c. (4abc 2 ) 0 6. Solve the following equations, and name the properties used for each step.

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1 Name: CC Algebra 9H Midterm Review Date:. Simplify the following: (3x + x 3) (x 5x + 7) (9 t t ) (8t + t ). Simplify the following (x + )(3x 8x + ) (x 3) c. (x + ) 3 3. Simplify the following using the laws of exponents. xy (xy ) 3 (-3x y) 5. Simplify the following radicals x y 3 xy 5 8a b 5. Let A = x 5x + 3 and B = 3x x 7. Find: c. (abc ) 0 A + B B A c. AB 6. Solve the following equations, and name the properties used for each step. 7 8x = 7( + 7x) 39 8n = -8(3 + n) + 3n 7. Solve the following equations. 3x x 5 x 7 x 3 (3x 0) 8. Solve each inequality for x and graph the solution on a number line. x 6 3 5x + 7 and 3x < 9 c. x + 8 > x 0 or 3 3 x 9. Find the x and y intercepts algebraically. 5x 3y = 5 x y = Calculate the slope of the line that passes through each pair of points: (-, ), (,-5) (-8, 0), (, 5) c. (-5, ½), (-5, 3) d. (0, 3.5), (-,.5). Find the slope and y-intercept of each equation: y = -x 7 y 6 = 3x c. -y = 6(5 3x). Write an equation in point-slope form for the line that has a slope of -3 and that passes through the point (-, 7).

2 3. Write an equation in point-slope form for the line that passes through the points (,3) and (-,-5).. Graph the following equations: y + = 3 (x + ) y = 5. Solve the following systems graphically: 3 - (x - 3) c. y + 3 = 7 (x - 5) 3xy xy 8 y x6 xy 8 6. Solve the following systems using substitution: 3x5y x y y x y x 7. Solve the following systems using elimination: x y 70 3x0y 5 3 x0y 0 x y Graph each linear inequality. Clearly indicate the solution area: y < 6x + x y 8 For #s 9-5, solve the following word problems algebraically: 9. A laboratory technician has one batch of antiseptic that is 0% alcohol and a second batch that is 60% alcohol. She would like to make 8 liters of solution that is 55% alcohol. How many liters of each batch should she use? 0. The sum of Wilbur s and Fred s age is 0 years. Wilbur s age year from now will be 9 times Fred s age year ago. Find their present ages.. Find four consecutive odd integers such that the sum of the first three exceed the fourth by 8.. A merchant wants to mix peanuts worth $3 per pound with jelly beans worth $.50 per pound to make 30 pounds of a mixture worth $.0 per pound. How many pounds of each should he use?

3 3. Bill invested some money at 5% annual interest, and Janette invested some at 7%. If their combined interest was $30 on a total investment of $5,000, how much did Bill invest?. A gardener is planting two types of trees: Type A is three feet tall and grows at a rate of 5 inches per year. Type B is four feet tall and grows at a rate of 0 inches per year. Algebraically determine exactly how many years it will take for these trees to be the same height. 5. Jacob and Zachary go to the movie theater and purchase refreshments for their friends. Jacob spends a total of $8.5 on two bags of popcorn and three drinks. Zachary spends a total of $7.50 for four bags of popcorn and two drinks. Write a system of equations that can be used to find the price of one bag of popcorn and the price of one drink. Using these equations, determine and state the price of a bag of popcorn and the price of a drink, to the nearest cent. 6. John is planning a party. He is going to buy wings and hot dogs. One package of wings costs $8 and hot dogs cost $ per pound. He must spend less than $0 and buy at least 5 pounds of hotdogs. Write and graph a system of linear inequalities based on the constraints. (Only quadrant I is needed and use the intercept method for graphing when needed). Clearly indicate the solution are 7. If f(x) = x and g(x) = ¾x + 6x, evaluate f(-3) f(6x) c. f(x + 5) d. g(-5) e. g() f. f(x ) 8. Write a piecewise function for each graph. Then, state the domain and range. 9. Graph the piecewise function below. 3x0, x f ( x) x, x x 6, x 8 Find f(-) c. Find f(0) d. For what value(s) of x is f(x) = -? e. What is the domain? f. What is the range? g. On what intervals is the function increasing? h. On what intervals is the function decreasing?

