Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Name _________________________________________________________________ ALGEBRA REVIEW PACKET DAY 1 1) Solve the equation 3x2 + x = 2 algebraically for x. 2) On the set of axes below, solve the following system of inequalities graphically. State the coordinates of a point in the solution set. 3) Given the graph of the function on the right: a) On what interval(s) is the function increasing? ________________________ b) On what interval(s) is the function decreasing? ________________________ page 1 x 2 ,3 x 2 4) Graph the following function on the set of axes below. f ( x) 6,2 x 7 5) Which of the following has the largest maximum? 1) 3) 2) y (2 x)(7 x) 4) y 4 x 2 10 x 1 page 2 6) The data table below shows water temperatures at various depths in an ocean. What is the value of the linear correlation coefficient for these data? Round your answer to the nearest thousandth. Explain what the correlation coefficient suggests in the context of this problem. The state the equation of the regression line (line of best fit) 7) Given M = 4x2 – 7x + 5 and N = -5x2 + 3x – 2, find, in simplest form: a) M + N b) M – N 8) Christine is hiring a photographer for her wedding. She narrowed her choices down to two companies. Pretty Pictures charges a flat rate of $80 per hour, which can be represented by P(x) = 80x, where x represents the number of hours of the event. Fabulous Photos charges $50 per hour plus a $300 equipment fee, which can be represented by F(x) = 50x + 300, where x represents the number of hours of the event. Determine, algebraically, the number of hours, x, that will make both photographers cost the same. Verify you algebraic solution using your graphing calculator. Explain what you would look for using your graphing calculator. page 3 9) Fifteen students were surveyed to find out how many songs they downloaded on their iPhones. The results are as follows: 120, 124, 132, 145, 200, 255, 260, 292, 308, 314, 342, 407, 421, 435, 452 Using an appropriate scale, construct a box plot for the 15 values. Then find the Range and the Inter-quartile Range 10) On the given axes, graph f ( x) 2 x . If g(x) = f(x) + 5, how is the graph of translated to form the graph of ? If h(x) = f(x + 1), how is the graph of translated to form the graph of ? page 4 11) Which function has the same y-intercept as the given graph? 1) y 8 6x 4 2) 5y x 20 3) 16 4 y 3x 4) y 4 x 12) Jennifer deposited $600 in an account in the Monopoly Bank, earning 5.7% interest, compounded annually. She made no deposits or withdrawals. Write an equation that can be used to find B, her account balance after t years. 13) Use the data below to write the linear regression equation for the raw test score based on the hours tutored. Round all values to the nearest hundredth. a) Equation: ____________________________________ b) Create a residual plot on the given axes, using the residual scores in the table. c) Based on the residual plot, state whether the equation is a good fit for the data. Justify your answer. page 5 14) The accompanying graph shows the heart rate, in beats per minute, of a jogger during a 4-minute interval. What is the domain and range of the function? 15) Determine if the following statements are always true, sometimes true, or never true: a) The sum of two integers is an integer. b) The sum of two irrational numbers is rational. c) The product of two irrational numbers is irrational. d) The product of two rational numbers is irrational. ___________________________ ___________________________ ___________________________ ___________________________ 16) Is the point (5,30) on the graph represented by y = x2 + 2x – 5? Explain how you know. 17) Tim has two less quarters than dimes in his wallet, for a total of $3.00. Write and solve an equation to determine how many dimes and how many quarters Tim has. page 6 18) The formula for the area of a semi-circle is A 1 2 r . 2 What is r, in terms of A and π? 19) What is the product of (7x – 1) and (3x – 4), expressed in simplest form? 20) Write a quadratic equation, in simplest standard form, that has roots of and 3. 21) What is a formula for the nth term of sequence B shown below? 1) 3) 2) 4) page 7 Name _________________________________________________________________ ALGEBRA REVIEW PACKET DAY 2 22) The diagrams below represent the first three terms of a sequence. Assuming the pattern continues, which formula determines 23) If 1) 3) 2) 4) and 1) 2)21 , the number of shaded squares in the nth term? , then 3) 11 4) 43 24) What is the value of x in the equation ? page 8 25) A gym charges a one-time initial fee and a monthly membership charge. The total cost is modeled by the function y = 30 + 19.99x. Which statement represents the meaning of each part of the function? 