Lesson G25

G25 Vector addition, subtraction, scalar multiplication and proofs Quiz: AQA Maths, Unit 4

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson G25, Vector addition, subtraction, scalar multiplication and proofs: 20 multiple choice questions for the AQA GCSE Maths (8300), Unit 4: Geometry and measures, written with Revision Ninja.

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The 20 questions

  1. Given a = (2, 5) and b = (1, -3), what is a + b?

    • (3, 8)
    • (2, -15)
    • (3, 2)
    • (1, 8)

  2. Given a = (2, 5) and b = (1, -3), what is a - b?

    • (-1, -8)
    • (3, 2)
    • (3, 8)
    • (1, 8)

  3. What is the result of the scalar multiplication 3 times (2, -1)?

    • (2, -3)
    • (5, 2)
    • (6, -3)
    • (6, -1)

  4. Which description matches the vector -a?

    • Double magnitude, same direction
    • Same magnitude and direction
    • Half magnitude, same direction
    • Same magnitude, opposite direction

  5. If a = (2, 1), what is 2a?

    • (2, 2)
    • (4, 1)
    • (2, 4)
    • (4, 2)

  6. What single vector does AB + BC equal?

    • BA
    • AC
    • AB - BC
    • CA

  7. When are two vectors parallel?

    • Their components sum to zero
    • One is a scalar multiple of the other
    • They have equal magnitudes only
    • They start at the same point

  8. What is the vector sum around a closed triangle path ABCA?

    • The zero vector
    • The vector CA
    • A vector AB
    • Twice AB

  9. Given a = (3, -2) and b = (-1, 4), what is 2a - b?

    • (7, -8)
    • (5, -8)
    • (7, 0)
    • (5, 0)

  10. Given a = (4, 1) and b = (2, 6), find the vector c such that a + c = b.

    • (-6, -7)
    • (6, 7)
    • (-2, 5)
    • (2, 5)

  11. Given p = (5, 2) and q = (-3, 4), what is 3p - q?

    • (18, 2)
    • (18, 10)
    • (12, 2)
    • (2, -2)

  12. OA = a and OB = b. Which vector equals BA?

    • a - b
    • -(a + b)
    • b - a
    • a + b

  13. OP = p and PQ = q. Which expression gives OQ?

    • q - p
    • 2p + q
    • p + q
    • p - q

  14. ABCD is a parallelogram with AB = a and AD = b. Which expression gives BD?

    • 2b - a
    • a + b
    • a - b
    • b - a

  15. If vector AB = 2 times vector BC, what can be concluded about the points A, B and C?

    • They form an equilateral triangle
    • They are collinear
    • They form a right angle
    • They lie on a circle

  16. If 2a = 3b and a = (3, 6), what is b?

    • (1, 2)
    • (4.5, 9)
    • (2, 4)
    • (6, 12)

  17. (H) OA = a and OB = b. What is the position vector of the midpoint M of AB?

    • a - b
    • (b - a) / 2
    • (a + b) / 2
    • a + b

  18. (H) PQ = 3x and QR = x - y. Which expression gives PR?

    • 4x - y
    • 4x + y
    • 2x + y
    • 3x - y

  19. (H) For A(1, 2), B(4, 6) and C(7, 10), what is the relationship between AB and BC?

    • AB = BC, so the points are collinear
    • AB = -BC, so the points form a triangle
    • AB and BC have different lengths
    • AB is perpendicular to BC

  20. (H) If k a + m b = 0 where a and b are not parallel, what must be true?

    • k = 1 and m = 1
    • k = m
    • k = -m
    • k = 0 and m = 0

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