Prior Content: GCSE/IGCSE Vectors
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Contents
- Whole Topic Notes
- 11A Introduction to 2D Vectors
- 11B i j and Unit Vectors
- 11C Magnitude & Direction
- 11D Position Vectors
- 11E Geometric Problems
- 11F Context Problems
- Whole Topic Summary Resources (Including Past Paper Questions)
Whole Topic Notes
Download Full Topic Slides
- Textbook Notes as PPTs (Courtesy of Owen134866)
Full Notes to Accompany Slides
Dr Frost
- Dr Frost Vectors Section
- Dr Frost Vector Slides✦
- Blank Notes to Follow Slides Word Doc & PDF (Courtesy of King’s Chester Maths Department)
Acute Learning Whole Chapter Problem Pairs
11A Introduction to 2D Vectors
Textbook resources
Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.
Dr Frost resources
Bicen Maths Live Lesson
Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths
Download Blank Notes
(Courtesy of King’s Chester Maths Department)
Download Slides
Extra Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 373a: Multiply a column vector by a positive scalar.
- 373c: Multiply a column vector by a negative scalar.
- 373e: Add or subtract vectors written in column vector form.
- 373g: Add or subtract scalar multiples of vectors.
- 373h: Solve equations formed in vector notation.
- 373j: Solve problems involving vectors where the points form a given shape.
- 474a: Determine if two vectors are parallel.
- 474b: Determine an unknown constant in a vector that is parallel to another.
- 474c: Determine the ratio of two vectors that are parallel to each other.
- 373: Exam Practice: Adding, subtracting and scaling column vectors
- 474: Exam Practice: Parallel vectors and straight line proofs using vectors
Other resources
Videos & Other Multimedia
Alternative Handouts
- Acute Learning Problem Pairs as PowerPoint or PDF
Activities
- PhET Vectors Interactive Resource
Worksheets
- Solomon Worksheet A✦ & Answers A✦
- MadAsMaths (T. Madas)
- Vector Algebra Introduction 2D Vectors Q18 (difficulty 5 of 5)
- Starting Points Maths
- Vectors in 2 Dimensions (by Segar Rogers) · PDF
Online Platforms
- Khan Academy
- Intro to vectors: Videos & practice
11B i j and Unit Vectors
Textbook resources
Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.
Dr Frost resources
Bicen Maths Live Lesson
Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths
Download Blank Notes
(Courtesy of King’s Chester Maths Department)
Download Slides
Extra Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 504a: Write a 2D column vector in textbfi-textbfj form.
- 504c: Write a vector in textbfi-textbfj form as a 2D column vector.
- 504f: Calculate the magnitude of a 2D vector written in textbfi-textbfj form.
- 504h: Determine a component of a 2D vector in textbfi-textbfj notation given its magnitude. (not yet active)
- 504j: Convert a 2D in either column vector or textbfi-textbfj form to a unit vector.
- 504: Exam Practice: Writing vectors in terms of unit vectors
Other resources
Other Videos
Courtesy of Maths Genie (Up to 6:12)
Alternative Handouts
- Acute Learning Problem Pairs as PowerPoint or PDF
Activities
- PhET Vectors Interactive Resource
Online Platforms
- Khan Academy
- Vector components: Videos & practice
11C Magnitude & Direction
Textbook resources
Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.
Note unit vectors are not included in these notes.
Dr Frost resources
Bicen Maths Live Lesson
Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths
Download Blank Notes
(Courtesy of King’s Chester Maths Department)
Download Slides
Extra Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 472a: Understand that a vector can be defined by its magnitude and direction, or its components. (not yet active)
- 472b: Calculate the magnitude of a 2D column vector.
- 472c: Determine the magnitude of a scalar multiple of a 2D column vector.
- 472d: Determine an unknown value in a 2D column vector given the magnitude.
- 472e: Determine the direction or bearing of a vector. (not yet active)
- 472f: Determine the components of a vector given its magnitude and direction. (not yet active)
- 472g: Determine the magnitude of the sum or difference of vectors given in component form. (not yet active)
- 472h: Determine the direction of the sum or difference of vectors given in component form. (not yet active)
- 506a: Determine the angle between a vector and the x or y axis.
- 506b: Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.
- 472: Exam Practice: Converting a vector between component form and magnitude and direction form
- 506: Exam Practice: Trigonometry involving vectors
Other resources
Other Videos
Courtesy of Maths Genie (From 6:12, Magnitude Only)
Alternative Handouts
- Acute Learning Problem Pairs as PowerPoint or PDF
Activities
- PhET Vectors Interactive Resource
- Transum
Worksheets
- Solomon Worksheet B✦ and Answers B✦
- Underground Maths ‘Hit the Spot✦‘
- MadAsMaths (T. Madas)
- Vector Algebra Introduction 2D Vectors Q4, 10 (difficulty 3 of 5)
Online Platforms
- Khan Academy
- Direction of vectors: Videos & practice
- Magnitude of vectors: Videos & practice
11D Position Vectors
Textbook resources
Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.
Dr Frost resources
Bicen Maths Live Lesson
Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths
Download Blank Notes
(Courtesy of King’s Chester Maths Department)
Download Slides
Extra Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 505a: Determine a 2D position vector given another position vector and the vector between them.
