Expressions and Formulae

    OCR
    GCSE

    Algebraic proficiency requires the rigorous application of operational laws to simplify expressions, expand brackets, and factorise linear and quadratic forms. Candidates must demonstrate accuracy in substituting numerical values into complex formulae, adhering strictly to the order of operations. The ability to rearrange formulae to change the subject is critical, serving as a prerequisite for solving equations and modelling physical relationships in scientific contexts. Mastery of algebraic fractions and identities distinguishes higher-level reasoning.

    0
    Objectives
    6
    Exam Tips
    8
    Pitfalls
    10
    Key Terms
    8
    Mark Points

    Subtopics in this area

    Expressions and Formulae
    Expressions and Formulae

    What You Need to Demonstrate

    Key skills and knowledge for this topic

    • Award B1 for correct partial simplification (e.g., collecting x terms correctly but making an error with constant terms)
    • Award M1 for a correct first step in rearranging a formula, such as isolating the term containing the subject or clearing a denominator
    • Award 1 mark for correct substitution of negative values, strictly requiring brackets for powers (e.g., (-3)² rather than -3²)
    • For algebraic proof, credit responses that define an integer as 'n' and an odd number as '2n+1' or '2n-1', rejecting numerical examples
    • Award B1 for correct partial factorisation (e.g., extracting the numerical factor but ignoring the common variable)
    • Award M1 for a correct first step in rearranging a formula, such as isolating the term containing the subject or clearing a denominator
    • Award 1 mark for correct substitution of negative numbers into a formula, specifically looking for the correct handling of signs
    • Allow Follow Through (FT) marks for subsequent algebraic manipulation errors only if the method remains mathematically sound and complexity is not reduced

    Example Examiner Feedback

    Real feedback patterns examiners use when marking

    • "You have correctly expanded the brackets, but check the sign of the final term—remember negative times negative is positive"
    • "Remember, you cannot combine x terms and x² terms—they are unlike terms and must remain separate"
    • "To get the marks for proof, you must use 'n' for an integer, not just test with n=3"
    • "When the subject is in the denominator, multiply both sides by the denominator as your first step to clear the fraction"

    Marking Points

    Key points examiners look for in your answers

    • Award B1 for correct partial simplification (e.g., collecting x terms correctly but making an error with constant terms)
    • Award M1 for a correct first step in rearranging a formula, such as isolating the term containing the subject or clearing a denominator
    • Award 1 mark for correct substitution of negative values, strictly requiring brackets for powers (e.g., (-3)² rather than -3²)
    • For algebraic proof, credit responses that define an integer as 'n' and an odd number as '2n+1' or '2n-1', rejecting numerical examples
    • Award B1 for correct partial factorisation (e.g., extracting the numerical factor but ignoring the common variable)
    • Award M1 for a correct first step in rearranging a formula, such as isolating the term containing the subject or clearing a denominator
    • Award 1 mark for correct substitution of negative numbers into a formula, specifically looking for the correct handling of signs
    • Allow Follow Through (FT) marks for subsequent algebraic manipulation errors only if the method remains mathematically sound and complexity is not reduced

    Examiner Tips

    Expert advice for maximising your marks

    • 💡When substituting negative numbers into formulae involving powers, always enclose the number in brackets to ensure the sign is handled correctly
    • 💡If the variable you are making the subject appears twice, move all terms containing it to one side and factorise immediately
    • 💡In 'Show that' questions involving algebraic proof, never substitute numbers; you must use n or k to represent a general number to access AO2 marks
    • 💡When substituting negative numbers, always place the number in brackets to ensure your calculator processes the sign and power correctly
    • 💡Distinguish command words carefully: 'Simplify' means collect terms/cancel; 'Factorise' means insert brackets; 'Solve' requires finding a value
    • 💡For 'Show that' questions involving algebraic identities, work from the left-hand side to the right-hand side showing every step of the expansion clearly

    Common Mistakes

    Pitfalls to avoid in your exam answers

    • Incorrectly simplifying 3a + 4b to 7ab by treating unlike terms as like terms
    • Evaluating -x² instead of (-x)² when substituting a negative value for x, resulting in a sign error
    • Failing to factorise the subject out when it appears twice in a formula (e.g., failing to move from ax = by + cx to x(a-c) = by)
    • Using specific numerical examples to 'prove' a statement instead of general algebraic terms, which caps the mark at zero for proof questions
    • Incorrectly expanding brackets with negative signs, typically resulting in sign errors for the second term (e.g., -3(x - 2) becoming -3x - 6)
    • Confusing 'expressions' with 'equations' by attempting to 'solve' an expression (e.g., setting 3x + 6 = 0 arbitrarily)
    • Failing to use brackets when substituting negative numbers into formulae involving powers (e.g., calculating -3² as -9 instead of 9)
    • In rearranging formulae, candidates often fail to factorise when the subject appears twice, leaving the subject on both sides of the equals sign

    Study Guide Available

    Comprehensive revision notes & examples

    Read Study Guide

    Key Terminology

    Essential terms to know

    Simplification and collection of like terms
    Expansion of brackets (linear, quadratic, cubic)
    Factorisation (common factors, quadratics, difference of two squares)
    Substitution and evaluation of formulae
    Rearranging formulae and changing the subject
    Algebraic fractions and proof of identities
    Algebraic notation and conventions
    Substitution of numerical values
    Changing the subject of a formula
    Deriving formulae from physical or geometric contexts

    Likely Command Words

    How questions on this topic are typically asked

    Simplify
    Substitute
    Rearrange
    Factorise
    Expand
    Show that

    Practical Links

    Related required practicals

    • •{"code":"Physics Formulae","title":"Kinematics Equations","relevance":"Rearranging v = u + at or s = ut + 0.5at² to find specific variables"}

    Ready to test yourself?

    Practice questions tailored to this topic