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Mathematics · Self Assessment

Practice Test: Vectors & Transformations

A 100-mark paper covering "Vectors: Notation, Arithmetic & Magnitude" and "Transformations: Translation, Reflection, Rotation & Enlargement" — multiple choice, true/false, fill-in-the-blank, column matching, and short answer, all auto-graded instantly.

EDUSAMBAM Editorial Team · 45 questions · 100 marks · Instant self-assessment

Questions

100

Marks

Sections

100%

Auto-Graded

Section	Questions	Marks Each	Total
A — Multiple Choice	15	2	30
B — True / False	10	2	20
C — Fill in the Blank	10	2	20
D — Column Matching	5 pairs	2	10
E — Short Answer	5	4	20
Total	45	—	100

Fill-in-the-blank and short-answer questions are checked automatically against accepted answers — exact wording doesn't need to match, but the key term should be present.

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Section A — Multiple Choice

30 marks

15 questions · 2 marks each.

1.A vector has:Basic2 pts

A. Only magnitude

B. Only direction

C. Both magnitude and direction

D. Neither

2.a = (2 over 5), b = (3 over −1). Find a + b.Basic2 pts

A. (5 over 4)

B. (5 over 6)

C. (−1 over 6)

D. (1 over 4)

3.a = (6 over 4), b = (2 over 7). Find a − b.Intermediate2 pts

A. (8 over 11)

B. (−4 over 3)

C. (4 over 11)

D. (4 over −3)

4.v = (3 over −5). Find 3v.Basic2 pts

A. (6 over −5)

B. (9 over −15)

C. (3 over −5)

D. (9 over 15)

5.The position vector of point A relative to origin O is written:Basic2 pts

A. →AO

B. |OA|

C. A²

D. →OA

6.A has position vector (1 over 2), B has position vector (7 over 6). Find →AB.Intermediate2 pts

A. (8 over 8)

B. (6 over 4)

C. (−6 over −4)

D. (4 over 3)

7.Find the magnitude of v = (8 over 15).Intermediate2 pts

A. 17

B. 23

C. 7

D. 120

8.A full description of a reflection must include:Basic2 pts

A. A scale factor

B. A centre point

C. The equation of the mirror line

D. A direction

9.Point B(5, 2) is reflected in the x-axis. Find B′.Intermediate2 pts

A. (−5, 2)

B. (5, −2)

C. (2, 5)

D. (−5, −2)

10.Point C(6, 1) is reflected in the line y = x. Find C′.Intermediate2 pts

A. (6, −1)

B. (−6, 1)

C. (−1, −6)

D. (1, 6)

11.A full description of a rotation must include:Intermediate2 pts

A. Only the angle

B. Only the centre

C. Centre, angle, AND direction

D. Only the direction

12.Point D(2, 7) is rotated 90° anticlockwise about the origin, using (x, y) → (−y, x). Find D′.Advanced2 pts

A. (−7, 2)

B. (2, −7)

C. (7, 2)

D. (7, −2)

13.A full description of an enlargement must include:Intermediate2 pts

A. Centre AND scale factor

B. A mirror line

C. A direction only

D. An angle only

14.Point E(3, 5) is enlarged by scale factor 2, centre the origin. Find E′.Intermediate2 pts

A. (5, 7)

B. (1.5, 2.5)

C. (6, 10)

D. (9, 15)

15.A negative scale factor produces an image that is:Advanced2 pts

A. On the same side, right-way up

B. On the opposite side of the centre, and upside down

C. Always larger, never smaller

D. The same size and position as the object

Section B — True / False

20 marks

10 questions · 2 marks each.

16.Two vectors are equal if they have the same magnitude and direction.Basic2 pts

True

False

17.If a and b are the position vectors of A and B, then →AB = a − b.Intermediate2 pts

True

False

18.Two vectors are parallel if one is a scalar multiple of the other.Intermediate2 pts

True

False

19.The magnitude of a column vector (x, y) is found using √(x² + y²).Basic2 pts

True

False

20.The position vector of the midpoint M of AB is a + b (not halved).Intermediate2 pts

True

False

21.A translation is fully described by a column vector.Basic2 pts

True

False

22.A rotation can be fully described using only the angle, with no centre needed.Intermediate2 pts

True

False

23.Under a reflection, every point on the mirror line is invariant.Intermediate2 pts

True

False

24.A negative scale factor always makes the image larger, never smaller.Advanced2 pts

True

False

25.Two translations applied one after another are equivalent to a single translation using the sum of the two vectors.Intermediate2 pts

True

False

Section C — Fill in the Blank

20 marks

10 questions · 2 marks each. Type the missing word or term.

26.A quantity with both magnitude and direction is called a ______.Basic2 pts

27.If a and b are the position vectors of A and B, then →AB = b − ______.Intermediate2 pts

28.The magnitude of vector (x, y) is √(x² + ______).Intermediate2 pts

29.Two vectors are ______ if one is a scalar multiple of the other.Intermediate2 pts

30.The position vector of the midpoint of AB is ______ (a + b).Intermediate2 pts

31.A translation is described fully using a column ______.Basic2 pts

32.A rotation must be described using a centre, an angle, and a ______.Intermediate2 pts

33.An enlargement is described using a centre and a ______ factor.Basic2 pts

34.A negative scale factor produces an image that is ______ down relative to the object.Advanced2 pts

35.The invariant point of an enlargement is the ______ of enlargement.Intermediate2 pts

Section D — Column Matching

10 marks

Match each term to its correct definition. Use the ▲▼ buttons to reorder Column B.

36–40.Match each term to its correct definition.Advanced10 pts

Column A

Translation

Reflection

Rotation

Enlargement

Parallel vectors

Column B

One vector is a scalar multiple of the other

Described fully by a column vector

Described fully by a centre and a scale factor

Described fully by the equation of the mirror line

Described fully by a centre, an angle, and a direction

Section E — Short Answer

20 marks

5 questions · 4 marks each. Answer in one or two sentences.

41.Explain how to find the vector from point A to point B, given their position vectors.Intermediate4 pts

42.Describe how to find the midpoint of a line segment using position vectors.Intermediate4 pts

43.Explain why a full description of a rotation must include the direction (clockwise or anticlockwise).Advanced4 pts

44.Describe what happens to a shape when it is enlarged by a negative scale factor.Advanced4 pts

45.Explain what an "invariant point" is, and give one example from a specific transformation.Advanced4 pts

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