MCR3U Skills Review. Study Tips. Unit 1 Polynomials and Functions

Transcription

1 MCR3U Skills Review Study Tips Read over the outline and rank the concepts for review by identifying which concepts you have the most difficulty with. Set GOALS. Start with an overall achievement goal, then identify specific study goals ie. Study for this length of time, study these concepts, re do my tests, etc. Make a PLAN. Look at your schedule and create a time line of when you will do what. Do not leave all your studying until the very last minute. Study by PRACTICING. Re do the practice questions assigned for a given lesson, re do quizzes and tests. Unit 1 Polynomials and Functions Simplifying Expressions Expanding Expressions Factoring Definition of a function Domain and Range Evaluating and combining functions

2 Expand and simplify. Factoring Common Factor Trinomial (a = 1) Trinomial (a 1) Special Product

3 What is the definition of a function? Examples? Non Examples? What is the domain of a given function? Range? State the domain and range for each function.

4 Evaluate for the function : A. B. Unit 2 Transformations Types of Parent Functions The Inverse of a Function Transformations

5 Sketch the graph of each parent function and write the general equation for each. Linear Quadratic Absolute Square Root Exponential Rational Sinusoidal Find the inverse of the function.

6 Connect the transformation rules to each parent function: Quadratic Rational Absolute Square Root Exponential Sinusoidal Transformation Rules State the transformations made to each function.

7 Mapping Points The point P( 3, 9) is transformed by a reflection in the y axis, a vertical compression by a factor of 0.5, moving the point up 7 units and to the left 4 units. Find the coordinates of the new point. Unit 3 Quadratic Functions Completing the square Simplifying radicals Solving quadratic functions (Quadratic Formula) Transformations of Quadratic Functions Applications of Quadratic Functions

8 Completing the Square Find the maximum or minimum for the function: Simplifying radicals. Simplify and report your answer as a mixed radical in simplest terms. A. B. C.

9 Solving quadratic equations. Find the roots. A. B. Applications of Quadratic Functions Vertex Form Factored Form Standard Form

10 Unit 4 Exponential Functions Exponent Laws Simplifying exponential expressions Applications of Exponential Functions Compound Interest Exponent Laws Multiplication Division Power of a Power

11 Exponent Laws Zero Exponent Negative Exponents Rational Exponents Simplifying Exponential Expressions

12 The Exponential Function Growth Decay Applications of Exponential Functions A. The population of a new town is growing at rate of 2.6% per year. If the present population of the town is 4000 people, determine the population of the town in 10 years. B. Marjorie is on a diet and she is losing weight at a rate of 3% per month. If Marjorie weights 286 lbs, how long will it take her to reach her goal weight of 145 lbs?

13 Compound Interest You borrow $ at 4.2%/a for a 5 year term. What amount do you owe at the end of the term if the interest was compounded monthly? Unit 5 Rational Functions Properties of Rational Functions Simplifying and graphing rational functions Adding and subtracting rational functions Multiplying and dividing rational functions Applications of Rational Functions

14 Properties of Rational Functions Simplifying and Graphing Rational Functions Simplify and state the restrictions. A. B.

15 Sketch the graph of each function. A. B. Multiplying and Dividing Rational Functions Simplify and state the restrictions.

16 Adding and Subtracting Rational Functions Simplify and state the restrictions. Applications of Rational Functions Fred drove his car a distance of 2x km in 3 hours. Later he drove x km in 2 hours. Use the equation for speed to find the simplified expression for the difference between his first speed and second speed.

17 Unit 6 Trigonometric Relationships Right triangle trigonometry (SOHCAHTOA) Acute/Obtuse trigonometry (Sine and Cosine Law) Problem Solving with Trigonometry Special Triangles Angles in Standard Position Solving Trigonometric Equations Proving identities Right Triangle Trigonometry SOHCAHTOA a 2 + b 2 = c 2

18 Acute/Obtuse Triangle Trigonometry Sine Law Cosine Law Problem Solving with Trigonometry Solve for d.

19 Special Triangles Draw the isosceles right triangle. Draw the triangle. Angles in Standard Position Draw the principal angle of 225 in standard position and state: a. the related angle b. possible values of x, y and r Sketch the principal angle 160 o. Determine the principle angle for the point P( 5, 12), and state all of the corresponding trigonometric ratios.

20 Angles in Standard Position Determine the principal angle represented by the point (3, 8) and state one co terminal angle. Solving Trigonometric Equations Solve for θ for 0 θ 360. a. b.