Logs and Exponentials
We have below bronze, silver and gold tutorials for our Higher Maths Logs and Exponentials 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:-
Higher Maths Maths; 4.2
- Exponential Graphs
- Logarithmic Graphs
Contents:-
14.1 - Simplifying numerical expressions
14.2 - Solving logarithmic equations
14.3 - Solving exponential equations
14.4 - Experimental data
14.1 - Simplifying numerical expressions
At bronze level we learn how to simplify basic logarithmic expressions by learning how they can be re-written as exponentials. At silver level, we learn how to combine logs...but only if they have the same base!
In the gold section we learn about a rule for logarithms which enables us to deal with constants at the start of our expressions.
Video 140: Outcome 1 - Simplifying numerical expressions. Grab a pen and your Rigour jotter. Make sure you try all the questions!
Video 141: Outcome 2 - Combining logs. Remember to copy down the worked examples and take notes. These will help you revise and remember!
Video 142: Outcome 3 - Bringing stuff "up/down". 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?
Do you need to check your working? If so, download the full solutions to the questions in the video lessons for 14.1 - Evaluating Numerical Expressions below;
Adobe Acrobat document [496.8 KB]
14.2 - Solving logarithmic equations
At bronze level we learn how to solve basic logarithmic equations by re-writing them as exponentials. In the silver section, we learn a 3-step strategy that will enable us to solve trickier equations.
Using our silver strategy, we then learn how to solve logarithmic equations involving brackets at gold level. Well worth a watch!
Video 143: Outcome 1 - Solving simple log equations. Grab a pen and your Rigour jotter. Make sure you try all the questions!
Video 144: Outcome 2 - Solving "standard" log equations. Remember to copy down the worked examples and take notes. These will help you revise and remember!
Video 145: Outcome 3 - Solving equations with brackets. 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?
Do you need to check your working? If so, download the full solutions to the questions in the video lessons for 14.2 - Solving Logarithmic Equations below;
Adobe Acrobat document [537.8 KB]
14.3 - Solving exponential equations
In this module, we learn how to solve exponential equations. At bronze level, we learn the basic skill. At silver level we learn how to evaluate "exam style" exponential equations.
At gold level, we learn how to calculate the 'half life' of an expoonential function. This video will give us the skills we need to try the pastpaper questions.
Video 146: Outcome 1 - Solving exponential equations. Grab a pen and your Rigour jotter. Make sure you try all the questions!
Video 147: Outcome 2 - Evaluating exponentials equations. Remember to copy down the worked examples and take notes. These will help you revise and remember!
Video 148: Outcome 3 - Finding the 'half life'. 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?
Do you need to check your working? If so, download the full solutions to the questions in the video lessons for 14.3 - Solving Exponential Equations below;
Adobe Acrobat document [640.8 KB]
14.4 - Experimental data
In this module, we learn about the connection between raw data, logarithims and straight lines. At bronze level we learn about equations of the form y = ax and at silver level we progress onto equations of the form y = kax.
In our gold module you will learn about equations of the form y = kxn. Once you have completed this module you should try the exam questions below.
Video 149: Outcome 1 - Equations of the form y = ax. Grab a pen and your Rigour jotter. Make sure you try all the questions!
Video 150: Outcome 2 - Equations of the form y = kax. Remember to copy down the worked examples and take notes. These will help you revise and remember!
Video 151: Outcome 3 - Equations of the form y = kxn. 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?
Do you need to check your working? If so, download the full solutions to the questions in the video lessons for 14.4 - Experimental Data below;
Adobe Acrobat document [643.5 KB]
Past Paper Questions
SQA Pastpaper Questions
You will find below a collection of Logs and Exponentials SQA pastpaper 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.
14.1 - Simplifying numerical expressions
- 2023 Paper 1 Question 7
- 2022 Paper 1 Question 2
- 2018 Paper 1 Question 6
- 2015 Paper 1 Question 6
- 2003 Paper 1 Question 12
- 2000 Paper 1 Question 9
14.2 - Solving logarithmic equations
- 2023 Paper 1 Question 3
- 2022 Paper 1 Question 8
- 2019 Paper 1 Question 14
- 2018 Paper 1 Question 11
- 2017 Paper 1 Question 12
- 2016 Paper 1 Question 14
- 2013 Paper 2 Question 5
- 2009 Paper 2 Question 3
- 2008 Paper 1 Question 23
- Specimen 1 Paper 1 Question 22
- 2007 Paper 2 Question 8
- 2005 Paper 2 Question 7
- 2004 Paper 1 Question 9
- 2002 Paper 2 Question 7
- 2001 Paper 1 Question 8
14.3 - Solving exponential equations
- 2023 Paper 2 Question 13
- 2022 Paper 2 Question 10
- 2019 Paper 2 Question 9
- 2018 Paper 2 Question 11
- 2016 Paper 2 Question 6
- Specimen Paper 2 Question 7
- 2009 Paper 2 Question 6
- 2006 Paper 2 Question 11
- 2005 Paper 2 Question 9
- 2004 Paper 2 Question 10
- 2001 Paper 2 Question 9
- 1992 Paper 2 Question 4
- 1989 Paper 1 Question 20
14.4 - Experimental Data
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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