Download Pre-Calculus Learning Targets 2016

Pre-Calculus Learning Targets 2016-17
Fundamental Concepts of Algebra
Unit P: Pre-Requisite Skills (From Chapter 1)
LT P.1 – Graphs
Skills assessed
1) Graph functions (linear, quadratic, cubic, and absolute value) by creating a table of values
2) Identify (from graph) the intercepts of a function.
3) Determine the intervals where a function is increasing and decreasing.
LT P.2 – Function Basics
Skills Assessed
1) Find the domain and range of a relation and determine if that relation is a function.
2) Determine whether an equation represents a function
3) Evaluate functions including piecewise functions
LT P.3 – Linear Functions
Skills Assessed
1) Graph and write an equation of a line in point-slope form, slope intercept form, and standard
form.
2) Graph and write equations of horizontal and vertical lines.
3) Find slopes and equations of parallel and perpendicular lines.
LT P.4 – Distance, Midpoint, and Equations of Circles
Skills Assessed
1) Find the distance and midpoint between two coordinates.
2) Write the equation of a circle in standard form.
3) Graph an equation of a circle in standard form and general form.
Unit1: Functions & Graphs
LT 1.1 – Functions and Their Graphs (Section 1.3)
Skills Assessed
1) Find maximum and minimum values of a function
2) Identify odd and even functions (and recognize their symmetry).
3) Graph piecewise functions.
4) Evaluate the difference quotient of a function.
LT 1.2 – More on Slope (Section 1.5)
Skills Assessed
1) Change equations of lines between general, point-slope, and slope-intercept forms.
2) Calculate average rate of change
3) Interpret slope as a rate of change (not assessed but discussed).
LT 1.3 – Transformations of Functions (Sections 1.6)
Skills Assessed
1) Graph common and uncommon functions by transformations.
Common functions include linear, absolute value, quadratic, square root, cubic, and cube
root functions.
Transformations include vertical/horizontal shifts, reflections, and vertical/horizontal
stretching.
LT 1.4 – Operations and Combinations of Functions (Section 1.7)
Skills Assessed
1) Find domain of a function
2) Combine functions using the sum, difference, product, and quotient rules.
3) Form composite functions and determine their domain.
LT 1.5 – Inverse Functions (Section 1.8)
Skills Assessed
1) Verify functions are inverses by composition of functions.
2) Find the inverse of a function algebraically and graphically.
3) Determine whether a relation (including graphs) has an inverse.
4) Determine whether a relation is a function from its graph. Find the domain and range of the
function from its graph.
LT 1.6 – Modelling Functions
Skills Assessed
1) Solve real world problems by setting up and solving functions.
Unit 2: Polynomial & Rational Functions
LT 2.1 – Complex Numbers
Skills Assessed
1) Perform operations with complex numbers including add, subtract, multiply, and divide.
2) Solve quadratic equations with complex solutions.
LT 2.2 – Quadratic functions
Skills Assessed
1) Graph parabolas in vertex and standard form
2) Find the maximum/minimum of a parabola
3) Solve real world problems involving quadratics.
LT 2.8 – Modeling Using Variation
Skills Assessed
1) Solve problems involving direct, indirect, combined, and joint variation.
LT 2.3 – Polynomial Functions and Their Graphs
Skills Assessed
1) Determine end behavior of a polynomial function.
2) Find the zeros of a polynomial by factoring.
3) Use the Intermediate Value Theorem to prove a zero exists
4) Graph a polynomial function.
LT 2.4 – Dividing Polynomials
Skills Assessed
1) Divide polynomials using long and synthetic division.
2) Use the factor theorem to solve equations involving polynomials.
LT 2.5 – Zeros of a Polynomial Function
Skills Assessed
1) Use the rational zero test to find possible zeros of a polynomial.
2) Find zeros of a polynomial (using a graphing utility to help find zeros)
3) Solve polynomial equations
4) Write a polynomial function given the zeros.
LT 2.6 – Rational Zeros and Their Graphs
Skills Assessed
1) Find the domain of a rational function
2) Identify vertical, horizontal, and slant asymptotes of a rational function.
3) Write vertical and horizontal asymptotes in limit notation.
4) Graph rational functions.
LT 2.7 – Polynomial and Rational and Inequalities
Skills Assessed
1) Solve polynomial and rational inequalities and write answers in interval notation.
Unit3: Exponential & Logarithmic Functions
LT 3.1 – Introduction to Exponential Functions
Skills Assessed
1) Evaluate exponential functions (including with base e)
2) Graph exponential functions (including with base e)
𝑟 𝑟𝑡
3) Use compound interest formulas including: A = P(1 + 𝑛) and A = Pe rt
LT 3.2 – Introduction to Logarithmic Functions
Skills Assessed
1) Change back and forth between logarithmic and exponential forms.
2) Evaluate logarithms without a calculator
3) Graph logarithmic functions
4) Find the domain of a logarithmic function.
5) Use logarithmic functions in applications.
LT 3.3 – Using Properties of Logarithms
Skills Assessed
1) Use the basic properties of logarithms (taught in section 3.2)
2) Use logarithmic properties (product, quotient, and power) to expand and condense logarithmic
expressions.
3) Use the change of base property.
LT 3.4 – Using Exponential and Logarithmic Equations
Skills Assessed
1) Use logarithms to solve exponential equations.
2) Use rules of logarithms to solve logarithmic equations.
3) Solve applied problems.
