Algebra 1 (ACP1) Summer Refresher Assignment

Transcription

1 Algebra 1 (ACP1) Summer Refresher Assignment This summer bridge assignment represents topics from the first chapter of the text. These topics will not be taught in class. However, please go to for extra help and resources. Vocabulary: Variables Algebraic expression Factors Product Power Base Exponent Evaluate Order of operations Open sentences Solution Equation Replacement set Set Element Solution set Inequality Additive identity Multiplicative identity Multiplicative Property of Zero Multiplicative inversese Reciprocals Closure property Distributive property Like terms Equivalent expressions Simplest form Coefficient Commutative property Associative property Function Coordinate system (plane) Ordered pair X-coordinate Y-coordinate Origin x- and y-axis Independent variable Dependent variable Relation Domain Range Term

2 1. Write an algebraic expression for each verbal expression. a. 8 increased by three times a number b. The product of 2 and the second power of y c. 9 less than g to the fourth power d. The difference of 17 and 5 times a number 2. Evaluate the expression. a. 8 2 b c Write a verbal expression for each algebraic expression. a. c + 2d b. 4 5n 4. Evaluate each expression. a (3 + 1) b c. 5 + [30 (6 1) 2 ] 5. Evaluate each expression if x = 6, y = 8, and z = 3. a. 2( + ) b. 6. The length of a rectangle is 3n + 2 and its width is n 1. The perimeter of the rectangle is twice the sum of its length and its width. a. Write an expression that represents the perimeter of the rectangle. b. Find the perimeter when n = 4 inches. 7. Find the solution of each equation using the given replacement set. a. + = ;,,1, b. ( +2) = ;,,,

3 8. Solve each equation. a. = b. = ( ) ( ) 9. Find the solution set for each inequality using the given replacement set. a > 12 ; 0, 3, 6, 9, 12, 15 b. > 2 ; 3, 4, 5, 6, 7, 8 c. 9 + < 17 ; 7, 8, 9, 10, A teacher has 15 weeks to teach 6 chapters. Write and then solve an equation that represents the number of lessons that teacher must teach per week if there is an average of 8.5 lessons per chapter. 11. Rewrite each expression using the Distributive Property. Then simplify. a. 7(b + 4) b. (c d)5 c. (5y 3)6 12. Simplify each expression. If not possible, write simplified. a. c 2 + 4d 2 d 2 b. 4(6p + 2q 2p) c. 3a 2 + 6a + 2b 2 d. 25t 3 17t The Ross family recently dined at an Italian Restaurant. Each of the four family members ordered a pasta dish that cost $11.50, a drink that cost $1.50, and a dessert that cost $2.75. a. Write an expression that could be used to calculate the cost of the Ross dinner before adding tax and a tip. b. What was the cost of dining out for the Ross family?

4 14. Simplify each expression. a. 3(2c + d) + 4(c + 4d) b. 6s + 2(t + 3s) + 5(s + 4t) c. (p + 2n) + 7p 15. Identify the graph that represents the height of a skydiver just before she jumps from a plane until she lands. 16. Identify the graph that displays the speed of a radio-controlled car as it moves along and then hits a wall.

5 17. During an experiment, the students of Ms. Roswell s class recorded the height of an object above the ground at several intervals after it was dropped from a height of 5 meters. Their results are in the table below. a. Identify the independent and dependent variables. b. Write a set of ordered pairs representing the data in the table. c. Draw a graph showing the relationship between the height of the falling object and time. 18. Paul is a pitcher for his school baseball team. Draw a reasonable graph that shows the height of the baseball from the ground from the time he releases the ball until the time the catcher catches the ball. Let the horizontal axis show the time and the vertical axis show the height of the ball. 19. Explain the appropriate use of each type of graph. a. Circle graph b. Bar graph c. Line graph 20. Oatmeal can be found in 80% of the homes in the United States. The circle graph shows favorite oatmeal toppings. Is the graph misleading? If so, explain why and tell how the graph can be fixed so that it is not misleading.

6 For questions 21 and 22, use the graph that shows the time of year people prefer to buy books. 21. Suppose the total number of books purchased for the year was 25 million. Estimate the number of books purchased in the spring. 22. Suppose the manager of a bookstore has determined that she sells about 15,000 books a year. Approximately how many books should she expect to sell during the summer? 23. The line graph shows the number of cable television systems in the United States from 1995 to Explain how the graph misrepresents the data.