Mathematics: Analysis and Approaches HL

Calculus

Higher-level differentiation, integration, optimization, rates, concavity, and differential equations.

Differentiate products of linear functions Develop differentiate products of linear functions through finite, exact AA HL practice aligned to current syllabus point AHL 5.6. Use implicit differentiation on circles Develop use implicit differentiation on circles through finite, exact AA HL practice aligned to current syllabus point AHL 5.14. Solve related-rate problems for circles Develop solve related-rate problems for circles through finite, exact AA HL practice aligned to current syllabus point AHL 5.14. Use second derivatives to classify concavity Develop use second derivatives to classify concavity through finite, exact AA HL practice aligned to current syllabus point AHL 5.7. Integrate composite powers by substitution Develop integrate composite powers by substitution through finite, exact AA HL practice aligned to current syllabus point AHL 5.16. Integrate polynomial-exponential products by parts Develop integrate polynomial-exponential products by parts through finite, exact AA HL practice aligned to current syllabus point AHL 5.16. Solve separable first-order differential equations Develop solve separable first-order differential equations through finite, exact AA HL practice aligned to current syllabus point AHL 5.18. Differentiate tangent composites Develop differentiate tangent composites through finite, exact AA HL practice aligned to current syllabus point AHL 5.15. Optimise functions on closed intervals Develop optimise functions on closed intervals through finite, exact AA HL practice aligned to current syllabus point AHL 5.14. Find points of inflexion on cubic graphs Develop find points of inflexion on cubic graphs through finite, exact AA HL practice aligned to current syllabus point AHL 5.8. Integrate inverse-tangent forms Develop integrate inverse-tangent forms through finite, exact AA HL practice aligned to current syllabus point AHL 5.15. Calculate areas between curves Develop calculate areas between curves through finite, exact AA HL practice aligned to current syllabus point AHL 5.11. Connect velocity acceleration and displacement Develop connect velocity acceleration and displacement through finite, exact AA HL practice aligned to current syllabus point AHL 5.9. Solve separable differential equations with initial values Develop solve separable differential equations with initial values through finite, exact AA HL practice aligned to current syllabus point AHL 5.18. Apply one Euler-method step Develop apply one euler-method step through finite, exact AA HL practice aligned to current syllabus point AHL 5.18. Evaluate indeterminate limits using l’Hôpital’s rule Develop evaluate indeterminate limits using l’hôpital’s rule through finite, exact AA HL practice aligned to current syllabus point AHL 5.13. Approximate exponential values with Maclaurin polynomials Develop approximate exponential values with maclaurin polynomials through finite, exact AA HL practice aligned to current syllabus point AHL 5.19. Find coefficients in Maclaurin sine series Develop find coefficients in maclaurin sine series through finite, exact AA HL practice aligned to current syllabus point AHL 5.19. Approximate logarithms with Maclaurin polynomials Develop approximate logarithms with maclaurin polynomials through finite, exact AA HL practice aligned to current syllabus point AHL 5.19. Solve exponential growth differential models Develop solve exponential growth differential models through finite, exact AA HL practice aligned to current syllabus point AHL 5.18. Apply two Euler-method steps Develop apply two euler-method steps through finite, exact AA HL practice aligned to current syllabus point AHL 5.18. Calculate volumes of revolution about the x-axis Develop calculate volumes of revolution about the x-axis through finite, exact AA HL practice aligned to current syllabus point AHL 5.17. Calculate areas between curves and the y-axis Develop calculate areas between curves and the y-axis through finite, exact AA HL practice aligned to current syllabus point AHL 5.17. Evaluate limits at infinity using l’Hôpital’s rule Develop evaluate limits at infinity using l’hôpital’s rule through finite, exact AA HL practice aligned to current syllabus point AHL 5.13. Integrate rational functions using partial fractions Develop integrate rational functions using partial fractions through finite, exact AA HL practice aligned to current syllabus point AHL 5.15. Differentiate quadratics from first principles Develop differentiate quadratics from first principles through finite, exact AA HL practice aligned to current syllabus point AHL 5.12. Solve logistic differential equations with initial values Develop solve logistic differential equations with initial values through finite, exact AA HL practice aligned to current syllabus point AHL 5.18. Solve homogeneous power differential equations Develop solve homogeneous power differential equations through finite, exact AA HL practice aligned to current syllabus point AHL 5.18. Calculate higher derivatives of polynomials Develop calculate higher derivatives of polynomials through finite, exact AA HL practice aligned to current syllabus point AHL 5.12. Evaluate scaled trigonometric limits Develop evaluate scaled trigonometric limits through finite, exact AA HL practice aligned to current syllabus point AHL 5.13. Evaluate exponential limits Develop evaluate exponential limits through finite, exact AA HL practice aligned to current syllabus point AHL 5.13. Optimise open-box volume Develop