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1 Student: Date: Assignment: Exponential and Radical Equations 1. Perform the indicated computation. Write the answer in scientific notation = (Use the multiplication symbol in the math palette as needed.) Evaluate. 7 Simplify the following expression. 5x 3 y 5 10x 4 y 3 4 5x 3 y 5 10x 4 y 3 4 = (Use positive exponents only.) Write the expression in radical form. 1 36x 7 = (Type a simplified fraction.) 1 The radical form of 36x is. 5. Write the following expression involving radicals in exponential notation. 7 x The expression in exponential notation is. (Use integers or fractions for any numbers in the expression.) 6. Rewrite the expression with rational exponents. 6 x 7 6 x 7 =

2 7. Simplify the radical expression. 75 = 75 (Type an exact answer, using radicals as needed.). Simplify the radical expression. 5 9m m m 3 9 m5 = (Simplify your answer. Type an exact answer, using radicals as needed.) 9. Simplify the radical expression. 30 1x x 5 = (Type an exact answer, using radicals as needed.) 10. Simplify the product. 3 3 = (Type an exact answer, using radicals as needed.) 11. Simplify the product. 7x 3 175x 5 7x 3 175x 5 = (Type an exact answer, using radicals as needed.) 1. Find a root that is a real number = 13. Simplify the radical expression. 7 5n11 16n 9 7 5n11 16n 9 = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)

3 14. 3h From a viewing height of h feet, the approximate distance d to the horizon, in miles, is given by the equation d =. a) To the nearest mile, what is the distance to the horizon from a height of 90 ft? 135 ft? 10 ft? b) How does the distance to the horizon increase as the height increases? a) A person could see miles from a height of 90 feet. (Simplify your answer. Type an exact answer, using radicals as needed. Rationalize all denominators.) A person could see miles from a height of 135 feet. (Simplify your answer. Type an exact answer, using radicals as needed. Rationalize all denominators.) A person could see miles from a height of 10 feet. (Simplify your answer. Type an exact answer, using radicals as needed. Rationalize all denominators.) b) Choose the correct answer below. A. The distance to the horizon increases by progressively larger amounts for equal changes in height. B. The distance to the horizon increases by equal amounts for equal changes in height. C. The distance to the horizon increases by progressively smaller amounts for equal changes in height. D. The distance to the horizon increases by random amounts for equal changes in height.

4 Student: Date: Assignment: Exponents and Functions 1. Simplify the following expression. 5 5 = (Type an integer or a simplified fraction.). Write the expression with positive exponents only. Then simplify, if possible = (Type a fraction.) 3. Evaluate the following expression for b = 6 and g =. g 0 b 3 g 0 b 3 = (Type an integer or a simplified fraction.) 4. Rewrite the following expression using each base only once = (Type exponential notation with positive exponents. Simplify your answer.) Multiply and simplify. b b 6 Simplify the expression The answer is b b 6 =. (Type your answer as one base to a nonnegative power.) = 7. Simplify the expression. y 9 7 y 9 7 = (Type exponential notation with positive exponents. Simplify your answer.)

5 . Simplify the expression. x 4 y x 3 4 x 4 y x 3 4 = (Simplify your answer. Type exponential notation with positive exponents. Use integers or fractions for any numbers in the expression.) 9. Simplify the following expression = (Simplify your answer. Type exponential notation with positive exponents.) 10. Simplify the expression. 1 x 1 x = (Use integers or fractions for any numbers in the expression. Use positive exponents only.)

6 Student: Date: Assignment: Foundations of Algebra 1. Write an English phrase that would translate into the following mathematical expression. 4z Which of the following is equivalent to the expression 4z? A. The quotient of 4 times a number z and B. 4 times the difference of a number z and C. 4 less than the product of and a number z D. less than 4 times a number z. Express the following English phrase using an algebraic expression. The product of 13 and a number n. Represent "The product of 13 and a number n" mathematically. 3. Find the value of the expression. = 4. Evaluate. 3 3 = 5. Evaluate the expression below for x = 5 and y = 4. x + 3(x + y) When x = 5 and y = 4, x + 3(x + y) =. (Type an integer or a decimal.) 6. Evaluate = 7. Evaluate the following exponential expression. 3 3 = (Type an integer or a simplified fraction.)

