Number & Proportion
Topics, misconceptions, and exam techniques for number & proportion.
Converting Fractions, Decimals and Percentages
Fractions, decimals and percentages are three different ways of writing the same value. Being able to convert fluently between them is essential for c...
Ratio and Proportion
A ratio compares quantities of the same kind. It tells us how much of one thing there is compared to another. Writing Ratios Ratios can be written as:...
Percentage Change and Reverse Percentages
Percentage of an Amount To find a percentage of an amount: Example: Find 15% of £80 Percentage Increase and Decrease Increase by a percentage: Example...
Standard Form
Standard form is a way of writing very large or very small numbers concisely. The Format where: - (A is between 1 and 10, including 1 but not 10) - is...
Indices (Powers)
What is an Index? In , the base is and the index (or power/exponent) is . Laws of Indices Multiplying (same base) — ADD the powers Example: Dividing (...
HCF, LCM and Prime Factorisation
Prime Numbers A prime number has exactly two factors: 1 and itself. First ten primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 Note: 1 is NOT a prime number...
Surds and Exact Trig Values H
A surd is an irrational root that cannot be simplified to a rational number. Examples include , , . Surds give exact answers — more precise than decim...
Error Intervals and Bounds H
When a number is rounded, the original value lies within a range called the error interval. The endpoints of this range are called bounds. Understandi...
Compound Interest and Depreciation
Compound interest and depreciation involve repeated percentage changes over time. Simple vs Compound Interest Simple interest: Interest is calculated...