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Maths

8 Dec 2025

2,765

16 pages

Year 9 Math Knowledge Organizer

user profile picture

katana @canelakaare

You're diving into Year 9 maths - the year where geometry, algebra, and numbers all come together to... Show more

YEAR 9 - REASONING WITH ALGEBRA...
Straight Line Graphs
@whisto_maths
What do I need to be able Keywords
to do?
ii Gradient: the steepness o

Maths and Money - Real-World Applications

Money maths isn't just about passing exams - it's about making smart financial decisions throughout your life. Whether you're comparing phone contracts, understanding your first payslip, or planning a trip abroad, these skills are genuinely essential.

Simple interest stays the same each year, while compound interest grows because you earn interest on your interest. If you invest £100 at 30% simple interest for 4 years, you'll have £220 total. With compound interest, you'd have £285.61 because each year's interest gets added to the pot.

Exchange rates work through direct proportion - if £1 = 1.40,then£200=1.40, then £200 = 280. Always check which direction you're converting and use the inverse operation to go backwards. When comparing unit prices, divide the total cost by the number of items to find the cost per unit.

Understanding VAT (Value Added Tax) is crucial - it's 20% added to most purchases in the UK. Essential items like food are VAT-free, but luxury items aren't. Your future salary will be taxed in brackets, so the more you earn, the higher percentage you'll pay on the top portion.

Key tip Always estimate your answers first - if your calculation seems wildly off, you've probably made an error!

YEAR 9 - REASONING WITH ALGEBRA...
Straight Line Graphs
@whisto_maths
What do I need to be able Keywords
to do?
ii Gradient: the steepness o

Ratio and Proportion - Sharing and Scaling

Ratio and proportion help you scale recipes, share costs fairly, and find the best deals. They're about relationships between quantities rather than the actual amounts.

Direct proportion means both quantities change by the same scale factor. If 4 cans cost £2.40, then 12 cans cost £7.20 (multiplying both by 3). Conversion graphs for changing currencies or units always create straight lines because of this constant relationship.

Inverse proportion works oppositely - as one quantity increases, the other decreases by the same factor. More workers means less time to complete a job. If 2 workers take 20 hours, then 8 workers take 5 hours.

Best buy problems require you to find the cost per unit or the amount per pound. Don't just compare total prices - a bigger pack might be worse value per item. Calculate cost per unit for both options and choose the cheaper one.

Key tip Always identify whether problems involve direct or inverse proportion before starting - it determines your entire approach!

YEAR 9 - REASONING WITH ALGEBRA...
Straight Line Graphs
@whisto_maths
What do I need to be able Keywords
to do?
ii Gradient: the steepness o

Forming and Solving Equations - Algebra in Action

Algebra might seem abstract, but it's actually about describing real situations mathematically. When you're sharing pizza costs or working out mobile phone deals, you're using algebraic thinking without realising it.

Inequalities work like equations but show ranges of values instead of exact answers. When you multiply or divide by a negative number, flip the inequality sign - this trips up many students! For example, if -3x > 15, then x < -5 notx>5not x > -5.

Equations with unknowns on both sides need you to collect like terms. Move all the x terms to one side and all the numbers to the other. Always do the same operation to both sides to keep the equation balanced.

Rearranging formulae is like solving equations backwards - you're making a different letter the subject. This is essential for science subjects where you need to rearrange equations like v = u + at. Use inverse operations in reverse order, just like unwrapping a mathematical parcel.

Key tip Always check your solutions by substituting back into the original equation - if it works, you've got the right answer!

YEAR 9 - REASONING WITH ALGEBRA...
Straight Line Graphs
@whisto_maths
What do I need to be able Keywords
to do?
ii Gradient: the steepness o

Rates and Calculations - Speed, Density, and Flow

Understanding rates helps you make sense of everything from speed cameras to recipe adjustments. A rate tells you how one quantity changes relative to another - like miles per hour or grams per cubic centimetre.

