Unit 2 Linear Equations and Inequalities in One Variable (Keystone Review)

Transcription

1 Keystone Review Unit Name: Date: Period: Unit Linear Equations and Inequalities in One Variable (Keystone Review) Part. Solving -Step Equations ) Solve: g 7 8 A) B) C) D) ) Solve: x 8 A) 6 B) C) 7 D) 6 ) During the first half of a basketball game, a team scored 8 points. They made only field goals, which are points each. Which of the following equations could you use to find the number of field goals g the team scored? g A) g 8 B) g 8 C) 8 D) g 8 ) Jessica has $0.00 she wants to spend on CDs, which are on sale for $.0 each. Which equation could you use to find out how many CDs she can afford to buy? A) c. 0 B) c. 0 C) 0c. D).c 0 ) A meteorologist forecast that the high temperature would reach one afternoon. The low temperature for the day was -. Which equation could you use to find out how many degrees d the temperature would need to rise to reach the predicted temperature for the day? A) d B) d C) d D) d ( ) 6) Which of the following is an expression that represents 6 times the difference of a number n and? A) 6n B) 6( n ) C) 6( n ) D) 6 n Part. Solving Multi-Step Equations 7) Using the formula, C ( F ), solve for C if F = 7. 9 A). 7 B) C). 8 D)

2 8) Solve: 8n n A) B) C) 6 D) 7 9) If a number is increased by and that number is doubled, the result is -8. What was the original number? A) 7 B). C) D) 6 0) The gas tank in Roy s car holds gal of gasoline. The car averages 9mi/gal. Roy filled up the tank and then drove 0 mi. About how many gallons of gasoline are left in the tank? A) 6 gal B) 7 gal C) 8 gal D) 9 gal ) Josie s goal is to run 0 miles each week. This week she has already run distances of. miles, 6. miles, and 6. miles. If she wants to spread out the remaining miles evenly over the next days, which equation can you use to find how many miles (m) per day she must run? A) m B) m C) m 0 D) m ) A cell phone company charges $. for the first minute but only $.0 every minute after that. Which equation can you use to find how many minutes m Eric talked if the bill for the call was $.? A) ( m ). B) m. C) ( m ). D) m. ) Albert Einstein made $.70 per hour and received a $0 bonus at the end of the week. If Mr. Einstein made a total of $70 last week, which equation best represents the situation? A).7 0h 70 B).7 0h 70 C).7h 0 70 D).7h 70 0 ) Solve: 9x (x ) 0 A) B) C) D) ) Solve: 8 r 6 A) 6 B) C) 8 D) 96 b 6) Solve: 7 8 A) 87 B) 8 C) 97 D)

3 7) The length of a rectangular garden is feet more than the width. The amount of fencing needed to enclose the garden is 6 ft. What is the length of the garden? A) 7 ft B) ft C) 7 ft D) ft Part. Equations with Variables on Both Sides 8) Solve: ( q ) q 9 A) No Solution B) All Real Numbers C) 0 D) 9 9) Solve: y y 0 A) 0 B) C) D) 0 0) Which of the following equations is NOT equivalent to the others? A) ( y ) 6y B) y 6 6y C) y D) y 6 ) Ace Truck Rental charges $.00 a day plus 9 cents per mile. Joe s Truck Rental charges $8.00 a day plus cents per mile. For how many miles will the cost of renting a truck for one day at Ace equal the cost at Joe s? A) 0 mi B) 70 mi C) 00 mi D) 8 mi ) Which equation is NOT equivalent to p 6p? A) p 6p 6 B) 6 p C) p 6 D) p ) A record store sells CDs for $.00 each. A music club offers free CDs and charges $.00 for each additional CD. Which equation can you use to find the number of CDs, x, that would cost the same under both plans? A) x x B) x x C) x ( x ) D) ( x ) x ) Solve: ( y ). y A). 6 B). C). 6 D) None of these ) Solve: 8 d ( d) A) 0 B) C) All Real Numbers D) No Solution

