Ready to master percentage changes and transformations? These topics might... Show more
Maths165 views·Updated May 26, 2026·4 pagesMastering Maths: Comprehensive Topic Review
Isha Patel@ishx_0119
1 / 4
1
of 4
Compound Changes
Ever wondered how your savings grow over time or why car values drop each year? Compound changes happen when you apply percentage changes repeatedly - like getting interest on your interest!
The magic formula is: compound value = original × (multiplier)ⁿ. Remember that 25% less means multiply by 0.75, whilst 5% more means multiply by 1.05. The 'n' tells you how many time periods you're dealing with.
Reverse problems work backwards from the final amount. If £3375 becomes your total after 3 years at 50% interest, divide by 1.5³ to find you started with £1000. For unknown time periods, you'll need logarithms - don't panic, your calculator can handle these!
Quick tip: When no original value is given, just pick a round number like £10,000 to make calculations easier.
2
of 4
Simple Interest and Transformations
Simple interest is much easier than compound - you earn the same amount each year using I = p × r × t. If you invest £300 for 2 years at 4% annually, you'll earn £24 total (£12 per year).
Now for something completely different - transformations! These are the four ways to move shapes around: translation (sliding with vectors), reflection (flipping across mirror lines), rotation (spinning around a centre), and enlargement (changing size from a centre point).
Vectors like (3, -4) mean 3 units right and 4 units down. Rotations need three pieces of info: direction , angle (usually 90°, 180°, or 270°), and the centre point coordinates.
Watch out: Negative enlargements cause the shape to flip 180° as well as change size!
3
of 4
Tricky Transformations and Invariant Points
Here's where many students get caught out! If two shapes look like one has been rotated but they're different sizes, it's actually an enlargement with a negative scale factor, not a rotation.
The only exception is when the scale factor equals -1 - this has exactly the same effect as a 180° rotation, so either description counts as correct. Your examiner will accept both answers!
Invariant points are spots that don't move during transformations. With translations, points only stay put if the vector is (0,0). For rotations, the centre point stays fixed (unless it's outside the shape). With enlargements, any point that sits exactly on the centre of enlargement won't budge.
Pro tip: Take your time finding all vertices after transformations - rushing leads to shapes drawn in completely wrong orientations!
4
of 4
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Maths165 views·Updated May 26, 2026·4 pagesMastering Maths: Comprehensive Topic Review
Isha Patel@ishx_0119
Ready to master percentage changes and transformations? These topics might seem tricky at first, but once you get the hang of the formulas and key principles, you'll be solving problems like a pro.
1
of 4Sign up to see the content. It's free!
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- Improve your grades
- Join milions of students
Compound Changes
Ever wondered how your savings grow over time or why car values drop each year? Compound changes happen when you apply percentage changes repeatedly - like getting interest on your interest!
The magic formula is: compound value = original × (multiplier)ⁿ. Remember that 25% less means multiply by 0.75, whilst 5% more means multiply by 1.05. The 'n' tells you how many time periods you're dealing with.
Reverse problems work backwards from the final amount. If £3375 becomes your total after 3 years at 50% interest, divide by 1.5³ to find you started with £1000. For unknown time periods, you'll need logarithms - don't panic, your calculator can handle these!
Quick tip: When no original value is given, just pick a round number like £10,000 to make calculations easier.
2
of 4Sign up to see the content. It's free!
- Access to all documents
- Improve your grades
- Join milions of students
Simple Interest and Transformations
Simple interest is much easier than compound - you earn the same amount each year using I = p × r × t. If you invest £300 for 2 years at 4% annually, you'll earn £24 total (£12 per year).
Now for something completely different - transformations! These are the four ways to move shapes around: translation (sliding with vectors), reflection (flipping across mirror lines), rotation (spinning around a centre), and enlargement (changing size from a centre point).
Vectors like (3, -4) mean 3 units right and 4 units down. Rotations need three pieces of info: direction , angle (usually 90°, 180°, or 270°), and the centre point coordinates.
Watch out: Negative enlargements cause the shape to flip 180° as well as change size!
3
of 4Sign up to see the content. It's free!
- Access to all documents
- Improve your grades
- Join milions of students
Tricky Transformations and Invariant Points
Here's where many students get caught out! If two shapes look like one has been rotated but they're different sizes, it's actually an enlargement with a negative scale factor, not a rotation.
The only exception is when the scale factor equals -1 - this has exactly the same effect as a 180° rotation, so either description counts as correct. Your examiner will accept both answers!
Invariant points are spots that don't move during transformations. With translations, points only stay put if the vector is (0,0). For rotations, the centre point stays fixed (unless it's outside the shape). With enlargements, any point that sits exactly on the centre of enlargement won't budge.
Pro tip: Take your time finding all vertices after transformations - rushing leads to shapes drawn in completely wrong orientations!
4
of 4Sign up to see the content. It's free!
- Access to all documents
- Improve your grades
- Join milions of students
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.
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Students love us — and so will you.
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The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan SiOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
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