For speed, distance, and time problems, remember that speed = distance ÷ time. Make sure your units match - if speed is in mph, time should be in hours and distance in miles. Distance-time graphs show journeys visually, where the gradient represents speed and horizontal lines mean staying still.

Density measures how much mass fits in a given volume using density = mass ÷ volume. This helps explain why oil floats on water (it's less dense) or why a small piece of gold feels surprisingly heavy. Always check your units match up in the formula.

Flow problems often involve containers filling at different rates. The key is understanding that as containers get narrower, the liquid level rises faster even though the flow rate stays constant. This creates curved graphs for oddly-shaped containers.

Key tip Draw diagrams for flow problems - visualising the container shape helps you understand how the depth changes over time!

YEAR 9 - REASONING WITH ALGEBRA...
Straight Line Graphs
@whisto_maths
What do I need to be able Keywords
to do?
ii Gradient: the steepness o

Constructing in 2D and 3D Shapes

3D shapes are everywhere around you - from the cylindrical cans in your kitchen to the rectangular prism that is your phone. Understanding these shapes helps you calculate everything from how much paint you need for your bedroom to how much space your luggage takes up.

Prisms are 3D shapes with identical ends and flat sides - imagine pushing a 2D shape through space. The cross-section (the shape you'd see if you sliced through it) is always the same. Cylinders behave similarly but aren't technically prisms because their sides are curved.

Surface area is all about imagining you're unwrapping the shape like a present - what would the net look like when laid flat? For cuboids, calculate the area of each face and add them up. For cylinders, you need two circles plus a rectangle whose width equals the circumference.

Volume tells you how much space is inside the shape. For prisms and cylinders, multiply the area of the cross-section by the height. Think of it as stacking identical slices on top of each other.

Key tip Draw nets when calculating surface area - it helps you visualise which faces you've counted!

YEAR 9 - REASONING WITH ALGEBRA...
Straight Line Graphs
@whisto_maths
What do I need to be able Keywords
to do?
ii Gradient: the steepness o

Rotation and Translation - Moving Shapes Around

Transformations are everywhere in the real world - from the spinning wheels on your bike to the sliding doors at the supermarket. Understanding how shapes move helps in everything from computer game design to engineering.

Rotational symmetry tells you how many times a shape fits into itself during a full turn. A regular pentagon has rotational symmetry of order 5 because it looks identical 5 times as you rotate it through 360°. Tracing paper is your best friend for checking this.

Rotation requires three pieces of information the centre of rotation, the direction (clockwise or anticlockwise), and the angle. Every point on the shape moves in a circle around the centre, staying the same distance away.

Translation moves every point the same distance in the same direction. Vector notation like (3, -2) tells you to move 3 units right and 2 units down. Unlike rotation, translation doesn't change the orientation of the shape.

Key tip Use tracing paper for rotations - it makes visualising the movement much easier and reduces errors!

YEAR 9 - REASONING WITH ALGEBRA...
Straight Line Graphs
@whisto_maths
What do I need to be able Keywords
to do?
ii Gradient: the steepness o

Pythagoras' Theorem - Finding Missing Sides

Pythagoras' theorem is like a mathematical superpower - it helps you find missing lengths in right-angled triangles, whether you're calculating the shortest route across a field or working out screen sizes. The hypotenuse is always the longest side, opposite the right angle.

The theorem states that a² + b² = c², where c is the hypotenuse. If you know two sides, you can find the third. To find the hypotenuse, add the squares of the shorter sides and take the square root. To find a shorter side, subtract the known shorter side squared from the hypotenuse squared, then square root.

You can use Pythagoras on coordinate axes by treating any line segment as the hypotenuse of a right-angled triangle. The horizontal and vertical distances become your two shorter sides. This is incredibly useful in navigation and computer graphics.

To check if a triangle is right-angled, test whether the theorem works. If 3² + 4² = 5² whichgives9+16=25which gives 9 + 16 = 25, then you've got a right-angled triangle. Knowing your square numbers up to 12² makes these calculations much faster.

