Vectors
We have below bronze, silver and gold tutorials for our Higher Maths Vectors topic. Typically as you work through the modules, the difficulty of the skills increase by one step ensuring smooth progression. Simply click on the video to play it and pause it at the relevant points for you to attempt the questions. Each tutorial has a corresponding worksheet for you to download if additional practice is required. Make sure you have a pen and paper handy! Be sure to mark your work for every exercise attempted and record your score and time taken in your recording grid.
Essential prior knowledge:-
National 5 Maths; App 1.2
- Vector calculations
- Calculating the magnitude of a vector
- 3D Coordinates
- Vector journeys
Contents:-
12.1 - Working with vector components
12.2 - Vector journeys
12.3 - Collinearity and ratio
12.4 - Scalar product
12.5 - Calculating the angle between 2 vectors
12.1 - Working with vector components
At bronze level we learn about position vectors and how to calculate the components of a journey between two points followed by, at silver level, revising how to find the magnitude of a vector.
Our gold section introduces us to unit vectors and how to perform calculations involving them.
Video 121: Outcome 1 - Using vector components. Grab a pen and your Rigour jotter. Make sure you try all the questions!
Video 122: Outcome 2 - The magnitude of a vector. Remember to copy down the worked examples and take notes. These will help you revise and remember!
Video 123: Outcome 3 - Unit vectors. This is the final video in this module. After completing the questions why don't you try the past paper questions on this section at the bottom of the page?
12.2 - Vector journeys
At bronze level we revise how to describe vector journeys in terms of 'p', 'q' and 'r'. At silver level we learn how to describe a vector journey by using our answer from the part before.
At gold level we learn how to calculate the components of a vector journey - well worth a watch!
Video 124: Outcome 1 - Describing a vector journey in terms of 'p', 'q' and 'r'. Grab a pen and your Rigour jotter. Make sure you try all the questions!
Video 125: Outcome 2 - Describing vector journeys using the previous answer. Remember to copy down the worked examples and take notes. These will help you revise and remember!
Video 126: Outcome 3 - Calculating the components of a vector journey. This is the final video in this module. After completing the questions why don't you try the past paper questions on this section at the bottom of the page?
12.3 - Collinearity and ratio
In part one of this module we revise, at bronze level, how to show that 2D points are collinear. At silver level we learn how to show that 3D points are collinear and how to find the ratio that the points divides the line in.
At gold level in this module we learn how to find the coordinates of a point dividing a line when given the ratio. This tricky skill is well worth a watch and a practise!
Video 127: Outcome 1 - 2D collinearity. Grab a pen and your Rigour jotter. Make sure you try all the questions!
Video 128: Outcome 2 - 3D collinearity. Remember to copy down the worked examples and take notes. These will help you revise and remember!
Video 129: Outcome 3 - Finding a point when given the ratio. This is the final video in this module. After completing the questions why don't you try the past paper questions on this section at the bottom of the page?
12.4 - Scalar product
At bronze level we learn how to calculate the scalar product when given a vector's components. In the silver section we learn how to show that two vectors are perpendicular and how to find missing terms in perpendicular vectors.
At gold level we learn how to calculate the scalar product from diagrams. We call this section "hard a.b stuff"! This "a/b" standard video is well worth a watch!
Video 130: Outcome 1 - The scalar product. Grab a pen and your Rigour jotter. Make sure you try all the questions!
Video 131: Outcome 2 - Perpendicular vectors. Remember to copy down the worked examples and take notes. These will help you revise and remember!
Video 132: Outcome 3 - 'Hard' a.b stuff. This is the final video in this module. After completing the questions why don't you try the past paper questions on this section at the bottom of the page?
12.5 - The angle between 2 vectors
In this video, we learn how to calculate the angle between two vectors. Knowing how to calculate the scalar product and the magnitude of a vector (see above moules) is essential prior knowledge before viewing this video!
Video 133: Outcome 1 - The angle between 2 vectors. This is the only video in this module. After completing the questions why don't you try the past paper questions on this section at the bottom of the page?
Past Paper Questions
SQA Exam Questions
You will find below a collection of Vectors SQA past paper questions. You should click on a question, pause the video when instructed and give the question your best shot. Then un-pause the video and watch the worked solution. If the question is from paper 1 you should NOT use a calculator. You should make this section a regular place to come back to when revising. Even if you get the correct answer, it is recommended that you try all these questions more than once at various stages throughout the year.
12.1 - Vectors introduction
12.2 - Vectors journeys
12.3 - Collinearity and Ratio
- 2019 Paper 1 Question 5
- 2018 Paper 1 Question 5
- 2016 Paper 1 Question 11
- 2009 Paper 1 Question 22
- 2004 Paper 1 Question 5
- 2001 Paper 1 Question 3
- 1997 Paper 1 Question 2
- 1996 Paper 1 Question 6
- 1994 Paper 1 Question 4
12.4 - Scalar product
12.5 - The angle between 2 vectors
Congratulations!
You have completed this module - well done! Remember to go back and redo any areas of weakness, that's how we improve. If you are happy with all areas, go back to the main menu and pick another topic to practice!
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