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Structure and calculation

15 lessons in Number.

135 exam questions · 297 marks

1.1 Place value and ordering numbers Place value in whole numbers and decimals, multiplying and dividing by powers of 10, and ordering integers, decimals, fractions and negative numbers using a number line and the symbols =, ≠, <, >, ≤ and ≥. AQA Edexcel OCR 1.2 Calculating with integers and negative numbers Formal written methods for adding, subtracting, multiplying and dividing whole numbers, and the rules for calculating with negative numbers, including problems in context. Most of this is tested without a calculator. AQA Edexcel OCR 1.3 Calculating with decimals Adding, subtracting, multiplying and dividing decimals without a calculator, lining up the decimal point, counting decimal places, dividing by a decimal, using a known fact, and checking by estimation. AQA Edexcel OCR 1.4 Order of operations and inverse operations The correct order of operations (BIDMAS) with brackets, powers, roots and fractions, using reciprocals, and using inverse operations to check calculations and to work backwards. AQA Edexcel OCR 1.5 Factors, multiples and prime numbers The vocabulary of factors, multiples, common factors, common multiples and prime numbers, finding factors in pairs, tests for divisibility, and recognising the primes up to 100. AQA Edexcel OCR 1.6 Prime factorisation, HCF and LCM Writing a number as a product of prime factors using a factor tree and index form, and using prime factorisation to find the highest common factor (HCF) and lowest common multiple (LCM), including with a Venn diagram and in problems. AQA Edexcel OCR 1.7 Systematic listing and the product rule for counting Counting outcomes with systematic lists, tables and diagrams so that none is missed or repeated, and (Higher tier) the product rule for counting: multiply the number of choices at each stage. AQA Edexcel OCR 1.8 Squares, cubes and roots Square numbers up to 15 × 15, cube numbers, powers of 2, 3, 4 and 5, square roots, cube roots and higher roots, estimating a root between two integers, and knowing that 1000 = 10³ and 1 million = 10⁶. AQA Edexcel OCR 1.9 Laws of indices The laws of indices for multiplying, dividing and raising a power to a power, and the meaning of zero and negative indices, with numbers and with algebraic terms. AQA Edexcel OCR 1.10 Fractional indices Higher tier: fractional indices, where a power of 1/n means the nth root and a power of m/n means a root and a power, including negative fractional indices and combining them with the index laws. Higher only AQA Edexcel OCR 1.11 Standard form Writing very large and very small numbers in standard form A × 10ⁿ with 1 ≤ A < 10, converting to and from ordinary numbers, comparing and ordering numbers in standard form, and reading standard form on a calculator. AQA Edexcel OCR 1.12 Calculating with standard form Multiplying and dividing numbers in standard form using the index laws, adding and subtracting after matching the powers of 10, using a calculator for standard form, and solving real problems with very large and very small numbers. AQA Edexcel OCR 1.13 Exact calculations with fractions and π Calculating exactly with fractions rather than rounded decimals, and leaving answers as multiples of π, for circles, semicircles, cylinders and rings; when to give an exact answer and when to round. AQA Edexcel OCR 1.14 Simplifying surds Higher tier: what a surd is, simplifying surds by taking out square factors, multiplying and dividing surds, adding and subtracting like surds, expanding brackets containing surds, and finding exact lengths. Higher only AQA Edexcel OCR 1.15 Rationalising the denominator Higher tier: rationalising the denominator, removing a surd from the bottom of a fraction by multiplying by the surd or by the conjugate, with exact answers and links to the difference of two squares. Higher only AQA Edexcel OCR