GCSE AQA Higher Further Maths · Topic 4 of 6
Choose a subtopic. Calculus covers Know what the gradient function gives, Know that the gradient of a function is the gradient of the tangent at that point, Differentiation of kx^n and the sum of such functions, and The equation of a tangent and normal at any point on a curve in GCSE AQA Higher Further Maths. 11 lessons in 9 subtopics.
Revise Calculus for GCSE AQA Higher Further Maths, including Know what the gradient function gives. 11 lessons across 9 subtopics.
11
Lessons
9
Subtopics
Calculus has 9 subtopics, including:
11 lessons, grouped by subtopic.
Go back to the full GCSE AQA Higher Further Maths topic list, or practise this topic with past-paper questions.
Calculus covers Know what the gradient function gives, Know that the gradient of a function is the gradient of the tangent at that point, Differentiation of kx^n and the sum of such functions, and The equation of a tangent and normal at any point on a curve in GCSE AQA Higher Further Maths. 11 lessons in 9 subtopics.
A stationary point of inflection is a stationary point where the gradient is momentarily zero but the curve does not actually turn: it flattens and then continues in the same direction. The Determining the Nature of Stationary Points notes cover this in full.
Split the fraction into separate terms, simplify using index laws, then differentiate. The Simplifying and Differentiating notes cover this in full.
The second derivative shows how the gradient is changing. The Introducing Second Derivatives notes cover this in full.
The nature of a stationary point describes whether it is a local maximum, a local minimum or a point of inflection. The Determining the Nature of Stationary Points notes cover this in full.
Find the tangent gradient, take its negative reciprocal, then use the same point in y − y₁ = m(x − x₁). The Finding Tangents and Normals notes cover this in full.
A function is increasing on an interval when its gradient dy/dx is positive throughout that interval, so as x increases, y also increases, like walking uphill. The Understanding Increasing and Decreasing Functions notes cover this in full.
Differentiate, substitute the x-value to get the gradient, then use y − y₁ = m(x − x₁). The Finding Tangents and Normals notes cover this in full.
The derivative of a constant is zero, because a horizontal line has zero gradient everywhere: 7 = 7x⁰, and 7 × 0 = 0. The Differentiating kx^n notes cover this in full.