HUDSONVILLE HIGH SCHOOL COURSE FRAMEWORK

Transcription

1 HUDSONVILLE HIGH SCHOOL COURSE FRAMEWORK COURSE / SUBJECT Algebra 2B KEY COURSE OBJECTIVES/ENDURING UNDERSTANDINGS OVERARCHING/ESSENTIAL SKILLS OR QUESTIONS RATIONAL AND RADICAL FUNCTIONS PROPERTIES AND ATTRIBUTES OF FUNCTIONS CONIC SECTIONS Analyze, write, solve and graph functions that are rational or involve radicals. Transform functions, analyze piecewise functions and take composites of functions Solve, graph, identify, and write equations for conic sections. PROBABILITY AND STATISTICS SEQUENCES AND SERIES TRIGONOMETRIC FUNCTIONS Explore permutations and combinations as well as dependent and independent events. Write and solve equations for series and sequences, arithmetic and geometric. Solve right angle trigonometric problems and non-right angle trigonometric problems. Use the unit circle to find trig ratios.

2 UNIT PACING LESSON # STANDARD UNIT LEARNING TARGETS Example Key FOUNDATIONS FOR FUNCTIONS 8.1 Classify and order real numbers Order and classify:.6, 2, 0, 5 2, Order real numbers and know set notation. 8.2 Identify and use properties of real numbers 2(x + y) = 2x + 2y Simplify expressions using properties. 8.3 Simplify, add, subtract, multiply and divide square roots Simplify 18 Simplify radical expressions. 8.4 Simplify and evaluate algebraic expressions Simplify x + 3xy 2y for x=4 and y =7 Evaluate according to properties. 8.5 Simplify expressions involving exponents. Use Scientific Notation Simplify ( ab4 b 7 )2 Use properties of exponents to simplify powers. 8.6 Use properties of Rewrite and simplify radical expressions using rational exponents Simplify 3 27x 6 exponents to rewrite expressions. 8.7 and transform radical functions f (x) = x using transform-ations rules. 8.8 Solve Radical Equations and Inequalities Solve x 2 = 3 Solve equations involving radicals.

3 UNIT PACING LESSON # STANDARD UNIT LEARNING TARGETS Example Key PROPERTIES AND ATTRIBUTES OF FUNCTIONS 9.1 Multiple representations of functions Kurt is rappelling down a 500-foot cliff at a rate of 6 feet per second. Create a table, equation, and graph. Solve problems using graphs, equations, and tables. 9.2 Write and graph piecewise functions Solve functions that are in pieces or parts. 9.4 Operations with functions Composite Functions. 9.5 Functions and their inverses Find the inverse of Find the inverse of a function. UNIT PACING LESSON # STANDARD UNIT LEARNING TARGETS Example Key CONIC SECTIONS 10.1 Introduction to Conic Sections (x 2) 2 + (y + 3) 2 = 16 Rewrite equations to solve for y to graph.

4 10.2 Circles Find the center and radius of (x 2) 2 + (y + 3) 2 = 16 graph circles Ellipses (x 2) (y + 3)2 16 = 1 graph ellipses Hyperbolas (x 2) 2 9 (y + 3)2 16 = 1 graph hyperbolas Parabolas 10.6 Identifying Conic Sections y 3 = 2(x 4) 2 Identify the conic section represented by 6x 2 + 9y 2 +12x 15y 25 = 0 graph parabolas. Use B 2 4AC to determine conic section.

5 PROBABILITY AND STATISTICS 11.1 Permutations and Combinations How many ways can a club select a president, a vice president, and a treasurer from a group of 5 people Solve problems involving Counting Techniques Theoretical and Experimental Probability A CD has 5 upbeat songs and 7 slow songs. What is the probability of randomly picking an upbeat song Find the probability of an event Independent and Dependent Events Find the probability of selecting two Aces from a deck of cards Find the probability of independent or dependent events Compound Events Find the probability of choosing an Ace or a Heart from a deck of cards Find the probability of compound events Measures of Central Tendency 11.6 Binomial Distribution Find the mean and standard of deviation from a set of numbers Expand Find measures of central tendency Binomial Expansion EXTENSION Normal Distribution A test has a mean of 50 and a standard of deviation of 4. Find the probabilities using normal distribution Find percentages of normal distribution graphs

6 SEQUENCES AND SERIES 12.1 Introduction to Sequences Write an explicit formula for the following sequence. 3, 6, 12, 24, 48,... Find the nth term of a sequence Series and Summation Notation Expand and evaluate Expand and Evaluation a series in sigma notation 12.3 Arithmetic Sequence and Series Find the indicated sum of the arithmetic series Find the sums of arithmetic series 12.4 Geometric Sequence and Series Find the indicated sum of the arithmetic series Find the sums of geometric series 12.5 Infinite Geometric Series Find the sum of the infinite geometric series Find the sum of a geometric series to infinity. EXTENSION Area Under a Curve Estimate the area under the curve over 0<x<5 Find the area underneath a curve using rectangles and technology

7 CONIC SECTIONS 13.1 Right Angle Trigonometry Find the value of sine, cosine, and tangent given the right triangle. Sine, cosine and tangent ratios Angles of Rotation Draw an angle with the given measure in standard position. θ = 200 Rotate around a circle, draw angles The Unit Circle Find the exact value of sine, cosine, and tangent of θ = 210 Know trig ratios of special right triangles and locate them around the unit circle Inverse Trigonometric Functions Find all possible values sin 1 ( 1 of 2 ) Given ratio, find the angle The Law of Sines 13.6 The Law of Cosines Solve ABC given m A = 49, m B = 40, and AC = 20 Solve ABC given AB = 54, m B = 65 and BC = 49 Use Law of Sines to solve triangles without a right angle. Use Law of Cosines to solve triangles without a right angle.