The Straight Line
We have below bronze, silver and gold tutorials for our Higher Maths Straight Line 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; E+F 1.4a, REL 1.1a, REL 1.1c, REL 1.4a
- Calculating the gradient of a straight line
- Rearranging an equation to find the gradient and y-intercept
- Calculating the equation of a straight line
- Solving equations
- Pythagoras' Theorem
Contents:-
1.1 - The gradient of a straight line
1.2 - The equation of a straight line
1.3 - Calculating the gradient when given the angle
1.4 - The distance between 2 points
1.5 - Calculating the midpoint of a line
1.6 - Parallel and perpendicular gradients
1.7 - Collinearity
1.8 - Lines associated with triangles
1.9 - Points of intersection 1
1.1 - The gradient of a straight line
In this module we revise how to calculate the gradient of a straight line. At gold level we learn how to work backwards to calculate missing values when given the gradient.
Video 1: Outcome 1 - The gradient of a straight line (whole numbers). Grab a pen and your Rigour jotter. Make sure you try all the questions!
Video 2: Outcome 2 - The gradient of a straight line (fractions). Remember to copy down the worked examples and take notes. These will help you revise and remember!
Video 3: Outcome 3 - Finding a point when given the gradient. 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?
If you feel you have mastered these skills why not try this short quiz under exam conditions? You will be provided with instant feedback so be sure to view it. Remember to re-do any video lessons for any questions you answered incorrectly. Once you have completed the quiz record the score in your profile. After this, check to see if there are any past paper questions for this module at the bottom of this page to try.
1.2 - The equation of a straight line
In this module we revise how to calculate the equation of a straight line. Extra practice should be put into the gold section when we look at how to deal with fractions.
Video 4: Outcome 1 - The equation of a straight line when given a point and the gradient. Grab a pen and your Rigour jotter. Make sure you try all the questions!
Video 5: Outcome 2 - The equation of a straight line when given 2 points. Remember to copy down the worked examples and take notes. These will help you revise and remember!
Video 6: Outcome 3 - The equation of a straight line (with fractions!). 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?
If you feel you have mastered these skills why not try this short quiz under exam conditions? You will be provided with instant feedback so be sure to view it. Remember to re-do any video lessons for any questions you answered incorrectly. Once you have completed the quiz record the score in your profile. After this, check to see if there are any past paper questions for this module at the bottom of this page to try.
1.3 - Calculating the gradient when given the angle
In this module we learn how to calculate the gradient when given the angle that the line makes with the positive direction of the x-axis. We also discover that we can calculate the angle when given the gradient. We finish off with a brief introduction to some exact values.
Video 7: Outcome 1 - Calculating the gradient when given the angle. Grab a pen and your Rigour jotter. Make sure you try all the questions!
Video 8: Outcome 2 - Calculating the angle when given the gradient. Remember to copy down the worked examples and take notes. These will help you revise and remember!
Video 9: Outcome 3 - Finding the gradient and angle with an introduction to exact values. 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?
If you feel you have mastered these skills why not try this short quiz under exam conditions? You will be provided with instant feedback so be sure to view it. Remember to re-do any video lessons for any questions you answered incorrectly. Once you have completed the quiz record the score in your profile. After this, check to see if there are any past paper questions for this module at the bottom of this page to try.
1.4 - The distance between 2 points
In this module we learn two different methods that can be used to calculate the distance between 2 points.
Video 10: Outcome 1 - The distance between two points. Grab a pen and your Rigour jotter. Make sure you try all the questions!
If you feel you have mastered these skills why not try this short quiz under exam conditions? You will be provided with instant feedback so be sure to view it. Remember to re-do any video lessons for any questions you answered incorrectly. Once you have completed the quiz record the score in your profile. After this, check to see if there are any past paper questions for this module at the bottom of this page to try.
1.5 - Calculating the Midpoint
This module shows us how to calculate the midpoint of a straight line. We also learn how to calculate the coordinates of an end-point when given the midpoint.
Video 11: Outcome 1 - Calculating the Midpoint (for positive numbers). Grab a pen and your Rigour jotter. Make sure you try all the questions!
Video 12: Outcome 2 - Calculating the angle when given the gradient. Remember to copy down the worked examples and take notes. These will help you revise and remember!
Video 13: Outcome 3 - Finding an end point when given the Midpoint. 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?
If you feel you have mastered these skills why not try this short quiz under exam conditions? You will be provided with instant feedback so be sure to view it. Remember to re-do any video lessons for any questions you answered incorrectly. Once you have completed the quiz record the score in your profile. After this, check to see if there are any past paper questions for this module at the bottom of this page to try.
1.6 - Parallel and perpendicular gradients
In this module we learn how to calculate the equations of parallel and perpendicular lines. We finish at gold level with a recap of some exact values.
Video 14: Outcome 1 - Parallel gradients. Grab a pen and your Rigour jotter. Make sure you try all the questions!
Video 15: Outcome 2 - Perpendicular gradients. Remember to copy down the worked examples and take notes. These will help you revise and remember!
Video 16: Outcome 3 - Parallel and perpendicular gradients with exact values. 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?
