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Differentiation

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Limits, first principles and the power rule
1Evaluate limits and test continuityOpen, set of 8LessonPractice
2Gradient of a tangent from first principlesOpen, set of 8LessonPractice
3Differentiate power functions and evaluate a derivativeOpen, set of 8LessonPractice
4Expand and factor polynomial expressionsOpen, set of 8LessonPractice
5Pascal rows and binomial coefficient structureOpen, set of 8LessonPractice
6Simplify and combine algebraic fractionsOpen, set of 8LessonPractice
7Evaluate a polynomial or recover a coefficient parameterOpen, set of 8LessonPractice
8Substitute values into a formulaOpen, set of 8LessonPractice
9Solve a linear equationOpen, set of 8LessonPractice
Gradient graphs and smooth joins
10Test or construct a smooth piecewise joinOpen, set of 8LessonPractice
11Read and construct a gradient function from a function graphOpen, set of 8LessonPractice
12Analyse a cubic graph or determine its ruleOpen, set of 8LessonPractice
13Evaluate and determine function rulesOpen, set of 8LessonPractice
Tangents, normals and derivative conditions
14Equation of a tangent or normal lineOpen, set of 8LessonPractice
15Recover a polynomial rule from derivative and tangent conditionsOpen, set of 8LessonPractice
16Find the gradient of a line through two pointsOpen, set of 8LessonPractice
17Find the equation of a line from its graph or from its intercept and slopeOpen, set of 8LessonPractice
18Form an equation of a parallel or perpendicular lineOpen, set of 8LessonPractice
19Solve a pair of simultaneous linear equationsOpen, set of 8LessonPractice
20Determine parameters in a polynomial identityOpen, set of 8LessonPractice
21Solve a linear equationOpen, set of 8LessonPractice
Exponential derivatives and rate models
22Differentiate natural exponential functions and solve simple derivative conditionsOpen, set of 8LessonPractice
23Exponential growth and decay rate modelsOpen, set of 8LessonPractice
24Simplify and combine algebraic fractionsOpen, set of 8LessonPractice
25Round to decimal places and significant figuresOpen, set of 8LessonPractice
Trigonometric differentiation and rates
26Differentiate sine, cosine and tangent functions and solve simple derivative conditionsOpen, set of 8LessonPractice
27Geometric optimisation with a trigonometric modelOpen, set of 8LessonPractice
28Sinusoidal models and their rates of changeOpen, set of 8LessonPractice
29Solve a practical right-angled-triangle problemOpen, set of 8LessonPractice
30Perimeter and area of standard shapesOpen, set of 8LessonPractice
31Round to decimal places and significant figuresOpen, set of 8LessonPractice
Newton’s method and numerical accuracy
32Approximate a cubic root using Newton's methodOpen, set of 8LessonPractice
Chapter 4Chapter 6