University:
College Entrance Preparation
Course:
ACT Preparation (Mathematics)
Academic year:

2019
Views:

113

Pages:

14
Author:

Quintin Ware

H. Algebra 2 Honors Alg 2 Second Semester Final Review Name: Date: Hour: 12.1 Arithmetic Sequences Write an explicit rule and a recursive rule for each sequence. 1. | n | 1 | 2 | 3 | 4 | 5 | |---|---|---|---|---|---| | f(n) | 8 | 12 | 16 | 20 | 24 | Recursive: f(1) = 8, f(n) = f(n-1) + 4 Explicit: f(n) = 8 + 4(n-1) 2. | n | 1 | 2 | 3 | 4 | 5 | |---|---|---|---|---|---| | f(n) | 11 | 7 | 3 | -1 | -5 | Recursive: f(1) = 11, f(n) = f(n-1) - 4 Explicit: f(n) = 11 - 4(n-1) Solve 3. The explicit rule for an arithmetic sequence is f(n) = -13 + 6(n-1). Find the first four terms of the sequence. -13, -7, -1, 5 4. A recursive rule for an arithmetic sequence is f(1) = 7, f(n) = f(n-1) - 4 for n ≥ 2. Write an explicit rule for this sequence. f(n) = 7 - 4(n-1) 12.2 Geometric Sequences Each rule represents a geometric sequence. If the given rule is recursive, write it as an explicit rule. If the rule is explicit, write it as a recursive rule. Assume that f(1) is the first term of the sequence. 1. f(n) = 11 * 2^(n-1) for n ≥ 1 f(1) = 11, f(n) = 2 * f(n-1) for n ≥ 2 2. f(1) = 2.5; f(n) = -2 * f(n-1) for n ≥ 2 f(n) = 2.5 * (-2)^(n-1) 12.3 Geometric Series Determine the values of a, n, and r for each geometric series. Then use the summation formula to find the sum. 1. 1 + 6 + 36 + 216 + 1296 a = 1, r = 6, n = 5 S(n) = a(1-r^n) / (1-r) = 1(1-6^5) / (1-6) = 1296 2. 0 - 12 + 72 - 432 a = 0, r = -6, n = 4 S(n) = 0(1-(-6)^4) / (1-(-6)) = 0 3. Determine the number of terms in each geometric series. Then evaluate the sum. 3 + 15 + 75 + ... + 148,875 a = 3, r = 5 58593 4. 2 - 6 + 18 - ... + 1458 a = 2, r = -3, n = 7 1094 5. A geometric series has 9 terms, starts with -2, and has a common ratio of -4. S(9) = -2(1-(-4)^9) / (1-(-4)) = -109,858 13.1 Exponential Growth Functions 1. Given the function g(x) = ½(2)^(x+3) + 3 complete the following: a) Tell the transformations that have been applied to the graph of f(x) = 2^x to produce the graph of g(x). - Vertical shrink by a factor of 1/2 - Horizontal shift left 3 units - Vertical shift up 3 units b) Identify the asymptote, reference point, and at least two other points to graph the function. - Asymptote: y = 3 - Reference point: (0, 1) -> (-3, 3.5) - Other points: (-2, 4), (-1, 5) c) Give the domain and range in set notation. Domain: (-∞, ∞) Range: (3, ∞) d) Describe end behavior. As x -> -∞, y -> 3 As x -> ∞, y -> ∞ 2. The annual sales for a fast food restaurant are $650,000 and are increasing at a rate of 4% per year. a) Write the function f(t) that expresses the annual sales after t years. f(t) = 650,000(1.04)^t b) Find the annual sales after 5 years. f(5) = 650,000(1.04)^5 ≈ 790,824.39 13.2 Exponential Decay Functions 1. Given the function g(x) = -2(⅓)^(x+1) - 2 complete the following: a) Tell the transformations that have been applied to the graph of f(x) = (⅓)^x to produce the graph of g(x). - Flip over the x-axis - Vertical stretch by a factor of 2 - Horizontal shift left 1 unit - Vertical shift down 2 units b) Identify the asymptote, reference point, and at least two other points to graph the function. - Asymptote: y = -2 - Reference point: (0, 1) -> (-1, -4) - Other points: (-2, -8), (0, -2 ⅔) c) Give the domain and range in set notation. Domain: (-∞, ∞) Range: (-∞, -2) d) Describe end behavior. As x -> -∞, y -> -∞ As x -> ∞, y -> -2 2. The value of a company’s equipment is $25,000 and decreases at a rate of 15% per year. a) Write the function, f(t), that expresses the value of the equipment after t years. f(t) = 25,000(1 - 0.15)^t b) Find the value of the equipment in year eight. f(8) = 25,000(0.85)^8 ≈ 6,812.21 20.2 & 20.3 Independent and Dependent Events 1. Isabelle believes that right- and left-footed soccer players are equally likely to score goals. She collected data from 260 players from a local soccer league. Using the following two-way frequency table, show that being right-footed and scoring goals are independent events. | | Right-Footed | Left-Footed | Total | |---|---|---|---| | Has scored a goal | 13 | 52 | 65 | | Has not scored a goal | 195 | 90 | 285 | | Total | 208 | 142 | 260 | 2. Jim has 2 blue, 2 green, and 2 black socks in his drawer. He picks out 2 socks, one after the other. Determine the probability of him getting a matching pair of blue socks. Are these events Independent or Dependent? P(blue, blue) = 2/6 * 1/5 = 1/15 Dependent 3. A farmer wants to know if a particular fertilizer can cause blackberry shrubs to produce fruit early. Using the following two-way table, compute the probability of a plant producing fruit early without receiving fertilizer. | | Early Fruit | No Fruit | Total | |---|---|---|---| | Received Fertilizer | 37 | 3 | 40 | | Did not receive Fertilizer | 19 | 21 | 40 | | Total | 56 | 24 | 80 | P(Early Fruit | No Fertilizer) = 19/40 4. Are the events independent? Choose Yes or No for each situation. A. Picking a penny and a marble out of a jar of pennies and a jar of marbles. Yes No B. Drawing cards from a deck to form a 4-card hand. Yes No C. Choosing a color for a new shirt from a choice of red, yellow, or purple. Yes No 22.1 Data Gathering Techniques 1. The owner of a bakery wants to know whether customers like a new type of cake that is sold. Identify whether each sampling method is random, self-selected, convenience, systematic, stratified, or cluster. a) When the bakery isn't busy, ask all the customers who buy the cake what they think of it. Convenience b) Ask the opinion of every 5th customer who buys the cake. Systematic c) Give customers who buy the cake a survey form to fill out and mail in. Self-select 2. A teacher wants to know whether students in the class think a test was fair. Identify whether each sampling method is random, self-selected, convenience, systematic, stratified, or cluster. Then state whether the sampling method is likely to be representative of the population or biased.