Vectors and Transformations Practice Questions
IGCSE (Cambridge) · IGCSE Mathematics · 150 free MCQs with instant results and detailed explanations.
150
Total
58
Easy
73
Medium
19
Hard
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Sample Questions from Vectors and Transformations
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Q1
Easy
What is the resultant vector of A = (3, 4) and B = (1, 2)?
A.
(4, 6)
B.
(2, 2)
C.
(3, 2)
D.
(1, 6)
Show Answer & Explanation
Correct Answer: A
To find the resultant vector, add the corresponding components of vectors A and B: (3+1, 4+2) = (4, 6).
Q2
Easy
If vector A = (2, 3) is reflected over the x-axis, what is the new position of vector A?
A.
(2, -3)
B.
(-2, 3)
C.
(2, 3)
D.
(-2, -3)
Show Answer & Explanation
Correct Answer: A
Reflecting a vector over the x-axis changes the sign of its y-component. Therefore, the reflected vector will be (2, -3).
Q3
Easy
Which of the following transformations represents a translation of vector (4, -2)?
A.
Move 4 units right and 2 units down
B.
Move 4 units left and 2 units up
C.
Move 2 units right and 4 units down
D.
Move 2 units left and 4 units up
Show Answer & Explanation
Correct Answer: A
A translation by the vector (4, -2) means moving in the positive x-direction by 4 units and in the negative y-direction by 2 units.
Q4
Medium
A vector A has components (3, 4). What is the magnitude of vector A?
A.
5
B.
7
C.
6
D.
4
Show Answer & Explanation
Correct Answer: A
The magnitude of a vector A with components (x, y) is calculated using the formula √(x² + y²). Here, √(3² + 4²) = √(9 + 16) = √25 = 5.
Q5
Medium
Which of the following transformations will preserve the area of a shape?
A.
Reflection
B.
Enlargement
C.
Translation
D.
Rotation
Show Answer & Explanation
Correct Answer: A
Reflection preserves the area of a shape, as it does not alter the size or shape. Enlargements change the dimensions, translations and rotations keep the area unchanged but are not transformations that generate a new area.
Q6
Medium
If vector B = (2, -3) is translated by vector C = (1, 4), what are the new coordinates of vector B?
A.
(3, 1)
B.
(1, 1)
C.
(2, 1)
D.
(2, 7)
Show Answer & Explanation
Correct Answer: A
To find the new coordinates of vector B after translation by vector C, add the corresponding components: (2 + 1, -3 + 4) = (3, 1).
Q7
Medium
A shape is rotated 90 degrees counterclockwise about the origin. If a point on the shape is at (x, y), what are the new coordinates of that point?
A.
(-y, x)
B.
(y, -x)
C.
(-x, -y)
D.
(x, y)
Show Answer & Explanation
Correct Answer: A
When a point (x, y) is rotated 90 degrees counterclockwise about the origin, the new coordinates become (-y, x). This transformation effectively swaps the coordinates and changes the sign of the new x-coordinate.
Q8
Hard
A vector A has a magnitude of 10 units and is directed 30 degrees from the positive x-axis. What are the x and y components of vector A?
A.
(8.66, 5)
B.
(7.5, 6.5)
C.
(10, 0)
D.
(5, 8.66)
Show Answer & Explanation
Correct Answer: A
The x and y components of vector A can be calculated using cosine and sine functions. The x component is 10 * cos(30°) = 8.66 and the y component is 10 * sin(30°) = 5. Thus, the correct answer is (8.66, 5).
Q9
Hard
A vector A is given by (2, 3) and vector B is given by (1, -4). What is the resultant vector A + B?
A.
(3, -1)
B.
(1, -1)
C.
(2, -1)
D.
(2, 7)
Show Answer & Explanation
Correct Answer: A
The resultant vector A + B is obtained by adding the corresponding components. So, (2 + 1, 3 + (-4)) = (3, -1).
Q10
Hard
A transformation is represented by the matrix \( \begin{pmatrix} 2 & 0 \ 0 & 3 \end{pmatrix} \). If the point (1, 2) is transformed using this matrix, what are the coordinates of the transformed point?
A.
(2, 6)
B.
(1, 2)
C.
(0, 0)
D.
(3, 1)
Show Answer & Explanation
Correct Answer: A
To find the transformed coordinates, multiply the transformation matrix by the point vector: \( \begin{pmatrix} 2 & 0 \ 0 & 3 \end{pmatrix} \begin{pmatrix} 1 \ 2 \end{pmatrix} = \begin{pmatrix} 2 \times 1 + 0 \times 2 \ 0 \times 1 + 3 \times 2 \end{pmatrix} = \begin{pmatrix} 2 \ 6 \end{pmatrix} \).
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Vectors and Transformations — IGCSE (Cambridge) IGCSE Mathematics Practice Questions Online
This page contains 150 practice MCQs for the chapter Vectors and Transformations in IGCSE (Cambridge) IGCSE Mathematics. The questions are organized by difficulty — 58 easy, 73 medium, 19 hard — 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.