4 6) The perimeters of the rectangle and the triangle below are equal. Find the value of x. 6 in 6 in (x +) in (x+) in x in A) 6 B) 8 C) 0 D) Part. Solving -Step Inequalities 7) Which makes the inequality x x false? A) B) 0 C) D) 8) Which has the same solution as n? A) n B) n C) n D) n 9) Solve: 6y A) y 9 B) y 9 C) y 9 D) y 9 0) What is the least whole-number solution of k? A) B) C) 0 D) ) Employees must work at least 0 years in a company in order to receive full benefits upon retirement. Which inequality or graph does NOT describe this situation? A) y 0 B) y 0 C) 0 y D) ) Solve: n 0 0 A) n B) n C) n 8 D) n 8 ) Hector is flying his plane. To avoid a storm, he climbs,00 ft without going above his plane s maximum safe altitude of,000 ft. The inequality a,00, 000 represents his original altitude a in feet. Which of the following could have been the original altitude? A) 0, 00 ft B) 0, 000 ft C) 9, 70 ft D) 7, 70 ft

5 ) Describe the solution of inequality m 8. A) All real numbers less than or equal to B) All real numbers less than C) All real numbers greater than D) All real numbers greater than or equal to ) Which graph represents the solution of x 7? A) B) C) D) ) Determine which is a solution of a. A) B) 0 C) 7 D) 7) Solve: x A) x B) x C) x D) x Part. Solving Multi-Step Inequalities 8) Solve: x A) x B) x C) x D) x 9) Solve: x 8 x A) x B) x C) x D) x 0) Solve: n 6 7n A) n 8 B) n 8 C) n 8 D) n 8

6 Mass (kg) ) Great gifts pays its supplier $6 for each box of bells. The owner wants to determine the least amount x he can charge his customers per bell in order to make at least a 0% profit per box. Which inequality should he use? A) x.0(6) B) 6x.0() C) 0.0(x ) 6 D) 0.0(x ) 6 ) Solve: n 8 7 A) n B) n 7 C) n 7 D) n ) The Science Club hopes to collect at least 00 kg of aluminum cans for recycling this semester ( weeks). The graph at the right shows the first week s results. Let x represent the average mass of cans required per week for the remainder of the semester. Which inequality would you sue to find x? A) 00 x B) ( 00 8) x 0 Aluminum Cans Collected in Week Mon. Wed. Fri. Day C) ( 00 8) 00 x D) x Part.6 Compound Inequalities ) Solve: 0 x 8 8 A) x 8 B) x 6 C) 9 x 8 D) 9 x 0 ) Which graph represents the solution of x 7 or x? A) B) 6 7 C) D) ) Which value below is a solution of neither x 7 8 nor x? A) 6 B) 0 C) 0 D) 6

7 Part.7 Absolute Value Equations and Inequalities 7) Which compound inequality has the same meaning as x 8? A) x B) x C) x or x D) x or x 8) Which of the following is a solution of x? A) B) C) 6 D) 7 9) Solve: x 7 7 A) 9, B), C), D), 9 0) The ideal diameter of a metal rod for a lamp is. inches with an allowable error at most 0.00 inches. Which rod below would NOT but suitable? A) a rod with diameter.9 inches B) a rod with diameter. inches C) a rod with diameter. inches D) a rod with diameter. inches ) Water is in a liquid state if its temperature t, in degrees Fahrenheit, satisfies the inequality t 90. Which graph represents the temperature describes by this inequality? A) B) C) D) Part.8 Cumulative Review ) Which equation is NOT equivalent to the others? x A) x B) x C) D) x ) What is the value of the expression 8? A) 6 B) C) 8 D) 0

8 ) Which expression has a value of? I. ( ) II. ( ) III. ( ) A) I B) II C) III D) None of them ) Evaluate the expression xy for x and y. A) 6 B) C) 7 D) 7 6) Which equation is NOT equivalent to the others? m n A) q p B) m n qp C) qp n D) m pq n m x 7) If and ( y ) y, which of the following is true? A) x and y B) x and y C) x 6 and y D) x 6and y 8) Half of the money collected at a show was donated to charity. Tickets cost $00 per pair. The charity received $00. How many pairs of tickets were sold? A) 70 B) 700 C) 0 D) 00 9) Which of the following is a solution to the equation x x? A) 0 B) 7 C) 7 D) 60) Solve: a a A) B) C) D) 6) If 7x, find the value of x. A) B) 7 C) D) 7 6) Which of the following can be represented by this graph? 8 A) b B) b C) 8 b D) b 8

9 6) Which inequality can be represented by this graph 6 9 A) 9 d B) d 9 or d C) d or d 9 D) d or d 9