7 . Evaluate the expression below for s = 5 and t = 6. 3st s For s = 5 and t = 6, 3st s =. 9. Simplify the following expression. 3[( 4) 5 ] 3[( 4) 5 ] = 10. Simplify. 100 The principal square root is. 11. Evaluate the square root = (Type an integer or a fraction.) 1. Evaluate the square root = (Type an integer or a fraction. Simplify your answer.) 13. Evaluate the square root = (Type an integer or a decimal.) 14. Estimate the square root. Round to the nearest integer (Round to the nearest integer as needed.) 15. Use the commutative and associative properties as needed to simplify the expression. (15 + a) + 14 (15 + a) + 14 =

8 Student: Date: Assignment: Linear Functions 1. Determine whether the rate of change is constant. If it is, find the rate of change and explain what it represents. Airplane Descent Time (min) Elevation (ft) 0 50,000 49, , ,600 Determine whether the rate of change is constant. Choose the correct answer below. A. No, the rate of change is not constant. 00 ft B. Yes, the rate of change is constant and it equals. 1 min 100 ft C. Yes, the rate of change is constant and it equals. 1 min 100 ft D. Yes, the rate of change is constant and it equals. 1 min Now explain what the rate of change represents. Choose the correct answer below. A. It represents the speed of the airplane. B. It represents the number of feet the airplane descends per minute. C. It represents the number of feet the airplane will be from the ground after one minute.. Find the slope of the line. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The slope of the line is. (Simplify your answer. Type an integer or a fraction.) B. The slope is undefined Using the slope formula, find the slope of the line through the given points. (4,1) and (6,7) What is the slope of the line? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The slope of the line is. (Type an integer or a simplified fraction.) B. The slope of the line is undefined.

9 4. Find the slope of the line. y 4 x (-5,-4) (,-4) - What is the slope of the line? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The slope of the line is. (Type an integer or a simplified fraction.) B. The slope of the line is undefined. 5. Without graphing, tell whether the slope of a line that models the linear relationship is positive, negative, zero, or undefined. Then find the slope. The total cost, including shipping, for ordering five uniforms is $69. The total cost, including shipping, for ordering seven unifo Choose the correct answer below. A. The slope of the relationship is negative. B. The slope of the relationship is zero. C. The slope of the relationship is positive. D. The slope of the relationship is undefined. Find the slope. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The slope is. B. The slope is undefined.

10 6. State the independent variable and the dependent variable in the linear relationship. Then find the rate of change for the situation. The cost of admission is $ 66 for six people and $ 77 for seven people. Determine the independent variable. A. six people B. the cost of admission C. seven people D. $77 E. $66 F. the number of people Determine the dependent variable. A. $77 B. six people C. the cost of admission D. seven people E. the number of people F. $66 Find the rate of change. rate of change = (Type an integer or simplified fraction.) 7. Graph the equation. y = x y Use the graphing tool to graph the line. 6 4 x Find the slope and y intercept of the graph of the equation. y = 5x + 1 Select the correct choice and fill in any answer boxes in your choice below. A. The slope is. B. The slope is undefined. Select the correct choice and fill in any answer boxes in your choice below. A. The y intercept is. B. There is no y intercept.

11 9. Find the slope and y intercept of the line whose equation is given. y = 7x + 4 Determine the slope. Select the correct choice below and fill in any answer boxes in your choice. A. m = (Type an integer or a fraction.) B. The slope is undefined. Determine the y intercept. Select the correct choice below and fill in any answer boxes in your choice. A. b = (Type an integer or a fraction.) B. There is no y intercept. 10. Determine the equation of the line. y (Type an equation. Simplify your answer. Type your answer in slope intercept form.) x

12 Student: Date: Assignment: Solving Inequalities 1. Solve the inequality. Graph and check your solutions. 15 < y 4 y (1) Choose the graph of the solution. A B C D E (1) > <. Tell what number you would subtract from each side of the inequality to solve the inequality. x + 9 < 0 Subtract from each side of the inequality.

13 3. Solve the inequality. Graph and check your solution. m 4 5 m (1) Choose the correct graph below. A B C D E (1) < > 4. Solve the inequality. Check your solutions. 4x + 9 > 5 The solution is x (1). (1) > < 5. Solve for x. 5(x 3) 6x 1 The solution is x. (Simplify your answer. Type an inequality symbol, then type an integer.)

