Precal Exam Prep 2014
RED / YELLOW / GREEN
Unit 4 – Exponential & Logarithmic Functions
- in a functional analysis context, be able to use appropriate terminology to describe the characteristics of exponential & logarithmic fcns
- be able to prepare data tables & describe short term & long term (end) behavior and sketch graphs of these functions
- be able to apply basic transformations to parent functions of y = 2x, y = ex, y = log(x) and y = ln(x), in the form of y = af(b(x+c))+d & analyze the resultant graph for key features
- be able to sketch transformed functions by technology & by hand
- be able to convert from exponential to logarithmic form & vice-versa and then do simple evaluations of exp & log expressions
- be able to use graphic analysis to study the behaviour of more complex exp & log based functions
- be able to use equations to generate graphs & data tables and answer contextual problems of real world scenarios
- evaluate numeric expressions containing integral & rational exponents
- evaluate the nth root of a number using the rational exponents
- simplify numeric expressions by re-expressing powers in simplified bases
- be able to rewrite logarithms with different bases
- be able to convert from exponential to logarithmic form & vice-versa and then do simple evaluations of exp & log expressions
- be able to expand or condense exponential & logarithmic expressions & equations using exponent laws or logarithm laws
- be able to algebraically solve simple & complex exponential & logarithmic equations, using exponent laws or logarithm laws
- be able to use algebraic & numeric analysis to predict the behaviour of more complex exp & log based functions
- be able to use equations and then use algebraic analysis to answer contextual problems of real world scenarios
Unit 5 – Trigonometric Functions
- state the values of the six trig ratios in a triangle, given at least the measure of any two sides of a right triangle
- be able to state the values of all six trig ratios for an angle of 30°, 45°, 60° and then evaluate expressions involving these three angles without the use of a calculator (i.e. 2sin30cos30)
- state the value of an angle (30°, 45°, 60°) when given a ratio (i.e csc(x) = 2)
- draw and analyze a given angle in standard position
- state the trig ratios for any angle, wherein the terminal arm goes through a given coordinate (i.e P(5,12)).
- extend the knowledge of the two fundamental triangles and then apply these basics to determining the trig ratio for any angle of multiples of 30° in any quadrant (i.e. sin(150°), cos(-750°))
- apply the new definitions of trig ratios to understand & evaluate the trig ratios of quadrantal angles (90°,180°,270°,360°)
- be able to convert the units of angle measures between degrees and radians
- be able to state (without a calculator) the 6 fundamental trig ratios of special angles, now that the angle measure is given in radians (i.e. tan(-2p/3))
- evaluate expressions involving fundamental angles without the use of a calculator (i.e. 1-2sin2(-5p/6))
- be able to draw and analyze the parent functions of f(q)=sin(q), f(q)=cos(q) and f(q)=tan(q)
- be able to draw and analyze transformed sinusoidal functions in the form of y = Asin(K(q + C)) + D or y = Acos(K(q + C)) + D with and without technology
- be able to write equations of sinusoidal functions, based upon information presented in a word problem, a data table or a graph
- be able to use the equation (or graph) of a sinusoidal functions to answer contextual questions dealing with periodic phenomenon
- restrict the domain of y = sin(q), y = cos(q), y = tan(q) in order to ensure that the inverse relations are functions
- be able to graph by hand and using technology graphs of the inverse trig functions
- be able to state an angle (multiples of (30°,45°,60°)) when given a corresponding key ratio (i.e sin-1(1/2)=?) when expressed as an inverse trig equation
- be able to state which quadrants are used when evaluating trig inverse equations
- be able to evaluate expressions involving inverse trig involving composite functions (sin(cos-1(1/2)) = ? or tan-1(sin(-p/4))
- be able to evaluate expressions involving inverse trig involving composite functions (sin(cos-1(-4/7)) = ? when working in non-standard angles and ratios
Unit 6 – Analytical Trigonometry
- be able to solve simple “linear type” trig equations (eqns in the form of Asin(x) + D = 0 or eqns in the form of sink(x + C) = 0) or even more complicated linear trig equations (Asink(x + C) + D = 0)
- be able to solve “quadratic type” trig eqns, presented in factored form or “quadratic standard form” (i.e. (sinx – 0.5)(sinx + 1) = 0 or cosx(2sin(x) – 1) = 0 or sin2(x) – 2sin(x) + 1 = 0)
- be able to state solutions to equations when given a (i) restricted domain and (ii) an infinite domain.
