Math 11 Functions - Advanced

Expectations: be able to communicate and solve the following

Numerical skills

Functions

The parabola - quadratic functions

• Be able to complete the square for quadratic functions
• Finding the min/max of quadratic functions
• Solving quadratic functions
• Graphing of quadratic functions

Trigonometry and Trigonometric Functions

• Know the sine and cosine laws
• Be able to solve triangles using sine and cosine laws
  Be able to solve triangles using sine and cosine laws
• Be able to convert between radians and degrees
• Know basic trig identities
• Be able to prove trig identities
• Be able to graph sin(x), cos(x) and tan(x) functions
• Be able to solve trigonometric equations
• Understand the periodic behavior of functions
• Review of key concepts pp 442 - 447
• Chapter test

Loci Conics

• Finding equations of circles
  • Given the centre and radius
  • Given the centre and a point on the circle
• Finding equations of parabolas
• Finding equations of ellipses
  • Given the focal points and focal sum
  • Given the centre, major and minor axes
  • Given the centre and four points on the ellipse
Graphing of ellipses
• Finding equations of hyperbolas

Transformation of functions

• Understand vertical and horizontal transformations of functions
• Understand stretches and decompresses of functions
Understand refections of functions

Sequence and Series

• Solve problems involving arithmetic sequences and series
  Solve problems involving arithmetic sequences and series
  Solve problems involving arithmetic sequences and series
• Solve problems involving geometric sequences and series
  Solve problems involving geometric sequences and series
• Recursive functions
• Key concepts and chapter test: page 510 - 518

Compound Interest and Annuities

• Differentiate between simple and compound interest
• Sovling mortgage problems

Review of skills

• Exponent Laws - p.38
• Fact:
  ${\mathrm{(-1)}}^{\mathrm{n}}$ = -1 if n is odd
  and
  ${\mathrm{(-1)}}^{\mathrm{n}}$ = 1 if n is even
• Fact:
  = $a^{\mathrm{n}}$
• Solving Exponential Equations
• Polynomials
• Finding the GCF and LCM of polynomials - p.92
• GCF and LCM of polynomials - p.100
• Rational Exponents - p.45
• First-Degree Inequalities
• Radicals - p.169

• The Unit Circle
• The Factor Theorem for polynomials
• The Remainder Theorem for polynomials
• The Binomial Theorem for polynomials
• The Pascal Triangle for polynomials

Seqence and Series

• Sequences Summary P.462
• Arithmetic sequence P.471
• Arithmetic series P.498
• Geometric sequence P.482
• Geometric series P.506
• Recursion formulas P.490

Review of skills

• Completing the square - key concepts
• Maximum or Minimum of a Quadratic Function by Completing the Square
• Roots of (Solving) Quadratic Equations
  • Solving quadratic equations by completing the square
  • Solving quadratic equations by factoring
  • Solving quadratic equations by the quadratic formula
  • Summary
• Standard forms of Quadratic Equations
• Transformations (stretch, translate) of Quadratic Equations

• Function: key concepts
• Vertical line test
• Evaluating functions
• Domain and Range of functions
• Analysis of f(x) = $\sqrt{x}$ and f(x) =
• Horizontal and Vertical Translations of Functions
• Reflections of Functions
• Inverse Functions
• Stretches of Functions
• Combinations of Transformations

• Reviewing the Trigonometry of Right Triangles
• The Sine and the Cosine of Angles Greater Than 90°
• The Sine Law and the Cosine Law
• The Sine Law: The Ambiguous Case
• Applications
  • Ship Navigation

• Radians and Angle Measure
• Trigonometric Ratios of Any Angle
• Positive and Negative Angles of Rotation
• Modelling Periodic Behaviour
• Investigation: Sketching the Graphs of f(x) = sin x, f(x) = cos x, and f(x) = tan x
• Stretches of Periodic Functions
• Translations and Combinations of Transformations
• Trigonometric Identities
• Trigonometric Equations

• The Circle
• The Ellipse
• The Hyperbola
• The Parabola
• Conic Sections With Equations in the Form ax2 + by2 + 2gx + 2fy + c = 0
• Intersections of Lines and Conics

• Investigation: Simple Interest, Arithmetic Sequences, and Linear Growth
• Compound Interest
• Investigation: Compound Interest, Geometric Sequences, and Exponential Growth
• Present Value
• Amount of an Ordinary Annuity
• Present Value of an Ordinary Annuity
• Mortgages

1. P648.29 Geometry