2.07+PRE-CALCULUS

"The learner will . . ." || **Standard(s)** || **No. of Days** || **Vocabulary Terms** || **Resources** || **Student Learning Activities** || **Assessment** || 12.1.3[a] 12.3.3[g,h] ||  || integer, rational, irrational, intersection, union || textbook, chapter 1 || practice exercises, notes || HW, quizzes, test || 12.1.3[a,b,c] 12.3.3[b] ||  || growth and decay, laws of exponents || textbook, chapter 1 || practice exercises, notes || HW, quizzes, test || 12.2.2[a,b,c] 12.2.4[a] 12.3.1[c,e] || 1 || coordinates, x-axis, y-axis, origin, quadrants, x-coordinate, y-coordinate, graph, x-intercept, y-intercept, linear equation, general form, solution || textbook, chapter 1 || practice exercises, notes || HW, quizzes, test || 12.3.3[f,g] || 1 || point-slope form, intercept form, || textbook, chapter 1 || practice exercises, notes || HW, quizzes, test ||
 * Teacher****: Jerry Arnold**
 * Textbook**: Precalculus: Mathematics for Calculus, 2012
 * ~ (1) ||~ (2) ||~ (3) ||~ (4) ||~ (5) ||~ (6) ||~ (7) ||~ (8) ||~ (9) ||
 * **Obj #** || **Unit** || **Objective:**
 * 1 || 1 || understand and apply the properties of real numbers || 12.1.1[b] 12.1.2[a,b]
 * 2 || 1 || define and apply integral exponents and rational exponents || 12.1.1[a,b]
 * 3 || 1 || manipulate and solve basic algebraic equations || 12.3.3[c,d,e,i,l] ||  || variable, monomial, binomial, polynomial || textbook, chapter 1 || practice exercises, notes || HW, quizzes, test ||
 * 4 || 1 || simplify, perform algebraic operations on and solve rational expressions || 12.3.1[b] 12.3.3[j,k,o] ||  || domain, compound fraction || textbook, chapter 1 || practice exercises, notes || HW, quizzes, test ||
 * 5 || 1 || find the intersection of two lines and find the length and midpoint of a segment || 12.1.4[a,b]
 * 6 || 1 || find the slope of a line and determine whether two lines are parallel, perpendicular, or neither || 12.2.2[a] 12.3.1[c,d,e] || 1 || slope, parallel, perpendicular, rise, run, slope-intercept form, negative reciprocal || textbook, chapter 1 || practice exercises, notes || HW, quizzes, test ||
 * 7 || 1 || find an equation of a line given certain geometric properties of the line || 12.2.2[a] 12.3.1[c,d,e]
 * 8 || 1 || model real-world situations by means of linear functions || 12.1.4[a,b]

12.2.4.ab 12.3.1.abcdef || 1 || function, domain, range, zero || textbook, chapter 1 || practice exercises, notes || HW, quizzes, test || 12.3.2[d] 12.3.3[e,l] ||  || polynomial, terms, coefficients, leading term, degree, maxima, minima, leading term || textbook, chapter 3.2 || practice exercises, notes || HW, quizzes, test || 12.3.3[d,e] ||  || complex number, imaginary number, pure imaginary, complex conjugates || textbook, chapter 3.5 || practice exercises, notes || HW, quizzes, test || 12.3.3[b,d,e,j,k,l] ||  || horizontal, vertical and slant asymptote || textbook, chapter 3.7 || practice exercises, notes || HW, quizzes, test || chapter 8 || practice exercises, notes || HW, quizzes, test || chapter 8 || practice exercises, notes || HW, quizzes, test || chapter 8 || practice exercises, notes || HW, quizzes, test || negative relationships, pythagorean relationships, cofunction relationships || textbook, chapter 8 || practice exercises, notes || HW, quizzes, test || chapter 8 || practice exercises, notes || HW, quizzes, test || chapter 9 || practice exercises, notes || HW, quizzes, test || chapter 9 || practice exercises, notes || HW, quizzes, test || chapter 9 || practice exercises, notes || HW, quizzes, test || chapter 9 || practice exercises, notes || HW, quizzes, test || chapter 9 || practice exercises, notes || HW, quizzes, test || chapter 10 || practice exercises, notes || HW, quizzes, test || chapter 10 || practice exercises, notes || HW, quizzes, test || chapter 10 || practice exercises, notes || HW, quizzes, test || chapter 10 || practice exercises, notes || HW, quizzes, test || chapter 11 || practice exercises, notes || HW, quizzes, test || chapter 11 || practice exercises, notes || HW, quizzes, test || chapter 11 || practice exercises, notes || HW, quizzes, test || chapter 11 || practice exercises, notes || HW, quizzes, test || geometric sequence || textbook, chapter 13 || practice exercises, notes || HW, quizzes, test || chapter 13 || practice exercises, notes || HW, quizzes, test || chapter 13 || practice exercises, notes || HW, quizzes, test || chapter 13 || practice exercises, notes || HW, quizzes, test || chapter 13 || practice exercises, notes || HW, quizzes, test || chapter 13 || practice exercises, notes || HW, quizzes, test || chapter 19 || practice exercises, notes || HW, quizzes, test ||
 * 9 || 1 || solve quadratic equations using different methods || 12.3.1[e] 12.3.3[e,f,g,h,i] ||  || quadratic equation, discriminant, quadratic formula, completing the square, root || textbook, chapter 1 || practice exercises, notes || HW, quizzes, test ||
 * 10 || 2 || identify a function, determine the domain, range, and zeros of a function, graph a function || 12.3.1[a,b,c,d,e,h,i] ||  || dependent variable, independent variable, domain, range, vertical line test || textbook, chapter 2 || practice exercises, notes || HW, quizzes, test ||
 * 11 || 2 || perform operations on functions and determine domains of resulting functions || 12.3.3[c,d,n] ||  || sum, difference, product, quotient, composition || textbook, chapter 2 || practice exercises, notes || HW, quizzes, test ||
 * 12 || 2 || reflect graphs and use symmetry to sketch graphs || 12.2.3[a,b] ||  || reflection, line of symmetry, point of symmetry || textbook, chapter 2 || practice exercises, notes || HW, quizzes, test ||
 * 13 || 2 || determine periodicity and amplitude from graphs, stretch and shrink graphs both vertically and horizontally, translate graphs || 12.2.3[a,b] ||  || periodic, fundamental period, amplitude, stretching, shrinking, translating || textbook, chapter 2 || practice exercises, notes || HW, quizzes, test ||
 * 14 || 2 || find the inverse of a function, if the inverse exists || 12.3.1[e,h] ||  || inverse, horizontal line test, one-to-one function || textbook, chapter 2 || practice exercises, notes || HW, quizzes, test ||
 * 15 || 3 || define and graph quadratic functions || 12.3.1[a,b,d,e] 12.3.2[a,c,d] 12.3.3[i] ||  || quadratic function, vertex, axis of symmetry, parabola || textbook, chapter 3.1 || practice exercises, notes || HW, quizzes, test ||
 * 16 || 3 || model real-world situations using quadratic functions || 12.2.4[b] 12.3.1[a,e] 12.3.2[a,d] ||  || curve-fitting, quadratic model || textbook, chapter 3.1 || practice exercises, notes || HW, quizzes, test ||
 * 17 || 3 || graph a polynomial function and determine end behavior and zeros || 12.3.1[a,d,e,i]
 * 18 || 3 || use long and synthetic division and apply the remainder and factor theorems || 12.3.3[b,c,d,e] ||  || synthetic division, factor theorem, remainder theorem || textbook, chapter 3.3 || practice exercises, notes || HW, quizzes, test ||
 * 19 || 3 || solve polynomial equations by various methods of factoring, including the use of the rational root theorem || 12.3.1[d] 12.3.3[d,e,i] ||  || rational root theorem || textbook, chapter 3.4 || practice exercises, notes || HW, quizzes, test ||
 * 20 || 3 || add, subtract, multiply and divide complex numbers || 12.1.1[a,b] 12.1.3[a]
 * 21 || 3 || apply general theorems about polynomial equations || 12.1.3[a] 12.3.3[d,e] ||  || fundamental theorem of algebra, complex conjugates theorem || textbook, chapter 3.6 || practice exercises, notes || HW, quizzes, test ||
 * 22 || 3 || manipulate, simplify and graph rational functions, determining end behavior and asymptotes || 12.3.1[a,b,d,e]
 * ||  || write a polynomial function for a given situation and find the maximum or minimum value of the function || 12.2.5.a || 2 || cubic functions, maximum, minimum ||   ||   ||   ||
 * ||  ||   ||   || 1 || location principle ||   ||   ||   ||
 * 21 || 1 || graph functions of two variables in a two-dimensional coordinate system and read such graphs || 12.3.1.a, 12.3.2.ad || 1 || curves of constant values || textbook, chapter || practice exercises, notes || HW, quizzes, test ||
 * 22 || 1 || form functions of one variable from a verbal description and determine the minimum or maximum value of the function || 12.2.4.b, 12.2.5.af, 12.3.2.ad || 1 ||  || textbook, chapter || practice exercises, notes || HW, quizzes, test ||
 * 23 || 1 || define and apply integral exponents and rational exponents || 12.1.1.b, 12.1.3.b, 12.3.1.a, 12.3.2.d || 2 || growth and decay, laws of exponents || textbook, chapter 5 || practice exercises, notes || HW, quizzes, test ||
 * 24 || 1 || define and use exponential functions || 12.3.1.a, 12.3.2.a, 12.3.2.d || 1 || rule of 72, half-life || textbook, chapter 5 || practice exercises, notes || HW, quizzes, test ||
 * 25 || 1 || define and apply the natural exponential function || 12.3.1.a, 12.3.2.a, 12.3.2.d || 1 || natural exponential function, compound interest, effective annual yield || textbook, chapter 5 || practice exercises, notes || HW, quizzes, test ||
 * 26 || 1 || define and apply logarithms and prove and apply laws of logarithms || 12.1.3 || 2 || common logarithm, natural logarithm || textbook, chapter 5 || practice exercises, notes || HW, quizzes, test ||
 * 27 || 1 || solve exponential equations and change logarithms from one base to another || 12.1.3.b, 12.3.3 || 1 || exponential equation, change-of-base formula || textbook, chapter 5 || practice exercises, notes || HW, quizzes, test ||
 * 28 || 1 || find equations of circles, ellipses, hyperbolas and parabolas and graph them || 12.2.1.g, 12.3.1.d, 12.3.1.e || 4 || circle, ellipse, hyperbola, parabola, conic sections, center, radius, focus, foci, directrix, asymptotes || textbook, chapter 6 || practice exercises, notes || HW, quizzes, test ||
 * 29 || 1 || solve systems of second-degree equations || 12.3.3 || 1 ||  || textbook, chapter 6 || practice exercises, notes || HW, quizzes, test ||
 * 30 || 1 || define conic sections in terms of eccentricity and classify the graph of a second-degree equation by examining the coefficients || 12.3.2.d || 1 || eccentricity, non-degenerate conic sections || textbook, chapter 6 || practice exercises, notes || HW, quizzes, test ||
 * 31 || 2 || find the measure of an angle in either degrees or radians and find coterminal angles || 12.2.5 || 1 || initial ray, terminal ray, revolution, degree, minutes, seconds, radian, standard position, coterminal || textbook, chapter 7 || practice exercises, notes || HW, quizzes, test ||
 * 32 || 2 || find the arc length and area of a sector of a circle and solve problems involving apparent size || 12.2.5, 12.2.5.e, 12.3.2 || 1 || arc length, sector, apparent size || textbook, chapter 7 || practice exercises, notes || HW, quizzes, test ||
 * 33 || 2 || use the definitions of sine and cosine to find values of these functions and solve simple trigonometric equations || 12.2.1, 12.2.2, 12.3.1 || 1 || sine, cosine, unit circle || textbook, chapter 7 || practice exercises, notes || HW, quizzes, test ||