- 505c: Determine the vector between two 2D position vectors.
- 505e: Determine a position vector involving the midpoint of a line segment.
- 505f: Determine the position vector of a point that divides the vector between positions in a given ratio.
- 505g: Calculate the distance between two 2D position vectors.
- 505i: Determine a component of a 2D position vector given the distance between two points. (not yet active)
- 505k: Determine the coordinate of a point given a mixture of position vectors and vectors between them.
- 505l: Determine an unknown component of a 2D position vector for collinear points.
- 505: Exam Practice: Position vectors and the distance between two points from their position vectors
Other resources
Alternative Handouts
- Acute Learning Problem Pairs as PowerPoint or PDF
Worksheets
- MadAsMaths (T. Madas)
- Vector Algebra Introduction 2D Vectors Q1–2 (difficulty 2 of 5)
11E Geometric Problems
Textbook resources
Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.
Dr Frost resources
Bicen Maths Live Lesson
Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths
Download Blank Notes
(Courtesy of King’s Chester Maths Department)
Download Slides
Extra Questions
- Dr Frost Questions (Short)
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 473a: Determine a vector between two points using an appropriate path.
- 473b: Determine a vector involving a midpoint.
- 473c: Determine a vector involving a fraction of the distance between two points.
- 473d: Determine a vector involving half of a subroute.
- 473e: Determine a vector involving a fraction of a subroute.
- 473f: Determine a vector when one vector is extended out by a ratio.
- 473g: Prove that points form a parallelogram or rectangle using vector variables. (not yet active)
- 474d: Prove that two vectors in a diagram are parallel.
- 474e: Prove that points form a trapezium using vector variables.
- 474f: Prove that three points are collinear using vector variables.
- 474g: Prove that three points are collinear using column vectors.
- 475a: Determine a vector by equating coefficients for two different scalars/routes.
- 475b: Determine a ratio by writing a vector using two different scalars/routes.
- 475c: Determine a ratio of vectors by extending out a vector.
- 505n: Prove that position vectors form a given shape. (not yet active)
- 473: Exam Practice: Vectors using variables
- 474: Exam Practice: Parallel vectors and straight line proofs using vectors
- 475: Exam Practice: Solving vector problems by introduction of a scalar
- 505: Exam Practice: Position vectors and the distance between two points from their position vectors
Other resources
Worksheets
- MadAsMaths (T. Madas)
- Vector Algebra Introduction 2D Vectors Q3, 5, 7–9, 11–17 (difficulty 3–5 of 5)
- Vectors Exam Questions Part A Q5, 12, 22, 30, 33, 44, 54, 57, 69, 89, 112, 148, 149, 156 (difficulty 2–5 of 5)
- Vectors Practice Part A Vector Algebra & Geometry Q1–12 (difficulty 2–5 of 5)
11F Context Problems
Textbook resources
Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.
Dr Frost resources
Bicen Maths Live Lesson
Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths
Download Blank Notes
(Courtesy of King’s Chester Maths Department)
Download Slides
Extra Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 660a: Determine the speed of a particle given its velocity vector.
- 660b: Determine the angle of direction associated with a velocity vector.
- 660c: Determine the bearing of a moving particle given two displacements.
- 660d: Use the formula textbfrB = textbfrA + textbfvt to determine the position of a particle after a given time or vice versa.
- 660e: Determine the velocity or speed of a particle given a displacement vector textbfrB = textbfrA + textbfvt
- 660f: Use the formula textbfrB = textbfrA + textbfvt to determine the velocity or speed of a particle given two displacements.
- 554a: Determine the resultant vector of forces expressed in i and j notation.
- 554c: Determine the magnitude of a force vector.
- 554d: Determine the direction of a force vector as an angle.
- 660: Exam Practice: Vector calculations for displacement or velocity with constant velocity
- 554: Exam Practice: Forces as vectors
Other resources
Alternative Handouts
- Acute Learning Problem Pairs as PowerPoint or PDF
Activities
- Lord Franklin Vectors The Chalk Face
Online Platforms
- Khan Academy
- Vector word problems: Videos & practice
Whole Topic Summary Resources (Including Past Paper Questions)
Download PPQs as WW Powerpoint for AS Vectors
External Whole Topic Past Paper Style Questions
- WW Dr Frost Style QQQs (Version 1) Word Doc, PDF (Q’s Only) or PDF (Q’s & Sol.)
- WW Dr Frost Style QQQs (Version 2) Word Doc, PDF (Q’s Only) or PDF (Q’s & Sol.)
- Jethwa Maths Worksheet, Topic Test (coming soon) & Starter Activity
- PMT
Activities
- NRICH (student problems)
- MEI
- Andy Lutwyche
Worksheets
- MathedUp
- Vectors: Questions
- Maths Genie
- Vectors: Questions · Solutions · Lesson · Topic page
- Jethwa Maths
- Year 1 Vectors: Worksheets✦
- Vectors mini-tests/starters✦
- Mathsaurus (Kevin Olding)
- Physics & Maths Tutor
- Vectors: Questions 2021–24 · Mark scheme · Model answers · Questions 2018–21 (with MS) · Model answers
- Dr Austin Maths
✦ Links marked ✦ are also featured and recommended by Jo Morgan on Resourceaholic.