Pre-Calculus. Concepts: Relations and Functions. Distinguish between relations and functions, identify domain and range, evaluate f(c)

Transcription

1 Pre-Calculus Standards and Relations and Functions PC 1.4 PC 1.4 Distinguish between relations and functions, identify domain and range, evaluate f(c) Compose and find inverses of functions Determine if inverse is a function Graph linear equations and inequalities Use the midpoint, slope, and distance formulas and apply to parallel and perpendicular lines, be able to write equations of parallel and perpendicular lines given a linear equation and a point on the line Know the linear equation forms and be able to convert from one form to another Systems of Equations and Matrices, PC 1.3, PC 9.3 Solve systems of linear equations Operate with matrices add, subtract, multiply, scalar multiplication Find determinant using diagonal method and expansion by minors Solve matrix equations by multiplying by the inverse matrix Find the inverse of a 2 by 2 matrix Solve a system of linear equations using augmented matrices Solve systems of linear inequalities using the concept of vertex points of convex polygonal regions Apply systems of linear inequalities to situations (word problems)

2 Standards Concepts Graphing PC 1.5, PC 1.6 PC 1.7 PC 1.4, PC 1.7 PC 1.9 Identify types of symmetry of a functions, identify as even or odd or neither Identify and use graphing transformations: reflection, translations and dilations Graph inverses of functions by reflecting across the y=x line, find the equation of an inverse algebraically Find the vertical, horizontal, and slant asymptotes of rational functions, and graph function Graph inequalities Find the derivative of a polynomial function, find the slope and equation of the tangent line to a point on a function, find and identify types of critical points of a function Identify the end behavior of a polynomial function as a graphing tool Polynomial and Rational Functions,, PC 9.5 Know and apply the Fundamental Theorem of Algebra to find the number of solutions, factor and solve polynomial functions Solve and graph quadratic equations using quadratic formula, completing the square, and factoring. Use the discriminate to identify the type of roots. Apply the factor and remainder theorem to find solutions and identify factors of a polynomial function. Apply the rational root theorem to list possible solutions, then use synthetic division to find roots. Solve rational and radical equations and check solutions for extraneous roots.

3 Trigonometry PC 4.2 PC 4.2, PC 3.3 PC 4.1 PC 4.3 PC 3.1, PC 4.11 PC 3.1, PC 3.2 Be able to convert angles to degree and radians. Find the reference angle on the unit circle. Use trigonometry to find arc length, sector area and triangle area. Know the six trigonometric functions and how they apply to the unit circle. Apply the six trigonometric functions to the special angles 30,45,60 etc. around the unit circle and in triangles. Know and apply right triangle trigonometry to solve for lengths and angles in a right triangle. Use the Law of Sines and the Law of Cosines to find parts of nonright triangles. Graphs and Inverses of Trigonometric Functions PC 4.5, PC 4.6, PC 4.7 PC 4.6, PC 9.1, PC 9.2, PC 4.4, PC 4.7 PC 4.8 PC 4.9 PC 4.9, PC 9.2 PC 4.4, PC 9.1, PC 9.2 Graph trigonometric functions, identify the domain and range of each function, and use graphs to find values at specific angles. Understand and graph trig functions using amplitude, period and phase shift. Find the amplitude period and phase shift given the equation, write equations from the given information and apply to word problems. Define and graph inverse trigonometric functions and identify the domain and range of each. Find values of the inverse trigonometric functions using the unit circle and graphing calculators. Find the solutions of principal value functions and distinguish the difference between principal value solutions and general value solutions. Solve simple harmonic motion problems.

4 Trigonometric Identities and Equations PC 5.1 PC 5.2, PC 9.3, PC 5.3, PC 5.5, PC 9.3, PC 9.5, PC 9.5, PC 9.5 PC 5.6, PC 9.1 Know and apply the Pythagorean and reciprocal identities Verify trigonometric identities. Work with double, half, sum and difference formulas to solve numerical problems. Solve trigonometric equations with a given domain, with principal values, and with general value solutions. Write linear equations in normal form and convert from standard to normal and back. Find the distance from a point to a line and apply to finding the distance between two parallel lines, given their equations and to finding the equation of the line which bisects the angle formed by two intersecting lines Apply trigonometry to solve word problems. Vectors and Parametric Equations PC 3.2, PC 9.2 PC 1.8, PC 9.1 Add, subtract, and use scalar multiplication with vectors algebraically and geometrically. Do the algebra for three-dimensional vectors. Use the concepts of dot product and cross product to determine perpendicular vectors. Apply vectors to the Law of Sines and the Law of Cosines and apply to problems in physics. Write linear equations in parametric form and use to model motion. Polar Coordinate System and Complex Numbers PC 6.1 PC 6.2 Define polar coordinate and convert from polar to rectangular and vice versa. Write equations in polar and rectangular form. Convert from one to the other as needed.

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6 PC 6.3 PC 6.4 PC 6.5 Graph polar equations by plotting points on polar graph paper and by using a graphing calculator. Review complex number operations. Write complex numbers in polar form then add, subtract, multiply and divide. Apply DeMoivre s Theorem to find powers and roots of polar form complex numbers. Exponential and Logarithmic Functions PC 2.3 PC 2.1, PC 9.2, PC 9.1, PC 2.4, PC 2.3 Review properties of exponents and apply to rational and irrational exponents, simplify exponential expressions. Graph exponential functions. Solve problems using logarithmic and exponential functions. Apply the properties of logarithms. Graph logarithmic functions and relate to exponential function graphs. Sequences and Series PC 7.1 PC 7.2 PC 7.4 PC 7.5 PC 7.6, PC 9.1 PC 7.1 Work with arithmetic and geometric sequences and write in sigma notation. Expand sigma notation and evaluate. Find the sum of infinite geometric series. Write the equation of a series using recursive formulas. Find the limit of a sequence, if it exists. Solve application problems. Use Pascal s triangle and the Binomial Theorem to expand binomials. Also use the sigma form of the Binomial Theorem to find a specific term of a binomial expansion.

7 PC 9.6 Define mathematical induction and use the method of mathematical induction to prove formulas are true. Data Analysis PC 8.1 PC 8.1,8.2 PC 8.2, 8.3 PC 8.2, 8.3 Plot data in a scatter plot; identify best fit line, find equation for best fit line Calculate standard deviation & correlation coefficient using formula and technology Use Excel to get graph and correlation coefficients for linear and exponential data Identify data as linear or exponential PC 8.3 Predict using best fit line or exponential model for equations by substitution of x or y