Vectors and Transformation Practice Questions
WAEC (West Africa) · WAEC Mathematics · 145 free MCQs with instant results and detailed explanations.
145
Total
48
Easy
72
Medium
25
Hard
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Sample Questions from Vectors and Transformation
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Q1
Easy
If vector **a** = 3i + 4j and vector **b** = 2i - j, what is the resultant vector **r** = **a** + **b**?
A.
5i + 3j
B.
6i + 5j
C.
1i + 5j
D.
5i + 4j
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Correct Answer: A
The resultant vector **r** is obtained by adding vectors **a** and **b** element-wise. Therefore, **r** = (3i + 4j) + (2i - j) = (3 + 2)i + (4 - 1)j = 5i + 3j.
Q2
Easy
A point P(2, 3) is translated by the vector **v** = 4i - 2j. What are the new coordinates of point P after the translation?
A.
(6, 1)
B.
(6, 5)
C.
(2, 5)
D.
(6, 2)
Show Answer & Explanation
Correct Answer: B
To find the new coordinates after the translation, add the vector **v** to the coordinates of point P. Thus, (2 + 4, 3 - 2) = (6, 5).
Q3
Easy
Which of the following vectors is perpendicular to vector **a** = 5i + 12j?
A.
12i - 5j
B.
5i + 12j
C.
-12i + 5j
D.
5j - 12i
Show Answer & Explanation
Correct Answer: A
A vector is perpendicular to another if their dot product is zero. The dot product of **a** and option A (12i - 5j) is (5*12) + (12*-5) = 60 - 60 = 0, confirming they are perpendicular.
Q4
Medium
If vector A = 3i + 4j and vector B = -2i + j, what is the resultant vector A + B?
A.
i + 5j
B.
i + 3j
C.
5i + 5j
D.
i - 3j
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Correct Answer: A
Adding the vectors A and B results in (3i - 2i) + (4j + j) = i + 5j, making option A the correct answer.
Q5
Medium
A point P has coordinates (2, 3). If it is translated by the vector (4, -1), what are the new coordinates of point P?
A.
(6, 2)
B.
(6, 4)
C.
(2, 2)
D.
(4, 3)
Show Answer & Explanation
Correct Answer: A
Translating point P (2, 3) by vector (4, -1) results in (2+4, 3-1) = (6, 2), confirming option A.
Q6
Medium
If vector C = 5i - 3j and you need to find a unit vector in the direction of C, what is the unit vector?
A.
(1/โ34)(5i - 3j)
B.
(1/โ34)(-5i + 3j)
C.
(5/โ34)i - (3/โ34)j
D.
(5/โ34)j + (3/โ34)i
Show Answer & Explanation
Correct Answer: C
The magnitude of vector C is โ(5^2 + (-3)^2) = โ34, and the unit vector is (5/โ34)i - (3/โ34)j, confirming option C.
Q7
Medium
A vector D is defined as D = 2i + 5j. What is the angle ฮธ between vector D and the positive x-axis?
A.
tanโปยน(5/2)
B.
tanโปยน(2/5)
C.
sinโปยน(2/โ29)
D.
cosโปยน(5/โ29)
Show Answer & Explanation
Correct Answer: A
The angle ฮธ can be found using ฮธ = tanโปยน(y/x) = tanโปยน(5/2), which corresponds to option A.
Q8
Hard
A vector A has coordinates (3, -2) and vector B has coordinates (-1, 4). What is the resultant vector R when A and B are added together?
A.
(2, 2)
B.
(4, 6)
C.
(1, 2)
D.
(2, -6)
Show Answer & Explanation
Correct Answer: A
The resultant vector R is found by adding the corresponding components of vectors A and B. Thus, R = (3 + (-1), -2 + 4) = (2, 2).
Q9
Hard
If a vector P is represented by the coordinates (4, 3) and is reflected across the y-axis to produce vector Q, what are the coordinates of vector Q?
A.
(-4, 3)
B.
(4, -3)
C.
(3, 4)
D.
(-3, 4)
Show Answer & Explanation
Correct Answer: A
When reflecting a point across the y-axis, the x-coordinate changes sign while the y-coordinate remains the same. Therefore, vector Q has coordinates (-4, 3).
Q10
Hard
A vector \( \mathbf{a} = 3\mathbf{i} - 4\mathbf{j} \) is transformed by the matrix \( \begin{pmatrix} 2 & 0 \ 0 & 3 \end{pmatrix} \). What is the resulting vector after the transformation?
A.
6\mathbf{i} - 12\mathbf{j}
B.
6\mathbf{i} + 12\mathbf{j}
C.
2\mathbf{i} - 4\mathbf{j}
D.
3\mathbf{i} + 12\mathbf{j}
Show Answer & Explanation
Correct Answer: A
The transformation is performed by multiplying the vector \( \mathbf{a} \) by the matrix. Thus, \( \begin{pmatrix} 2 & 0 \ 0 & 3 \end{pmatrix} \begin{pmatrix} 3 \ \ -4 \end{pmatrix} = \begin{pmatrix} 2*3 + 0*-4 \ \ 0*3 + 3*-4 \end{pmatrix} = \begin{pmatrix} 6 \ \ -12 \end{pmatrix} \), so the resulting vector is \( 6\mathbf{i} - 12\mathbf{j} \).
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Vectors and Transformation โ WAEC (West Africa) WAEC Mathematics Practice Questions Online
This page contains 145 practice MCQs for the chapter Vectors and Transformation in WAEC (West Africa) WAEC Mathematics. The questions are organized by difficulty โ 48 easy, 72 medium, 25 hard โ so you can choose the right level for your preparation.
Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit.