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Structure and calculation
Structure and calculation covers integer, fraction, root, index and standard-form methods, with attention to exact arithmetic, calculator interpretation and efficient order-of-operations working.
17
Objectives
85
Flashcards
85
Questions
90 min
Study time
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17 objective pages available
Ordering numbers and inequality notation1 objectives
- [Foundation and Higher] Order positive and negative integers, decimals and fractions and use =, !=, <, >, <= and >= correctly.
Operations and place value2 objectives
- [Foundation and Higher] Apply the four operations to integers, decimals, simple fractions and mixed numbers, including positive and negative values.
- [Foundation and Higher] Use place value with very large numbers, very small numbers and decimal calculations, including financial contexts.
Inverse operations and priority of operations2 objectives
- [Foundation and Higher] Use relationships between operations, including inverse operations, to simplify calculations and expressions.
- [Foundation and Higher] Apply conventional priority of operations using brackets, powers, roots and reciprocals.
Factors, multiples and prime factorisation2 objectives
- [Foundation and Higher] Use vocabulary and methods for primes, factors, multiples, common factors, common multiples, HCF, LCM and prime factorisation.
- [Foundation and Higher] Write products of prime factors using index notation and apply the uniqueness of prime factorisation.
Systematic listing and counting2 objectives
- [Foundation and Higher] Apply systematic listing strategies using lists, tables and diagrams.
- [Higher only] Use the product rule for counting where the specification requires it.
Powers and roots2 objectives
- [Foundation and Higher] Use positive integer powers and associated roots, including square, cube and higher roots.
- [Foundation and Higher] Recognise powers of 2, 3, 4 and 5 and estimate powers and roots of positive numbers.
Indices and roots2 objectives
- [Foundation and Higher] Calculate with roots and integer indices.
- [Higher only] Calculate with fractional indices.
Exact calculation2 objectives
- [Foundation and Higher] Calculate exactly with fractions and exact multiples of pi.
- [Higher only] Calculate exactly with surds, simplify surd expressions involving squares and rationalise denominators.
Standard form2 objectives
- [Foundation and Higher] Calculate with and interpret standard form A x 10^n, where 1 <= A < 10 and n is an integer.
- [Foundation and Higher] Interpret calculator displays involving standard form.
Key terms
fractionsoperationsplace valueinverse operationspriority of operationsprimesystematic listingproduct rulepowersrootsfractional indicessurds
Exam tips
- Ordering numbers and inequality notation exam tip 1: Write the method before the answer so the examiner can follow each step. Apply this to [Foundation and Higher] Order positive and negative integers, decimals and fractions and use =, !=, <, >, <= and >= correctly..
- Operations and place value exam tip 1: Write the method before the answer so the examiner can follow each step. Apply this to [Foundation and Higher] Apply the four operations to integers, decimals, simple fractions and mixed numbers, including positive and negative values..
Common mistakes
- Ordering numbers and inequality notation common mistake 1: Show the method first, then give the final answer in the required form. Apply this directly to Ordering numbers and inequality notation.
- Operations and place value common mistake 1: Show the method first, then give the final answer in the required form. Apply this directly to Operations and place value.
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