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Precalculus

Course Outline

Day Page Objectives
1 10 Determine domain & range; Evaluate functions; Determine restrictions on domain.
2 17 Perform operation on functions; Find composite functions.
24 Graph linear equations; Find the zeros of linear functions.
3 30 Write equations for lines given points and/or slopes.
36 Determine if lines are parallel or perpendicular; Write equations for parallel or perpendicular lines.
4 49 Graph piecewise defined functions.
5 Test 01 Determine domain & range (1.1); Evaluate a function for a given value (1.1); Determine the domain of an equation (1.1); Add, subtract, multiply, and/or divide functions (1.2); Find the composition of functions (1.2); Graph linear equations (1.3); Write the equation of a line (1.4); Write the equation of a line parallel or perpendicular to a given line (1.5); Graph absolute value and piecewise functions (1.7)
6 134 Determine symmetry of functions
7 143 Identify transformations of graphs; Use transformations to graph functions.
8 156 Determine the inverse of a function; Graph functions and their inverses.
9 166 Determine continuity of a function at a point; Determine continuity of a function; Determine end behavior of a function.
10 Test 02 Determine the symmetries of a function (3.1); given a partial graph and its symmetry relation, complete the graph (3.1); Given an equation, describe its transformation in relation to its parent graph (3.2); Graph a function given its parent graph (3.2); Find the inverse of a function and determine if the inverse if a function (3.4); Graph a function and its inverse on the same set of axes (3.4); Determine if a function is continuous at a point (3.5); Determine the end behavior of a function (3.5); Determine the interval(s) for which a function is increasing and decreasing (3.5)
11 947 Determine limits of functions at specified values.
781 Determine limits of functions as x approaches ± infinity.
12   Find the derivatives of functions using the definition of the derivative.
13 958 Use derivative rules to find the derivative.
14   Determine relative minimum and maximum values of polynomial functions; Determine inflection points; Graph polynomial functions.
15 Test 03 Determine limits as n approaches a constant, and as n approaches ± infinity (Worksheet, 12.3); Find the derivative of a function using the definition (Worksheet); Find the derivative of a function using derivative rules (15.2); Find local minimum and maximum values of a function (Worksheet); Find inflection points of a function (Worksheet); Graph a function using its extrema (Worksheet)
16 186 Determine asymptotes of functions; Graph rational functions.
17 210 Determine the number of complex roots (Fundamental Theorem of Algebra); Given the roots, write a polynomial of least degree.
18 219 Solve quadratic equations by completing the square and quadratic formula; Discuss the nature of the roots of polynomial functions.
19 226 Determine if a binomial is a factor of a polynomial; Use the Remainder & Factor Theorems to find roots of polynomials.
20 Test 04 Determine all horizontal, vertical and/or oblique asymptotes for a rational function (3.7); Determine if a rational function has a hole (3.7); Graph rational functions (3.7); Write a polynomial equation of least degree given its roots (4.1); Solve a quadratic equation by completing the square, and by using the quadratic formula (4.2); Use the discriminant to discuss the nature of the roots of a quadratic equation (4.2); Use the Factor and/or Remainder Theorems to determine the binomial factors of a polynomial (4.2)
21 233 Determine possible rational roots of a polynomial (Rational Roots Theorem); Determine the maximum number of real positive and real negative roots of a polynomial (Descartes' Rule of Signs).
22 240 Approximate the location of the real roots of a polynomial function; Determine the upper and lower bounds for the real roots of a polynomial.
23 247 Solve rational equations and inequalities; Complete partial fraction decompositions.
24 255 Solve radical equations and inequalities.
25 Test 05 List all possible rational roots of a polynomial equation, then determine which ones are actual roots (4.4); Determine the number of possible positive real and negative real roots of a polynomial equation (4.4); Determine between which consecutive integers the roots of a polynomial are located (4.5); approximate the zeros of a function to the nearest hundredth (4.5); Determine the least upper bound and the greatest lower bound for the roots of a polynomial function (4.5); Solve rational equations (4.6); Solve radical equations and inequalities (4.7).
26 700 Simplify numerical & algebraic expressions involving exponents (use the rules of exponents).
27 708 Graph exponential functions.
28 714 Solve problems involving e.
29 723 Convert between logarithmic & exponential form; Evaluate logarithmic expressions; Solve logarithmic equations.
