Directions: Show all of your work. Use units and labels and remember to give complete answers.

Size: px

Start display at page:

Download "Directions: Show all of your work. Use units and labels and remember to give complete answers."

Christian Nash
5 years ago
Views:

1 AMS II QTR 4 FINAL EXAM REVIEW TRIANGLES/PROBABILITY/UNIT CIRCLE/POLYNOMIALS NAME HOUR This packet will be collected on the day of your final exam. Seniors will turn it in on Friday June 1 st and Juniors will turn it in on Wednesday June 6 th, Thursday June 7 th or Friday June 8 th depending on when their final exam is. You may prepare a single 8 ½ X 11 sheet of paper with any notes, examples, rules, equations, etc. you would like to use on the Final Exam. Your note sheet will NOT be allowed on the no calculator unit circle questions. Directions: Show all of your work. Use units and labels and remember to give complete answers. TRIANGLES 1. Phil lives miles west of college and Mark lives 8 2 miles north of the college. Find the shortest distance between the friend s homes. Your answer should be exact and simplified. Include a well labeled sketch. EXPLAIN OR SHOW YOUR WORK!!!!! 2. The hypotenuse of a right isosceles triangle is 3 24 feet. Find the exact simplified perimeter. Include a well labeled sketch. EXPLAIN OR SHOW YOUR WORK!!!!!

2 3. Find the exact simplified area of the triangle below. EXPLAIN OR SHOW YOUR WORK!!!!! a) Find the smallest angle in a triangle with side lengths 14, 18 and 30. Show work and include a well labeled sketch of the situation. b) Find the area of the triangle. show work 5. Find m A. T M A 5.4 M M 6. Under what circumstances is the Law of Cosines the appropriate way to find a side length or angle measure?

3 7. The area of an equilateral triangle is 16 3 sq. km. Find the exact perimeter of the triangle. show work. 8. ABC, a = 7.02", m B = 101.8, and c = 12.75". Find the length of the third side of the triangle. show work and include a well labeled sketch. 9. Specifically when,using Law of Sines, are there two possible answers? UNIT CIRCLE This part of the final exam will be NO CALCULATOR and NO NOTES. 1. You will be given a blank unit circle on the exam but not asked or required to completely fit it out like on the unit circle quiz. You should be able to determine all degree and radian measurements, as well as, determine the coordinates of the points around the circle to answer questions related to unit circle. 2. Convert each angle measure to the other form. Show your work. a) π 10 b) 140 o

4 3. Find the exact values of the following trigonometric functions. a) cos 480 o b) sin ( 17π 6 ) c) tan (11π ) 4 d) cos ( 35π 6 ) e) sin -495o f) tan ( π 2 ) 4. Solve each of the following equations on the given interval. Make sure that you are careful to give answers in radians if the interval is given in radians. Also make sure you give all solutions in the interval. a) cos θ = 2 2 on the interval 0o < θ < 360 o (degrees) b. sin θ = 1 2 on the interval 0 < θ < 2π (radians) c. cos θ = 3 2 on the interval 0o < θ < 720 o (degrees)

5 PROBABILITY 1. In an overpopulated country, a plan to limit growth was instituted. A family can have, at most, four children; however if there are two boys born before they reach the maximum of 4 kids, a family must stop having children. The frequency table below shows 100 such families. a) Find the average number of children per family. NO. OF CHILDREN FREQUENCY IN FAMILY b) If a county has more than 2 children per family, the population will increase because the number of children will be greater than simply replacing the parents in the next generation. Will the population increase, decrease, or stay the same over time? 2. Billy and Gina are creating a simple dice game. They will each roll a tetrahedral die (4-sides) and they will subtract the smaller number from the larger number. This means that the only possible differences between the dice are 0, 1, 2 or 3. a) Billy suggests that he should win if the difference is a 0 or a 1 and Gina should win if the difference is a 2 or a 3. Assume that this suggestion becomes part of the rules. Calculate the probability of Billy winning and calculate the probability of Gina winning. Hint: Neither has a 50% chance of winning! b) Gina quickly realizes that she is losing way more often than she is winning when they play the game using Billy s suggestion. How could you alter Billy s suggestion from part a so that both players have an equal probability of winning?

