course framework hudsonville high school...6.4a y = log x 6.4b y = 3log(x 2) +5 6.4c f(x) = e x...

6/4/2019 Algebra 2B Curriculum map - Google Docs

https://docs.google.com/document/d/12jwn7fuB2d9JqMz7Sz54FmSSnPSTTaZ8e5t2f50kI74/edit 1/15

HUDSONVILLE HIGH SCHOOL COURSE FRAMEWORK

Course: Algebra 2B

KEY COURSE OBJECTIVES/ENDURING UNDERSTANDINGS (Important ideas and core processes)

OVERARCHING/ESSENTIAL SKILLS OR QUESTIONS (ideas/skills that transcend disciplinespecific learning)

Exponential and Logarithmic Functions Rational functions Sequences and series Trigonometric functions Probability and statistics

Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning.



UNIT

LESSON #

STANDARD (Which standards does this address?)

UNIT LEARNING TARGETS

(By the end of the unit, students will be able to. . . )

EXAMPLES KEY CONCEPTS

Exponential Growth and

Decay

6.1

HSASSE.B.3c HSFIF.C.7e HSFIF.C.8b HSFLE.A.2 HSFLE.B.5

6.1A Evaluate an exponential expression for a given value of x 6.1B Tell whether the function is exponential growth (b>1) or exponential decay (0<b<1) and sketch a graph no calculator 6.1C Calculate Compound Interest

6.1A when x 3x = − 2 6.1B Tell whether the function represents exponential growth or decay:

.75y = x

6.1C You deposit $3000 into a bank account that pays 1.25% annual interest, compounded semiannually. How much interest does the account earn after 4 years?

Graph exponential growth and decay

functions

Use exponential models to solve reallife

problems

The Natural Base e

6.2 HSFIF.C.7e HSFLE.B.5

6.2A Simplify expressions using power rules with base e 6.2B Tell whether the function is exponential growth (pos expo) or exponential decay (neg expo) and sketch a graph no calculator 6.2C Graph and Identify Domain and Range 6.2D Use erA = P t

6.2A e e5 * 3

6.2B ey = −2x 6.2C ey = x+2 6.2D You invest $4000 in an account to save for college. a. Option 1 pays 5% annual interest compounded semiannually. What would be the balance in the account after 2 years? b. Option 2 pays 4.5% annual interest compounded continuously. What would be the balance in the account after 2 years? c. At what time t (in years) would Option 1 give you $100 more than Option 2?

Define and use the natural base e

Graph natural base

functions

Solve reallife problems



Logarithms and Logarithmic Functions

6.3 HSFIF.C.7e HSFBF.B.4a HSFLE.A.4

6.3A Rewrite the equation in exponential form (no calc) 6.3B Rewrite the equation in logarithmic form (no calc) 6.3C Evaluate the logarithm (no calc) 6.3D Evaluate the logarithm (with calc) 6.3E Simplify logarithmic expressions (no calc) 6.3F Find the inverse of the log or expo function

6.3A log 2 8=3 6.3B 642 = 1 6.3C log 5 125 6.3D log 5 6.3E log 4 4 3x

6.3F 3y = x

Define and evaluate logarithms. Graph logarithmic functions.

Transformations of Exponential and Logarithmic

Functions

6.4 HSFIF.C.7e HSFBF.B.3

6.4A Graph the log function and determine the Domain, Range and asymptote 6.4B Describe the transformation 6.4C Write a rule that represents the indicated transformation

6.4A log xy = 6.4B log(x ) y = − 3 − 2 + 5 6.4C translation 2 units left and(x) ef = −x 3 units up, followed by a vertical stretch by a factor of 2

Transform graphs of exponential functions. Transform graphs of logarithmic functions. Write transformations of graphs of exponential and logarithmic functions.

Properties of Logarithms

6.5 HSASSE.A.2 HSFLE.A.4

6.5A No calculator use properties to evaluate 6.5B Condense the log expression 6.5C Use the change of base formula to evaluate

6.5A use log 5 3 = .8833 and log 5 6= 1.113 to evaluate the logarithm : log 5 2 6.5B log 7 3 + log 7 5 6.5C log 3 5

Use the properties of logarithms to evaluate logarithms. Use the properties of logarithms to expand or condense logarithmic expressions. Use the changeofbase formula to evaluate logarithms.

Solving Exponential and Logarithmic Equations

6.6 HSAREI.A.1 HSFLE.A.4

6.6A Solve Exponential and Logarithmic Equations 6.6B Determine the relationship, given a table and explain why 6.6C Write an exponential Function whose graph passes through the given points

6.6A 93x+1 = x−3 6.6A log 6 (5x+4) = 2 6.6B

X 1 2 3 4 5

f(x) 800 400 200 100 50

6.6C (1,2) and (4, 16)

Solve exponential equations and

logarithmic equations.

