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

# Grade 12 Math

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