 * 34 || 2 || use reference angles, calculators or tables, and special angles to find values of the sine and cosine functions and sketch graphs of these functions || 12.2.1, 12.2.2, 12.3.1 || 2 || reference angle, latitude || textbook, chapter 7 || practice exercises, notes || HW, quizzes, test ||
 * 35 || 2 || find values of the tangent, cotangent, secant, and cosecant and sketch the functions graphs || 12.2.1, 12.2.2, 12.3.1 || 1 || tangent, cotangent, secant, cosecant || textbook, chapter 7 || practice exercises, notes || HW, quizzes, test ||
 * 36 || 2 || find values of inverse trigonometric functions || 12.2.1, 12.2.2, 12.3.1, 12.3.1.h || 1 ||  || textbook, chapter 7 || practice exercises, notes || HW, quizzes, test ||
 * 37 || 2 || solve simple trigonometric equations and apply them and find angles of inclination || 12.3.2, 12.3.3 || 1 || angle of inclination || textbook,
 * 25 || 1 || define and apply the natural exponential function || 12.3.1.a, 12.3.2.a, 12.3.2.d || 1 || natural exponential function, compound interest, effective annual yield || textbook, chapter 5 || practice exercises, notes || HW, quizzes, test ||
 * 26 || 1 || define and apply logarithms and prove and apply laws of logarithms || 12.1.3 || 2 || common logarithm, natural logarithm || textbook, chapter 5 || practice exercises, notes || HW, quizzes, test ||
 * 27 || 1 || solve exponential equations and change logarithms from one base to another || 12.1.3.b, 12.3.3 || 1 || exponential equation, change-of-base formula || textbook, chapter 5 || practice exercises, notes || HW, quizzes, test ||
 * 28 || 1 || find equations of circles, ellipses, hyperbolas and parabolas and graph them || 12.2.1.g, 12.3.1.d, 12.3.1.e || 4 || circle, ellipse, hyperbola, parabola, conic sections, center, radius, focus, foci, directrix, asymptotes || textbook, chapter 6 || practice exercises, notes || HW, quizzes, test ||
 * 29 || 1 || solve systems of second-degree equations || 12.3.3 || 1 ||  || textbook, chapter 6 || practice exercises, notes || HW, quizzes, test ||
 * 30 || 1 || define conic sections in terms of eccentricity and classify the graph of a second-degree equation by examining the coefficients || 12.3.2.d || 1 || eccentricity, non-degenerate conic sections || textbook, chapter 6 || practice exercises, notes || HW, quizzes, test ||
 * 31 || 2 || find the measure of an angle in either degrees or radians and find coterminal angles || 12.2.5 || 1 || initial ray, terminal ray, revolution, degree, minutes, seconds, radian, standard position, coterminal || textbook, chapter 7 || practice exercises, notes || HW, quizzes, test ||
 * 32 || 2 || find the arc length and area of a sector of a circle and solve problems involving apparent size || 12.2.5, 12.2.5.e, 12.3.2 || 1 || arc length, sector, apparent size || textbook, chapter 7 || practice exercises, notes || HW, quizzes, test ||
 * 33 || 2 || use the definitions of sine and cosine to find values of these functions and solve simple trigonometric equations || 12.2.1, 12.2.2, 12.3.1 || 1 || sine, cosine, unit circle || textbook, chapter 7 || practice exercises, notes || HW, quizzes, test ||
 * 34 || 2 || use reference angles, calculators or tables, and special angles to find values of the sine and cosine functions and sketch graphs of these functions || 12.2.1, 12.2.2, 12.3.1 || 2 || reference angle, latitude || textbook, chapter 7 || practice exercises, notes || HW, quizzes, test ||
 * 35 || 2 || find values of the tangent, cotangent, secant, and cosecant and sketch the functions graphs || 12.2.1, 12.2.2, 12.3.1 || 1 || tangent, cotangent, secant, cosecant || textbook, chapter 7 || practice exercises, notes || HW, quizzes, test ||
 * 36 || 2 || find values of inverse trigonometric functions || 12.2.1, 12.2.2, 12.3.1, 12.3.1.h || 1 ||  || textbook, chapter 7 || practice exercises, notes || HW, quizzes, test ||
