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Find a connected rate of change from a stated relation · Check your progress
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Differentiate composite functions, products and quotients exactly · Check your progress
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Find the complete normal to a polynomial curve at a stated input · Check your progress
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Find every input where a polynomial is increasing or decreasing · Check your progress
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Form a polynomial model from a described situation and find its optimum · Check your progress
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Differentiate power sums on the stated input interval · Check your progress
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Find a complete second derivative on the stated input interval · Check your progress
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Find the complete tangent to a polynomial at a stated input · Check your progress
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Find and classify every stationary point of a polynomial · Check your progress
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Find the greatest polynomial value and every attaining input on a closed interval · Check your progress
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Find the least polynomial value and every attaining input on a closed interval · Check your progress
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Model and evaluate a nonnegative polynomial curve–line region with vertical strips · Check your progress
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Find a connected rate of change from a stated relation · Check again
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Differentiate composite functions, products and quotients exactly · Check again
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Find the complete normal to a polynomial curve at a stated input · Check again
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Find every input where a polynomial is increasing or decreasing · Check again
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Form a polynomial model from a described situation and find its optimum · Check again
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Differentiate power sums on the stated input interval · Check again
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Find a complete second derivative on the stated input interval · Check again
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Find the complete tangent to a polynomial at a stated input · Check again
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Find and classify every stationary point of a polynomial · Check again
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Find the greatest polynomial value and every attaining input on a closed interval · Check again
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Find the least polynomial value and every attaining input on a closed interval · Check again
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Model and evaluate a nonnegative polynomial curve–line region with vertical strips · Check again
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Find a connected rate of change from a stated relation · Retention check
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Differentiate composite functions, products and quotients exactly · Retention check
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Find the complete normal to a polynomial curve at a stated input · Retention check
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Find every input where a polynomial is increasing or decreasing · Retention check
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Form a polynomial model from a described situation and find its optimum · Retention check
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Differentiate power sums on the stated input interval · Retention check
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Find a complete second derivative on the stated input interval · Retention check
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Find the complete tangent to a polynomial at a stated input · Retention check
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Find and classify every stationary point of a polynomial · Retention check
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Find the greatest polynomial value and every attaining input on a closed interval · Retention check
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Find the least polynomial value and every attaining input on a closed interval · Retention check
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Model and evaluate a nonnegative polynomial curve–line region with vertical strips · Retention check
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Practise: Find a connected rate of change from a stated relation
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Practise: Differentiate composite functions, products and quotients exactly
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Practise: Find the complete normal to a polynomial curve at a stated input
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Practise: Find every input where a polynomial is increasing or decreasing
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Practise: Form a polynomial model from a described situation and find its optimum
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Practise: Differentiate power sums on the stated input interval
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Practise: Find a complete second derivative on the stated input interval
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Practise: Find the complete tangent to a polynomial at a stated input
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Practise: Find and classify every stationary point of a polynomial
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Practise: Find the greatest polynomial value and every attaining input on a closed interval
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Practise: Find the least polynomial value and every attaining input on a closed interval
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Practise: Model and evaluate a nonnegative polynomial curve–line region with vertical strips
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Next step
Revision notes
Connect derivatives with tangents, stationary points, rates and optimisation, then recover antiderivatives and calculate positive areas.
Key ideas
- Function, gradient and local change
Distinguish function value from local rate of change and connect derivative tests to curve behaviour.
- Power, chain, product and quotient rules
Choose differentiation rules from the expression structure, retain real domains, and verify combined derivatives by another form.
- Stationary points, tangents and normals
Interpret derivative signs, classify stationary points, and distinguish local behaviour from extrema on a stated domain.
- Connected rates and optimisation
Connect changing dimensions and net rates, then justify constrained optima using the original model and feasible domain.
- Antiderivatives and positive area
Recover antiderivatives with their conditions, then select the correct boundaries and vertical separation for positive area.
From the G2 Additional Mathematics 2027 syllabus
Show all 16 syllabus statements
- Derivative of f (x) as the gradient of the tangent to the graph of y = f (x) at a point
- Derivative as rate of change
- Use of standard notations f′(x), f″(x), dy/dx, d²y/dx² = d/dx(dy/dx)
- Derivatives of x^n , for any rational n, together with constant multiples, sums and differences
- Derivatives of products and quotients of functions
- Use of Chain Rule
- Increasing and decreasing functions
- Stationary points (maximum and minimum turning points and stationary points of inflexion)
- Use of second derivative test to discriminate between maxima and minima
- Apply differentiation to gradients, tangents and normals, connected rates of change and maxima and minima problems
- Integration as the reverse of differentiation
- Integration of x^n for any rational n, (excluding n = −1 ), together with constant multiples, sums and differences
- Integration of (ax + b)n for any rational n, (excluding n = −1 )
- Definite integral as area under a curve
- Evaluation of definite integrals
- Finding the area of a region bounded by a curve and line(s) (excluding area of region between 2 curves)