Welcome to your essential maths concepts guide! This summary covers...
Maths166 views·Updated 26 Jul 2026·7 pagesMaths Revision for Non-Calculator and Calculator Papers
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Eve @eve_06adb
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1
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Non-Calculator Topics Overview
Getting comfortable with non-calculator maths is essential for exam success. The topics you'll need to master include using the correct order of operations (BIDMAS) and finding error intervals for rounded numbers.
You'll also learn how to estimate calculations including roots and powers, which helps check if your answers make sense. Working with fractions and surds (square roots that can't be simplified to whole numbers) is another key skill.
These topics build your mathematical foundation and help you solve more complex problems. Don't worry if they seem tricky at first – with practice, they'll become second nature!
💡 Remember: Non-calculator questions test your understanding of mathematical concepts, not just your ability to compute numbers.
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of 7
Order of Operations & Error Intervals
When solving calculations, always follow the correct order of operations: Brackets, Indices, Division, Multiplication, Addition, Subtraction (BIDMAS). This ensures you get the right answer every time.
Error intervals show the possible range for a number that's been rounded. If a number rounds to 30 to the nearest ten, it could be any value from 25 to 34.999... (written as 25 ≤ x < 35). Numbers 5 and above round up, while 4 and below round down.
When estimating calculations, you can make problems easier by rounding values. For example, × 8 can be estimated as × 10 = 700. For square roots, think about perfect squares: √17 must be between √16 (4) and √25 (5), closer to 4.
🔑 Estimating is a powerful skill that helps you spot errors in your work – if your exact answer is dramatically different from your estimate, double-check your calculation!
3
of 7
Fractions and Surds
Working with fractions requires finding equivalent fractions with common denominators. To find a fraction of an amount, divide by the denominator, then multiply by the numerator. For example, to find of 100: divide 100 by 10 , then multiply by 7 to get 70.
When multiplying surds, multiply the numbers outside the square root sign separately from those inside. For example: 3√2 × 4√3 = (3×4) × √(2×3) = 12√6. Remember that √a × √a = a, so √7 × √7 = 7.
For dividing surds, divide the numbers inside and outside the square root separately. For example: 8√15 ÷ 2√3 = (8÷2) × √(15÷3) = 4√5. Always look to simplify your answer after performing these operations.
💡 Perfect squares hiding in surds are your friends! Always check if you can simplify expressions like √50 to 5√2 by spotting that 50 = 25 × 2.
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of 7
Expanding Brackets with Surds and Percentage Change
When expanding brackets with surds, multiply each term in the first bracket by each term in the second bracket. For example, with √3+4$$√3+5, multiply each term: √3×√3=3, √3×5=5√3, 4×√3=4√3, and 4×5=20. Then combine like terms: 5√3+4√3=9√3 and 3+20=23, giving 23+9√3.
The process uses the same principle as regular bracket expansion but requires applying surd laws when multiplying terms. Remember that √a × √a = a and that like surds can be combined.
Percentage change calculations help you understand how values increase or decrease. To find the percentage change: find the difference between new and original values, divide by the original value, then multiply by 100. If a price increases from £20 to £25, the calculation is: ÷20×100=25% increase.
🔍 In real life, you'll use percentage change constantly – from calculating discounts while shopping to understanding inflation rates in the economy!
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Calculator Topics Overview
While calculators help with computations, you still need to understand the underlying concepts. The calculator topics you'll study include term-to-term rules and position-to-term rules for sequences.
You'll also learn to confidently multiply and divide negative numbers, understanding the patterns of when answers will be positive or negative. Prime factor decomposition breaks numbers into their prime building blocks.
Working with fractions on your calculator is also essential, particularly multiplying fractions and simplifying the results. These calculator skills allow you to tackle more complex problems efficiently.
💡 Even with a calculator, understanding the mathematical concepts is crucial – the calculator is just a tool to help you work more efficiently.
6
of 7
Sequences and Their Rules
Term-to-term rules tell you how to find the next term in a sequence using previous terms. For arithmetic sequences, you add or subtract a fixed value (e.g., 2, 4, 6, 8... add 2). For geometric sequences, you multiply by a constant value (e.g., 3, 6, 12, 24... multiply by 2).
Position-to-term rules (or nth term) are more powerful as they let you find any term directly without calculating all previous terms. This is especially useful for finding terms far along in the sequence.
Percentage change calculations follow a simple formula: find the difference between new and original values, divide by the original value, and multiply by 100. For example, if a price increases from £20 to £25: ÷20×100 = 25% increase.
🧠 Understanding sequences helps develop your pattern recognition skills, which is useful not just in maths but in many other subjects and real-world situations!
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of 7
Negative Numbers and Prime Factors
When multiplying negative numbers, remember that two negatives make a positive, while a negative and a positive make a negative. For example, -5 × -2 = 10, but -2 × 5 = -10. The same principles apply to division: -10 ÷ -5 = 2, while -10 ÷ 2 = -5.
Prime factor decomposition breaks down a number into its prime building blocks. You can use a factor tree to help: start with any factor pair, then continue breaking down non-prime factors until all branches end in prime numbers. For example, 56 = 2³ × 7 (or 8 × 7).
To multiply fractions, multiply the numerators together and the denominators together, then simplify if possible. For example: after simplifying.
👍 Prime factorization might seem tedious at first, but it's incredibly useful for simplifying fractions, finding LCM and HCF, and solving many other mathematical problems!