- be able to graphically verify any solution developed algebraically
- be able to work with fundamental identities: the reciprocal identities, (ii) the Quotient Identities & (iii) the Pythagorean Identities in simple proofs of identities
- be able to work with fundamental identities: the reciprocal identities, (ii) the Quotient Identities & (iii) the Pythagorean Identities in solving simple equations wherein a fundamental identity can be used to simplify an equation
- be able to work with addition/subtraction identities in simple proofs of identities, simple evaluations & simple equations.
- be able to work with double/half angle identities in simple proofs of identities, simple evaluations & simple equations
- be able to graphically verify any solution developed algebraically
- be able to solve for unknown sides or angles in a right triangle using the three fundamental trig ratios (sine, cosine, tangent)
- be able to use the tools of right triangle trig to work through real world problems wherein right triangles are used to model the application/context
- be able to solve for unknown sides or angles in non-right triangles using Law of Sines and/or the Law of Cosines
- be able to use the tools of right triangle trig & Law of Sines and/or the Law of Cosines to work through real world problems wherein right triangles are used to model the application/context
1. Blank Copy of our March 2014 Exp & Logs Unit Test
2. Here is a copy of the Solution Key for this Unit Test
3. Blank Copy of our April 2014 Trig Functions Unit Test
4. Here is a copy of the Solution Key for this Unit Test
5. Blank copy of our May 2014 Analytical Trig Unit Test
6. Here is a copy of the Solution Key for this Unit Test
7. Here is a link to the Larson Text, Chapter 3 REV (Exp & Logs)
8. Here is a link to the Larson Text, Chapter 4 REV (Trig Functions)
9. Here is a link to the Larson Text, Chapter 5 REV (Analytical Trig)
10. Here is a link to the HOLT Text, Chapter 5 REV (Exp & Logs)
a. You can work through p403-7, Q11,15,22,23,29,31,33,35,40,44,45,47,49,50,52,61,63,71,75
11. Here is a link to the HOLT Text, Chapter 6 REV (Trig Functions - Basics)
a. You can work through p464-467, Q19,21,29,31,33,35,44,51,54
12. Here is a link to the HOLT Text, Chapter 7 REV (Graphs of Trig Fcns)
a. You can work through p516-519, Q7,13,24,26,29,32,33
13. Here is a link to the HOLT Text, Chapter 8 REV (Analytical Trig – Solving Eqns)
a. You can work through p564-565, Q9,11,13,17,21,27,33,34,37
14. Here is a link to the HOLT Text, Chapter 9 REV (Analytical Trig - Identities)
a. You can work through p611-613, Q30,44,46
15. Here is a link to the Sullivan Text, Chapter 6 REV (Exp/Log Functions)
a. You can work through p497-498, Q26,27,28,29,35,36,37,39,41,46,49,51,59,61,71,73,77,79,83
16. Here is a link to the Sullivan Text, Chapter 7 REV (Trig Functions)
a. You can work through p595-596, Q13,15,21,35,37,49,65,71,75,77
17. Here is a link to the Sullivan Text, Chapter 8 REV (Analytical Trig)
a. You can work through p664-666, Q4,5,6,9,13,21,25,33,73,75,77,79,81,91,99,101,113,117
18. Here is a link to the Sullivan Text, Chapter 9 REV (Applications of Trig Fcns)
a. You can work through p707-708, Q15,17,19,21,25,29,38,39,40,41,42