If you feel you have mastered these skills why not try this short quiz under exam conditions? You will be provided with instant feedback so be sure to view it. Remember to re-do any video lessons for any questions you answered incorrectly. Once you have completed the quiz record the score in your profile. After this, check to see if there are any past paper questions for this module at the bottom of this page to try.
1.7 - Collinearity
Do you know what collinear means? How could you show that 3 points are collinear? Find out how in the module below. Well worth a watch!
Video 17: Outcome 1 - Collinearity. Grab a pen and your Rigour jotter. Make sure you try all the questions!
If you feel you have mastered these skills why not try this short quiz under exam conditions? You will be provided with instant feedback so be sure to view it. Remember to re-do any video lessons for any questions you answered incorrectly. Once you have completed the quiz record the score in your profile. After this, check to see if there are any past paper questions for this module at the bottom of this page to try.
1.8 - Lines associated with triangles
In this module we learn how to calculate the equation of medians, altitudes and perpendicular bisectors. Learning the key steps is crucial here. Well worth a watch!
Video 18: Outcome 1 - Medians. Grab a pen and your Rigour jotter. Make sure you try all the questions!
Video 19: Outcome 2 - Altitudes. Remember to copy down the worked examples and take notes. These will help you revise and remember!
Video 20: Outcome 3 - Perpendicular bisectors. 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?
If you feel you have mastered these skills why not try this short quiz under exam conditions? You will be provided with instant feedback so be sure to view it. Remember to re-do any video lessons for any questions you answered incorrectly. Once you have completed the quiz record the score in your profile. After this, check to see if there are any past paper questions for this module at the bottom of this page to try.
1.9 - Points of intersection 1
In this module we learn how to calculate the point of intersection between 2 straight lines. Particular attention should be spent on the gold section when we will be dealing with fractions.
Video 21: Outcome 1 - The point of intersection between 2 straight lines for positive 'x'. Grab a pen and your Rigour jotter. Make sure you try all the questions!
Video 22: Outcome 2 - The point of intersection between 2 straight lines for negative 'x'. Remember to copy down the worked examples and take notes. These will help you revise and remember!
Video 23: Outcome 3 - The point of intersection between 2 straight lines (with fractions!). 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?
If you feel you have mastered these skills why not try this short quiz under exam conditions? You will be provided with instant feedback so be sure to view it. Remember to re-do any video lessons for any questions you answered incorrectly. Once you have completed the quiz record the score in your profile. After this, check to see if there are any past paper questions for this module at the bottom of this page to try.
Straight Line - Cheat Sheet
Download this handy Straight Line Cheat Sheet consisiting of key steps and exam strategies to help you answer the past paper questions below - all on one handy sheet of A4 paper.
Continually reviewing strategies helps ensure you learn them!
Adobe Acrobat document [237.4 KB]
Past Paper Questions
Multiple Choice Questions
We have below a selection of Multiple Choice Exam questions. Although the exam is not in this format any more these questions provide an excellent opportunity to quickly test you on your knowledge of the topic before you try the longer questions in the section after this. To try the questions, just click on the links below.
SQA Exam Questions
You will find below a collection of Straight Line 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.
1.3 - Calculating the gradient when given the angle
- 2022 Paper 1 Question 5
- 2018 Paper 1 Question 8
- 2005 Paper 1 Question 1
- 2004 Paper 2 Question 1
- 2000 Paper 1 Question 3
1.6 - Parallel and perpendicular gradients
- 2022 Paper 1 Question 1
- 2019 Paper 1 Question 7
- 2017 Paper 1 Question 11
- 2016 Paper 1 Question 1
- Specimen Paper 1 Question 5
- 2007 Paper 1 Question 1
- 2006 Paper 2 Question 1
- 2003 Paper 1 Question 1
- 2001 Paper 1 Question 1
1.7 - Collinearity
1.8 - Lines associated with triangles
- 2023 Paper 1 Question 2
- 2023 Paper 2 Question 1
- 2018 Paper 1 Question 1
- 2017 Paper 1 Question 7
- 2016 Paper 2 Question 1
- Specimen Paper 1 Question 9
- 1995 Paper 1 Question 5
- 1999 Paper 2 Question 1
- 1998 Paper 1 Question 1
- 1988 Paper 1 Question 1
1.9 - Points of intersection 1
- 2022 Paper 2 Question 1
- 2019 Paper 2 Question 1
- 2018 Paper 2 Question 5
- 2017 Paper 2 Question 1
- 2015 Paper 2 Question 1
- Exemplar Paper 1 Question 6
- 2014 Paper 2 Question 1
- 2013 Paper 2 Question 2
- 2012 Paper 1 Question 23
- 2011 Paper 1 Question 21
- 2010 Paper 1 Question 21
- 2009 Paper 1 Question 21
- 2008 Paper 2 Question 1
- Specimen Paper 1 Question 1
- 2006 Paper 1 Question 1
- 2004 Paper 1 Question 1
- 2002 Paper 2 Question 1
- 1999 Paper 1 Question 2
- 1996 Paper 2 Question 2
- 1992 Paper 1 Question 2
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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