Further Mathematics

    OCR
    GCSE

    This subject will help you develop key knowledge and skills required for exam success.

    27

    Topics

    0

    Objectives

    89

    Exam Tips

    103

    Pitfalls

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    Study Guides

    27 revision guides for OCR GCSE Further Mathematics

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    Key Features

    • Master key concepts
    • Develop exam technique
    • Apply knowledge effectively

    What Gets Top Grades

    A*/Grade 9

    Knowledge & Understanding

    Demonstrates comprehensive and accurate knowledge

    • Uses correct subject-specific terminology
    • Shows detailed understanding of concepts
    • Makes accurate connections between topics
    • Demonstrates depth beyond surface-level knowledge

    Application

    Applies knowledge effectively to new contexts

    • Selects relevant knowledge for the question
    • Adapts understanding to unfamiliar scenarios
    • Uses examples appropriately
    • Shows awareness of context

    Analysis & Evaluation

    Develops sophisticated analytical arguments

    • Constructs logical chains of reasoning
    • Considers multiple perspectives
    • Weighs evidence to reach justified conclusions
    • Acknowledges limitations and nuances

    Key Command Words

    OCR
    State
    1 mark

    Give a single fact or term

    Identify
    1 mark

    Name or select

    Describe
    2-4 marks

    Account of process or features

    Explain
    3-6 marks

    Give reasons with BUSINESS-FACING outcomes

    Analyse
    6-9 marks

    Examine methodically showing cause→effect→outcome

    Evaluate
    9-12 marks

    Judge, weigh up evidence, reach SYNOPTIC conclusion

    Common Exam Mistakes

    Pitfalls to avoid in your exams

    • •Squaring individual terms instead of expanding brackets, e.g., claiming $(3+\sqrt{2})^2$ equals $9+2$ rather than $11+6\sqrt{2}$
    • •Dividing only the first term of the numerator by the denominator after rationalising, e.g., reducing $\frac{4+2\sqrt{2}}{2}$ to $2+2\sqrt{2}$
    • •Confusing the square root of a sum with the sum of roots, leading to invalid simplifications like $\sqrt{16+9} = 4+3$
    • •Reverting to decimal approximations from a calculator, which results in zero marks for method in 'Show that' or 'Exact value' questions
    • •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
    • •Leaving the final answer in 'non-standard' form (e.g., 12.5 × 10⁵) rather than adjusting to 1.25 × 10⁶

    Top Examiner Tips

    Expert advice for exam success

    • •When asked to 'Show that', work forwards from the given expression; never substitute the final answer back into the start to prove it
    • •Always simplify surds (e.g., $\sqrt{75} \to 5\sqrt{3}$) before attempting addition or subtraction to easily identify like terms
    • •In geometric questions involving triangles or circles, keep values in surd form throughout intermediate steps to avoid rounding errors affecting the final accuracy mark
    • •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
    • •In non-calculator papers, convert numbers to ordinary form for addition/subtraction if the powers differ by only 1 or 2
    • •When squaring a value in standard form, remember to square the coefficient AND multiply the index by 2

    Specification Topics

    27 topics

    Surds

    0 objectives3 tips4 pitfalls

    Indices

    0 objectives3 tips3 pitfalls

    Standard Form

    0 objectives3 tips4 pitfalls

    Error Intervals

    0 objectives3 tips3 pitfalls

    Algebraic Fractions

    0 objectives4 tips4 pitfalls

    Simultaneous Equations

    0 objectives4 tips4 pitfalls

    Inequalities

    0 objectives3 tips4 pitfalls

    Completing the Square

    0 objectives3 tips4 pitfalls

    Functions

    0 objectives3 tips4 pitfalls

    Proof

    0 objectives3 tips4 pitfalls

    Sequences

    0 objectives4 tips4 pitfalls

    Iteration

    0 objectives4 tips4 pitfalls

    Equation of a Circle

    0 objectives3 tips4 pitfalls

    Equation of a Tangent to a Circle

    0 objectives3 tips4 pitfalls

    Parallel and Perpendicular Lines

    0 objectives3 tips4 pitfalls

    Vectors

    0 objectives3 tips3 pitfalls

    Circle Theorems

    0 objectives3 tips4 pitfalls

    Similar Shapes

    0 objectives4 tips4 pitfalls

    Trigonometry

    0 objectives4 tips4 pitfalls

    Pythagoras' Theorem in 3D

    0 objectives3 tips3 pitfalls

    Constructions

    0 objectives4 tips4 pitfalls

    Transformations of Functions

    0 objectives4 tips4 pitfalls

    Histograms

    0 objectives3 tips4 pitfalls

    Cumulative Frequency

    0 objectives3 tips3 pitfalls

    Box Plots

    0 objectives3 tips4 pitfalls

    Probability

    0 objectives3 tips4 pitfalls

    Set Notation

    0 objectives3 tips4 pitfalls

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