Powers and roots

    OCR
    GCSE

    This topic governs the arithmetic and algebraic manipulation of indices, requiring candidates to fluently apply the three fundamental laws of indices to simplify expressions and solve equations. Assessment ranges from basic recall of square and cube numbers to the complex evaluation of negative and fractional indices, which serves as the theoretical underpinning for surds and logarithms. Mastery is critical for handling standard form in scientific contexts and provides the necessary fluency for differentiation and integration in advanced calculus.

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

    What You Need to Demonstrate

    Key skills and knowledge for this topic

    • Award B1 for correct evaluation of integer powers or roots, e.g., stating 3 cubed is 27 or square root of 64 is 8.
    • Award M1 for correct application of index laws in a multi-step problem, such as adding indices for multiplication or subtracting for division.
    • Award M1 for interpreting a negative index as a reciprocal, e.g., x^-n = 1/x^n, before attempting further calculation.
    • Award B1 for correctly simplifying algebraic terms involving powers, ensuring coefficients are raised to the power as well (e.g., (2x)^3 = 8x^3).

    Marking Points

    Key points examiners look for in your answers

    • Award B1 for correct evaluation of integer powers or roots, e.g., stating 3 cubed is 27 or square root of 64 is 8.
    • Award M1 for correct application of index laws in a multi-step problem, such as adding indices for multiplication or subtracting for division.
    • Award M1 for interpreting a negative index as a reciprocal, e.g., x^-n = 1/x^n, before attempting further calculation.
    • Award B1 for correctly simplifying algebraic terms involving powers, ensuring coefficients are raised to the power as well (e.g., (2x)^3 = 8x^3).

    Examiner Tips

    Expert advice for maximising your marks

    • 💡For negative fractional indices, apply the negative sign (reciprocal) first, then the root, then the power to minimize arithmetic errors.
    • 💡Memorize square numbers up to 15^2 and cubes up to 5^3 and 10^3, as these frequently appear in non-calculator papers where 'Evaluate' is the command.
    • 💡When simplifying expressions like (2x^3)^4, handle the number (2^4) and the algebra (x^(3*4)) separately to ensure accuracy.

    Common Mistakes

    Pitfalls to avoid in your exam answers

    • Calculating a power as a multiplication, such as stating 4^3 = 12 (4x3) instead of 64.
    • Failing to apply the power to the coefficient in algebraic expressions, e.g., writing (3x)^2 as 3x^2 rather than 9x^2.
    • Misinterpreting fractional indices, often halving the base number instead of finding the square root (e.g., 16^1/2 = 8 instead of 4).
    • Confusing the operation for raising a power to a power, adding indices instead of multiplying them (e.g., (x^2)^3 = x^5 instead of x^6).

    Study Guide Available

    Comprehensive revision notes & examples

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    Key Terminology

    Essential terms to know

    Laws of Indices (Multiplication, Division, Power of a Power)
    Negative and Fractional Indices
    Standard Form (Scientific Notation)
    Surds and Exact Calculation

    Likely Command Words

    How questions on this topic are typically asked

    Calculate
    Evaluate
    Simplify
    Write
    Estimate

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