Mathematics

    AQA
    A-Level

    Specification: 7357

    Mathematics builds your numerical fluency and problem-solving abilities across algebra, geometry, statistics and more. You'll develop logical reasoning skills applicable to science, finance and everyday decisions.

    3

    Topics

    0

    Objectives

    9

    Exam Tips

    11

    Pitfalls

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    Key Features

    • Master algebraic manipulation
    • Solve multi-step problems
    • Apply statistics and probability
    • Develop proof and reasoning

    Assessment Objectives

    AO1
    60%

    Use and apply standard techniques Learners should be able to: • select and correctly carry out routine procedures • accurately recall facts, terminology and definitions

    AO2
    20%

    Reason, interpret and communicate mathematically Learners should be able to: • construct rigorous mathematical arguments (including proofs) • make deductions and inferences • assess the validity of mathematical arguments • explain their reasoning • use mathematical language and notation correctly

    AO3
    10%

    Solve problems within mathematics and in other contexts Learners should be able to: • translate problems in mathematical and non-mathematical contexts into mathematical processes • interpret solutions to problems in their original context, and, where appropriate, evaluate their accuracy and limitations • translate situations in context into mathematical models • use mathematical models • evaluate the outcomes of modelling in context, recognise the limitations of models and, where appropriate, explain how to refine them

    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

    AQA
    State
    1 mark

    Give a single fact or term

    Identify
    1 mark

    Name, select, or recognise

    Outline
    2 marks

    Set out main features briefly

    Describe
    2-4 marks

    Give an account of what something is like or what happens

    Explain
    3-6 marks

    Give reasons with developed cause→effect chains

    Compare
    2-4 marks

    State similarities AND differences (both required)

    Analyse
    6-9 marks

    Examine in detail showing cause→effect→consequence chains

    Evaluate
    6-12 marks

    Weigh up BOTH sides, reach JUSTIFIED conclusion

    Assess
    6-12 marks

    Make judgments about importance with justification

    Calculate
    2-4 marks

    Show formula→substitution→calculation→answer with units

    Common Exam Mistakes

    Pitfalls to avoid in your exams

    • •Subtracting vectors in the wrong order when finding a displacement vector (e.g., calculating a - b instead of b - a for vector AB)
    • •Neglecting to square negative components correctly when calculating magnitude, resulting in a negative term under the square root
    • •Omitting vector notation (underlines or arrows) in handwritten work, leading to confusion between scalars and vectors in algebraic manipulation
    • •Assuming vectors are parallel solely based on visual inspection without showing one is a scalar multiple of the other
    • •Dividing an equation by a common trigonometric factor (e.g., dividing by cos(x)) without considering the case where cos(x) = 0, leading to lost solutions
    • •Failure to adjust the domain when solving for a compound angle (e.g., solving sin(2x) = 0.5 for 0 < x < 360 requires checking the range 0 < 2x < 720)
    • •Incorrect signs when expanding compound angles, particularly assuming cos(A + B) = cos(A) + cos(B) or forgetting the sign change in the expansion
    • •Using degree mode on the calculator when evaluating small angle approximations or calculus-based trigonometric questions, which strictly require radians

    Top Examiner Tips

    Expert advice for exam success

    • •When proving points are collinear, explicitly state that the vectors share a common point AND are scalar multiples of each other
    • •Always draw a sketch for geometric vector problems to visualize the path; remember the triangle law AB + BC = AC
    • •In 3D problems, handle the k-component with the same algebraic rules as i and j; errors often occur when forgetting the third dimension in distance calculations
    • •When proving identities, always manipulate the more complex side (usually LHS) to match the simpler side; do not move terms across the equals sign as this invalidates the proof structure
    • •For 'Show that' questions, explicitly state the standard identity being used (e.g., 'Using sin²x + cos²x = 1') before substituting to secure method marks even if calculation errors follow
    • •Always sketch the relevant trigonometric graph when solving equations to visually verify the number of solutions expected in the interval
    • •When asked to 'Show that' events are independent, you must calculate P(A) x P(B) and P(A n B) separately and explicitly state they are equal
    • •Use Venn diagrams for questions involving 'at least one' or 'neither' to visually verify which regions to sum

    Specification Topics

    3 topics

    Vectors

    0 objectives3 tips4 pitfalls

    Trigonometry

    0 objectives3 tips4 pitfalls

    Probability

    0 objectives3 tips3 pitfalls

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