GCSE (91) Higher Mathematics is broken down into six main areas:
NUMBER:H 

1. Order positive and negative integers, decimals and fractions; Use the symbols =, ≠, <, >, ≥, ≤ 
2. Apply the 4 operations (+, –, ×, ÷), including formal written methods, to integers, decimals and simple fractions (proper and improper), and mixed numbers, positive or negative Understand and use place value (e.g. when working with very large or very small numbers, and decimals. Divide a decimal by a whole number or a decimal, including negative decimals, without a calculator. Fractions: 
3. Recognise and use relationships between operations, including inverse operations Use conventional notation for priority of operations, including brackets, powers, roots and reciprocals (BIDMAS) Cancellation to simplify calculations and expressions: 
4. Use the concepts and vocabulary of prime numbers, factors (divisors), multiples, common factors, common multiples, highest common factor, lowest common multiple, prime factorisation, including using product (e.g. 2×2×3) notation Express a whole number as a product of its prime factors. Find the HCF and LCM of two whole numbers from their prime factorisations What are the factors of 20? 
5. Apply systematic listing strategies including use of the product rule for counting 
NUMBER:H 

6. Use positive integer powers and associated real roots (square, cube and higher), recognise powers of 2, 3, 4, 5; Estimate powers and roots of any given positive number 
7. Calculate with roots, and with integer indices 
8. Calculate exactly with fractions, surds and multiples of π Simplify surd expressions involving squares 
9.Calculate with and interpret standard form A × 10^{n} where 1 ≤ A < 10, and n is an integer Add, subtract, multiply and divide numbers in standard form, without a calculator. 
10. Work interchangeably with terminating decimals and their corresponding fractions Change recurring decimals into their corresponding fractions and vice vers 
11. Identify and work with fractions in ratio problems 
12. Interpret fractions and percentages as operators 
13. Use standard units of mass, length, time, money and other measures (including standard compound measures) using decimal quantities where appropriate 
14. Estimate answers; check calculations using approximation and estimation, including answers obtained using technology 
15. Round numbers and measures to an appropriate degree of accuracy (e.g. to a specified number of decimal places or significant figures); Use inequality notation to specify simple error intervals due to truncation or rounding

16. Apply and interpret limits of accuracy including upper and lower bounds 