Number

    AQA
    GCSE

    AS Unit 2: Applied Mathematics A provides a foundational introduction to the practical application of mathematics in two core disciplines: Statistics and Mechanics. Students learn to model and analyze real-world phenomena, from interpreting data and understanding probability to studying the motion of objects and the forces that influence them. This unit emphasizes the translation of physical situations into mathematical models, the application of standard techniques to solve them, and the critical interpretation of the results in context. Mastery of this content is crucial for developing the problem-solving and analytical skills required for further study in STEM, finance, and data-driven fields.

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    Objectives
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    Exam Tips
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    Pitfalls
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    Key Terms
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    Mark Points

    Learning Objectives

    What you need to know and understand

    • Order positive and negative integers, decimals and fractions; use the symbols =, ≠, <, >, ≤, ≥
    • Apply the four operations, including formal written methods, to integers, decimals and simple fractions (proper and improper), and mixed numbers – all both positive and negative
    • Understand and use place value (eg when working with very large or very small numbers, and when calculating with decimals)
    • Recognise and use relationships between operations, including inverse operations (eg cancellation to simplify calculations and expressions)
    • Use conventional notation for priority of operations, including brackets, powers, roots and reciprocals
    • 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 notation and the unique factorisation theorem
    • Apply systematic listing strategies for counting
    • Use the product rule for counting
    • 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
    • Calculate with roots, and with integer indices
    • Calculate with fractional indices
    • Calculate exactly with fractions and multiples of pi
    • Calculate exactly with surds; simplify surd expressions and rationalise denominators
    • Calculate with and interpret standard form A x 10^n, where 1 ≤ A < 10 and n is an integer
    • Work interchangeably with terminating decimals and their corresponding fractions
    • Change recurring decimals into their corresponding fractions and vice versa
    • Identify and work with fractions in ratio problems
    • Interpret fractions and percentages as operators
    • Use standard units of mass, length, time, money and other measures (including standard compound measures) using decimal quantities where appropriate
    • Estimate answers; check calculations using approximation and estimation, including answers obtained using technology
    • Round numbers and measures to an appropriate degree of accuracy (eg to a specified number of decimal places or significant figures)
    • Use inequality notation to specify simple error intervals due to truncation or rounding

    Key Terminology

    Essential terms to know

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