1) y is the total cost, x is the number of months of membership, $30 is the initial fee, and $19.99 is the membership charge per month. 2) y is the total cost, x is the number of months of membership, $19.99 is the initial fee, and $30 is the membership charge per month. 3) x is the total cost, y is the number of months of membership, $30 is the initial fee, and $19.99 is the membership charge per month. 4) x is the total cost, y is the number of months of membership, $19.99 is the initial fee, and $30 is the membership charge per month. 26) Factor Completely: x 4 x 2 12 27) What are the zeros of the function f(x) = (x – 3)2 – 36? page 9 28) Given the following tables, determine if they represent linear, quadratic, or exponential functions. Explain your choices. a) b) c) 29) The owner of a men's clothing store bought six belts and eight hats for $140. A week later, at the same prices, he bought nine belts and 6 hats for $132. Write a system of equations that can be used to find the price of one belt and one hat. Using these equations, determine and state the price of one belt and one hat. 30) A student was given the equation x2 + 12x = –22 to solve by completing the square. The step in the student’s process was x2 + 12x + c = –22 + c. State the value of c that creates a perfect square trinomial. Explain how the value of c is determined. page 10 31) Solve the inequality below to determine and state the smallest possible value for x in the solution set. 3(x + 3) < 5x – 3 32) Solve the equation 4x2 + 8x – 5 = 0 algebraically for x. 33) A local business was looking for a cleaning service to work on their property. They narrowed their choices down to two companies. Molly Maids company charges a flat rate of $100 per hour. Sparkly Clean Company charges $80 per hour plus a $260 equipment fee. a) Write an equation, M(x), that represents the total cost of hiring Molly Maids for x hours. Write an equation, S(x), that represents the total cost of hiring Sparkly Clean Company for x hours. b) Determine and state the number of hours that must be worked for the cost of both companies to be the same. page 11 34) Let f be the function represented by the graph below. Let g be the function such that g ( x) 1 2 x 3x 1 . 2 Determine which function has the larger maximum value. Justify your answer. 35) Frank bought hamburgers and hot dogs for a BBQ at his house. He spent $2.25 for each hamburger and $1.30 for each hot dog. Frank spent a total of $98.70 on hamburgers and hot dogs and bought a total of 54 hamburgers and hot dogs. a) Write a system of equations that can be used to find how many hot dogs and how many hamburgers Frank purchased. b) Using these equations, determine and state how many hot dogs and how many hamburgers Frank purchased for the BBQ. page 12 36) Solve the following system of inequalities graphically on the set of axes below. 3x y 1 y State the coordinates of a point in the solution set. 2 x4 3 37) The price of an Apple increases according to the equation A(x) = 6x2, where x equals the number of months. The price of a Samsung stock increases according to the equation S(x) = 8x + 8. Graph both equations on the accompanying grid and label them A(x) and S(x). page 13 37 continued State all price(s) when both stock values were the same. Explain how you determined your answer. If Robert only wants to invest in the stock for 3 months, should he invest in Apple or Samsung? Justify your answer. 38) Hailey deposited $6550 in an account in Johnson’s National Bank, earning 3.4% interest, compounded annually. She made no deposits or withdrawals. a) Write an equation that can be used to find B, her account balance after t years. b) Using the equation from part a, determine, to the nearest dollar, how much money Hailey will have in the account after 10 years. 39) Graph the following function on the set of axes below. x, x 2 f ( x) x 3, x 2 page 14 40) Is the equation change per time period? a model of exponential growth or exponential decay, and what is the rate (percent) of 1) exponential growth and 12% 2) exponential decay and 12% 3) exponential growth and 88% 4) exponential decay and 88% 41) A population that initially has 20 birds approximately doubles every 10 years. Which graph represents this population growth? 1) 2) 3) 4) 42) The box plot below represents a set of grades in a college statistics class. Which interval contains exactly 50% of the grades? 1) 63-88 2) 75-81 3) 63-95 4) 75-88 page 15