Survey

* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project

Survey

Document related concepts

Structure (mathematical logic) wikipedia , lookup

Automatic differentiation wikipedia , lookup

Quadratic equation wikipedia , lookup

System of linear equations wikipedia , lookup

Corecursion wikipedia , lookup

Signal-flow graph wikipedia , lookup

History of algebra wikipedia , lookup

Transcript

Take Home Review Packet Algebra 2 Midterm 2014-2015 Chapter 1 Recursive Formulas 1. State whether each recursive formula defines a sequence that is arithmetic, geometric, shifted geometric, or none of these. State whether a graph of the sequence would be linear or curved. Then list the first five terms of the sequence. a. a0 = 13 b. u0 = 125 an = an-1 – 9 un = (1-0.20)un-1 2. Ted just bought a new car for $17,500. Suppose the value of the car decreases by 18% each year. a. Write a recursive formula for calculating the value of the car after n years. b. What will be the value of the car after 5 years? c. After how many years will the car be worth less than $5,000? 3. Rashid is conducting a biology study involving fruit flies. This table shows the number of fruit flies in his sample at the end of each day for a week. Day 1 2 3 4 5 6 7 Number of flies 40 46 54 62 72 81 94 a. Find a recursive formula to model the population growth. b. Predict the number of flies in his sample at the end of 3 weeks. c. According to your model, when will the number of fruit flies first exceed 100,000? Chapter 3 Linear Equations and Systems 1. Consider the arithmetic sequence –19, –12, –5, 2, 9, 16, …. a. Write a recursive formula that describes this sequence. Use u0 for the starting term. b. Write an explicit formula for this sequence. c. Determine the value of u27. d. If you were to plot the points (n, un) for this sequence and then draw a line through the points, what would be the slope and y-intercept of the line? 2. Given the recursive formula below, answer the following questions u0 = 6.3 un = un-1 + 2.5 a) Write an explicit formula for the sequence. b) Use the formula to find the value of u35. c) Use the formula to figure out the value of n when un is equal to 78. 3. Write an equation (x and y) of the line that contains the points. 4. Write an explicit formula for the recursive formulas below. a. b. 5. Write an equation for each graph below: 6. Write an equation for the line that passes through (5, –4) and is perpendicular to the graph of 5x – 2y = -6. 1 5 4 3 1 2 4 4 7. Write an equation in slope-intercept form of the line through (– , ) and ( , – ). 8. When Great Adventure first opened (year 0) there were 13 zebras. Year # of Zebras 1 17 2 25 a. Create a scatter plot and draw a line of best fit. b. Find the equation to your line of best fit. c. What is the real-world meaning of the slope? d. What is the real-world meaning of the y-intercept? e. On the safari’s 10th birthday approximately how many zebras will there be? 3 20 4 26 9. For Questions a and b, use the set of data in the table. The table below shows the relationship between distance traveled and elapsed time. Distance d (km) 40 75 110 150 160 Time t (min) 30 60 80 110 150 a. Draw a scatter plot for the data. b. Use two ordered pairs to write a prediction equation. Then use your prediction equation to predict the time for a distance of 160 kilometers. Compare your prediction to the one given in the table. 