Pearson Edexcel International GCSE in Mathematics (Specification A) · 4MA1 · Free · no account needed
Vectors — exam questions
9 original Incandio exam-style questions on vectors, 21 marks, about 25 minutes of writing. Each one carries the command word, the tariff and the specification statement it assesses, exactly as a paper presents them. This is an original Incandio practice question, written to reflect the structure and demands of the qualification. It is not an official Pearson Edexcel past-paper question.
This is the practice set for Vectors — the module that teaches it. Read the module first if the idea is new; come here when you want to find out whether you can turn it into marks. Completely free, no account needed to read.
What these questions ask of you
8 command words run through this set, and on Pearson Edexcel International GCSE Mathematics A each one means something precise. Answering the wrong command is the commonest way a candidate who understands the module still loses the mark.
- Write down (1–2 marks)
- a value that needs no working — read off, recalled or stated
- Work out (1–5 marks)
- a calculated result, with the working that produced it
- Calculate (1–5 marks)
- a numerical answer obtained by calculation
- Explain why (1–2 marks)
- one short justification — mathematics almost never asks for extended explanation
- Simplify (1–3 marks)
- an equivalent expression in its simplest form
- Find (1–5 marks)
- a value or expression obtained by a method the learner chooses
- Show that (2–5 marks)
- every step of a derivation to a value that is already printed in the question Misread as: stating the printed answer again instead of deriving it
- Prove (2–5 marks)
- a general argument, valid for every case, not a demonstration on one example
Assessed on Paper 1 and Paper 2.
Where these sit in the specification
Pearson Edexcel International GCSE Mathematics A (4MA1) — statement 5.1. Incandio is aligned to this specification; it is not published by, endorsed by or affiliated with Pearson, and it reproduces none of Pearson's wording.
The 9 questions
Answer them on paper, then open the module's exam practice to have them marked. The mark scheme, the accepted and rejected answers and the annotated model answer are in Incandio and are not printed here — an answer beside its question is not practice.
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(1)Write down
The column vector p is (3, -1). Write down the column vector 2p.
(Total for Question 1 = 1 mark)
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(2)Work out
Vector c is (4, 7) and vector d is (-2, 3). Work out c + 2d as a column vector.
(Total for Question 2 = 2 marks)
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(2)Calculate
A vector has components (5, 12). Calculate its magnitude.
magnitude = ............................
(Total for Question 3 = 2 marks)
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(1)Explain why
The vector from P to Q is 2a + 4b and the vector from R to S is a + 2b. Explain why PQ and RS are parallel.
(Total for Question 4 = 1 mark)
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(2)Simplify
Simplify 3(2a - b) + 2(a + 4b).
(Total for Question 5 = 2 marks)
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(3)Find
Figure 2 shows triangle OAB, in which M is the midpoint of AB. Find the vector from O to M in terms of a and b.
Diagram NOT accurately drawn
Figure 2 (Total for Question 6 = 3 marks)
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(3)Show that
Figure 3 shows triangle OXY, in which P lies on XY so that XP : PY = 1 : 2. Show that the vector from O to P is (2x + y)/3.
Diagram NOT accurately drawn
Figure 3 (Total for Question 7 = 3 marks)
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(3)Work out
A is the point (2, 5) and the vector from A to B is (6, -3). Work out the coordinates of the midpoint of AB.
(Total for Question 8 = 3 marks)
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(4)Prove
The vector from P to Q is 3m + 2n and the vector from Q to R is 6m + 4n. Prove that P, Q and R lie on a straight line.
(Total for Question 9 = 4 marks)
Have them marked, then defend the answer
Practice tells you the mark; teaching it back tells you whether you understand it. On Incandio a topic counts as mastered only once you have taught it and defended it.
- Mark these questions — 9 questions, marked on Incandio against the authored scheme, with the mistake you actually made named.
- Teach it — explain vectors to Ember, an AI pupil who does not have it yet and asks the awkward question.
- Defend it — argue it against Simon Stevin over three rounds, marked against descriptors you can read first.
Completely free. No subscriptions, no paywalls, no account needed to start.
Back to the module
- Vectors — Column vectors, magnitude, and the a-and-b algebra of geometric proof — the topic that ends most Higher papers. Higher Tier.
- All of Incandio Mathematics · Incandio Exam Practice