Key tip Always check your triangle has a right angle before using Pythagoras - it only works for right-angled triangles!

YEAR 9 - REASONING WITH ALGEBRA...
Straight Line Graphs
@whisto_maths
What do I need to be able Keywords
to do?
ii Gradient: the steepness o

Using Percentages - Real-World Applications

Percentages are probably the most useful maths skill for adult life. From understanding pay rises to comparing discounts, percentages help you make informed financial decisions.

Percentage increase and decrease use multipliers - values greater than 1 for increases, less than 1 for decreases. A 15% increase means multiplying by 1.15, while a 30% decrease means multiplying by 0.70. This method is much faster than calculating the percentage separately.

Reverse percentages work backwards from a result. If 40% of a number is 16, then 10% must be 4, so 100% is 40. This technique is essential for understanding sale prices and tax calculations.

Percentage change always compares to the original value. If you buy something for £200 and sell it for £125, the percentage loss is (75 ÷ 200) × 100 = 37.5%. Remember, the denominator is always the starting value.

Key tip Learn your percentage-decimal-fraction equivalents by heart - knowing that 25% = 0.25 = ¼ speeds up every calculation!

YEAR 9 - REASONING WITH ALGEBRA...
Straight Line Graphs
@whisto_maths
What do I need to be able Keywords
to do?
ii Gradient: the steepness o

Reasoning with Geometry - Angles and Parallel Lines

Ever wondered how architects ensure buildings are perfectly aligned? It all comes down to understanding parallel lines and the angles they create. When a transversal (a line that crosses other lines) cuts through parallel lines, it creates predictable angle patterns that are incredibly useful.

There are three key angle relationships you need to master. Alternate angles are equal - they're the Z-shaped pairs that appear on opposite sides of the transversal. Corresponding angles are also equal - think of them as being in the same relative position at each intersection. Co-interior angles always add up to 180° - they're the C-shaped pairs on the same side of the transversal.

When solving angle problems, link everything back to algebra. Set up equations using the angle rules you know, then solve for the unknown. For example, if two angles on a straight line are 2x and 4x, you know that 2x + 4x = 180°, so x = 30°.

Making conjectures about shapes means spotting patterns and testing whether they're always true. Remember, you only need one counterexample to prove a conjecture wrong, but you need logical proof to show it's always correct.

Key tip Always state your angle facts clearly when solving problems - examiners love to see your reasoning!

YEAR 9 - REASONING WITH ALGEBRA...
Straight Line Graphs
@whisto_maths
What do I need to be able Keywords
to do?
ii Gradient: the steepness o

Number Types and Operations - Building Strong Foundations

Numbers come in different families, and understanding these families helps you work more efficiently. Rational numbers can be written as fractions, while irrational numbers like √2 have decimal expansions that never end or repeat.

Directed numbers (positive and negative) follow predictable rules. When multiplying or dividing, same signs give positive results, different signs give negative results. Think of it as a friendship rule - friends of friends are friends, but friends of enemies are enemies!

HCF and LCM help solve practical problems like finding when buses arrive together or cutting materials into equal pieces. The Highest Common Factor is the biggest number that divides into both numbers, while the Lowest Common Multiple is the smallest number that both numbers divide into.

Standard form (like 3.4 × 10⁵) makes huge numbers manageable. Scientists use it for distances to stars or sizes of atoms. The power of 10 tells you how many places to move the decimal point.

Key tip When adding fractions, find a common denominator first - it's like making sure you're comparing apples with apples!

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Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.

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This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.

David K

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The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!

Sudenaz Ocak

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In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.

Greenlight Bonnie

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very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.

Rohan U

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I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.

Xander S

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THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮

Elisha

iOS user

This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now

Paul T

iOS user

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 S

iOS 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.

Samantha Klich

Android user

Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.

Anna

iOS user

Best app on earth! no words because it’s too good

Thomas R

iOS user

Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.

Basil

Android user

This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.

David K

iOS user

The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!

