INTEGRATED 3 Final Exam 2012 Topic List:A. Reasoning Unit 1:

a) Know how to use the conditional to make the converse, inverse, and contrapositive b) Know the 3 characteristics of a well designed experiment - Random Assignment / Sufficient number of subjects / Control Groupc) Identify the treatment and response variable in a studyd) Determine if a study is subject blind, evaluator blind, or double blinde) Identify the placebo effect and if a lurking variable existsf) Determine if the result of the difference of two means is statistically significant – meaning does it fall in the outer 2.5% of the data

B. Similar and Congruent triangles Unit 3: a) Know the triangle shortcuts for similarity ~ ( AA, SAS, SSS)b) Know how to find the scale factor after you know 2 triangles are similarc) Know how to use the scale factor in order to find the lengths of missing sidesd) Use similar triangles to find geometric concepts (area, perimeter)e) Know how to use law of sines and cosines to solve for sides or angles of trianglesf) Know the triangle congruence shortcuts (ASA, SSS, SAS, AAS, HL)g) Know how to prove 2 triangles are congruent.h) Use definitions of midpoint, and properties of parallel lines cut by a transversal to prove triangles are congruent.i) Properties of quadrilaterals

C. Properties of circles Unit 6:a) Know how to use chords and Pythagorean theorem to find lengths inside the circleb) Know properties of tangent lines and angles formed when tangent lines meet the radiusc) Know properties of central angles, inscribed angles and intercepted arcsd) Know how to write the equation of a circle

D. Trigonometry with calculator accessa) Know how to find coterminal angles in radians and degreesb) Know how to find the compliment and supplement in radians and degrees

Trigonometry without calculator accessc) Know how to find a trig ratio (exact value) given an angle in radians and in degreesd) Know how to solve for an angle in radians and degrees when given a trig ratio (exact value)e) Know how to graph sine and cosinef) Know what the amplitude does to the sine and cosine function ex. Y=4sinxg) Know what a vertical shift does to the sine and cosine function ex. Y=Sinx +1

E. Statistics Unit 4:a) Know how to graph a normal curve and label with the mean and standard deviation; label the approximate percentages with the Empirical ruleb) Know how to find the z score given a value, standard deviation and meanc) Know how to use the z score to find the percentiled) Know how to determine if a situation is binomiale) Know how to determine if a binomial distribution is approximately normalf) Know how to use the normalcdf function on the calculator to determine the proportion below a given scoreg)Know how to use the invnorm function on the calculator to determine the score given a percentile

h) Know how to find the expected number of successesi) Know how to use the binomial probability formula, and the binomial PDF in the calculatorj) Know how to do the binomial formula by hand to find a cumulative distribution probability and how to compute with the binomialCDF programk) Know how to calculate mean and standard deviation in a binomial distribution

F. Recursion Unit 7:a) Write a Now-Next rule or recursive notation to model population, balances, or interest

FINAL EXAM REVIEWA Unit 1 ReasoningA1. Consider the true statement “People taller than 4ft 6 in are allowed to ride Expedition Everest at Disney World.”

a. Write an if-then statement

a. Identify the hypothesis of the sentence above.

b. Identify the conclusion of the sentence above.

c. Write the converse of the if-then sentence.

d. Write the inverse of the if-then sentence.

e. Write the contrapositive of the if-then sentence.

A2. In each section determine if the information allows you to conclude that a ll b and tell why.

A3. In the diagram below a ll b and m<4 + m<15 = 180. Prove that m<1 + m<11 = 180

A4. Janna wanted to determine whether 11th graders did better when they took a math test in silence or when Mozart was being played. Twenty six students were randomly divided into the two treatment groups. Students were given the test and their scores were recorded.

a. What are the treatments for this experiment?

b. Is this experiment subject blind? Explain your reasoning.

c. Explain how to make the study evaluator blind.

A5. Kayla conducted a study of how the color of water affects its evaporation rate. She filled each of ten identical containers to a height of 6.5 inches and then placed the containers on a windowsill. She then added red food coloring to the water in five randomly chosen containers. After one week, she measured the height of the water left in each of the containers. Her measurements are given below.

a. What are the treatments for this experiment?

b. Find the value of mean height clear - mean height red.

c. The randomization distribution below provides the results of 200 random assignments. Eachvalue plotted in the histogram is mean height clear - mean height red for one run.

