Differentiation
Differentiate y = 3x^4 - 5x^2 + 7 and state the gradient when x = 2.
A strong answer shows dy/dx = 12x^3 - 10x, then substitutes x = 2 to get 96 - 20 = 76. The common lost mark is substituting before differentiating.
For official specifications and assessment wording, cross-check AQA, Pearson Edexcel and OCR alongside this guide.
A-Level Maths Revision Made Simple
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AQAEdexcelOCRWJECEduqasCCEACIESQAIBAP
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A-Level Mathematics is one of the most challenging and rewarding subjects you can study. Whether you're working through pure maths topics like calculus and trigonometry, or applied topics like statistics and mechanics, StudyVector breaks concepts into clear, manageable steps. Our tutor explains topics patiently, clearly, with worked examples that actually make sense, and now with curated launch guides for the highest-friction routes. We support AQA, Edexcel, OCR, Cambridge International A-Level, IB Mathematics AA and AI, and AP Calculus where coverage is live.
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A-Level and Further Maths explanations reviewed
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Core A-Level Maths topics
Start with the strand that is costing you marks, then move into full practice once the method is secure. Topic depth varies by board, so check your exact specification alongside these launch guides.
Proof (Pure Mathematics)AQAEdexcelOCRWJECEduqasCCEACIESQAIBAPDifferentiation (Pure Mathematics)AQAEdexcelOCRWJECEduqasCCEACIESQAIBAPIntegration (Pure Mathematics)AQAEdexcelOCRWJECEduqasCCEACIESQAIBAPTrigonometry (Pure Mathematics)AQAEdexcelOCRWJECEduqasCCEACIESQAIBAPStatistical Hypothesis Testing (Statistics)AQAEdexcelOCRWJECEduqasCCEACIESQAIBAPKinematics (Mechanics)AQAEdexcelOCRWJECEduqasCCEACIESQAIBAP
Example questions
Quick checks before full practice
Statistics
A random variable follows X ~ B(20, 0.3). What does P(X <= 4) mean in context?
It means the probability of four or fewer successes in 20 independent trials, each with success probability 0.3. State the context before using calculator probabilities.
Mechanics
A particle starts from rest and accelerates uniformly at 2.5 m s^-2 for 8 seconds. Find its speed.
Use v = u + at with u = 0, a = 2.5 and t = 8, so v = 20 m s^-1. Include units because mechanics marks often reward correct physical interpretation.
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A-Level Maths
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AQAEdexcelOCRWJEC
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We cover AQA, Edexcel, OCR, Cambridge IGCSE, Cambridge International A-Level, IB Mathematics AA & AI, and AP Calculus AB & BC.
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