Inverse Variation

7.1 HSACED.A.1

7.1A Classify Direct and Inverse Variation from an equation

7.1A and y 7x = 3xy =

Classify direct and inverse variation.



HSACED.A.2 HSACED.A.3

7.1B Classify Direct and Inverse Variation from a table 7.1C Write an inverse variation function given x and y 7.1D SAT prep/real life

7.1B

x 1 2 3 4 6

y 24 12 8 6 4

7.1C x = 6 and y = 5 7.1D The current y in a certain circuit varies inversely with the resistance x in the circuit. If the current is 8 amperes when the resistance is 20 ohms, what will the current be when the resistance increases to 25 ohms?

Write inverse variation

equations.

Graphing Rational Functions

7.2 HSAAPR.D.6 HSFBF.B.3

7.2A Compare the graph with the graph of 1/x 7.2B Give the Domain, Range and asymptotes of a rational function 7.2C Give the Domain and Range with calculator by using graph 7.2D Rewrite the function in the form y = a/(xh)+k by using long division 7.2E Solve Real Life Applications

7.2A y = x−20

7.2B y = 1

x+3 − 5 7.2C y = 1

x−2 + 4 7.2D g(x) = x+2

3x+7 7.2E You are creating statues made of cement. The mold costs $300. The material for each statue costs $22. a. Estimate how many statues must be made for the average cost per statue to fall below $30.

b. What happens to the average cost as more statues are created?

Graph simple rational functions. Translate simple rational functions. Graph other rational functions.

Multiplying and Dividing Rational Expressions

7.3

HSAAPR.D.6 HSAAPR.D.7

7.3A Simplify the rational expression 7.3B Find the product of the rational expression 7.3C Find the quotient of the rational expression

7.3A x −4x−52

x −7x+102 7.3B *y4

54x y4 2 x y3 2

9x y5 3 7.3C 3x +6x4 3

x −x−62 ÷ 6x3x−3

Simplify, multiply and divide rational expressions



Adding and Subtracting Rational

Expressions

7.4 HSAAPR.D.6 HSAAPR.D.7

7.4A Adding or subtracting with a common denominator 7.4B Find the least common multiple 7.4C Adding or subtracting with unlike denominators simplify complex fractions

7.4A +5x12 3

5x 7.4B , x x2 − 9 − 3 7.4C + 14

x −7x−1826x+9

Add or subtract rational expressions Simplify complex fractions

Solving Rational Equations

7.5 HSACED.A.4 HSAREI.A.1 HSAREI.A.2

7.5A Solve the rational equation by cross multiplying 7.5B Identify the LCD 7.5C Solve by using the LCD 7.5D Determine if the inverse is a function

7.5A = 4x+21

6x−2

7.5B =3x

x+5 x8

x2

7.5C 4

x−5 + x1 = x−5

x−1 7.5D f(x)= 2

x−4

Solve equations by cross multiplying. Solve rational equations by using the least common denominator. Use inverses of functions *extraneous solutions

Defining and Using

Sequences and Series

8.1 HSFIF.A.3

Day 1 8.1A Give the first 6 terms of a sequence (give the first 2 terms no calc) (with a calculator you can use y= and hit 2nd table) 8.1B Describe the pattern, write the next term, and write a rule for the nth term Day 2 8.1C Write the series using summation notation 8.1D Find the sum NO CALCULATOR (check it on your calculator) 2nd stat math 5 8.1E Find the sum with a calculator

8.1A a n = n 3 + 2 8.1B 3.1, 3.8, 4.5, 5.2, . . . 8.1C 7 + 10 + 13 + 16 + 19+ ….

8.1D x∑6

x=12

8.1E ∑8

x=4

xx+1

Use sequence notation to write terms of sequences. Write a rule for the n th term of a sequence. Sum the terms of a sequence to obtain a series and use summation notation. sequence, terms of a sequence, series, summation notation, sigma notation

Analyzing Arithmetic


8.2 HSFIF.A.3 HSFBF.A.2 HSFLE.A.2

8.2A Tell whether the sequence is arithmetic and explain how you know 8.2B Write a rule for the nth term of the sequence. Then find a sub 20 8.2C Write a rule for the nth term of the sequence given a term

8.2A 12, 6, 0, 6, 12, . . . . 8.2B 12, 20, 28, 36, . . . 8.2C a 11 = 43, d = 5

Identify arithmetic sequences. Write rules for arithmetic sequences. Find sums of finite arithmetic sequences



