Chapter 4 & 5 Review

Chapter 2 & 3 Review

5.5 Trigonometric Equations Take up Homework
Chapter 1. Test. pg. 114

5.5 Trigonometric Equations

• Take up Homework
• Solving Trigonometric Equations

• Take up Homework
• Solving Trigonometric Equations

5.4 Inverse Trigonometric Equations III

• Take up Homework
• Evaluating Trig Expressions
• Graphs of Trigonometric Equations

5.4 Inverse Trigonometric Functions II

• Take up Homework
• Evaluating Trigonometric Expressions
• Solving Inv. Trig. Equations

ASSESSMENT 7
Sections 5.1 to 5.3

5.4 Inverse Trigonometric Functions I

1. Take up Homework
2. Inverse Trigonometric Functions
3. Composition of Trigonometric Functions and Their Inverses

1. Take up Homework
2. Inverse sin Function: sin^-1x

1. Double-Angle Formulas & Identities
2. Half-Angle Formulas & Identities

Final Exam Outline

5.2 Verification of Trigonometric Identities III

1. Cofunctions
2. Complex Identities

5.2 Verification of Trigonometric Identities II

1. Homework Review
2. Identities that Involve (α ± β)
3. Cofunctions

5.2 Verification of Trigonometric Identities I

1. Fundamental Trigonometric Identities
2. Verifying Indentities: Factor, Conjuagte, Reduction to Sine and Cosine

Section 5.1. Trigonometric Functions of Acute Angles

1. Applications Involving Right Triangles
2. Trigonometric Functions of Any Angle
3. Questions 71-76
4. Connecting Concepts

Section 5.1. Trigonometric Functions of Acute Angles

1. Take up Questions 1-17
2. Quadrantal and Reference Angles

1. Cumulative Review, p. 355
2. Section 5.1. Trigonometric Functions of Acute Angles

1. Take Up Assessment 6
2. Cumulative Review pp. 354-355

1. Assessment #6: Sections 4.1 to 4.4
2. Section 4.5: Graphing Techniques: Translation of Trigonometric Functions

Online 'Recognize Functions' Quiz

Online 'Recognize Functions' Quiz

Online 'Recognize Functions' Quiz

Trigonometric Applet Package

Six Trig Functions Applet

Six Trig Functions Applet

Six Trig Functions Applet

Manipula Math Applets
Trigonometry, Calculus, Vectors, etc.
Explore for inspiration!

Determine the ratio of the area of a circle to it's inscribed square.

Model Solution for
Question 58, Page 263.

As we recapped in Lesson 40's T&C section, the log of a sum is not the sum of the logs.

However, for some combinations it is true. Solve for x in terms of y for the following equation:

Solve for x:

(Tricky)
Is

?

Is

?

239-240:
1-33 (odd)
39-51 (odd)
57-71 (odd)

On a single Cartesian Plane, draw the graphs of f(x)=e^x and g(x)=e^-x.

Now, overlay the graphs of

and

224-226:
1-47 (odd)

Simplify the expression,

224-226:
1-47 (odd)

196-197:
11-39 (odd)
45-69 (odd)

1. Introduction
2. Graphs of Inverse Functions
3. Composition of a Functon and its Inverse
4. Finding the Inverse of a Function

Can a function be its own inverse?

212-213:
1-45 (odd)

1. Slant Asymptotes
2. Asymptotic behaviour of degree greater than 1
3. Squeezing the lemon:
   

Can a function cross its horizontal asymptote?

189:
35-57 (odd)

1. Definition of a Vertical Asymptote
2. Definition of a Horizontal Asymptote
3. Theorem on Horizontal Asymptotes (p.180) (comparing the degrees of numerator and denominator)
4. Domain and Range Intervals
5. RAI²D²S

Can a function have more than one vertical asymptote?

Can a function have more than one horizontal asymptote?

189:
1-29 (odd)

1. Definition of a Vertical Asymptote
2. Definition of a Horizontal Asymptote
3. Domain and Range Intervals

Can a function cross it's vertical asymptote?

How about its horizontal asymptote?

189:
1-29 (odd)

1. Number of Zeros of a Polynomial Function
2. Rational Zero Theorem

164-165:
1-16 (odd)
37-58 (every 5th)
59-63 (odd)

1. Turning Points
2. Relative and Absolute Extrema (Max/Min)
3. Real Zeros of a Polynomial
4. Even and Odd Multiplicity of Factors

For the polynomial P(x), if
P(a)·P(b)<0
must P have a zero in the interval [a,b]?

