# Definition and Rules for Exponents

The Final Exam is worth 35% of your final grade. You must score at least 35% on the final exam to pass the course, regardless of your term mark. You will be given 3 hours to write the exam. The exam is open book. Makes sure to have handy any formula sheets, mine or yours, as well as pencils, erasers, a small plastic ruler and your Casio (or other) calculator. Prepared formula sheets you may want to have handy include (1) Definition and Rules for Exponents; Factoring Flowchart (note that formulas for difference of squares, sum and differences of cubes are included)(2) Solving Equations (note that the quadratic formula is on the back), (3) Some Strategies for solving Equations, (4) Some “Common” Functions” and their Graphs (you may want to add the basic exponential and logarithmic graphs), (5) Properties of Logarithms, (6) “Trig Formulas” and (7) “Trigonometric Identities”. You may also want to have handy (1) a detailed sketch of the sine and cosine “wave” functions, (2) a list of the restricted domains for the inverse sine, cosine and tangent functions and (3) the formulas for the transformed sine and cosine “waves”, including the formula for the period of such waves. The exam covers material from the entire course. Refer to the term test outlines for specifics on text questions worth studying and make sure to do and understand Assignment #6 on Trigonometry (especially seeing you have not been tested on Trigonometry on either term test). Likely Topics on the Final Exam: (final exam will likely be a total of 85 – 90 marks) 1. 1.1 Converting between interval, set and number line notation and determining the intersection and/or union of sets of numbers given in interval notation. See Test #1 [3 marks]. 2. 1.2 Simplifying using rules for exponents. See: Test #1 [3 marks]. 3. 1.3 Factoring algebraic expressions. See: Test #1 [5 marks]. 4. 1.4 Simplifying (adding, subtracting, multiplying, dividing, compound fractions) algebraic expressions. See: Test #1 [ 4 – 5 marks]. 5. 1.4, 2.1, 2.2, 2.3, 4.3 Domains (meaningful replacements) for algebraic expressions and functions. See: Tests #1 and #2 [6 marks). 6. 1.5 and 4.5 and 7.4 Solving equations and solving “formulas” for an indicated (asked for) variable – linear, quadratic, fractional, radical, or one with higher degree or fractional exponents, exponential and logarithmic, trigonometric and absolute value equations. See: Tests #1 and #2 as well as post term test material for solving a trigonometric equation over the interval [00, 360°) or (0,2Pi] [22 marks] 7. 1.8 Solving linear, nonlinear and (NOT THIS YEAR) rational (fractional) inequalities. See: Test #1 [2 marks] 8. 2.1, 2.2, 2.3, 2.7 and other sections. Evaluating outputs of functions given inputs, given either a table of values, graph (piecewise-defined or otherwise) or equation of the function. (This will include a question where one would be asked to find and simplify the difference quotient for a function, and a question involving a composite function). See: mostly Test #2 (there was one question on evaluating a function at points given a graph of the function on Test #1). [7 marks] 9. 4.1, 4.2 and 4.3 Evaluating Logarithmic and Exponential expressions with and without a calculator. See: See Test #2 (included within other topics shown). 10.3.6 Sketch the graph of a Rational Function, after calculating all intercepts, determining where vertical and horizontal asymptotes occur and performing either a “sign diagram” or select table of values. See Test #2 [10 marks). 11.5.2, 6.2 and 6.3 Finding exact trigonometric function values of angles (usually given in standard position)- using definitions of the trigonometric ratios, “special” triangles, knowledge of the x-y coordinate system and quadrant designations, and reference angles. (33 – 44 in Chapter 6 review exercises, 7 – 16 in Chapter 5 review exercises). See: post term test #2 material and Assignment #6 [5 marks) 12.5.3 Given the equation of a transformed sine or cosine function, determine the amplitude, period, phase shift and vertical shift of the “wave”, then neatly sketch the graph of such a wave. (29-36 in the Chapter 5 review exercises, 33 – 46 in 5.3. [The problem will likely involve you having to “factor” the argument of the trigonometric function – such as in questions 33 — 36 in the Chapter 5 review exercises) See: post term test #2 material and Assignment #6 [6 marks]. 13.5.5 and 6.4 Evaluate inverse trigonometric functions (usually, if not always, giving answers “in terms of “). See: post term test #2 material and Assignment #6 [3 marks]. See 49 and 50 in the Chapter 5 review exercises and 61 and 62 in the Chapter 6 review exercises. 14.5.5 and 6.4 Evaluate a “composite” trigonometric function/inverse trigonometric function. See post term test #2 material and Assignment #6 (combines topics 12 and 14 above). See also 49 – 52 in Chapter 5 review exercises and 63 and 64 in the Chapter 6 review exercises. 15.2.2 Graphing a piecewise-defined function. See Test #2 [5 marks) 16.6.3 A question like #41 – 54 on page 499. See post term test #2 material and Assignment #6 [5 marks) 17. 