SL 1.1—Using standard form
SL 1.2—Arithmetic sequences and series
Arithmetic sequences and series. Use of the formulae for the nth 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.
approximate common differences.
SL 1.3—Geometric sequences and series
Geometric sequences and series
Use of the formulae for the nth term and the sum of the first n terms of the sequence.
Use of sigma notation for the sums of geometric sequences.
Applications
Examples include the spread of disease, salary increase and decrease and population growth
SL 1.4—Financial apps – compound int, annual depreciation
Financial applications of geometric sequences and series:
compound interest
annual depreciation
SL 1.5—Intro to exponents and logs
Laws of exponents with integer exponents.
Introduction to logarithms with base 10 and e. Numerical evaluation of logarithms using technology
SL 1.6—Simple proof
SL 1.7—Laws of exponents and logs
Laws of exponents with rational exponents.
Laws of logarithms.
log(xy) = log(x) + log(y)
log(x/y)=log(x) - log(y)
log(x^m)= mlog(x)
Change of base of a logarithm.
log_a (x) = (log_c (x))/(log_c (a)) for a, c, x > 0
SL 1.8—Sum of infinite geo sequence
Sum of infinite convergent geometric sequences.
SL 1.9—Binomial theorem where n is an integer
The binomial theorem: expansion of (a + b)n , n ∈ ℕ.
Use of Pascal’s triangle and nCr
AHL 1.10—Perms and combs, binomial with negative and fractional indices
AHL 1.13—Polar and Euler form
AHL 1.14—Complex roots of polynomials, conjugate roots, De Moivre’s, powers & roots of complex numbers
AHL 1.15—Proof by induction, contradiction, counterexamples
AHL 1.16—Solution of systems of linear equations