Mathematics: Analysis and Approaches HL

Functions

Advanced function behaviour, transformations, inverses, composites, polynomial/rational/exponential/logarithmic models, and parametric representations.

Use equations and gradients of straight lines Free Develop use equations and gradients of straight lines through finite, exact AA HL practice aligned to current syllabus point AHL 2.1. Use function notation, domain, range and inverses Develop use function notation, domain, range and inverses through finite, exact AA HL practice aligned to current syllabus point AHL 2.2. Sketch and label graphs from equations Develop sketch and label graphs from equations through finite, exact AA HL practice aligned to current syllabus point AHL 2.3. Determine key graph features and intersections Develop determine key graph features and intersections through finite, exact AA HL practice aligned to current syllabus point AHL 2.4. Use composite and inverse functions Develop use composite and inverse functions through finite, exact AA HL practice aligned to current syllabus point AHL 2.5. Connect the three forms of a quadratic function Develop connect the three forms of a quadratic function through finite, exact AA HL practice aligned to current syllabus point AHL 2.6. Solve quadratic equations and inequalities Develop solve quadratic equations and inequalities through finite, exact AA HL practice aligned to current syllabus point AHL 2.7. Analyse reciprocal and rational functions Develop analyse reciprocal and rational functions through finite, exact AA HL practice aligned to current syllabus point AHL 2.8. Evaluate logarithms exactly Develop evaluate logarithms exactly through finite, exact AA HL practice aligned to current syllabus point AHL 2.9. Use exponential and logarithmic inverse relationships Develop use exponential and logarithmic inverse relationships through finite, exact AA HL practice aligned to current syllabus point AHL 2.9. Connect exponential and logarithmic functions Develop connect exponential and logarithmic functions through finite, exact AA HL practice aligned to current syllabus point AHL 2.9. Solve exponential equations exactly Develop solve exponential equations exactly through finite, exact AA HL practice aligned to current syllabus point AHL 2.9. Combine logarithms exactly Develop combine logarithms exactly through finite, exact AA HL practice aligned to current syllabus point AHL 2.9. Solve exponential equations using technology Develop solve exponential equations using technology through finite, exact AA HL practice aligned to current syllabus point AHL 2.10. Solve equations using graph intersections Develop solve equations using graph intersections through finite, exact AA HL practice aligned to current syllabus point AHL 2.10. Map points under graph translations Develop map points under graph translations through finite, exact AA HL practice aligned to current syllabus point AHL 2.11. Map points under graph reflections Develop map points under graph reflections through finite, exact AA HL practice aligned to current syllabus point AHL 2.11. Map points under graph stretches Develop map points under graph stretches through finite, exact AA HL practice aligned to current syllabus point AHL 2.11. Apply composite graph transformations Develop apply composite graph transformations through finite, exact AA HL practice aligned to current syllabus point AHL 2.11. Apply the remainder theorem Develop apply the remainder theorem through finite, exact AA HL practice aligned to current syllabus point AHL 2.12. Apply the factor theorem Develop apply the factor theorem through finite, exact AA HL practice aligned to current syllabus point AHL 2.12. Find polynomial coefficients from factors Develop find polynomial coefficients from factors through finite, exact AA HL practice aligned to current syllabus point AHL 2.12. Find sums of polynomial roots Develop find sums of polynomial roots through finite, exact AA HL practice aligned to current syllabus point AHL 2.12. Find products of polynomial roots Develop find products of polynomial roots through finite, exact AA HL practice aligned to current syllabus point AHL 2.12. Use polynomial root relationships Develop use polynomial root relationships through finite, exact AA HL practice aligned to current syllabus point AHL 2.12. Connect polynomial zeros and factors Develop connect polynomial zeros and factors through finite, exact AA HL practice aligned to current syllabus point AHL 2.12. Find vertical asymptotes of rational functions Develop find vertical asymptotes of rational functions through finite, exact AA HL practice aligned to current syllabus point AHL 2.13. Find oblique asymptotes of rational functions Develop find oblique asymptotes of rational functions through finite, exact AA HL practice aligned to current syllabus point AHL 2.13. Find y-intercepts of rational functions Develop find y-intercepts of rational functions through finite, exact AA HL practice aligned to current syllabus point AHL 2.13. Analyse key features of rational functions Develop analyse key features of rational functions through finite, exact AA HL practice aligned to current syllabus point AHL 2.13. Determine whether functions are odd or even Develop determine whether functions are odd or even through finite, exact AA HL practice aligned to current syllabus point AHL 2.14. Evaluate restricted inverse functions Develop evaluate restricted inverse functions through finite, exact AA HL practice aligned to current syllabus point AHL 2.14. Analyse affine inverse composition Develop analyse affine inverse composition through finite, exact AA HL practice aligned to current syllabus point AHL 2.14. Solve polynomial inequalities Develop solve polynomial inequalities through finite, exact AA HL practice aligned to current syllabus point AHL 2.15. Compare functions using inequalities Develop compare functions using inequalities through finite, exact AA HL practice aligned to current syllabus point AHL 2.15. Solve equations involving modulus functions Develop solve equations involving modulus functions through finite, exact AA HL practice aligned to current syllabus point AHL 2.16. Solve inequalities involving modulus functions Develop solve inequalities involving modulus functions through finite, exact AA HL practice aligned to current syllabus point AHL 2.16. Analyse reciprocal transformations Develop analyse reciprocal transformations through finite, exact AA HL practice aligned to current syllabus point AHL 2.16. Map points under transformations of f(ax+b) Develop map points under transformations of f(ax+b) through finite, exact AA HL practice aligned to current syllabus point AHL 2.16. Solve equations between modulus functions Develop solve equations between modulus functions through finite, exact AA HL practice aligned to current syllabus point AHL 2.16. Solve lower-bound modulus inequalities Develop solve lower-bound modulus inequalities through finite, exact AA HL practice aligned to current syllabus point AHL 2.16.