LT 3.5 – Modeling Data Using Exponential Growth or Decay
Skills Assessed
1) Model exponential growth or decay with an equations (including base e).
2) Use logistic growth models.
3) Use Newton’s Law of Cooling
Unit 4: Trigonometric Functions
LT 4.1 – Introduction to Angles
Skills Assessed
1) Convert back and forth between radian and degree measure.
2) Find coterminal angles.
3) Find arc length.
4) Use linear and angular speed to describe motion on a circular path.
LT 4.2 – Introduction to the Unit Circle
Skills Assessed
1) Evaluate the six trigonometric functions (sin, cos, tan, csc, sec, and cot) using the Unit Circle
(NO CALCULATORS)
2) Use Pythagorean Identities to solve trigonometric equations.
Taught but not assessed at this time
1) Domain and range of sine and cosine functions.
2) Even and odd trigonometric functions.
3) Periodic properties of the six trig functions.
LT 4.3 – Using Right Triangle Trigonometry
Skills Assessed
1) Use right triangles to complete this missing measurements of a right triangle.
2) Use right triangle trigonometry to solve applied problems.
LT 4.4 – Trigonometric Functions of Any Angle
Skills Assessed
1) Use reference angles to evaluate trigonometric functions. (NO CALCULATORS)
LT 4.5 – Graphing the Sine and Cosine Functions.
Skills Assessed
1) Graph the Sine function (including transformations).
2) Graph the Cosine function (including transformations).
3) Model periodic behavior.
LT 4.6 – Graphing the Tangent, Cotangent, Cosecant, and Secant functions.
Skills Assessed
1) Graph the tangent and cotangent functions (including transformations).
2) Graph the cosecant and secant functions (including transformations).
LT 4.7 – Inverse Trigonometric Functions
Skills Assessed
1) Find exact values of the inverse of sine, cosine, and tangent functions (NO CALCULATORS)
LT 4.8 – Applications of Trigonometric Functions
Skills Assessed
1) Solve problems involving a right triangle, bearings, or simple harmonic motion.
Unit5: Analytic Trigonometry
LT 5.1- Verifying Trigonometric Identities
Skills Assessed
1) Use the fundamental trigonometric identities to verify identities.
LT 5.2 – Sum and Difference Identities
Skills Assessed
1) Use the sum and difference formulas for cosine, sine, and tangent.
LT 5.3 – Double-Angle and Half-Angle Formulas
Skills Assessed
1) Use double angle and half angle formulas to find exact values.
2) Verify identities using double angle and half angle formulas.
LT 5.4 – Product to Sum and Sum to Product Formulas
Skills Assessed
1) Rewrite expressions using product to sum and sum to product formulas.
2) Verify identities using product to sum and sum to product formulas.
LT 5.5 – Trigonometric Equations
Skills Assessed
1) Solve trigonometric equations with multiple solutions.
2) Solve equations with multiple angles.
3) Solve trigonometric equations involving quadratic form and factoring.
4) Use identities to solve trigonometric equations.
Unit 6: Additional topics in Trigonometry
LT 6.1 – Law of Sines
Skills Assessed
1) Use the Law of Sines to solve oblique triangles (including the ambiguous case).
2) Find the area of an oblique triangle using the sine function.
3) Solve applied problems using the Law of Sines
LT 6.2 – Law of Cosines
Skills Assessed
1) Use the Law of Cosines to solve oblique triangles.
2) Solve applied problems using the Law of Cosines
3) Use heron’s formula to find the area of a triangle.
LT 6.3 – Introduction to Polar Coordinates
Skills Assessed
1) Plot points in the polar coordinate system (including multiple sets).
2) Convert back and forth between polar and rectangular coordinates.
3) Convert back and forth between polar and rectangular equations.
LT 6.4 – Introduction to Graphing in the Coordinate Plane
Skills Assessed
1) Use point plotting to graph polar equations.
Unit 7: Systems of Equations
LT 7.1 – Systems of Linear Equations in Two Variables
Skills Assessed
1) Use substitution to solve a system of equations (including no solutions and infinite solutions)
2) Use addition to solve a system of equations (including no solutions and infinite solutions)
LT 7.2 – Systems of Linear Equations with Three Variables
Skills Assessed
1) Solve systems of linear equations in three variables.
LT 7.3 – Systems of Nonlinear Equations in Two Variables (Section 7.4)
Skills Assessed
1) Solve nonlinear system by substitution.
2) Solve nonlinear system by addition.
LT 7.4 – Systems of Inequalities (Section 7.5)
Skills Assessed
1) Graph linear and nonlinear inequalities.
2) Graph a system of inequalities.
LT 7.5 – Linear Programming (Section 7.6)
Skills Assessed
1) Use linear programming to solve problems.
Unit10: Mathematical Sequences and Induction
LT 10.1 – Introduction to Sequences and Series
Skills Assessed
1) Find particular terms of a sequence.
2) Use recursion formulas.
3) Use summation notation.
LT 10.2 – Arithmetic Sequences
Skills Assessed
1) Write terms of an arithmetic sequence.
2) Use the formula for the sum of the first n terms of an arithmetic sequence.
LT 10.3 – Geometric Sequences and Series
Skills Assessed
1) Write terms of a geometric sequence (including using the formula for a general term).
2) Use the sum of the first n terms of a geometric sequence.
3) Find the sum of an infinite geometric series.
LT 10.4 – Mathematical Induction
Skills Assessed
1) Prove statements using mathematical induction.