8 free calculus resources for Year 12: 5 worksheets, 3 study guides. Answers included.
Differentiation and integration. In Year 12, Year 12 is the final year, assessed for the HSC, VCE, QCE, WACE, SACE or equivalent.
Students will practise: finding stationary points by solving f′(x) = 0; classifying stationary points with the second derivative or a sign table; finding points of inflection and intervals where a function is increasing or decreasing; setting up and solving optimisation problems, including justifying the maximum or minimum; finding antiderivatives of polynomial, linear-power, exponential, reciprocal and trigonometric functions; evaluating definite integrals using the fundamental theorem of calculus; finding the area between a curve and the x-axis, including regions below the axis; finding the area between two curves and approximating area with the trapezoidal rule.
Printable practice with an answer sheet.
Differentiate polynomial functions using the power rule. A challenge set for students ready to stretch further. This Year 12 worksheet has…
Differentiate polynomial functions using the power rule. A challenge set for students ready to stretch further. This Year 12 worksheet has…
Find indefinite integrals of polynomials and evaluate simple definite integrals. Expected-level practice for this year group. This Year 12…
Find indefinite integrals of polynomials and evaluate simple definite integrals. A challenge set for students ready to stretch further.…
Clear explanations, examples and tips.
An HSC/VCE-style study guide to using the first and second derivatives to find and classify stationary points and points of inflection,…
An HSC/VCE-style study guide to definite integrals and area: the standard integrals, the fundamental theorem of calculus, areas below the…
Introduces integration as the reverse of differentiation, sets out the power rule for integrating, explains the constant of integration,…
Step-by-step solutions to model the method.
Ten exam-style calculus questions covering differentiation (product, quotient and chain rules with exponentials, logarithms and…
Differentiation and integration. At Year 12, our resources focus on: finding stationary points by solving f′(x) = 0; classifying stationary points with the second derivative or a sign table; finding points of inflection and intervals where a function is increasing or decreasing; setting up and solving optimisation problems, including justifying the maximum or minimum.
Read the study guide first, then start with the Level 1 or Level 2 worksheet. Finish with the topic test.
Yes — every worksheet has an answer sheet. Maths answer sheets show the working; English tasks include model answers or success criteria.
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