Sudenaz Ocak

Android user

In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.

Greenlight Bonnie

Android user

very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.

Rohan U

Android user

I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.

Xander S

iOS user

THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮

Elisha

iOS user

This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now

Paul T

iOS user

 

Maths

2,765

8 Dec 2025

16 pages

Year 9 Math Knowledge Organizer

user profile picture

katana

@canelakaare

You're diving into Year 9 maths - the year where geometry, algebra, and numbers all come together to build the foundation for your GCSE studies. These topics might seem challenging at first, but they're actually incredibly useful for solving real-world... Show more

YEAR 9 - REASONING WITH ALGEBRA...
Straight Line Graphs
@whisto_maths
What do I need to be able Keywords
to do?
ii Gradient: the steepness o

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Maths and Money - Real-World Applications

Money maths isn't just about passing exams - it's about making smart financial decisions throughout your life. Whether you're comparing phone contracts, understanding your first payslip, or planning a trip abroad, these skills are genuinely essential.

Simple interest stays the same each year, while compound interest grows because you earn interest on your interest. If you invest £100 at 30% simple interest for 4 years, you'll have £220 total. With compound interest, you'd have £285.61 because each year's interest gets added to the pot.

Exchange rates work through direct proportion - if £1 = 1.40,then£200=1.40, then £200 = 280. Always check which direction you're converting and use the inverse operation to go backwards. When comparing unit prices, divide the total cost by the number of items to find the cost per unit.

Understanding VAT (Value Added Tax) is crucial - it's 20% added to most purchases in the UK. Essential items like food are VAT-free, but luxury items aren't. Your future salary will be taxed in brackets, so the more you earn, the higher percentage you'll pay on the top portion.

Key tip: Always estimate your answers first - if your calculation seems wildly off, you've probably made an error!

YEAR 9 - REASONING WITH ALGEBRA...
Straight Line Graphs
@whisto_maths
What do I need to be able Keywords
to do?
ii Gradient: the steepness o

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Ratio and Proportion - Sharing and Scaling

Ratio and proportion help you scale recipes, share costs fairly, and find the best deals. They're about relationships between quantities rather than the actual amounts.

Direct proportion means both quantities change by the same scale factor. If 4 cans cost £2.40, then 12 cans cost £7.20 (multiplying both by 3). Conversion graphs for changing currencies or units always create straight lines because of this constant relationship.

Inverse proportion works oppositely - as one quantity increases, the other decreases by the same factor. More workers means less time to complete a job. If 2 workers take 20 hours, then 8 workers take 5 hours.

Best buy problems require you to find the cost per unit or the amount per pound. Don't just compare total prices - a bigger pack might be worse value per item. Calculate cost per unit for both options and choose the cheaper one.

Key tip: Always identify whether problems involve direct or inverse proportion before starting - it determines your entire approach!

YEAR 9 - REASONING WITH ALGEBRA...
Straight Line Graphs
@whisto_maths
What do I need to be able Keywords
to do?
ii Gradient: the steepness o

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Forming and Solving Equations - Algebra in Action

Algebra might seem abstract, but it's actually about describing real situations mathematically. When you're sharing pizza costs or working out mobile phone deals, you're using algebraic thinking without realising it.

Inequalities work like equations but show ranges of values instead of exact answers. When you multiply or divide by a negative number, flip the inequality sign - this trips up many students! For example, if -3x > 15, then x < -5 notx>5not x > -5.

Equations with unknowns on both sides need you to collect like terms. Move all the x terms to one side and all the numbers to the other. Always do the same operation to both sides to keep the equation balanced.

Rearranging formulae is like solving equations backwards - you're making a different letter the subject. This is essential for science subjects where you need to rearrange equations like v = u + at. Use inverse operations in reverse order, just like unwrapping a mathematical parcel.

Key tip: Always check your solutions by substituting back into the original equation - if it works, you've got the right answer!