(point) and the common difference (slope) 8.2D Write a rule for the nth term of the sequence given two terms (two points) 8.2E Write a rule for the nth term of the sequence given the graph 8.2F Find the sum of the arithmetic sequence using the formula 8.2G Find the sum of the arithmetic sequence using your calc (2nd stat math 5)

8.2D a 5 = 41, a 10 = 96

8.2E

8.2F x∑20

x=12 − 3

8.2G − .1 x∑39

x=14 + 4

Analyzing Geometric


8.3 HSASSE.B.4 HSFIF.A.3 HSFBF.A.2 HSFLE.A.2

8.3A Tell whether the sequence is geometric and explain your reasoning 8.3B Write a rule for the nth term of the sequence. Then find a sub 7 8.3C Write a rule for the nth term of the sequence given a term (point) and the common ratio (constant multiplier) you don't need to graph 8.3D Write a rule for the nth term of the sequence given two terms (two points) 8.3E Write a rule for the nth term of the sequence given the graph

8.3A 96, 48, 24, 12, 6 8.3B 4, 20, 100, 500, . . . 8.3C a 3 =4. r =2 8.3D a 2 =28, a 5 = 1792

8.3E

Identify geometric sequences. Write rules for geometric sequences. Find sums of finite geometric series



8.3F Find the sum of the geometric sequence given summation notation 8.3G Find the sum of the geometric sequence given the first 4 terms (and write a rule) 8.3H Real Life Application

8.3F (7)∑9

x=16 x−1

8.3G Find the sum of the first 8 terms: 12, 48, 192, 768. . . 8.3H A regional soccer tournament has 64 participating teams. In the first round of the tournament, 32 games are played. In each successive round, the number of games decreases by a factor of 2

1 a. Write a rule for the number of

games played in the n th round. For what values of n does the rule make sense? Explain.

b. Find the total number of games played in the regional soccer tournament

Finding Sums of Infinite

Geometric Series

8.4 HSASSE.B.4

8.4A Describe what happens in the sequence 8.4B Find the sum of the infinite geometric series 8.4C Write the repeating decimal as a fraction in simplest form

8.4A + + + + . . .12 6

1 118

154

8.4B ( )∑∞

x=18 5

1 x−1

8.4C .22222222

Find partial sums of infinite geometric series. Find sums of infinite geometric series

Using Recursive Rules with Sequences

8.5 HSFIF.A.3 HSFBF.A.1a HSFBF.A.2

8.5A Write the first six terms of the sequence given the recursive rule 8.5B Write a recursive rule for the sequence given the sequence 8.5C Write a recursive rule for the sequence given the graph 8.5D Write a recursive rule for the sequence given the explicit rule 8.5E Write an explicit rule given the recursive rule 8.5F SAT real life application

8.5A a 1 = 1, an = a n1 +3 8.5B 21, 14, 7, 0, 7. . .

8.5C 8.5D a n = 3+4n 8.5E a 1 = 3, an = a n1 6 8.5F The value of a car is given by the recursive rule a 1 = 25, 600, a n = .86a n1 , where n is the number of years since the car was new. Write an explicit rule for the value of the car after n years.

Evaluate recursive rules for sequences. Write recursive rules for sequences. Translate between recursive and explicit rules for sequences. Use recursive rules to solve reallife problems



Right Triangle Trigonometry

9.1 HSFTF.A.1 HSFTF.A.2 HSFTF.B.5 HSFTF.C.8

9.1A Evaluate the six trig functions of the angle 9.1B Given one trig function, give the other five 9.1C Find the EXACT value of x no calc using special right triangles 9.1D Evaluate on your calculator 9.1E Given an angle and a side of an acute triangle, solve for the triangle 9.1F Solve real world problems using angle of elevation and angle of depression

9.1A 9.1B sin θ = 3

19

9.1C 9.1D tan 31 °

9.1E B = 36 a = 23 °

9.1F A parasailor is attached to a boat with a rope 80 feet long. The angle of elevation from the boat to the parasailor is Estimate the parasailor’s height above the boat. Round your answer to the nearest tenth.

Evaluate trigonometric functions of acute angles. Find unknown side lengths and angle measures of right triangles. Use trigonometric functions to solve reallife problems.

