Topics Grade boundaries Exam dates Yumio GCSE Maths Grade 5 Vectors
Vectors – GCSE Maths Foundation and Higher · Grade 5 · Non-calculator
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On this page Objectives Key points Examples Questions Mistakes Tips Worksheet Read, add, subtract and scale column vectors, and use them to describe translations on a grid. It is on Foundation and Higher, aimed at grade 5. Free questions with answers are on this page. Worked examples show each line before you try the questions.
A column vector ( 3 − 2 ) a − b a + ( − b ) 3 ( 2 − 1 ) = ( 6 − 3 ) ( 3 − 4 ) = 5
On a grid, A B = b − a a b a
Add tops and bottoms. Scalar: multiply both components. Magnitude x 2 + y 2
Objectives Add two column vectors. Multiply a vector by a scalar, and subtract one vector from another. Write the vector from one point to another. Key points Read a column vector: top number is the move across (+ − Add and subtract vectors component by component. Multiply a vector by a number (scalar) — multiply both components. Work out combinations such as 2 a − b Worked examples Example 1 Add the vectors (3, 1) and (2, 5).
2 marks
Add horizontal components: 3 + 2 = 5 Add vertical components: 1 + 5 = 6 Write as column vector: (5, 6) Answer: (5, 6)
Common slips Slip: Amber multiplied 3 × 2 = 6 Adding vectors means adding matching components. Slip: Amber multiplied 1 × 5 = 5 Do not multiply components. Slip: Adrian wrote (6, 5) The top number is 5, the bottom is 6. Example 2 Subtract the vector (1, 5) from (7, 2).
2 marks
Recognise order: "subtract (1, 5) from (7, 2)" means (7, 2) minus (1, 5) Calculate components: 7 - 1 = 6 and 2 - 5 = -3 Write resultant vector: (6, -3) Answer: (6, -3)
Common slips Slip: Boris worked out (1, 5) minus (7, 2) The vector after the word from is the one you start with. Work out (7, 2) minus (1, 5). Slip: Bernice added 7 + 1 and 2 + 5 Perform subtraction on each component. Slip: Bernice wrote (-6, 3) (-6, 3) is the right size but the wrong sign, because the subtraction was done the wrong way round. Example 3 Work out the column vector from (1, 2) to (4, 6).
3 marks
Formula for vector from A to B: B - A (end minus start) Calculate x-step: 4 - 1 = 3 Calculate y-step: 6 - 2 = 4, giving (3, 4) Answer: (3, 4)
Common slips Slip: Cedric did A - B Always subtract start coordinates from end coordinates. Slip: Cedric did 1 - 4 = -3 Going from 1 to 4 is +3. Slip: Cedric wrote (3, 8) Going from 2 to 6 is +4. Questions and answers GCSE Maths vectors questions and answers. Try each one, then open the answer. Easy questions come first.
Question 1 Easy 2 marks Add the vectors (1, 2) and (3, 4).
Show answer Answer: (4, 6)
x: 1 + 3 = 4. y: 2 + 4 = 6, vector is (4, 6). M1 — x: 1 + 3 = 4. A1 — y: 2 + 4 = 6, vector is (4, 6). Question 2 Easy 2 marks Add the vectors (2, 1) and (4, 3).
Show answer Answer: (6, 4)
x: 2 + 4 = 6. y: 1 + 3 = 4, vector is (6, 4). M1 — x: 2 + 4 = 6. A1 — y: 1 + 3 = 4, vector is (6, 4). Question 3 Medium 2 marks Multiply the vector (3, 4) by 2. Give the answer as a column vector.
Show answer Answer: (6, 8)
Double top: 3 × 2 = 6. Double bottom: 4 × 2 = 8, vector is (6, 8). M1 — Double top: 3 × 2 = 6. A1 — Double bottom: 4 × 2 = 8, vector is (6, 8). Question 4 Medium 2 marks Multiply the vector (2, 3) by 3. Give the answer as a column vector.
Show answer Answer: (6, 9)
Triple top: 2 × 3 = 6. Triple bottom: 3 × 3 = 9, vector is (6, 9). M1 — Triple top: 2 × 3 = 6. A1 — Triple bottom: 3 × 3 = 9, vector is (6, 9). Question 5 Hard 2 marks Subtract the vector (4, 2) from (1, 8).
Show answer Answer: (-3, 6)
x: 1 - 4 = -3. y: 8 - 2 = 6, vector is (-3, 6). M1 — x: 1 - 4 = -3. A1 — y: 8 - 2 = 6, vector is (-3, 6). Question 6 Hard 2 marks Work out the column vector from (2, 5) to (6, 1).
Show answer Answer: (4, -4)
End minus start x: 6 - 2 = 4. End minus start y: 1 - 5 = -4, vector is (4, -4). M1 — End minus start x: 6 - 2 = 4. A1 — End minus start y: 1 - 5 = -4, vector is (4, -4). Question 7 Exam-style 2 marks Add the vectors (2, 5) and (3, 1).
Show answer Answer: (5, 6)
Add horizontal components: 2 + 3 = 5. Add vertical components: 5 + 1 = 6, giving (5, 6). M1 — Adds matching components, one correct A1 — (5, 6) Common mistakes Most lost marks on this topic are one slip.
Multiplying components instead of adding
Vector addition adds corresponding x and y components
Subtracting in reverse order (start minus end)
Vector from A to B is B - A (end minus start)
Scaling only the top component
A scalar multiplier applies to both top and bottom components
Spot the slip Add the vectors (3, 1) and (2, 5). Ada multiplies the components. What is the sum?
(5, 6) (6, 5) (3, 5) Show the slip (5, 6) Add the x-components and add the y-components.
Exam tips Be ready to do this without a calculator. Paper 1 is the non-calculator paper. If the question says “show that”, the result is given. The marks are for the steps that reach it. The method is the same on AQA-style and Edexcel-style papers. Show the scalar multiple as its own vector before subtracting — one method mark, and it exposes sign slips. For a translation, check with a second vertex: the same vector must take it to its image. Printable worksheet The same questions are in a PDF you can print. Answers start on a later page.
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Questions students ask Is Vectors Foundation or Higher? Vectors is on Foundation and Higher, aimed at grade 5.
What is a common slip on Vectors? Multiplying components instead of adding. Vector addition adds corresponding x and y components.
Where can I get Vectors questions and answers? The questions on this page are free. Open Show answer under each one, or download the worksheet PDF. Start free to practise this topic in the app.
Related topics More on Vectors Previous topic Exact trig values Next topic Similar shapes: area & volume AQA-style and Edexcel-style questions. Yumio is not affiliated with, endorsed by or connected to AQA, Pearson Edexcel or any other exam board.
Last updated 9 November 2026.