 * 37 || 2 || solve simple trigonometric equations and apply them and find angles of inclination || 12.3.2, 12.3.3 || 1 || angle of inclination || textbook,
 * 38 || 2 || find equations of different sine and cosine curves and apply these equations || 12.3.2, 12.3.3 || 2 || period, amplitude || textbook,
 * 39 || 2 || use trigonometric functions to model periodic behavior || 12.3.1, 12.3.2, 12.3.3 || 2 || axis of the wave || textbook,
 * 40 || 2 || simplify trigonometric expressions and prove trigonometric identities || 12.3.1, 12.3.2, 12.3.3 || 1 || reciprocal relationships,
 * 41 || 2 || use trigonometric identities or technology to solve more difficult trigonometric equations || 12.3.1, 12.3.2, 12.3.3 || 2 ||  || textbook,
 * 42 || 2 || use trigonmetry to find unkown sides or angles of a right triangle || 12.3.1, 12.3.2, 12.3.3 || 1 || angle of elevation, angle of depression || textbook,
 * 43 || 2 || find the area of a triangle given the lengths of two sides and the measure of the included angle || 12.2.5, 12.3.3 || 1 || included angle || textbook,
 * 44 || 2 || use the law of sines find unkown parts of a triangle || 12.3.2, 12.3.3 || 1 || law of sines || textbook,
 * 45 || 2 || use the law of cosines find unkown parts of a triangle || 12.3.2, 12.3.3 || 1 || law of cosines || textbook,
 * 46 || 2 || use trigonometry to solve navigation and surveying problems || 12.2.4, 12.3.1, 12.3.2, 12.3.3 || 1 || compass bearing, course || textbook,
 * 47 || 2 || derive and apply sum and difference formulas for sine and cosine || 12.3.1, 12.3.2, 12.3.3 || 1 ||  || textbook,
 * 48 || 2 || derive and apply sum and difference formulas for tangent || 12.3.1, 12.3.2, 12.3.3 || 1 ||  || textbook,
 * 49 || 2 || derive and apply double and half angle formulas for sine, cosine, and tangent || 12.3.1, 12.3.2, 12.3.3 || 2 ||  || textbook,
 * 50 || 2 || use identities to solve trigonometric equations || 12.3.1, 12.3.2, 12.3.3 || 2 ||  || textbook,
 * 51 || 2 || convert polar to rectangular and rectangular to polar coordinates and graph polar equations || 12.2.2, 12.3.1, 12.3.2, 12.3.3 || 1 || polar coordinates, polar equation, polar graph || textbook,
 * 52 || 2 || write complex numbers in polar form and find products in polar form || 12.2.2, 12.3.1, 12.3.2, 12.3.3 || 1 || argand diagram, complex number plane, polar angle || textbook,
 * 53 || 2 || use DeMoivre's theorem to find powers of complex numbers || 12.2.2, 12.3.1, 12.3.2, 12.3.3 || 1 || DeMoivre's theorem || textbook,
 * 54 || 2 || find roots of complex numbers || 12.2.2, 12.3.1, 12.3.2, 12.3.3 || 1 ||  || textbook,
 * 55 || 3 || identify an arithmetic or geometric sequence and find a formula for its nth term || 12.3.1, 12.3.2, 12.3.3 || 1 || arithmetic sequence,
 * 56 || 3 || use sequences defined recursively to solve problems || 12.3.1, 12.3.2, 12.3.3 || 1 || recursive definition || textbook,
 * 57 || 3 || find the sum of the first n terms of arithmetic or geometric series || 12.3.1, 12.3.2, 12.3.3 || 1 || finite sequences, finite series, infinite sequences, infinite series || textbook,
 * 58 || 3 || find or estimate the limit of an ifinite sequence or determine that the limit does not exist || 12.3.1, 12.3.2, 12.3.3 || 1 || infinite limits || textbook,
 * 60 || 3 || find the sum of an infinite geometric series || 12.3.1, 12.3.2, 12.3.3 || 1 || converge, diverge || textbook,
 * 61 || 3 || represent series using sigma notation || 12.3.1, 12.3.2, 12.3.3 || 1 || sigma notation, summand, limits of summation, index || textbook,
 * 62 || 4 || find the limit of a function or the quotient of two functions and to determine whether a function is continuous || 12.3.1, 12.3.2, 12.3.3 || 1 || continuous || textbook,