These SmartGirl Study Notes Include:
Summary of proofs (for Trigonometry & Euclidean Geometry) Algebra, Sequences & Series & Polynomials:
Revision of grade 11 concepts
Linear, Quadratic & Exponential Patterns
Arithmetic Series
Geometric Series
Geometric Series - sum to infinity
Sigma notation
Practical Applications of Sequences & Series
Polynomials
Trigonometry & Trig graphs:
Revision of basic trigonometry
Summary of grade 11 concepts: trig identities, reduction formulae, special angles & specific & general solutions
Trig graphs
Compound angles
Double angles
Using double angles with identities
General & specific solutions with double & compound angles
Equations with compound & double angles
Restrictions on identities & equations
Trigonometry in 3 dimensions
Functions:
Parabolas
Hyperbolas
Exponential Functions
Functions & Inverse Functions
Exponential & Log functions
Probability & Statistics:
Notation
Mutually exclusive events, complementary events, independent & dependent events
The product rule & the addition rule
Venn diagrams, tree diagrams & contingency tables
The fundamental counting principle (includes examples)
Five number summaries & percentiles
Histograms & Frequency polygons
Variance & standard deviation
Ogives
Normal distribution, symmetrical & skewed data
Scatter plots
Regression lines
Correlation coefficients
Interpolation & extrapolation
Euclidean & Analytical Geometry:
Grade 11 Revision of Analytical Geometry Formulas
Equations of circles
Tangents to a circle
Problem solving with circles
Summary of basic Euclidean geometry concepts (from grade 8 - 10)
Summary of circle geometry (grade 11)
Congruency
Similar polygons
The midpoint theorem
The proportionality theorem
Equiangular triangles
Triangles with proportional sides & similarity
The Pythagorean theorem & similarity
Proofs
Summary of grade 12 theorems
Financial Mathematics:
Simple growth and decay
Compound growth and decay
The effects of different compounding periods
Timelines (interest rate changes and additional withdrawals & deposits)
Nominal & Effective Interest Rates
Future Value Annuities
Present Value Annuities
Loan Values
Differing Final payments
Deferred Payments
Sinking Funds
Pyramid Schemes
Differential Calculus & Cubic Graphs:
Differential Calculus
Limits
First Principles
Rules of Differentiation
Differentiation shortcut
Gradient at a point
Equation of a tangent
Stationary points
Cubic graphs
Calculus & Problem solving
