Indices

    OCR
    GCSE

    The manipulation of indices forms the bedrock of algebraic fluency, extending arithmetic operations to include integer, negative, and fractional powers. Candidates must rigorously apply the laws of indices to simplify complex algebraic expressions and solve exponential equations where the variable resides in the exponent. This topic is critical for advanced calculus, specifically in the differentiation and integration of polynomial and exponential functions, requiring precise conversion between radical and index forms.

    0
    Objectives
    3
    Exam Tips
    3
    Pitfalls
    4
    Key Terms
    4
    Mark Points

    What You Need to Demonstrate

    Key skills and knowledge for this topic

    • Award M1 for correctly applying the power law (a^m)^n = a^mn to both coefficient and variable
    • Award B1 for correct conversion of a negative index to a reciprocal form
    • Award M1 for expressing different bases as powers of a common prime base (e.g., writing 4^x and 8 as powers of 2)
    • Award A1 for the final simplified expression, ensuring it matches the specific form requested (e.g., a^n or no negative indices)

    Example Examiner Feedback

    Real feedback patterns examiners use when marking

    • "You correctly identified the root, but forgot to apply the negative sign as a reciprocal — remember the 'flip'"
    • "Don't forget that the power applies to the coefficient too: (2x)^3 is 8x^3, not 2x^3"
    • "Excellent work equating the bases; now ensure you solve the resulting linear equation carefully"
    • "Check the question requirements: did it ask for positive indices only?"

    Marking Points

    Key points examiners look for in your answers

    • Award M1 for correctly applying the power law (a^m)^n = a^mn to both coefficient and variable
    • Award B1 for correct conversion of a negative index to a reciprocal form
    • Award M1 for expressing different bases as powers of a common prime base (e.g., writing 4^x and 8 as powers of 2)
    • Award A1 for the final simplified expression, ensuring it matches the specific form requested (e.g., a^n or no negative indices)

    Examiner Tips

    Expert advice for maximising your marks

    • 💡When simplifying expressions like (27x^6)^(1/3), handle the number and the algebra separately to avoid arithmetic errors
    • 💡Always convert roots to fractional indices immediately (e.g., sqrt(x) to x^(1/2)) to facilitate the application of index laws
    • 💡In 'Show that' questions involving indices, work clearly down the page one step at a time; skipping steps often leads to loss of method marks

    Common Mistakes

    Pitfalls to avoid in your exam answers

    • Failing to apply the index to the coefficient within a bracket, e.g., expanding (3x^2)^3 as 3x^6 instead of 27x^6
    • Incorrectly processing negative fractional indices by confusing the root and the power, or omitting the reciprocal step
    • Attempting to solve exponential equations like 3^x = 9^(x-1) by dividing terms rather than equating exponents after matching bases

    Key Terminology

    Essential terms to know

    Laws of indices (multiplication, division, power of a power)
    Negative and fractional indices
    Solving exponential equations by equating bases
    Hidden quadratics in exponential form

    Likely Command Words

    How questions on this topic are typically asked

    Evaluate
    Simplify
    Solve
    Show that
    Write

    Ready to test yourself?

    Practice questions tailored to this topic