1. General Form:a_nxⁿ+a_n-1x^n-1+...+a₀
2. Far-Left and Far-Right Behaviour
3. The Power form: xⁿ
4. Turning points
   

Watch this animation and then determine how much area is 'under' the function, f(x)=x³ over the same closed interval, [1,4].

1. The Remainder Theorem
2. Evaluating a Polynomial Usinfg the Remainder Theorem
3. The Factor Theorem
4. Reduced Polynomials
   

1. Division of Polynomials
2. Synthetic Division
3. The Remainder Theorem
4. The Factor Theorem
   

1. Composition of Functions

1. 
   Operations Worksheet
2. Composition of Functions
3. The Difference Quotient

1. Geometric Transformations:
   1. Symmetry
      1. Even: f(-x)=f(x)
      2. Odd: f(-x)=-f(x)
   2. Translations
      1. Vertical: y=f(x)+c
      2. Horizontal: y=f(x+c)
   3. Reflections
      1. x-axis: y= -f(x)
      2. y-axis: y= f(-x)
   4. Stretching & Compressing
      1. Horizontal: y= f(c·x)
      2. Vertical: y= c·f(x)

Which of the following geometric transformations does NOT modify the real solutions of f(x)?

1. ASSESSMENT: Sections 1.4 & 1.5

What transformation of f(x) is defined by -f(-x)?

1. Homework Review: Section 1.5
3. y-axis Symmetry: IMAGE-f(x)
   1. f(x) = f(-x) (even)
   2. f(x) = - f(-x) (odd)
4. Symmetry wrt a Point
5. Geometric Transformations:
   1. Translations

What are the necessary conditions for the maximum value of f(x) = ax²+bx+c
to be c?

1. Read the question over at least twice writing down the data as functions (include units and watch for restrictions)
2. Sketch a well-labelled graph
3. Do the algebra, starting from a general model, gradually replacing with the details from part 1. (Keep an eye on what the question is asking for!!)
4. Conclude with the answer the question is seeking, with units.

1. CNML Contests
2. Definition: Quadratic Function
3. Definition: Symmetry wrt a Line
4. Standard Form: f(x) = a(x-h)²+k
5. Vertex of a Parabola
6. Vertex Formula

1. Check Homework
2. (Physics) Point of Impact
3. Points of Discussion
4. Infinitesimal

1. Verify Real solutions as x-intercepts
2. f₁(x) = f₂(x) <=> f₁(x) - f₂(x)=0
3. (Business) Cost, Revenue and Profit functions
4. (Business) Break-Even Point
5. ab=0 <=> a=0 or b=0 or a=b=0
6. Parallel and Perpendicular Lines
7. Pythagorean Triples

1. Definition: f(x)=mx+b
2. Slope as Change
3. Horizontal and Vertical Lines
4. Slope-Intercept Form
5. Point-Slope Form
6. Real solutions and x-intercepts

What is the two-intercept form of a linear relation?

1. Increasing, Decreasing and Constant Functions
2. One-to-One Mapping: Horizontal Line Test
3. The Greatest Integer Function (Floor Function: [x], or int(x)
4. Topics for Discussion (page 43)

True or False?
The terms, reciprocal and inverse, are synomyms.

1. Vertical Line Test

1. A relation is a set of ordered pairs.
2. A function ia a relation in which no two ordered pairs have the same first coordinate (x-value or abscissa)
3. Functional notation: y=f(x)
4. Piecewise functions
5. Domain and range of a function

1. Identifying the circle by Completing the Square
2. Work period to complete the numerous questions I've assigned. If you come prepared to roll up your sleeves and get to work, the dividends will be realized immediately.

1. Identifying the circle by Completing the Square
2. Graphing: Equations (=) vs InEquations(<,>)
3. Graphs from a Table of Values
4. Intercepts

1. Algebra Assessment
2. A line vs a line segment
3. The Midpoint and Distance formulas
4. The Equation of a Circle centered at C(h,k) with radius, r: (x-h)²+(y-k)²=r²

1. Algebra PreAssessment
2. Cartesian Coordinate Systems: R, R×R, R×R×R, or R, R², R³
3. (x,y)=(abscissa, ordinate)

1. Solving Quadratic Equalities: Factoring
2. Solving Quadratic InEqualities(<, >)

1. Rank (<,>)
2. set-builder and interval notation
3. absolute value |x| and distance