Angles and Radian Measure

9.2 HSFTF.A.1

Day 1 9.2A Draw an angle in standard position 9.2B Find one pos angle and one neg angle that are coterminal with the given angle

9.2A 110 ° 9.2B 70 °

Draw angles in standard position. Find coterminal angles. Use radian measure



9.2C Convert from degrees to radians 9.2D Convert from radians to degrees 9.2E Use a calculator to evaluate the trig functions Day 2 9.2F Find arc length given the angle and radius 9.2G Find area of a sector given the angle and radius 9.2H Find the angle, given the arc length and radius

9.2C 315 ° 9.2D 4

3π 9.2E sin 8

7π 9.2F and 9.2G In the men’s shot put event at the 2012 summer olympic games, the length of the winning shot was 21.89 meters. A shot put must land within a sector having a central angle of 34.92 ° to be considered fair.

a. 9.2F The officials draw an arc across the fair landing area, marking the farthest throw. Find the length of the arc.

b. 9.2G All fair throws in 2012 Olympics landed within a sector bounded by the arc in part (a). What is the area of this sector?

c. 9.2H A corn maize design has an outer path in the shape of a circle with 29 foot long spokes to the center of the circle. Two spokes intersect the outer path 48 feet apart, approximate the angle measure, to the nearest degree between the spokes.

Find Arc Length and area of a sector

Trigonometric

Functions of Any Angle

9.3 HSFTF.A.2 9.3A Evaluate six trig functions, given a point

9.3A

Evaluate trigonometric functions of any angle. Find and use reference angles to



9.3B Use the unit circle to evaluate the 6 trig functions of theta (not given the unit circle) 9.3C Sketch the angle then find its reference angle 9.3D Use a reference angle to evaluate the function WITHOUT A CALCULATOR

9.3B θ = 2

π 9.3C 100 °

9.3D sec 135 °

evaluate trigonometric functions.

Graphing Sine and Cosine Functions

9.4 HSFIF.C.7e HSFBF.B.3

9.4A Determine whether a graph is periodic, if so state the period 9.4B Given a graph, state the period and amplitude 9.4C Given a sin or cos equation state the period and amplitude 9.4D Given the period and amplitude, give the function 9.4E Describe the transformation of the sin or cos function

9.4A 9.4B

9.4C g(x) = 3 sin 2x 9.4D amplitude: 10 period: 5 9.4E f(x) = 2 cos (x )π + 1

Explore characteristics of sine and cosine functions. Stretch, shrink, translate and reflect graphs of sine and cosine functions.

Sample Spaces and Probability

10.1 HSSCP.A.1

10.1A Find sample space 10.1B Find Theoretical probabilities

10.1A You flip a coin and draw a marble at random from a bag containing two purple marbles and one white marble. 10.1B What is the probability of rolling snake eyes?

Find sample spaces. Find theoretical and experimental probabilities.



10.1C Find Experimental probabilities 10.1D Find the geometric probability 10.1E Given a table, find the experimental probability and theoretical 10.1F SAT, real life application 10.1G Tell if events are unlikely or likely,

10.1C Each section of a spinner has the same area. The spinner was spun 20 times. The table shows the results. What was the experimental probability of landing on green?

10.1D You throw a dart at the board show, Your dart is equally likely to hit any point inside the square board. What is the probability your dart lands in the yellow region?

10.1E A bag contains 5 marbles that are each a different color A marble is drawn, its color is recorde, and then the marble is place back in the bag. This process is repeated until 30 marbles have been drawn. Th table shows the results. For which marble is the experimental probability of drawing the marble the same as the theoretical probability?

10.1G Refer to the chart. Order the following events from least likely to most likely.



10.1H Given experimental data, make a prediction (defects)

a. It rains on Sunday. b. It does not rain on Saturday c. It rains on Monday d. It does not rain on Friday

10.1H A manufacturer tests 1,200 computers and finds that 9 of them have defects. Find the probability that a computer chosen at random has a defect. Predict the number of computers with defects in a shipment of 15,000 computers. Explain your reasoning.

Independent and Dependent Events

10.2 HSSCP.A.1 HSSCP.A.2 HSSCP.A.3 HSSCP.A.5 HSSCP.B.6 HSSCP.B.8

10.2A Determine whether events are independent or dependent 10.2B Determine whether the events are independent 10.2C Find probabilities of independent events 10.2D Find probabilities of dependent events 10.2E Use a table to find conditional probabilities 10.2F Find the missing Probability using the formula

10.2A You roll a six sided die and flip a coin 10.2B You have one red apple and three green apples in a bowl. You randomly select one apple to eat now and another apple for your lunch. 10.2C Two cards are drawn from a deck of 52. (10.2A) Determine whether the events are independent or dependent. Find the probability. a. (10.2C) selecting two hearts when the first card is replaced. b. (10.2D) selecting two hearts when the first card is not replaced . 10.2E. The table shows the number of male and female college students who played collegiate basketball and collegiate soccer in the United States in a recent year. Express your answer as a percent

10.2F Events A and B are independent. P( A ) = .5, P( A and B ) = .125, Find P( B ).

