What this topic covers
Number has 3 subtopics:
- Knowledge and use of numbers and the number system
- The product rule for counting
- Manipulation of surds, including rationalising the denominator
← Back to topics
GCSE AQA Higher Further Maths · Topic 1 of 6
Number – GCSE AQA Higher Further Maths revision notes
Choose a subtopic. Number covers Knowledge and use of numbers and the number system, The product rule for counting, and Manipulation of surds, including rationalising the denominator in GCSE AQA Higher Further Maths. 4 lessons in 3 subtopics.
Revise Number for GCSE AQA Higher Further Maths, including Knowledge and use of numbers and the number system and The product rule for counting.
4
Lessons
3
Subtopics
Number lessons by subtopic
4 lessons, grouped by subtopic.
Knowledge and use of numbers and the number system
- Mastering Number Systems: Fractions, Decimals, and Percentages: Explore the relationship between fractions, decimals, and percentages, and practice converting between them.
- Ratio, Proportion, and Order of Operations: Understand and apply ratio and proportion, and reinforce skills in order of operations (BIDMAS/PEMDAS).
The product rule for counting
- Introduction to the Product Rule for Counting: Learn the product rule for counting and apply it to calculate the number of possible outcomes in various scenarios.
Manipulation of surds, including rationalising the denominator
- Surd Manipulation and Rationalising Denominators: Learn how to manipulate surds, including simplifying expressions and rationalising denominators.
More in this course
Go back to the full GCSE AQA Higher Further Maths topic list, or practise this topic with past-paper questions.
Frequently asked questions
What is Number?
Number covers Knowledge and use of numbers and the number system, The product rule for counting, and Manipulation of surds, including rationalising the denominator in GCSE AQA Higher Further Maths. 4 lessons in 3 subtopics.
How do you divide fractions?
To divide fractions, use Keep-Change-Flip: keep the first fraction, change the division to multiplication and flip the second fraction. The Mastering Number Systems: Fractions, Decimals, and Percentages notes cover this in full.
How do you calculate percentage decrease?
Percentage decrease = change ÷ original value × 100. The Mastering Number Systems: Fractions, Decimals, and Percentages notes cover this in full.
What is the product rule for counting?
The product rule for counting states that if a task has several sequential stages, the total number of ways to complete all stages is the number of ways for each stage multiplied together. The Introduction to the Product Rule for Counting notes cover this in full.
What is a surd?
A surd is a root of a positive integer that is itself irrational, so it cannot be written as a fraction of two integers. The Surd Manipulation and Rationalising Denominators notes cover this in full.
How do you write an improper fraction as a mixed number?
An improper fraction, where the numerator is bigger than the denominator, is written as a mixed number by taking out the whole number part. The Mastering Number Systems: Fractions, Decimals, and Percentages notes cover this in full.
How do you rationalise the denominator?
To rationalise a denominator of the form a/√b, multiply the top and bottom of the fraction by √b, which is the same as multiplying by 1. The Surd Manipulation and Rationalising Denominators notes cover this in full.
How do you simplify a ratio?
To simplify a ratio, divide all parts by their highest common factor (HCF). The Ratio, Proportion, and Order of Operations notes cover this in full.
What is BIDMAS?
BIDMAS is the priority order for operations: Brackets first, then Indices (powers and roots), then Division and Multiplication together, working left to right, then Addition and Subtraction together, working left to right. The Ratio, Proportion, and Order of Operations notes cover this in full.