Use this randomization distribution to record your result from “b” mean height clear - mean height red and determine if the difference is statistically significant.

B Unit 3 TrianglesSolve for the missing sides and angles of the Triangle

B1. m<A=41o, m<C=52o and a=6

B2. a=18, b=25, c=12

B3. m<B=2o, m<C= 119o, and b=9

B4. m<A=57, a=12, and b=40

B5. m<A=135o, b=6, c=7

Similar TrianglesB6. Prove the two triangles are similar.Given: BC ║ ADProve: Δ BCE ~ Δ DAE

B7. Given: lengths marked and <C and <F are right anglesProve : Δ BCA ~ Δ EFD

B8. Prove the two triangles are similar if BE ║ CD

B9. If Δ ABE ~ Δ ACD and AB = 20, BC = 5, BE = 6. Find DC.

B10. Use new measurements AB = 14, m<EAB = 25o, and m<AEB=110o, find BE

Congruent TrianglesB11. Prove the triangles are congruent

B12.

B13.

B14. Determine if each pair of triangles are congruent, similar, or neither. If they are congruent of similar, write a congruence or similarity relation showing the correspondence between vertices and cite an appropriate congruence or similarity theorem to support your conclusion.

C. Circles Unit 6C1. Find the missing angles and arcs.

AB= ______ BC = ________ <ACB = _______ <ABC = _______ <BAC = ________

C2. In the OM, chords BR=CR and BM and MC are radii. Find the central angle, inscribed angle, and two arcs.

C3. In the OP, arc AB is 160o. Find the following missing parts

C4. The length of the diameter of circle O is 26 inches. BC is a chord 10 in long. How far away from the center is the chord? Draw a diagram to help.

C5. Write the equation of a circle with the center at (5,-2) and a radius of 4

C6. If the equation of a circle is ( x+4 )2+ ( x−5 )2=144 what is the center and radius?

QuadrilateralsC7. List the quadrilaterals that have the following properties. Choose from parallelogram, rectangle, rhombus, square, trapezoid, isosceles trapezoid, kite

a. Diagonals are perpendicularb Both pair of opposite angles are equalc. Diagonal bisect opposite anglesd. All sides are equale. All angles are equalf. Regular quadrilateralg. Diagonals are congruent

D. Trigonometry WITH CALCULATORFor the following angles give a) 2 coterminal angles 1 positive and 1 negative and b) the complement and supplement.

Positive coterminal Negative coterminal Complementary SupplementaryD1. 35o

D2. 87o

D3. 210o

D4. -40o

D5. 2 π3

D6. π9

D7. 5π/6

D8. π/4

Find the following trigonometric ratios WITHOUT A CALCULATOR

D9. tan 2 π3

D10. sec 210o

D11. sin 45o

D12. cos 11π

6

D13. tan π

D14. sin (-135)

D15. cot 60o

D16. cos 3 π4

Solve each trig equation for degrees [0,360o) and radians [0, 2π ¿ WITHOUT A CALCULATOR

D17. cos x = √22

D18. sin x = -1

D19. tan x = - √33

D20. csc x = 2

D21. tan x = 1

D22. cos x = - √32

D23. Graph y=sinθ ¿0¿2 π without a calculator

D24. Graph y=cosθ from 0¿2 π without a calculator

Write down the amplitude of the function and compare it to the parent.D25 D26 D27

Write the vertical shift of the function and compare it to the parent.D28 D29 D30

E. StatisticsE1. The weights of 19-day-old pigs are approximately normally distributed with a mean weight of 11.9 pounds and standard deviation of 2.7 pounds.a. Find the standardized value for a 19-day-old pig that weighs 15 pounds. Write a sentence explaining

what the standardized value means.

b. Mason has a 19-day-old pig that weighs only 7.85 pounds. What is the pig’s percentile for weight? Write a sentence explaining what the percentile means.

c. Graciela has a big 19-day-old pig. When she looks at a chart, she realizes that only 10% of 19-day-old pigs are bigger than her pig. Approximately how much does Graciela’s pig weigh?

d. Use your calculator to find the percentage of pigs weigh between 10 and 13 pounds?

e. If your pig is in the bottom 10 percentile, what is his weight? Use your calculator.

E2. Approximate the mean and standard deviation from the following histogram.