10. Draw a line of fit for each plot below. Then write the equation of your line. Assume the scale of the graph is 1 unit. a. b. 11. Solve each system of equations using any method. a) 4x + 3y = 7 b) 2x – y = 8 c) 4x – 3y = 5 6x – 4y = -7 d) -x + 6y = 11 e) 3x – 4y = 7 2x – 2y = 5 5x + 2y = 12 y = 5 + 2x x – 3y = -30 f) 5x – 4y = 5 2x + 10y = 2 g) 2m = 5 – n h) 6m + 3n = 15 i. 1 3 1 2 k. 1 2 y = −2 1 2 3 y–x=6 a+b+ =0 3 4 l. 2 3 x– 4 5 -3x – 3y = -15 j. x– 1 2 1 4 5 y=1 5 2a = 4 – 2 b m. 3y = 1 – x 0.2 c + 1.5 d = –2.7 1.2 c – 0.5 d = 2.8 1 2 1 x+3y=1 x + 4y = –1 9 x–3y=–4 Chapter 4 Functions and Transformations 1. Write the equation of the graphed function. a. b. c. d. e. f. g. h. i. 2. Make a graph to match the description. Label your axes. Does this represent a function? Why or why not? A restaurant decides to have a special day each week where beverages will be served at a discount! For the first two hours that the restaurant is open, the drinks will cost just $0.25. Every half hour, the drinks will increase in price by $0.50. 3. Tell whether each relation is a function. a. b. c. y = 3x – 1 4. Suppose f(x) = x2 – 5 and g ( x) x 1 . a. Find f(g(–2)) and g(f(–2)) b. Find f(g(x)) and g(f(x)). 5. Let f(x) = -2x + 7, g(x) = x2 – 2, and h(x) = (x + 1)2 Find: a. f(g(3)) e. g(f(a)) b. g(h(-2)) f. h(f(a)) c. h(f(-1)) d. f(g(a)) 6. Solve for y. a. 2x – 3y = 6 b. (y + 1)2 – 3 = x c. 1 y2 2 x 7. Solve for x. 2 a. 4 x 2 10 8. The graph of y = f(x) is shown here. a. Find f(–3). b. Find all x for which f(x) = 3. c. Graph y = f(x + 2) – 3 x 5 b. 3 x3 4 c. 2 Partial Chapter 5 – Exponents and Radicals 1. Milo invested some money in an account that earned a fixed-percent interest compounded annually. After 4 years, his investment was worth $4,254.27. After 6 years, it was worth $4,690.33. a. What is the annual interest rate for Milo’s investment? b. How much did Milo initially invest? c. How many years will it take for the value of Milo’s investment to triple? 2. Given the equation for the exponential curve as f(x) = 125(0.6)x. a. Find the y-intercept and ratio for the curve. b. Find another point on the curve and use it to write an equation in point-ratio form. c. Use algebra to show that the two equations (the original and the one from part b) are equivalent. Give a reason for each step. 3. Austin deposits $5,000 into an account that pays 3.5% annual interest. a. Write and solve an equation for the amount of money Austin will have in his account after 5 years and 3 months if he doesn’t deposit any more money. b. When will Austin’s bank account be worth double what he started with if he doesn’t deposit any more money and the interest rate stays the same? (Give your answer to the nearest month.) 4.. Rewrite each expression in the form axn or xn. a) 4x6●2x6 6x5 d) b) 3 (-5x3)●(-2x4) 20x7 e) 3x g) c) -2 72x7 6x f) x-4 4x x6 ● x 6 h) (3x2)-3 x-4● x7 i) x6 x3 5. Rewrite each expression as a fraction without exponents or as an integer. a) 5-3 b) -3-4 b) (5/3)x = 27/125 c) (-12)-2 d) (3/4)-2 6. Solve. a) 3x = 1/9 x d) 25) 10 =5 √b8 = 14.3 c) (1/3)x = 243 e) 2x2/3 = 32 f) 6 26) 1 27) (5√d)7 = 23 /√c = 0.55 √a = 4.2 7. Match all expressions that are equivalent. a) 5 √x2 b) x2.5 c) 3 d) x5/2 e) x0.4 f) (1/x)-3 g) (√x)5 h) x3 i) x1/3 j) x2/5 √x 8. Write an exponential function whose graph passes through (0, –0.3) and (2, –10.8). 9. Solve 24𝑥 ⋅ 321 − 𝑥 = 8𝑥 + 2. 10. ECONOMICS The Jones Corporation found that its annual profit could be modeled by the exponential equation y = 10(0.99)𝑡 , while the Davis Company’s annual profit is modeled by y = 8(1.01)𝑡 . For both equations, profit is given in millions of dollars, and t is the number of years since 1990. a. Find each company’s annual profit for the years between 1990 and 2000 to the nearest dollar. b. In which company would you prefer to own stock? Explain your reasoning. c. Indicate how a comparison of the two profit equations would support your decision