optimise open-box volume through finite, exact AA HL practice aligned to current syllabus point AHL 5.14. Apply L’Hôpital’s rule repeatedly Develop apply l’hôpital’s rule repeatedly through finite, exact AA HL practice aligned to current syllabus point AHL 5.13. Solve sphere related-rate problems Develop solve sphere related-rate problems through finite, exact AA HL practice aligned to current syllabus point AHL 5.14. Differentiate inverse-sine composites Develop differentiate inverse-sine composites through finite, exact AA HL practice aligned to current syllabus point AHL 5.15. Integrate completed-square inverse-tangent forms Develop integrate completed-square inverse-tangent forms through finite, exact AA HL practice aligned to current syllabus point AHL 5.15. Differentiate secant and cosecant composites Develop differentiate secant and cosecant composites through finite, exact AA HL practice aligned to current syllabus point AHL 5.15. Solve linear differential equations with constant coefficients Develop solve linear differential equations with constant coefficients through finite, exact AA HL practice aligned to current syllabus point AHL 5.18. Analyse logistic equilibrium and maximum growth Develop analyse logistic equilibrium and maximum growth through finite, exact AA HL practice aligned to current syllabus point AHL 5.18. Find coefficients in cosine Maclaurin series Develop find coefficients in cosine maclaurin series through finite, exact AA HL practice aligned to current syllabus point AHL 5.19. Find coefficients in arctangent Maclaurin series Develop find coefficients in arctangent maclaurin series through finite, exact AA HL practice aligned to current syllabus point AHL 5.19. Model Newton cooling with differential equations Develop model newton cooling with differential equations through finite, exact AA HL practice aligned to current syllabus point AHL 5.18. Differentiate ellipse equations implicitly Develop differentiate ellipse equations implicitly through finite, exact AA HL practice aligned to current syllabus point AHL 5.14. Differentiate exponential and logarithmic bases Develop differentiate exponential and logarithmic bases through finite, exact AA HL practice aligned to current syllabus point AHL 5.15. Calculate implicit second derivatives Develop calculate implicit second derivatives through finite, exact AA HL practice aligned to current syllabus point AHL 5.14. Evaluate limits using Maclaurin coefficients Develop evaluate limits using maclaurin coefficients through finite, exact AA HL practice aligned to current syllabus point AHL 5.13. Integrate repeated-factor partial fractions Develop integrate repeated-factor partial fractions through finite, exact AA HL practice aligned to current syllabus point AHL 5.15. Optimise rectangle area for fixed perimeter Develop optimise rectangle area for fixed perimeter through finite, exact AA HL practice aligned to current syllabus point AHL 5.14. Calculate volumes of revolution about the y-axis Develop calculate volumes of revolution about the y-axis through finite, exact AA HL practice aligned to current syllabus point AHL 5.17. Solve variable-coefficient equations with integrating factors Develop solve variable-coefficient equations with integrating factors through finite, exact AA HL practice aligned to current syllabus point AHL 5.18. Use substitutions in homogeneous differential equations Develop use substitutions in homogeneous differential equations through finite, exact AA HL practice aligned to current syllabus point AHL 5.18. Apply Euler’s method to difference slopes Develop apply euler’s method to difference slopes through finite, exact AA HL practice aligned to current syllabus point AHL 5.18. Solve cone related-rate problems Develop solve cone related-rate problems through finite, exact AA HL practice aligned to current syllabus point AHL 5.14. Differentiate inverse-cosine composites Develop differentiate inverse-cosine composites through finite, exact AA HL practice aligned to current syllabus point AHL 5.15. Determine constants in antiderivative families Develop determine constants in antiderivative families through finite, exact AA HL practice aligned to current syllabus point AHL 5.15. Solve reciprocal separable initial-value equations Develop solve reciprocal separable initial-value equations through finite, exact AA HL practice aligned to current syllabus point AHL 5.18. Integrate logarithms by parts Develop integrate logarithms by parts through finite, exact AA HL practice aligned to current syllabus point AHL 5.16. Integrate linear-trigonometric products by parts Develop integrate linear-trigonometric products by parts through finite, exact AA HL practice aligned to current syllabus point AHL 5.16. Apply repeated integration by parts to quadratic exponentials Develop apply repeated integration by parts to quadratic exponentials through finite, exact AA HL practice aligned to current syllabus point AHL 5.16. Expand rational binomial powers Develop expand rational binomial powers through finite, exact AA HL practice aligned to current syllabus point AHL 5.19. Obtain substituted exponential Maclaurin series Develop obtain substituted exponential maclaurin series through finite, exact AA HL practice aligned to current syllabus point AHL 5.19. Optimise closed cylinders with fixed volume Develop optimise closed cylinders with fixed volume through finite, exact AA HL practice aligned to current syllabus point AHL 5.14. Calculate washer volumes about the x-axis Develop calculate washer volumes about the x-axis through finite, exact AA HL practice aligned to current syllabus point AHL 5.17.