QuestionQuestionConceptConceptDocumentDocument

1 Number and algebra

Start with Concept to understand a topic, then use Question Bank to check what you know.

2 topics · 16 learning objectives

Your progress

Sign in to see your mastery and mistakes.

  1. 1.1 Number and algebra - SL content

    1. SL 1.1Scientific notation

      • Use numbers in the form a x 10^k where 1 <= a < 10 and k is an integer. • Calculator/computer notation such as 5.2E30 is not acceptable.

    2. SL 1.2Arithmetic sequences and series

      • Use nth-term, finite-sum and sigma notation for arithmetic sequences. • Identify first term and common difference; apply to contexts such as simple interest.

    3. SL 1.3Geometric sequences and series

      • Use nth-term, finite-sum and sigma notation for geometric sequences. • Identify first term and common ratio; apply to growth/decay contexts.

    4. SL 1.4Financial applications

      • Apply geometric sequences to compound interest and annual depreciation. • Use technology/financial packages; consider inflation and compounding frequency.

    5. SL 1.5Integer exponents and logarithms

      • Use laws of exponents with integer exponents. • Understand base-10 and natural logarithms; ax=b is equivalent to log_a(b)=x.

    6. SL 1.6Deductive proof

      • Write simple numerical and algebraic deductive proofs. • Use equality/identity notation and LHS-to-RHS proof layout; check results.

    7. SL 1.7Rational exponents and logarithm laws

      • Use rational exponent laws and logarithm laws. • Use change of base and logarithms to solve exponential equations.

    8. SL 1.8Infinite geometric series

      • Find sums of infinite convergent geometric sequences. • Use |r| < 1 and modulus notation for convergence.

    9. SL 1.9Binomial theorem

      • Expand (a+b)^n for n in N using the binomial theorem. • Use Pascal's triangle and nCr, with formula and technology.

  2. 1.2 Number and algebra - AHL content

    1. AHL 1.10 (HL)—Counting and extended binomial theorem

      • Use counting principles, permutations and combinations. • Extend binomial expansion to fractional and negative indices. • Exclude identical-object permutations, circular arrangements and proof of the theorem.

    2. AHL 1.11 (HL)—Partial fractions

      • Decompose rational expressions into partial fractions. • Denominators have at most two distinct linear terms; numerator degree is lower than denominator degree.

    3. AHL 1.12 (HL)—Complex numbers

      • Use i where i^2 = -1 and Cartesian form z=a+bi. • Know real/imaginary parts, conjugate, modulus, argument and the Argand diagram.

    4. AHL 1.13 (HL)—Polar and Euler forms

      • Use polar form z=r(cos theta + i sin theta)=r cis theta and Euler form z=re^(i theta). • Convert between Cartesian, polar and Euler forms; interpret sums, products and quotients geometrically.

    5. AHL 1.14 (HL)—Complex roots and De Moivre's theorem

      • Know complex conjugate roots of real-coefficient polynomial equations. • Use De Moivre's theorem for powers and roots of complex numbers. • Include induction proof for positive integer powers; be aware of rational exponent extension.

    6. AHL 1.15 (HL)—Advanced proof

      • Use proof by mathematical induction and proof by contradiction. • Use counterexamples to disprove statements, with explanation of why the counterexample works.

    7. AHL 1.16 (HL)—Systems of linear equations

      • Solve up to three linear equations in three unknowns algebraically and with technology. • Identify unique, infinite or no solutions; find general solutions where appropriate.