Maths177Updated 26 Sept 20267 pages

Maths Revision for Non-Calculator and Calculator Papers

Report

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 examples to help you tackle these problems confidently.

Maths non calc and calc revision – page 1

By signing up you accept Terms of Service and Privacy Policy

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.

Maths non calc and calc revision – page 2

By signing up you accept Terms of Service and Privacy Policy

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, $101-34$ × 8 can be estimated as $100-30$ × 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!

Maths non calc and calc revision – page 3

By signing up you accept Terms of Service and Privacy Policy

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 $\frac{7}{10}$ of 100: divide 100 by 10 $=10$ , 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.

Maths non calc and calc revision – page 4

By signing up you accept Terms of Service and Privacy Policy

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 $\sqrt3+4$$\sqrt3+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: $25-20$ ÷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!

Maths non calc and calc revision – page 5

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.

Maths non calc and calc revision – page 6

By signing up you accept Terms of Service and Privacy Policy

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: $25-20$ ÷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!

Maths non calc and calc revision – page 7

By signing up you accept Terms of Service and Privacy Policy

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: $\frac{2}{3} \times \frac{1}{4} = \frac{2 \times 1}{3 \times 4} = \frac{2}{12} = \frac{1}{6}$ 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.

Comprehensive revision of key sociological theories including Functionalism, Marxism, Feminism, and Interpretivism. Explore concepts like value freedom, identity formation, and the critique of social control. Ideal for AQA A-Level Sociology students preparing for exams. This summary covers essential theories and their implications in sociology, providing a clear understanding of each perspective.

1231,968852

Maths

Comprehensive Maths Concepts

1180,4966,331

Criminology

Criminal Justice Overview

Explore key concepts in criminal justice, including the trial process, roles of court personnel, types of offenses, and evidence handling. This comprehensive summary covers essential topics such as jury strengths and weaknesses, the role of the CPS, and the impact of media on trials. Ideal for students preparing for assessments in criminology. Achieved a B grade.

133,69878

Criminology

Criminal Justice Evidence Rules

Explore the essential rules governing the use of evidence in criminal cases, including reliability, admissibility, and relevance. This summary covers key concepts such as the roles of personnel in investigations, the impact of witness testimonies, and the implications of plea bargaining. Ideal for Year 13 criminology students preparing for assessments.

1211,400183

Students love us, and so will you.

4.6/5App Store

4.7/5Google Play

Stefan SiOS 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.

Samantha KlichAndroid 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.

AnnaiOS 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.

Maths Revision for Non-Calculator and Calculator Papers

Non-Calculator Topics Overview

Order of Operations & Error Intervals

Fractions and Surds

Expanding Brackets with Surds and Percentage Change

Calculator Topics Overview

Sequences and Their Rules

Negative Numbers and Prime Factors

We thought you’d never ask...

What is the Knowunity AI companion?

Where can I download the Knowunity app?

Is Knowunity really free of charge?

Similar content

Understanding BIDMAS

GCSE Circle Geometry Formulas

Improper Fractions to Mixed Numbers

Year 6 arithmetic paper 6

Kinematics: Displacement & Velocity

Matrix Transformations Explained

Most popular content: Pemdas

Understanding BIDMAS

Most popular content: Maths

Comprehensive Maths Concepts

GCSE Maths (Higher) // Revision Guide

Comprehensive Maths Concepts

Foundation Maths Exam Solutions

GCSE Maths 2018 Exam Insights

GCSE Higher Maths Essentials

GCSE Maths Foundation Checklist

Comprehensive Pure Mathematics

November 2017 QP - Paper 1 (F) Edexcel Maths GCSE

Most popular content

Sociology of Families: Comprehensive Revision

Sociology of Education Overview

Comprehensive Crime & Deviance Overview

AQA Biology: Key Concepts

An Inspector Calls: Character Insights

Sociological Theories Overview

Comprehensive Maths Concepts

Criminal Justice Overview

Criminal Justice Evidence Rules

Students love us, and so will you.