YEAR 9 - REASONING WITH ALGEBRA...
Straight Line Graphs
@whisto_maths
What do I need to be able Keywords
to do?
ii Gradient: the steepness o

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Rates and Calculations - Speed, Density, and Flow

Understanding rates helps you make sense of everything from speed cameras to recipe adjustments. A rate tells you how one quantity changes relative to another - like miles per hour or grams per cubic centimetre.

For speed, distance, and time problems, remember that speed = distance ÷ time. Make sure your units match - if speed is in mph, time should be in hours and distance in miles. Distance-time graphs show journeys visually, where the gradient represents speed and horizontal lines mean staying still.

Density measures how much mass fits in a given volume using density = mass ÷ volume. This helps explain why oil floats on water (it's less dense) or why a small piece of gold feels surprisingly heavy. Always check your units match up in the formula.

Flow problems often involve containers filling at different rates. The key is understanding that as containers get narrower, the liquid level rises faster even though the flow rate stays constant. This creates curved graphs for oddly-shaped containers.

Key tip: Draw diagrams for flow problems - visualising the container shape helps you understand how the depth changes over time!

YEAR 9 - REASONING WITH ALGEBRA...
Straight Line Graphs
@whisto_maths
What do I need to be able Keywords
to do?
ii Gradient: the steepness o

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Constructing in 2D and 3D Shapes

3D shapes are everywhere around you - from the cylindrical cans in your kitchen to the rectangular prism that is your phone. Understanding these shapes helps you calculate everything from how much paint you need for your bedroom to how much space your luggage takes up.

Prisms are 3D shapes with identical ends and flat sides - imagine pushing a 2D shape through space. The cross-section (the shape you'd see if you sliced through it) is always the same. Cylinders behave similarly but aren't technically prisms because their sides are curved.

Surface area is all about imagining you're unwrapping the shape like a present - what would the net look like when laid flat? For cuboids, calculate the area of each face and add them up. For cylinders, you need two circles plus a rectangle whose width equals the circumference.

Volume tells you how much space is inside the shape. For prisms and cylinders, multiply the area of the cross-section by the height. Think of it as stacking identical slices on top of each other.

Key tip: Draw nets when calculating surface area - it helps you visualise which faces you've counted!

YEAR 9 - REASONING WITH ALGEBRA...
Straight Line Graphs
@whisto_maths
What do I need to be able Keywords
to do?
ii Gradient: the steepness o

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Rotation and Translation - Moving Shapes Around

Transformations are everywhere in the real world - from the spinning wheels on your bike to the sliding doors at the supermarket. Understanding how shapes move helps in everything from computer game design to engineering.

Rotational symmetry tells you how many times a shape fits into itself during a full turn. A regular pentagon has rotational symmetry of order 5 because it looks identical 5 times as you rotate it through 360°. Tracing paper is your best friend for checking this.

Rotation requires three pieces of information: the centre of rotation, the direction (clockwise or anticlockwise), and the angle. Every point on the shape moves in a circle around the centre, staying the same distance away.

Translation moves every point the same distance in the same direction. Vector notation like (3, -2) tells you to move 3 units right and 2 units down. Unlike rotation, translation doesn't change the orientation of the shape.

Key tip: Use tracing paper for rotations - it makes visualising the movement much easier and reduces errors!

YEAR 9 - REASONING WITH ALGEBRA...
Straight Line Graphs
@whisto_maths
What do I need to be able Keywords
to do?
ii Gradient: the steepness o

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Pythagoras' Theorem - Finding Missing Sides

Pythagoras' theorem is like a mathematical superpower - it helps you find missing lengths in right-angled triangles, whether you're calculating the shortest route across a field or working out screen sizes. The hypotenuse is always the longest side, opposite the right angle.

The theorem states that a² + b² = c², where c is the hypotenuse. If you know two sides, you can find the third. To find the hypotenuse, add the squares of the shorter sides and take the square root. To find a shorter side, subtract the known shorter side squared from the hypotenuse squared, then square root.