E3. As a summer job, Juliette works for the Empire Pencil Company. She runs a machine that makes pencils, which are supposed to have a mean length of 8 inches. But like all processes, the pencils do not come out exactly 8 inches long each time. The machine is supposed to be set so that the distribution of the lengths of the pencils is normal and the standard deviation of the lengths of the pencils is 0.05 inches.

a. Sketch the distribution of the lengths of pencils when the machine is under control. Mark onthe horizontal scale the mean and one, two, and three standard deviations from the mean.

b. If the machine is set correctly, what percentage of the pencils will be more than 8.1 inches long? Less than 7.85 inches long?

E4. The scores on the math section of the SAT Reasoning Test are normally distributed with a mean of 520 and standard deviation of 115. a. Taylor’s score placed her in the 90th percentile. What was Taylor’s score?

b. Use the calculator to verify the response in a. What is Taylor’s score if she scored in the 90th percentile? Write what you typed into the calc.

c. Use the calculator and determine the score of a student who scored in the top 15% of the scores. Write what you typed into the calc.

d. If a student scored a 445 on the SAT math section, what is the proportion below him? Use your calculator to find this and show a sketch and what you typed in.

e. If a student scored a 700 on the SAT math section, what is the percent that scored ABOVE him? Use your calculator to find this and show a sketch ad what you typed in.

E5. According to The Condition of Education 2007, 84.5% of the 2004 high school graduates completed at least one foreign language class. You randomly select 200 people in the United States who graduated from high school in 2004.a. How many do you expect to have completed at least one foreign language class?

b. Is the binomial distribution of the number of people in the sample who completed at least one foreign language class approximately normal?

c. What is the standard deviation of this distribution?σ=√n ∙ p ∙ (1− p )

d. Find the probability that in your sample you would have 160 or fewer people who completed at least one foreign language class. Use the binomial probabilities in your calculator to answer; show your set up!

e. Find the probability that in your sample you would have exactly 120 people who completed at least one foreign language class. Use the binomial probabilities in your calculator to answer; show your set up!

f. Find the probability that in your sample you would have more than 185 people who completed at least one foreign language class. Use the binomial probabilities in your calculator to answer; show your set up!

g. Find the probability that in your sample you would have at least 150 who completed at least one foreign language class. Use the binomial probabilities in your calculator to answer; show your set up!

h. P(155<x<190)

E6. You move to a new school in Guam that is very small with only 14 people in the graduating class. Reports say that 92% of that graduating class is successful in math. Assume the situation is binomial. Calculate the following probabilities by HAND!

P ( x=k )=(nk) pk (1−p )n−k

a. What is the probability that exactly 12 are successful?

b. What is the probability that less than 3 are successful? You can set this up by hand, but the numbers are so small, that you should use your calc. to complete this problem.

c. What is the probability that more than 12 are successful?

d. What is the probability that at least 11 are successful?

H) Recursion48. The population of fish in a lake at the end of each month can be modeled by the recursive function Pn = .92Pn-1 +1200. If P0 = 4000 and none of the conditions change from year to year.a. What is P4?

b. What will be the approximate long-term population of fish in the lake?

51. Eva has a credit card balance of $2,528. Since this balance is more than one month old, the credit card company adds an interest charge each month until it is paid in full. The annual interest rate on this balance is 21%. Suppose that Eva makes monthly payments of $200 and does not make any additional charges to this card.a. What is the monthly interest rate for this balance?

b. Write a recursive formula use NOW –NEXT rule or recursive notation that can be used to find the credit card balance at the end of each month.

c. Complete the table below indicating the balance after each of the following number of months.

d. How many months will it take her to reach a zero balance?

54. Suppose that approximately 5% of trees in a forest die each year due to weather and disease-related conditions. In a particular region of a forest, there are currently 5,000 trees. The forestry company has plans to cut down 200 trees each year.a. Write a recursive formula or now-next that represents this situation. Be sure to specify the initial value.

b. How many trees will be in this section of the forest after 5 years?

c. How many years will it be before there are fewer than 1,000 trees left in this section of the forest?

56. Suppose that James opens a savings account with an initial deposit of $2,000. The account will earn 6% interest each year, and James will deposit an additional $600 each year. Assume that James does not take any money out of the account.

a. Write a recursive formula that shows how the amount of money in the account changes from month to month. Find monthly rate first. Be sure to include an initial value.

b. How much money will be in the account after 6 months?

c. How many months will it take for James to have at least $20,000 in the account?