30 Test 06 Simplify numerical and variable expressions involving exponents (11.1); Convert between radical & exponential notation (11.1); Solve equations involving exponents (11.1);; Graph exponential functions (11.2); Solve problems involving exponential functions (11.2); Convert between exponential & logarithmic form (11.4); Solve equations involving logarithms (11.4); Graph logarithmic functions (11.4).
31 730 Use properties of logarithms to evaluate logarithmic expressions; Use the change of base formula; Solve logarithmic & exponential equations;Graph logarithmic equations.
32 736 Convert between logarithmic & exponential form; Solve logarithmic & exponential equations.
33 281 Convert between decimal degree and degree minute second notation; Find coterminal angles; Determine reference angles.
34 288 Use trigonometry to determine the measure of the angles of right triangles.
296 Use trigonometry on the unit circle.
35 Test 07 Evaluate logarithms using the change of base formula (11.5 & 11.6); Solve exponential and/or logarithmic equations (11.5 & 11.6); Convert between decimal degrees and degree minute second notation (5.1); Find the measure of the reference angle (5.1); given 2 sides of a right triangle, find all 6 trigonometric values for one of its acute angles (5.2); Given the measure of a central angle on the unit circle, find the values of all 6 trigonometric functions (5.2); Given an ordered pair that lies on the terminal side of a central angle, find the values of all 6 trigonometric functions (5.2); Given one trigonometric value and the quadrant the terminal side of the angle lies in, find the values of the remaining 5 trigonometric functions (5.2).
36 348 Convert between radian and degree measure; Find arc length; Find the area of a sector.
37 364 Use the graphs of sine and cosine.
38 373 Determine amplitude and period for sine & cosine; Graph sine & cosine functions.
39 383 Determine the phase shift for sine & cosine; Graph sine & cosine functions.
40 Test 08 Convert between degree and radian measure (6.1); Use the arc length formula(6.1); Use the area of a sector formula (6.1); Identify the period, amplitude, and phase shift of the graph of a trigonometric function (6.4 & 6.5); Graph trigonometric functions (6.4 & 6.5).
41 400A Graph tangent & cotangent.
42 400B Graph secant & cosecant.
43 410 Determine the inverse of trigonometric functions; Graph trigonometric functions & their graphs.
44 427A Identify & use basic trigonometric identities.
45 Test 09 Identify the period, amplitude, and phase shift of the graph of a trigonometric function (6.4, 6.5, 6.7); Graph trigonometric functions (6.4, 6.5, 6.7); Graph trigonometric functions and their inverses (6.8); Simplify trigonometric expressions (7.1).
46 427B Verify trigonometric identities.
47 434 Verify trigonometric identities.
48 442 Use sum & difference identities to evaluate trigonometric functions.
49 454 Use double & half angle identities to evaluate trigonometric functions.
50 Test 10 Given the value of a trigonometric function and a quadrant, find the exact value of another trigonometric function (7.1); Express a trigonometric function as a related function in the first quadrant (7.1); Verify trigonometric identities (7.2); Use the sum and/or difference identities to find the exact value of a trigonometric function (7.3); find the exact value of sine, cosine, and/or tangent, given the values of sine and/or cosine (7.3); Use the double and/or half angle formulas to find the exact value of a trigonometric function (7.4); Given the value of sin x, cos x, or tan x, find the exact value of sin 2x, COs 2x, tan 2x, sin (1/2x), COs (1/2x), and/or tan(1/2x) (7.4).
51 459 Solve trigonometric equations.
52 491 Determine the magnitude and direction of vectors; Add & subtract vectors; Find equal, opposite & parallel vectors.
53 497 Add, subtract, & multiply vectors; Find the magnitude of resultants; Find ordered pairs that represent vectors.
54 509 Determine if two vectors are perpendicular.
55 Test 11 Solve trigonometric equations for the principal solution or over a specified interval (7.5); Determine the magnitude and direction of a vector (8.1); Find the magnitude and direction of the resultant when adding, subtracting and/or multiplying two vectors (8.1); Given vectors a and b, find the ordered pair that represents vector ab, and the magnitude of vector ab (8.2); Find the ordered pair that represents the sum, difference and/or scalar product of two vectors (8.2); Find the magnitude of a vector and write the vector as the sum of unit vectors (8.2); Find the inner product of two vectors and determine if the vectors are perpendicular (8.4); Solve problems representing applications of vectors (8.5).