You can use Pythagoras on coordinate axes by treating any line segment as the hypotenuse of a right-angled triangle. The horizontal and vertical distances become your two shorter sides. This is incredibly useful in navigation and computer graphics.

To check if a triangle is right-angled, test whether the theorem works. If 3² + 4² = 5² whichgives9+16=25which gives 9 + 16 = 25, then you've got a right-angled triangle. Knowing your square numbers up to 12² makes these calculations much faster.

Key tip: Always check your triangle has a right angle before using Pythagoras - it only works for right-angled triangles!

YEAR 9 - REASONING WITH ALGEBRA...
Straight Line Graphs
@whisto_maths
What do I need to be able Keywords
to do?
ii Gradient: the steepness o

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Using Percentages - Real-World Applications

Percentages are probably the most useful maths skill for adult life. From understanding pay rises to comparing discounts, percentages help you make informed financial decisions.

Percentage increase and decrease use multipliers - values greater than 1 for increases, less than 1 for decreases. A 15% increase means multiplying by 1.15, while a 30% decrease means multiplying by 0.70. This method is much faster than calculating the percentage separately.

Reverse percentages work backwards from a result. If 40% of a number is 16, then 10% must be 4, so 100% is 40. This technique is essential for understanding sale prices and tax calculations.

Percentage change always compares to the original value. If you buy something for £200 and sell it for £125, the percentage loss is (75 ÷ 200) × 100 = 37.5%. Remember, the denominator is always the starting value.

Key tip: Learn your percentage-decimal-fraction equivalents by heart - knowing that 25% = 0.25 = ¼ speeds up every calculation!

YEAR 9 - REASONING WITH ALGEBRA...
Straight Line Graphs
@whisto_maths
What do I need to be able Keywords
to do?
ii Gradient: the steepness o

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Reasoning with Geometry - Angles and Parallel Lines

Ever wondered how architects ensure buildings are perfectly aligned? It all comes down to understanding parallel lines and the angles they create. When a transversal (a line that crosses other lines) cuts through parallel lines, it creates predictable angle patterns that are incredibly useful.

There are three key angle relationships you need to master. Alternate angles are equal - they're the Z-shaped pairs that appear on opposite sides of the transversal. Corresponding angles are also equal - think of them as being in the same relative position at each intersection. Co-interior angles always add up to 180° - they're the C-shaped pairs on the same side of the transversal.

When solving angle problems, link everything back to algebra. Set up equations using the angle rules you know, then solve for the unknown. For example, if two angles on a straight line are 2x and 4x, you know that 2x + 4x = 180°, so x = 30°.

Making conjectures about shapes means spotting patterns and testing whether they're always true. Remember, you only need one counterexample to prove a conjecture wrong, but you need logical proof to show it's always correct.

Key tip: Always state your angle facts clearly when solving problems - examiners love to see your reasoning!

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Number Types and Operations - Building Strong Foundations

Numbers come in different families, and understanding these families helps you work more efficiently. Rational numbers can be written as fractions, while irrational numbers like √2 have decimal expansions that never end or repeat.

Directed numbers (positive and negative) follow predictable rules. When multiplying or dividing, same signs give positive results, different signs give negative results. Think of it as a friendship rule - friends of friends are friends, but friends of enemies are enemies!

HCF and LCM help solve practical problems like finding when buses arrive together or cutting materials into equal pieces. The Highest Common Factor is the biggest number that divides into both numbers, while the Lowest Common Multiple is the smallest number that both numbers divide into.

Standard form (like 3.4 × 10⁵) makes huge numbers manageable. Scientists use it for distances to stars or sizes of atoms. The power of 10 tells you how many places to move the decimal point.

Key tip: When adding fractions, find a common denominator first - it's like making sure you're comparing apples with apples!

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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.

Samantha Klich

Android user

Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.

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iOS user

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Thomas R

iOS user

Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.

Basil

Android user

This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.

David K

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Android user

very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.

Rohan U

Android user

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iOS user

THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮

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iOS user

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