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Vectors

Free Printable Vectors PDF Worksheets, Revision Guide & GCSE Past Paper Questions (Grade 5)

Download free vectors worksheets (PDF), GCSE maths past paper questions and worked solutions for Vectors (5X). This is a Grade 5 geometry topic from the GCSE questions by topic collection for Foundation and Higher tier crossover GCSE Maths (Edexcel, AQA, OCR and IGCSE).

The free PDF worksheets table below brings together printable question booklets (Qs) and worked answers or mark schemes (Ans) from Maths Genie, Maths4Everyone, Corbett Maths, Maths Made Easy, Dr Frost, 1st Class Maths, Dr Austin, Metatutor, GCSE Maths Rocket, E Classroom and PMT, along with past paper question booklets.

Below the worksheet links you can read our vectors revision notes and worked examples with diagrams, try real GCSE past paper vectors questions with step-by-step solutions, or download a PDF of all vectors worksheet links.

Free Vectors PDF Worksheets & Answers

Grade 5 • Topic 5X
Resource Questions Answers
GCSE past paper questions & solutions
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Graded exam questions & solutions
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GCSE 9–1 practice booklet & solutions
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Practice Questions & answers
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MME worksheet & model answers
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GCSE worksheet & solutions
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Edexcel exam questions & solutions
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AQA exam questions & solutions
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Topic worksheet & worked solutions
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GCSE topic booklet & answers
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PMT (Edxl)
Edexcel GCSE topic questions & solutions
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PMT (AQA)
AQA GCSE topic questions & solutions
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PMT (IGCSE)
Edexcel IGCSE topic questions & solutions
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Online topic notes & examples
 Page
Interactive online lesson & practice
 Page
Grade 5 topics
5A - Combining ratios5B - Direct and inverse proportion
5C - Reverse percentages5D - Standard form
5E - Speed5F - Changing the subject
5G - Quadratic expressions5H - Solving quadratic equations
5J - Drawing quadratic graphs5K - Cubic/reciprocal graphs
5L - Simultaneous equations5M - Sector areas and arc lengths
5N - Sim. equ. graphically5P - Midpoint of a line segment
5Q - Gradient of a line5R - Equation of a line
5S - Spheres and cones5T - Similar shapes (lengths)
5U - Trigonometry (SOHCAHTOA)5V - Exact trig. values
5W - Probability trees5X - Vectors
5Y - Venn diagrams5Z - Density
5AA - Pressure
GCSE Maths Grade 5 Revision Notes & Method

Guide to Vectors: Explanation, Diagrams & Worked Examples

Download Printable One Page Guide (PDF)

Explanation:

A column vector writes horizontal movement on top (+ right, − left) and vertical movement on the bottom (+ up, − down). In geometric vector diagrams, going against an arrow reverses the sign (BA = −AB), and to travel from A to B via O you add the vectors: AB = AO + OB = −a + b = b − a.

Two vectors are parallel if one is a scalar multiple of the other (for example, 2a + 4b = 2(a + 2b) is parallel to a + 2b).

Example 1: Given column vectors a = (4, −1) and b = (−2, 5), work out 3a − 2b.

Solution:

Multiply each component: 3a = (12, −3) and 2b = (−4, 10)
Top component: 12 − (−4) = 16
Bottom component: −3 − 10 = −13
Answer: (16, −13) as a column vector

Example 2: In ▵OAB, OA = 2a and OB = 4b. M is the midpoint of AB. Find OM in terms of a and b.

Solution:

AB = AO + OB = −2a + 4b
AM = 12AB = −a + 2b
OM = 2a + (−a + 2b)
Answer: a + 2b
O A B M 2a 4b a+2b
Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Vectors Questions & Answers

Past Paper Example 1 OCR Jun 2023 2F Q17 3 marks
Full Paper (PDF) • Mark Scheme (PDF)
Vector a = (32) and vector b = (1-4).
(a) On the grid, draw vector a. [1 mark]
(b) On the grid, draw vector a + b. [2 marks]
Worked Solution & Mark Scheme (3 marks)
Part (a) Solution:
Vector a goes 3 right and 2 up. B1
a
Answer (a): Directed line segment going 3 units right and 2 units up with direction arrow.
Part (b) Solution:
a + b = (3 + 1, 2 − 4) = (4, −2): 4 right and 2 down. M1 A1
a + b
Answer (b): Directed line segment going 4 units right and 2 units down with direction arrow.
Past Paper Example 2 OCR Jun 2024 2F Q20 3 marks
Full Paper (PDF) • Mark Scheme (PDF)
Vector **a** is drawn on this grid.
a
(a) Write vector **a** as a column vector. [2 marks]
(b) Write this vector in terms of **a**. [1 mark]
Worked Solution & Mark Scheme (3 marks)
Part (a) Solution:
Vector a goes 2 units right and 3 units down M1
⇒ (2, −3). A1
Answer (a): (2-3)
Part (b) Solution:
Same length and parallel to a, but in the opposite direction ⇒ −a. B1
Answer (b): -a
Past Paper Example 3 Eduqas Nov 2017 1H Q3 4 marks
Full Paper (PDF) • Mark Scheme (PDF)
p = (54) and q = (1-1.5)
(a) Work out the column vector 2p - q. [2 marks]
(b) The grid shows the vector q.
On the same grid, draw the vector -3q. [2 marks]
q
Worked Solution & Mark Scheme (4 marks)
Part (a) Solution:
2p - q = 2(54) - (1-1.5) = (108) - (1-1.5) = (99.5). M1 A1
Answer (a): (99.5)
Part (b) Solution:
-3q = -3(1-1.5) = (-34.5) M1
From start point, move 6 grid squares left and 9 grid squares up, with arrow pointing top-left. A1
q–3q
Answer (b): Vector of length 3 times q pointing in the opposite direction (-34.5).

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