q7
Medium
Which of the following statements is true regarding vectors?
A.
Vectors can be added in any order.
B.
Vectors can only be added if they are of the same magnitude.
C.
The sum of two vectors is always a scalar.
D.
Vectors cannot be subtracted.
Show Answer & Explanation
Correct Answer: A
Vectors can be added in any order due to the commutative property, meaning A + B = B + A, regardless of their magnitudes.
Q8
Hard
A car travels 60 km north and then 80 km east. What is the magnitude of the displacement of the car from its starting point?
A.
100 km
B.
140 km
C.
80 km
D.
60 km
Show Answer & Explanation
Correct Answer: A
To find the resultant displacement, we apply the Pythagorean theorem. The car travels 60 km north and 80 km east, forming a right triangle. The displacement is the hypotenuse, calculated as โ(60ยฒ + 80ยฒ) = โ(3600 + 6400) = โ10000 = 100 km.
Q9
Hard
Two vectors A and B have magnitudes of 5 units and 12 units, respectively. If the angle between them is 90ยฐ, what is the magnitude of the resultant vector R?
A.
13 units
B.
7 units
C.
17 units
D.
60 units
Show Answer & Explanation
Correct Answer: A
When two vectors are perpendicular, the magnitude of the resultant vector can be found using the Pythagorean theorem: R = โ(Aยฒ + Bยฒ). Here, A = 5 and B = 12, thus R = โ(5ยฒ + 12ยฒ) = โ(25 + 144) = โ169 = 13 units.
Q10
Hard
A force of 10 N is applied at an angle of 30 degrees to the horizontal. What is the horizontal component of the force?
A.
5 N
B.
8.66 N
C.
17.32 N
D.
10 N
Show Answer & Explanation
Correct Answer: B
The horizontal component of a force can be calculated using the formula F_horizontal = F * cos(ฮธ). Here, F = 10 N and ฮธ = 30 degrees. Thus, F_horizontal = 10 * cos(30ยฐ) = 10 * (โ3/2) = 8.66 N.
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Scalars and Vectors โ WAEC (West Africa) WAEC Physics Practice Questions Online
This page contains 147 practice MCQs for the chapter Scalars and Vectors in WAEC (West Africa) WAEC Physics. The questions are organized by difficulty โ 45 easy, 79 medium, 23 hard โ so you can choose the right level for your preparation.
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