Mathematics: Analysis and Approaches HL

Number and algebra

Proof, complex numbers, polynomials, partial fractions, inequalities, and advanced sequences for Mathematics AA HL.

Operate with scientific notation Free Develop operate with scientific notation through finite, exact AA HL practice aligned to current syllabus point AHL 1.1. Divide and normalize scientific notation Develop divide and normalize scientific notation through finite, exact AA HL practice aligned to current syllabus point AHL 1.1. Find terms of arithmetic sequences Develop find terms of arithmetic sequences through finite, exact AA HL practice aligned to current syllabus point AHL 1.2. Sum arithmetic sequences using sigma notation Develop sum arithmetic sequences using sigma notation through finite, exact AA HL practice aligned to current syllabus point AHL 1.2. Model applications with arithmetic sequences Develop model applications with arithmetic sequences through finite, exact AA HL practice aligned to current syllabus point AHL 1.2. Find terms of geometric sequences Develop find terms of geometric sequences through finite, exact AA HL practice aligned to current syllabus point AHL 1.3. Sum finite geometric sequences Develop sum finite geometric sequences through finite, exact AA HL practice aligned to current syllabus point AHL 1.3. Model growth and decay with geometric sequences Develop model growth and decay with geometric sequences through finite, exact AA HL practice aligned to current syllabus point AHL 1.3. Calculate compound interest and depreciation Develop calculate compound interest and depreciation through finite, exact AA HL practice aligned to current syllabus point AHL 1.4. Use periodic compounding in financial models Develop use periodic compounding in financial models through finite, exact AA HL practice aligned to current syllabus point AHL 1.4. Calculate real value after inflation Develop calculate real value after inflation through finite, exact AA HL practice aligned to current syllabus point AHL 1.4. Apply laws of integer exponents Develop apply laws of integer exponents through finite, exact AA HL practice aligned to current syllabus point AHL 1.5. Evaluate logarithms and exponential equivalences Develop evaluate logarithms and exponential equivalences through finite, exact AA HL practice aligned to current syllabus point AHL 1.5. Construct numerical deductive arguments Develop construct numerical deductive arguments through finite, exact AA HL practice aligned to current syllabus point AHL 1.6. Prove algebraic identities from one side Develop prove algebraic identities from one side through finite, exact AA HL practice aligned to current syllabus point AHL 1.6. Apply laws of rational exponents Develop apply laws of rational exponents through finite, exact AA HL practice aligned to current syllabus point AHL 1.7. Combine expressions using logarithm laws Develop combine expressions using logarithm laws through finite, exact AA HL practice aligned to current syllabus point AHL 1.7. Use change of base for logarithms Develop use change of base for logarithms through finite, exact AA HL practice aligned to current syllabus point AHL 1.7. Solve exponential equations using logarithms Develop solve exponential equations using logarithms through finite, exact AA HL practice aligned to current syllabus point AHL 1.7. Decide convergence of geometric series Develop decide convergence of geometric series through finite, exact AA HL practice aligned to current syllabus point AHL 1.8. Calculate infinite geometric sums Develop calculate infinite geometric sums through finite, exact AA HL practice aligned to current syllabus point AHL 1.8. Counting principles and generalized binomial expansions Apply permutations and combinations to distinct-object restrictions, and expand binomials with fractional or negative indices. Use Pascal triangle and binomial coefficients Develop use pascal triangle and binomial coefficients through finite, exact AA HL practice aligned to current syllabus point AHL 1.9. Partial fractions with linear factors Decompose proper rational expressions whose denominators contain no more than two distinct linear factors. Expand binomials with positive integer powers Develop expand binomials with positive integer powers through finite, exact AA HL practice aligned to current syllabus point AHL 1.9. Complex numbers in Cartesian form Represent complex numbers on an Argand diagram and perform exact Cartesian operations using conjugates, modulus, and argument. Find a specified term in a binomial expansion Develop find a specified term in a binomial expansion through finite, exact AA HL practice aligned to current syllabus point AHL 1.9. Complex numbers in polar and Euler form Convert between Cartesian, polar, and Euler forms and use modulus-argument rules for exact multiplication and division. Solve equations involving binomial coefficients Develop solve equations involving binomial coefficients through finite, exact AA HL practice aligned to current syllabus point AHL 1.9. De Moivre theorem and complex roots Use De Moivre theorem for powers and roots, and use conjugate root structure in real-coefficient polynomials. Apply permutations and combinations Develop apply permutations and combinations through finite, exact AA HL practice aligned to current syllabus point AHL 1.10. Proof by induction, contradiction, and counterexample Construct complete proofs by induction and contradiction, and disprove universal statements with valid counterexamples. Count arrangements with restrictions Develop count arrangements with restrictions through finite, exact AA HL practice aligned to current syllabus point AHL 1.10. Systems of linear equations Solve and classify systems of at most three linear equations using algebra, row reduction, and technology where appropriate. Use generalized binomial expansions Develop use generalized binomial expansions through finite, exact AA HL practice aligned to current syllabus point AHL 1.10. Decompose using distinct linear partial fractions Develop decompose using distinct linear partial fractions through finite, exact AA HL practice aligned to current syllabus point AHL 1.11. Decompose using repeated linear partial fractions Develop decompose using repeated linear partial fractions through finite, exact AA HL practice aligned to current syllabus point AHL 1.11. Operate with complex numbers in Cartesian form Develop operate with complex numbers in cartesian form through finite, exact AA HL practice aligned to current syllabus point AHL 1.12. Use conjugate, modulus and argument on an Argand diagram Develop use conjugate, modulus and argument on an argand diagram through finite, exact AA HL practice aligned to current syllabus point AHL 1.12. Convert complex numbers between Cartesian and polar forms Develop convert complex numbers between cartesian and polar forms through finite, exact AA HL practice aligned to current syllabus point AHL 1.13. Multiply and divide complex numbers in polar form Develop multiply and divide complex numbers in polar form through finite, exact AA HL practice aligned to current syllabus point AHL 1.13. Use conjugate roots of real polynomials Develop use conjugate roots of real polynomials through finite, exact AA HL practice aligned to current syllabus point AHL 1.14. Apply De Moivre theorem to powers Develop apply de moivre theorem to powers through finite, exact AA HL practice aligned to current syllabus point AHL 1.14. Find roots of complex numbers Develop find roots of complex numbers through finite, exact AA HL practice aligned to current syllabus point AHL 1.14. Prove results by mathematical induction Develop prove results by mathematical induction through finite, exact AA HL practice aligned to current syllabus point AHL 1.15. Build proofs by contradiction Develop build proofs by contradiction through finite, exact AA HL practice aligned to current syllabus point AHL 1.15. Disprove statements with explained counterexamples Develop disprove statements with explained counterexamples through finite, exact AA HL practice aligned to current syllabus point AHL 1.15. Solve systems of three linear equations algebraically Develop solve systems of three linear equations algebraically through finite, exact AA HL practice aligned to current syllabus point AHL 1.16. Classify linear systems using row reduction Develop classify linear systems using row reduction through finite, exact AA HL practice aligned to current syllabus point AHL 1.16.