7.1 Verifying trigonometric identities (using the formula sheet of identities and algebra). (1 – 11 for example in Chapter 7 review exercises). See post term test #2 material and Assignment #6 [3 – 4 marks) course, regardless of your term mark. You will be given 3 hours to write the exam. The exam is open book. Makes sure to have handy any formula sheets, mine or yours, as well as pencils, erasers, a small plastic ruler and your Casio (or other) calculator. Prepared formula sheets you may want to have handy include (1) Definition and Rules for Exponents: Factoring Flowchart (note that formulas for difference of squares, sum and differences of cubes are included), (2) Solving Equations (note that the quadratic formula is on the back), (3) Some Strategies for solving Equations, (4) Some “Common” Functions” and their Graphs (you may want to add the basic exponential and logarithmic graphs), (5) Properties of Logarithms, (6) “Trig Formulas” and (7) “Trigonometric Identities”. You may also want to have handy (1) a detailed sketch of the sine and cosine “wave” functions, (2) a list of the restricted domains for the inverse sine, cosine and tangent functions and (3) the formulas for the transformed sine and cosine “waves”, including the formula for the period of such waves. The exam covers material from the entire course. Refer to the term test outlines for specifics on text questions worth studying and make sure to do and understand Assignment #6 on Trigonometry (especially seeing you have not been tested on Trigonometry on either term test). Likely Topics on the Final Exam: (final exam will likely be a total of 85 – 90 marks) 1. 1.1 Converting between interval, set and number line notation and determining the intersection and/or union of sets of numbers given in interval notation. See Test #1 [3 marks]. 2. 1.2 Simplifying using rules for exponents. See: Test #1 [3 marks]. 3. 1.3 Factoring algebraic expressions. See: Test #1 [5 marks]. 4. 1.4 Simplifying (adding, subtracting, multiplying, dividing, compound fractions) algebraic expressions. See: Test #1 [ 4 – 5 marks). 5. 1.4, 2.1, 2.2, 2.3, 4.3 Domains (meaningful replacements) for algebraic expressions and functions. See: Tests #1 and #2 [6 marks). 6. 1.5 and 4.5 and 7.4 Solving equations and solving “formulas” for an indicated (asked for) variable – linear, quadratic, fractional, radical, or one with higher degree or fractional exponents, exponential and logarithmic, trigonometric and absolute value equations. See: Tests #1 and #2 as well as post term test material for solving a trigonometric equation over the interval [0°, 360°) or (0,2Pi] [22 marks] 7. 1.8 Solving linear, nonlinear and (NOT THIS YEAR) rational (fractional) inequalities. See: Test #1 [2 marks] 8. 2.1, 2.2, 2.3, 2.7 and other sections. Evaluating outputs of functions given inputs, given either a table of values, graph (piecewise-defined or otherwise) or equation of the function. (This will include a question where one would be asked to find and simplify the difference quotient for a function, and a question involving a composite function). See: mostly Test #2 (there was one question on evaluating a function at points given a graph of the function on Test #1). [7 marks] 9. 4.1, 4.2 and 4.3 Evaluating Logarithmic and Exponential expressions with and without a calculator. See: See Test #2 (included within other topics shown). 10.3.6 Sketch the graph of a Rational Function, after calculating all intercepts, determining where vertical and horizontal asymptotes occur and performing either a “sign diagram” or select table of values. See Test #2 [10 marks] . 11.5.2, 6.2 and 6.3 Finding exact trigonometric function values of angles (usually given in standard position) – using definitions of the trigonometric ratios, “special” triangles, knowledge of the x-y coordinate system and quadrant designations, and reference angles. (33 – 44 in Chapter 6 review exercises, 7 – 16 in Chapter 5 review exercises). See: post term test #2 material and Assignment #6 [5 marks) 12.5.3 Given the equation of a transformed sine or cosine function, determine the amplitude, period, phase shift and vertical shift of the “wave”, then neatly sketch the graph of such a wave. (29-36 in the Chapter 5 review exercises, 33 – 46 in 5.3. [The problem will likely involve you having to “factor” the argument of the trigonometric function – such as in questions 33 — 36 in the Chapter 5 review exercises) See: post term test #2 material and Assignment #6 [6 marks] 13.5.5 and 6.4 Evaluate inverse trigonometric functions (usually, if not always, giving answers in terms of “). See: post term test #2 material and Assignment #6 [3 marks] . See 49 and 50 in the Chapter 5 review exercises and 61 and 62 in the Chapter 6 review exercises. 14. 5.5 and 6.4 Evaluate a “composite” trigonometric function/inverse trigonometric function. See post term test #2 material and Assignment #6 (combines topics 12 and 14 above). See also 49 – 52 in Chapter 5 review exercises and 63 and 64 in the Chapter 6 review exercises. 15.2.2 Graphing a piecewise-defined function. See Test #2 [5 marks). 16.6.3 A question like #41 – 54 on page 499. See post term test #2 material and Assignment #6 [5 marks] 17. 7.1 Verifying trigonometric identities (using the formula sheet of identities and algebra). (1 – 11 for example in Chapter 7 review exercises). See post term test #2 material and Assignment #6 [3 – 4 marks)

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