56 524 Convert between parametric equations & linear equations; Write the vector equation parallel to a given line.
57 531 Solve motion problems using parametric equations.
58 558 Graph points in polar coordinates; Graph polar equations; Find the distance between two points.
59 565 Graph polar equations; Write polar equations that meet specified conditions.
60 Test 12 Solve problems representing applications of vectors (8.5, 8.7); Write the vector equation of a line passing through a given point parallel to a given vector (8.6); Convert between parametric equations for a line and slope-intercept form (8.6); Graph points given in polar form (9.1); Find the distance between two points given in polar form (9.1); Graph polar equations (9.2).
61 572 Convert between polar & rectangular coordinates; Convert equations between polar & rectangular form.
62 467 Convert equations between linear & normal form; Find the length & angle of the normal from the origin.
63 475 Find the distance from a point to a line; Find the distance between two parallel lines; Write equations of lines that bisect angles.
64 578 Convert equations between polar & rectangular form.
65 Test 13 Convert points & equations between polar & rectangular form (9.3); Write the standard form of an equation given the length of the normal segment & the angle the normal segment makes with the positive x-axis (7.6); Write a standard form equation in normal form & find the length of the normal & the measure of the angle it makes with the positive x-axis (7.6); Find the distance between a point and a line (7.7); Find the distance between two parallel lines (7.7); Convert equations between rectangular and polar form (9.4); Graph polar equations (9.4).
66 583 Simplify expressions involving complex numbers.
67 590 Solve equations involving complex numbers; Convert numbers between complex & polar form.
68 620

Find distance & midpoint; Prove statements using coordinate proofs.

69 627 Write equations form and graph circles.
70 Test 14 Simplify expressions containing complex numbers (9.5); Solve equations involving complex numbers (9.6); Graph complex numbers and find their absolute value (9.6); Write complex numbers in polar form (9.6); Find the length and midpoint of a segment, given its endpoints (10.1); Prove statements using coordinate proofs (10.1); Convert between general and standard forms for the equations of circles (10.2); Graph circles (10.2); Given a graph, write the equation for a circle (10.2).
71 638 Write equations for and graph ellipses.
72 650 Write equations for and graph hyperbolas.
73 659 Write equations for and graph parabolas.
74 667 Graph conic sections; Convert equations for conic sections between rectangular & polar form.
75 Test 15 Convert between general & standard forms for the equations of ellipses (10.3); and hyperbolas (10.4); Graph ellipses (10.3); and hyperbolas (10.4); Given a graph, write the equation for an ellipse (10.3); and a hyperbola (10.4); Determine if an equation's graph is a circle, parabola, ellipse, or hyperbola, then graph it (10.5); Rewrite a general form equation into standard form, then identify the conic section and graph it (10.6).
76 763 Determine the next terms of arithmetic sequences; Find the sum of arithmetic sequences.
77 771 Determine the next terms of geometric sequences; Find the sum of geometric sequences.
78 781 Write repeating decimals as fractions; Determine if the sum of an infinite series converges or diverges.
79 791 Determine if an infinite series converges or diverges.
80 Test 16 Find the common difference and the next several terms in an arithmetic sequence (12.1); Find the specified term of an arithmetic sequence (12.1); Find the sum of an arithmetic sequence (12.1); Find the common ratio and the next several terms of a geometric sequence (12.2); Given the common ratio and a term in a geometric sequence, find the first term (12.2); Determine if the sum of a series exists, and if it does, find the sum (12.3); Use the ratio and/or comparison test to determine if a series is convergent or divergent (12.4).
81 798 Use sigma notation; Expand a binomial; Write a series using sigma notation.
82 804 Use Pascal's triangle & the Binomial Theorem to expand a binomial.
83 812 Use the exponential & trigonometric series & Euler's Formula to estimate values for e, the natural logarithm, and trigonometric functions.
84 Test 17 Write an expression in expanded form and then find its sum (12.5); Write a series using sigma notation (12.5); Use Pascal's triangle to expand a binomial (12.6); Use the Binomial Theorem to expand a binomial (12.6); Find the specified term for a binomial expansion (12.6); Use the exponential series to find an approximation for e to a power or the natural logarithm of a number (12.7); Use the trigonometric series to approximate sine or cosine (12.7); Use Euler's formula to write a complex number in exponential form (12.7)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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