14 6. Solve the inequality. 6 6x 0 The solution is x (1). (1) < > 7. Solve the inequality. 3(x ) + 4x 3 The solution is x (1). (1) > <. Your test scores in one class are 79 and 3. What possible scores can you earn on your next test to have a test average between 1 and 7, inclusive? Your score on the third test must be between and, inclusive. (Use ascending order.) 9. Write a compound inequality that represents the following phrase. Graph the solutions. all real numbers that are between 6 and 5, inclusive Write a compound inequality that represents the phrase. Choose the correct answer below. A. 6 < n 5 B. 6 n 5 C. 6 n < 5 D. 6 < n < 5 Graph the solutions. Choose the correct graph below. A. B C. D

15 10. Solve the inequality. Graph the solutions. 6t 3 or 4t Solve the inequality. Choose the correct answer below. A. t 6 or t B. t 6 or t C. t 5 or t 3 D. t 6 or t E. t 5 or t 3 F. t 5 or t 3 G. t 5 or t 3 H. t 6 or t Graph the solutions. Choose the correct graph below. A. B C. D E. F G. H

16 Student: Date: Assignment: Solving Linear Equations 1. Toucans and blue and yellow macaws are both tropical birds. The length of the toucan in the picture to the right is about two thirds of the length of the blue-and-yellow macaw. The toucan is about 16 in long. What is the length of the blue-and-yellow macaw? 16 in The length of the blue and yellow macaw is about in.. Solve the problem using multiplication or division. Check your answer. 5a = 0.5 a = (Type an integer or a decimal.) 3. A delivery person uses a service elevator to bring boxes of books up to an office. The delivery person weighs 170 lb and each box of books weighs 60 lb. The maximum capacity of the elevator is 140 lb. How many boxes of books can the delivery person bring up at one time? The delivery person can bring up (Type a whole number.) boxes of books. 4. Solve the equation. Check your answer. g 4 = g = 5. Solve the equation. Check your answer. 17 = 5x + x x = 6. Solve the equation. 4( 5x ) = 9 x = 7. Solve the equation. Check your answer. (r + 9) = 1 r = (Simplify your answer. Type an integer or a fraction.)

17 . Solve the equation below. Choose the method you prefer to use. Check your answer. n 7n 1 = 4 4 n = (Type an integer or a simplified fraction.) 9. Solve. x = 7x + 11 = 3x 5 (Simplify your answer. Type an integer or a fraction.)

18 Student: Date: Assignment: System Of Equations 1. Solve the system of equations by graphing. y = 5x + 5 y = x y Use the graphing tool to graph the system. x Select the correct choice below and fill in any answer boxes present in your choice. A. The solution of the system is. (Type an ordered pair.) B. There are infinitely many solutions. C. There is no solution A cell phone provider offers a plan that costs $ 30 per month plus $ 0.10 per text message sent or received. A comparable plan costs $ 50 per month but offers unlimited text messaging. Complete parts a. and b. below. a. How many text messages would have to be sent or received in order for the plans to cost the same each month? In order for the plans to cost the same, (Simplify your answer. Type an integer or a decimal.) text messages would have to be sent or received. b. If you send or receive an average of 100 text messages each month, which plan would you choose? Why? The plan with (1) because () than text messages are sent or received each month. (1) the charge per text message unlimited text messages () less more 3. Solve the system of equations by substitution. x + y = 0 y = 9x The solution of the system is. (Simplify your answer. Type an ordered pair.) 4. Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total of 10 people took the trip. She was able to purchase coach tickets for $ 30 and first class tickets for $ She used her total budget for airfare for the trip, which was $ 0. How many first class tickets did she buy? How many coach tickets did she buy? number of first class tickets bought = number of coach tickets bought =

19 5. Solve the system using elimination. x + 16y = 6 4x 16y = 1 The solution is. (Type an ordered pair.) 6. Solve the system using elimination. x 4y = 7 x + 3y = 5 The solution is. (Simplify your answer. Type an ordered pair.) 7. Your school's talent show will feature 1 solo acts and 3 ensemble acts. The show will last 93 minutes. The 6 solo performers judged best will give a repeat performance at a second 63 minute show, which will also feature the 3 ensemble acts. Each solo act lasts x minutes, and each ensemble act lasts y minutes. Use this information to answer parts (a) and (b). a) Write a system of equations to model the situation. A. 3x + 1y = 63 3x + 6y = 93 B. 3x + 1y = 93 3x + 6y = 63 C. 1x + 3y = 63 6x + 3y = 93 D. 1x + 3y = 93 6x + 3y = 63 b) Solve the system from part (a). (Type an ordered pair.) How long is each solo act? minute(s) How long is each ensemble act? minute(s). Determine whether the ordered pair is a solution of the given inequality. y 3 x + 7; (, 5) Is (, 5) a solution of the given inequality? No Yes

20 9. Graph the inequality. y x 10 y Use the graphing tool on the right to graph the inequality. 6 4 x Graph the system of inequalities. y > 4x 3 3y x y Use the graphing tool on the right to graph the system of inequalities. 4 x

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