6 3. A game of chance requires you to roll a 10 sided die numbered 1 through 10. If the die lands on an even number, the player win $1.50. If the die lands on an odd number, the player win $4. a) What is the fair price to charge if you are running the game? b) Explain why you would or wouldn t charge the fair price if you were running the game? 4. A newly proposed scratch off lottery ticket costs $2. You can win the jackpot of $10000 or smaller prizes of $1000, $250, $25, $10, $2 or nothing (lose your $2). You work for the state lottery and are responsible for checking to ensure the lottery makes certain profits on new games. The table below shows the probability of winning each prize and has taken the cost of the ticket into consideration. Profit (in dollars) Probability 1/1000 5/ / / / / /1000 a) Calculate the expected value (theoretical average) of a single lottery ticket. b) Based on your answer to part a, would you accept this new game or not? Explain your reasoning. Remember that you are responsible for ensuring the lottery makes a profit!!! 5. You are picking a single Starburst candy from a bag of original flavors (orange, yellow, red, pink candies) containing 100 candies. You can assume that there is the same number of each colored candy in the bag. a) What is the probability of choosing a yellow candy (the best flavor by the way)? b) What is the probability of NOT choosing a yellow candy?

7 c) Suppose you choose and eat a candy, then a second, then a third. Calculate: P(yellow, orange, yellow). Give answer as a reduced fraction. Recall that this notation means that you are selecting a yellow candy first, followed by an orange candy, followed by another yellow candy. 6. Suppose that you roll a pair of 6-sided dice and find the sum. Let event A be rolling a 3 on exactly one of the dice and event B be rolling a sum of eight. What is P(A B)? 7. Taylor High School surveyed its juniors and seniors about their experiences at school. One question asked if the student had been challenged to do his or her best work during that school year. The results are in the table at right. Suppose you randomly pick one of the students in order to gather follow-up information. Find each probability. Challenged to Not Challenged Total Do Best Work to Do Best Work Junior Senior Total a) P(student is a junior) b) P(student is a junior OR student was challenged to do best work) c) P(student is a junior AND was challenged to do best work) d) P(student is a junior student was challenged to do best work) e) Use one of the three formulas available to decide whether or not being a junior and being challenged to do his/her best work are independent events. 8. Explain what it means when two events are mutually exclusive.

8 POLYNOMIALS 1. Consider the functions f(x) = 2x 3 + 8x 2 + 3x 2 and g(x) = x 4 8x x a) Identify the degree of each function. b) Without graphing the functions, explain what the end behavior or each function looks like. c) Use your graphing calculator to estimate the coordinates of local maximum/minimum points of each function. d) Use your graphing calculator to estimate the coordinates of the zeroes for each function. 2. Consider the functions p(x) = 2x 2 + 4x + 1, q(x) = x 3 + 2x 2 + 3x + 7, r(x) = x 3 6x 2 8 and s(x) = x x. Write each of the following functions in standard form. a) p(x) + r(x) s(x) b) q(x) s(x) + p(x) 3. Factor each of the following polynomials into a product of linear factors. a) 4x 2 20x 96 b) x 3 8x x c) (x 2 16)(x 2 2x + 1) 4. Use the factored form of each polynomial in #3 to determine the x-intercepts.

9 5. A cubic polynomial d(x) has zeroes at 7, 3, and -2. a) Write the factored form for d(x). b) Expand d(x) into standard polynomial form. c) The graph of d(x) is supposed to have the end behavior on the right side heading towards infinity. What will the end behavior of the left side be? Is the polynomial you wrote in parts a and b correctly based on the end behavior? 6. The quartic polynomial w(x) = 1(x 2 6x + 9)(x x + 36). a) Factor the polynomial into a product of linear factors. b) Since the two x-intercepts both repeat, what will the graph of the polynomial look like? (end behavior, number of local minimums/maximums, interaction with the x-axis) 7. Rational numbers can be written as a fraction using only integers. The decimal form of a rational number is either a terminating or a repeating decimal. Some examples of rational numbers are 2, , 12 and 0. If a real number is not rational, it is irrational. Two examples of irrational 3 numbers that you are familiar with are 2 and π. Consider the following numbers e a) Which of the listed numbers are integers? π π 25 4 ( 5) 2 b) Which of the listed numbers are rational numbers? c) Which of the listed numbers are irrational numbers?

10 8. Consider the quadratic expression x 2 2x 5. a) Write the expression in equivalent vertex form. b) Find the coordinates of the vertex point and of the y-intercept. c) Determine the location of the x-intercepts. 9. Solve each of the following quadratic equations. a) 12 = 5(x 1) 2 33 b) 3x 2 = x c) 4x 2 + x = 0

6. a) Determine the probability distribution. b) Determine the expected sum of two dice. c) Repeat parts a) and b) for the sum of

6. a) Determine the probability distribution. b) Determine the expected sum of two dice. c) Repeat parts a) and b) for the sum of d) generating a random number between 1 and 20 with a calculator e) guessing a person s age f) cutting a card from a well-shuffled deck g) rolling a number with two dice 3. Given the following probability