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Maths166 views·Updated 26 Jul 2026·7 pagesMaths Revision for Non-Calculator and Calculator Papers
E
Eve @eve_06adb
Welcome to your essential maths concepts guide! This summary covers key non-calculator and calculator topics you need to master for your exams, from operations with numbers and surds to sequences and fractions. Each concept is explained in simple steps with...
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Non-Calculator Topics Overview
Getting comfortable with non-calculator maths is essential for exam success. The topics you'll need to master include using the correct order of operations (BIDMAS) and finding error intervals for rounded numbers.
You'll also learn how to estimate calculations including roots and powers, which helps check if your answers make sense. Working with fractions and surds (square roots that can't be simplified to whole numbers) is another key skill.
These topics build your mathematical foundation and help you solve more complex problems. Don't worry if they seem tricky at first – with practice, they'll become second nature!
💡 Remember: Non-calculator questions test your understanding of mathematical concepts, not just your ability to compute numbers.
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Order of Operations & Error Intervals
When solving calculations, always follow the correct order of operations: Brackets, Indices, Division, Multiplication, Addition, Subtraction (BIDMAS). This ensures you get the right answer every time.
Error intervals show the possible range for a number that's been rounded. If a number rounds to 30 to the nearest ten, it could be any value from 25 to 34.999... (written as 25 ≤ x < 35). Numbers 5 and above round up, while 4 and below round down.
When estimating calculations, you can make problems easier by rounding values. For example, × 8 can be estimated as × 10 = 700. For square roots, think about perfect squares: √17 must be between √16 (4) and √25 (5), closer to 4.
🔑 Estimating is a powerful skill that helps you spot errors in your work – if your exact answer is dramatically different from your estimate, double-check your calculation!
3
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Fractions and Surds
Working with fractions requires finding equivalent fractions with common denominators. To find a fraction of an amount, divide by the denominator, then multiply by the numerator. For example, to find of 100: divide 100 by 10 , then multiply by 7 to get 70.
When multiplying surds, multiply the numbers outside the square root sign separately from those inside. For example: 3√2 × 4√3 = (3×4) × √(2×3) = 12√6. Remember that √a × √a = a, so √7 × √7 = 7.
For dividing surds, divide the numbers inside and outside the square root separately. For example: 8√15 ÷ 2√3 = (8÷2) × √(15÷3) = 4√5. Always look to simplify your answer after performing these operations.
💡 Perfect squares hiding in surds are your friends! Always check if you can simplify expressions like √50 to 5√2 by spotting that 50 = 25 × 2.
4
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Expanding Brackets with Surds and Percentage Change
When expanding brackets with surds, multiply each term in the first bracket by each term in the second bracket. For example, with √3+4$$√3+5, multiply each term: √3×√3=3, √3×5=5√3, 4×√3=4√3, and 4×5=20. Then combine like terms: 5√3+4√3=9√3 and 3+20=23, giving 23+9√3.
The process uses the same principle as regular bracket expansion but requires applying surd laws when multiplying terms. Remember that √a × √a = a and that like surds can be combined.
Percentage change calculations help you understand how values increase or decrease. To find the percentage change: find the difference between new and original values, divide by the original value, then multiply by 100. If a price increases from £20 to £25, the calculation is: ÷20×100=25% increase.
🔍 In real life, you'll use percentage change constantly – from calculating discounts while shopping to understanding inflation rates in the economy!
5
of 7Sign up to see the content. It's free!
- Access to all documents
- Improve your grades
- Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Calculator Topics Overview
While calculators help with computations, you still need to understand the underlying concepts. The calculator topics you'll study include term-to-term rules and position-to-term rules for sequences.
You'll also learn to confidently multiply and divide negative numbers, understanding the patterns of when answers will be positive or negative. Prime factor decomposition breaks numbers into their prime building blocks.
Working with fractions on your calculator is also essential, particularly multiplying fractions and simplifying the results. These calculator skills allow you to tackle more complex problems efficiently.
💡 Even with a calculator, understanding the mathematical concepts is crucial – the calculator is just a tool to help you work more efficiently.
6
of 7Sign up to see the content. It's free!
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Sequences and Their Rules
Term-to-term rules tell you how to find the next term in a sequence using previous terms. For arithmetic sequences, you add or subtract a fixed value (e.g., 2, 4, 6, 8... add 2). For geometric sequences, you multiply by a constant value (e.g., 3, 6, 12, 24... multiply by 2).
Position-to-term rules (or nth term) are more powerful as they let you find any term directly without calculating all previous terms. This is especially useful for finding terms far along in the sequence.
Percentage change calculations follow a simple formula: find the difference between new and original values, divide by the original value, and multiply by 100. For example, if a price increases from £20 to £25: ÷20×100 = 25% increase.
🧠 Understanding sequences helps develop your pattern recognition skills, which is useful not just in maths but in many other subjects and real-world situations!
7
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Negative Numbers and Prime Factors
When multiplying negative numbers, remember that two negatives make a positive, while a negative and a positive make a negative. For example, -5 × -2 = 10, but -2 × 5 = -10. The same principles apply to division: -10 ÷ -5 = 2, while -10 ÷ 2 = -5.
Prime factor decomposition breaks down a number into its prime building blocks. You can use a factor tree to help: start with any factor pair, then continue breaking down non-prime factors until all branches end in prime numbers. For example, 56 = 2³ × 7 (or 8 × 7).
To multiply fractions, multiply the numerators together and the denominators together, then simplify if possible. For example: after simplifying.
👍 Prime factorization might seem tedious at first, but it's incredibly useful for simplifying fractions, finding LCM and HCF, and solving many other mathematical problems!
We thought you’d never ask...
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.
You can download the app from Google Play Store and Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
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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.
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