SL 1.1

• • Operations with numbers in the form a × 10k where 1 ≤ a < 10 and k is an integer.

SL 1.2

• • Arithmetic sequences and series.

  • Use of the formulae for the n th term and the sum of the first n terms of the sequence.

  • Use of sigma notation for sums of arithmetic sequences.

  • Applications.

  • Analysis, interpretation and prediction where a model is not perfectly arithmetic in real life

SL 1.3

• • Geometric sequences and series.

  • Use of the formulae for the n th term and the sum of the first n terms of the sequence.

  • Use of sigma notation for the sums of geometric sequences.

  • Applications.

SL 1.4

• • Financial applications of geometric sequences and series:

    • • • • compound interest

        • • annual depreciation.

SL 1.5

• • Laws of exponents with integer exponents.

  • Introduction to logarithms with base 10 and e.

  • Numerical evaluation of logarithms using technology.

SL 1.6

• • Simple deductive proof, numerical and algebraic; how to lay out a left-hand side to right-hand side (LHS to RHS) proof. The symbols and notation for equality and identity.

SL 1.7

• • Laws of exponents with rational exponents.

  • Laws of logarithms.

  • Change of base of a logarithm.

  • Solving exponential equations, including using logarithms.

SL 1.8

• • Sum of infinite convergent geometric sequences.

SL 1.9

• • The binomial theorem: expansion of (a + b) n , n ∈ ℕ.

  • Counting principles may be used in the development of the theorem.

  • Use of Pascal’s triangle

  • AHL 1.10 Counting principles, including permutations and combinations.

  • Extension of the binomial theorem to fractional and negative indices

AHL 1.11

• • Partial fractions.

AHL 1.12

• • Complex numbers: the number i, where i 2 = − 1. Cartesian form z = a + bi; the terms real part, imaginary part, conjugate, modulus and argument.

  • The complex plane.

AHL 1.13

• • Modulus–argument (polar) form: z = r(cosθ + isinθ) = rcisθ .

  • Euler form: z = reiθ

  • Sums, products and quotients in Cartesian, polar or Euler forms and their geometric interpretation

AHL 1.14

• • Complex conjugate roots of quadratic and polynomial equations with real coefficients.

  • De Moivre’s theorem and its extension to rational exponents.

  • Powers and roots of complex numbers

 AHL 1.15

• • Proof by mathematical induction.

  • Proof by contradiction.

  • Use of a counterexample to show that a statement is not always true.

AHL 1.16

• • Solutions of systems of linear equations (a maximum of three equations in three unknowns), including cases where there is a unique solution, an infinite number of solutions or no solution.