Prior content: AS Vectors (2D)
Previous Section: Integration
Next Section: A2 Pure General Support
Contents
- Whole Topic Notes
- 12A Introduction to 3D Vectors
- 12B i j k and Unit Vectors
- 12C Modelling with Vectors
- 12D Forces as Vectors
- 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 or PDF (Courtesy of King’s Chester Maths Department)
Acute Learning Whole Chapter Problem Pairs
12A Introduction to 3D Vectors
Textbook resources
Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.
Dr Frost resources
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
- 505b: Determine a 3D position vector given another position vector and the vector between them.
- 505d: Determine the vector between two 3D position vectors.
- 505h: Calculate the distance between two 3D position vectors.
- 505j: Determine a component of a 3D position vector given the distance between two points. (not yet active)
- 505: Exam Practice: Position vectors and the distance between two points from their position vectors
Other resources
Worksheets
- Mathshelper (Jon Stone)
- MadAsMaths (T. Madas)
- Vector Algebra Introduction 2D Vectors Q6; 3D Vectors Q1–25, 27–28 (difficulty 2–5 of 5)
12B i j k and Unit Vectors
Textbook resources
Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.
Dr Frost resources
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
- 504b: Write a column vector in textbfi-textbfj-textbfk form.
- 504d: Write a vector in textbfi-textbfj-textbfk form as a 3D column vector.
- 504e: Add and subtract vectors written in textbfi-textbfj-textbfk form.
- 504g: Calculate the magnitude of a 3D vector written in textbfi-textbfj-textbfk form.
- 504i: Determine a component of a 3D vector in textbfi-textbfj-textbfk notation given its magnitude. (not yet active)
- 504k: Convert a 3D vector in either column vector or textbfi-textbfj-textbfk form to a unit vector.
- 504: Exam Practice: Writing vectors in terms of unit vectors
Other resources
Other Videos
Courtesy of Maths Genie
Worksheets
- MadAsMaths (T. Madas)
- Vectors Exam Questions Part A Q2, 11, 15, 55 (difficulty 2–3 of 5)
- Vectors Practice Part A Vector Components & 3D Coordinates Q1–23
12C Modelling with Vectors
Textbook resources
Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.
Dr Frost resources
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
- 505k: Determine the coordinate of a point given a mixture of position vectors and vectors between them.
- 505m: Determine an unknown component of a 3D position vector for collinear points.
- 505n: Prove that position vectors form a given shape. (not yet active)
- 505o: Find the position vector of a point in a 3D diagram involving vector variables. (not yet active)
- 505p: Prove that two lines intersect in 3D using vector expressions. (not yet active)
- 505: Exam Practice: Position vectors and the distance between two points from their position vectors
Other resources
Online Platforms
- Khan Academy
- Vector word problems: Videos & practice
Worksheets
- MadAsMaths (T. Madas)
- Vectors Exam Questions Part A Q59, 116, 137 (difficulty 4 of 5)
12D Forces as Vectors
Textbook resources
Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.
Dr Frost resources
Download Blank Notes
(Courtesy of King’s Chester Maths Department)
Download Slides
Extra Questions
- Dr Frost Questions (No 3D Qs on Dr Frost to date with Vectors as Forces. Also Practice D question from the past paper Q’s using the link below)
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 554a: Determine the resultant vector of forces expressed in i and j notation.
- 554b: Determine unknown components in force vectors that gives a resultant vector or achieves equilibrium.
- 554c: Determine the magnitude of a force vector.
- 554d: Determine the direction of a force vector as an angle.
- 554e: Solve problems where the resultant vector is parallel to a given direction.
- 554: Exam Practice: Forces as vectors
Other resources
Online Platforms
- Khan Academy
- Adding vectors in magnitude & direction form: Videos & practice
Whole Topic Summary Resources (Including Past Paper Questions)
Download PPQs as WW Powerpoint for A2 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) and Starter Activity
- Solomon Worksheet (Q11 Onwards for 3D Vectors) and Answers
- PMT
- OCR MEI
- Vectors (Yr. 2) (No Calculus but Some Accessible Old Spec Questions)
- Cheat Sheet
- OCR MEI
Activities
- NRICH (student problems)
- Andy Lutwyche
Worksheets
- MathedUp
- Vectors: Questions
- Maths Genie
- Vectors: Questions · Solutions · Lesson · Topic page
- Jethwa Maths
- Year 2 Vectors: Worksheets
- Mathsaurus (Kevin Olding)
- Physics & Maths Tutor
- Vectors: Questions 2021–24 · Mark scheme · Model answers · Questions 2018–21 (with MS) · Model answers
- MME
- Dr Austin Maths
✦ Links marked ✦ are also featured and recommended by Jo Morgan on Resourceaholic.