Determine whether events are independent events. Find probabilities of independent and dependent events. Find conditional probabilities.

TwoWay Tables and Probability

10.3 HSSCP.A.4 HSSCP.A.5

10.3A Complete the two way table

10.3A

Make twoway tables. Find relative and conditional relative frequencies. Use conditional relative frequencies to find conditional probabilities.



10.3B Make a two way table 10.3C Use a twoway table to create a twoway table that shows the joint and marginal relative frequencies 10.4D Find relative and conditional relative frequencies

10.3B In a survey, 112 people feel that the amount of fresh water allowed to empty into the salt water river should be reduced, and 87 people did not feel that the amount of fresh water allowed to empty into the salt water river should be reduced. Of those who feel that the amount of fresh water released should be reduced, 98 people fish the salt water river. Of those that do not feel that the amount of fresh water released should be reduced, 12 people fish the salt water river. Organize these results in a twoway table. Then find and interpret the marginal frequencies. 10.3B and 10.3C b. Make a twoway table that shows the joint and marginal relative frequencies. 10.3D c. Make a twoway table that shows the conditional relative frequencies for each fish category.

Probability of Disjoint and Overlapping

Events

10.4 HSSCP.A.1 HSSCP.B.7

10.4A Find the probability of disjoint events (mutually exclusive) 10.4B Find the probability of overlapping events (mutually inclusive) 10.4C Use the formula to find the missing probability 10.4D Using the formula to find the P(A and B)

10.4A A group of students is donating blood during a blood drive. A student has a 9/20 probability of having type O blood and a ⅖ probability of having type A blood. Explain why the events “type O” and “type A” blood are mutually exclusive / disjoint. What is the probability that a student has type O or type A blood? 10.4B A card is drawn from a deck of 52. Find the probability of drawing a king or a heart 10.4C P( A ) = 0.25, P(B) = .75, and P(A or B) = 0.8, Find P( A and B ). 10.4D Out of 120 student parents, 90 of them can chaperone the Homecoming dance or the Prom. There are 40 parents who can chaperone the Homecoming dance and 65 parents who can chaperone the Prom. What is the probability that a randomly selected parent can chaperone both the Homecoming dance

Find probabilities of compound events. Use more than one probability rule to solve reallife problems.



and the Prom?

Permutations and

Combinations

10.5 HSAAPR.C.5 HSSCP.B.9

10.5A Use the fundamental counting principle 10.5B Evaluate the Combination or permutation expression 10.5C Calculate combinations and permutations real life applications

10.5A A password for a site consists of 4 digits followed by 2 letters. The letters A and Z are not used, and each digit or letter many be used more than once. How many unique passwords are possible? 10.5B 6 P 3 10.5C The three best essays in a contest will receive gold, silver, and bronze stars. There are 10 essays. In how many ways can the prizes be awarded?

Find Combinations and Permutations

Measures of Central

Tendencies

11.1 HSSID.A.3

11.1A Find Measures of Central Tendencies 11.1B Calculate weighted averages 11.1C Find Expected Value

11.1A Find the mean, median, and mode of the data.Deer at a feeder each hour: 3, 0, 2, 0, 1, 2, 4, 3, 3, 3 11.1B Suppose there are 10 people in an elevator, 3 men and 7 women. The average weight of the men is 210, and the average weight of the women is 130. What is the average weight for all 10 people? 11.1C For 20 days in a row, a basketball player shoots three free throws at the end of practice and decides to record his / her results. The probability distribution of successful free throws for the player’s practice set is given below. Find the expected value for the set data.

Mean, Median Mode, weighted

averages, expected value

Box and Whisker Plots and Standard Deviation

11.2 HSSID.A.1 HSSID.A.3

11.2A Make a box and whisker plot and answer questions about it 11.2B Find IQR 11.2C Find Standard Deviation and understand what it means 11.2D Calculate an outlier

11.2A and 11.2AB Make a boxandwhisker plot of the data. Find the interquartile range.

{6, 8, 7, 5, 10, 6, 9, 8, 4} 11.2C and 11.2D In some of the baseball games during the 20032004 American League Season, the New York Yankees scored the following numbers of runs against the Boston Red Sox: 2, 6, 4, 2, 4,

Box and Whisker Plots and Standard

Deviation



6, 6, 10, 3, 19, 4, 4, 2, 3. Find the mean and standard deviation. Identify if there are any outliers

course framework hudsonville high school...6.4a y = log x 6.4b y = 3log(x 2) +5 6.4c f(x) = e x...

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