4 30. Graph the piecewise function below., x f x x x x, x ( ), Find f(-3) c. Find f(0) d. For what value(s) of x is f(x) =? e. What is the domain? f. What is the range? g. On what intervals is the function increasing? h. On what intervals is the function decreasing? 3. A phone plan costs $0.0 per minute with a fee of $50 if you use up to 00 minutes. When you go over 00 minutes the phone company charges you $0.0 per minute. Write a piecewise function that gives the cost of your phone plan based on the number of minutes you talk on the phone. How much will you owe if you use 575 minutes? 3. You have a job that pays triple time for overtime, which is working over 0 hours in a week. After working 0 hours, the pay is 3 times your hourly rate of $0/hr. Write a piecewise function that gives your weekly pay P in terms of the number hours you work h. 33. Factor completely the following expressions: 3x 8x 0 9 x c. 5-8x x d. x 3 x x e. x - x 8 f. x 3 8x + x - 3. Complete the square for each of the following quadratics expressions. x + x 3 x x c. 3x 5x Solve the following quadratic equations. x x = 0 x + 8x 3 = 0 c. x + x = Simplify the following radicals 3x 0x 3 y 8 z 3 0 6x 08xy z c. x 98x yz Let X = 3x + 7 and Y = x + 3x 6. Write all answers in standard form. Express the sum of X and twice Y. Express the product of X and Y. c. Find Y 3X. d. Subtract Y from X.

5 38. Factor the following expression completely: 8x 8x 3 60y 3 8y 6y c. x 3 x d. x 3 y xy + 5x y 5y e.x 5 0x + 3x 3 f. 5n + 5n Solve by using the quadratic formul Give the solution in simplified radical form. -m m + 0 = 0m x + 3 = 6x c. 3d 8d + 3 =0 0. Solving by completing the square. Give the solution in simplified radical form. x x + = 0-3x 8x + = 0 c. 3x + 6x + = 0 For each word problem, only an algebraic solution will be accepted.. Leah is creating a rectangular flower bed such that the width is half of the length. The area of the flower bed is 3 square feet. Write and solve and equation to determine the width of the flower bed, to the nearest tenth of a foot.. A rectangular picture measures 6 inches by 8 inches. Steve wants to build a wooden frame for the picture so that the framed picture takes up an area of 00 square inches on his wall. The pieces of wood that he uses to build the frame all have the same width. Determine the width of the pieces of wood used for the frame to the nearest tenth of an inch. 3. Brian s rectangular patio measures 9 feet by feet. He wants to increase the patio s dimensions so its area will be twice the area it is now. He plans to increase both the length and the width by the same amount, x. Find x to the nearest hundredth of a foot.. Find consecutive positive even integers such that the product of the st and 3 rd number is 5 times the sum of the nd and th number. 5. Factor x 5x 36 completely. 6. Solve the equation -5x + 6x = -5 + x algebraically. 7. What are the zeros of the function f(x) = (x ) - 5? 8. Solve for x: x x Subtract 5x + x - from 3x + 8x - 7. Express the result as a trinomial. 50. Simplify (x + ) 5(x 7). 5. State whether the following relation is a function or not. Explain. {(, 6), (5, ), (, 8), (, 0)}.

6 5. State the domain and range of the following function. {(, 5), (3, ), (7, 8)} 53. State the domain of the following relation: {(, 5), (3, ), (7, 8),(,7),(3,-)} x y Determine if the following are either rational or irrational: c d. 7 7 e. 5 8 f The Key Club is planning a trip to a local amusement park. They plan on taking a bus which holds 3 people. It will cost $5 to park and the cost to enter the park is $.50 per person. The equation that models this situation is: c(n) =.5n + 5, where c represents the cost for the group to go to the park and n represents the number of people who go on this trip. Determine and state the domain. 56. Joe has an afterschool job at the local sporting goods store. He makes $6.50 an hour. He never works more than 0 hours in a week. The equation s(h) = 6.5h can be used to model this situation, where h represents the number of hours Joe works in a week. Determine and state the domain. 57. Perform each of the following conversions by showing all work. 36 km/hr to m/sec 0 cm/sec to m/hr