x when Algebra: Midterm Review Sheet Unit 1- Operations with Real Numbers, Properties & Expressions

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1 Name: Date: Algebra: Midterm Review Sheet Unit - Operations with Real Numbers, Properties & Expressions. Fill in each circle of the following flow diagram with one of the letters C for Commutative Property (for either addition or multiplication), A for Associative Property (for either addition or multiplication), or D for Distributive Property. 5. Evaluate the expression: x when 9 x

2 Unit - Solving Equations in One Variable. Solve the following equations; if appropriate write infinitely many solutions or no solution: a) 6 k 5 k 66 b) 0. x x 0 c) x 8 6x 0 d) 6 x 6 x 9 e) x 5 5 x x f) Solve for b : A h b b. Translate and solve the following word problem: Six more than three times a number is negative thirty-six.

3 Unit - Solving Inequalities in One Variable 5. Solve the following inequalities, graph the solutions. a) p 0 5 b) x Unit - Graphs & Functions 6. Which graph below most likely represents each of the following? Multiple Choice a) a person s body temperature as he enters a sauna and then cools off in a Jacuzzi b) the rise and fall of an elevator as it carries passengers from the ground floor to an observation tower c) the cost to mail a package based on weight categories a) II; IV; I b) II; III; IV c) I; III; II d) II; I; IV

4 7. Which diagram represents a function? Multiple Choice () () () () 8. The equation x x 6 f is an example of which type of function? Multiple Choice a) linear b) exponential c) step d) absolute value 9. Find the range of the function for the given domain. Show all work. y = x ; {,, }

5 0. Use the table below to answer the following questions. a) Plot the points (x,y) in this table on a graph (except when x is 5). y x b) The y-values in the table follow a regular pattern that can be discovered by computing the differences of consecutive y-values. Find the pattern and use it to find the y-value when x is 5.. Which function identifies the graph below? Multiple Choice a) f x x b) f x x c) f x x d) f x x 5

6 . Graph the following equations on the same graph: y x y x y Describe how graph () can be graph () using transformations. 5 obtained from x Unit 5 - Linear Relationships. Find the common difference of the arithmetic sequence and then find the next two numbers in sequence. Write the function. -5, -,,,,. Find the rate of change. Explain what the rate of change means for the situation. 6

7 5. Complete the table. Identify the slope, y-intercept, and write a function rule for the table. 6. Find the equation of the line that passes through the pair of points: A (, ) and B (, ) 7. Hans needs to rent a moving truck. The information is provided in the following table. Complete the table. total cost, C $60 0 $00 $0 days, d Write an algebraic equation for the total cost, C, based on the number of days, d. Truck Rental Company: 7

8 8. A trainer for a professional football team keeps track of the amount of water players consume throughout practice. The trainer observes that the amount of water consumed is a linear function of the temperature on a given day. The trainer finds that when it is 90 F the players consume about 0 gallons of water, and when it is 76 F the players consume about 78 gallons of water. Write a linear function to model the relationship between the gallons of water consumed and the temperature. Explain the meaning of the slope in the context of the problem. 9. Is (9, -) a solution to the equation y x 5? 0. The functions below represent pricing plans for car rentals, where d is the number of days and c is the cost. Order the car rentals from least to greatest based on their rate of change. Avis d 7 c Enterprise Total cost is $0 plus $5 per day. Hertz 7d 0.5c 0 8

9 Unit 6 - Systems of Equations & Linear Inequalities. Solve the system of equations algebraically, find the solution: y x 6x y What is the solution to the following system of linear equations? If there is no solution or infinitely many, explain why.. y x 7 y x y x

10 . Solve the system of linear inequalities by graphing. x y y x y x Name one point in the solution set Shopping at Savers Mart, Lisa buys her children four shirts and three pairs of pants for $ She returns the next day and buys three shirts and five pairs of pants for $5.00. What is the price of each shirt and each pair of pants? Only an algebraic solution will be accepted. 0