East Greenwich Mathematics Summer Review Material for Students Entering Algebra I

Transcription

1 East Greenwich Mathematics Summer Review Material for Students Entering Algebra I Directions: Print this document. Do all work on the review sheets. Be sure to show all work in order to earn credit. No calculator/technology.

2 Evaluating and Simplifying Helpful links: TOPIC: How to add, subtract multiply and divide fractions. Simplify each expression. Circle the answer when done x 2 3x Order of operations ( ) 6

3 11. (10 4) ( 3) (3 + 6) (7 10) Write each percent as a decimal and as a fraction % % % 23. Write 11 6 as a decimal. 24. About 83% of last year s senior class had been camping. There were 174 students in the senior class. How many students had never been camping?

4 Helpful links: Evaluate each of the following when a = 2, b = -3, x = 4, and y = b a xy 26. -b b a Solve each equation. Linear Equations and Inequalities in One Variable x = (3 2x) = 2(10 8x) (2x + 10) = 2( x + 5) + 12x c 3 5 = = b x 1= 1 4 x + 1 2

5 Solve each inequality and graph its solution x < k x + 4 < (x 4) x x > (3x 4)

6 Summer Review for Students Entering Linear Algebra Equations I in Two Variables Graph and LABEL the following points: A (0, 4) B (7,0) C (5,6) D (3, -1) E (9, -4) F (-4, -2) G (-7, 8) H (-1, 3) a) Using the points plotted, list points in quadrant I. b) Using the points plotted, list points in quadrant II. c) Using the points plotted, list points in quadrant III. d) Using the points plotted, list points in quadrant IV. 40. Graph the line y = 2 x + 3. Label at least two points on the line.

7 41. Graph the line 5x + 4y = 10. Label at least two points on the line. 42. Find the slope: a) of a line containing the two points, (4, 7) and (-2, 1). b) of a linear function described by the table. x y Solve the system by graphing. y = x + 3 3x 6y = Solve the system using substitution. y = 5x 10x + 2y = Solve the system using elimination. 2x + 4y = 10 x 2y = 7

8 Simplifying variable expressions Simplify. There should be no negative exponents in your final answer. 46. ( 7x 3 y 5 )( 4x 1 y 2 ) 47. 2x ( 2x5) 0 4x 49. ( 2x 5 ) (x 2 y 5 )(x 8 y) 51. x 2 x 4x 2 + 5x π 3π + 7 5π Reasoning with Numbers Helpful links: Use your estimation skills to place each of the following radicals onto the number line below. A) 3 B) 20 C)!"!! D) 5 E) 14 F) π G) -3.2 H) (.7) 2 I)!! J)!!

9 Using Mathematics Use problem solving skills. 1) Understand the problem (Use sketches, diagrams or tables to help with the understanding.) 2) Develop a plan 3) Execute the plan 4) Check. Does your answer make sense? The body of a 154-pound statue contains approximately 2 10 milligrams of gold and milligrams of aluminum. Based on this information, the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body. 55. Write the number 6 10!! in standard form. 56. The manager of a sporting goods store uses a markup rate of 60%. What is the selling price of a set of golf clubs that cost him $300? 57. The perimeter of a rectangle is 144 feet. The length of the rectangle is three times the width. Find the length, width, and area of the rectangle.

10 58. The table shows the results of a random survey of students in grade 7 and grade 8. Every student surveyed gave a response. Each student was asked if he or she exercised less than 5 hours last week or 5 or more hours last week. Based on the results of the survey, which statements are true? Select each correct statement. a. More grade 8 students were surveyed than grade 7 students. b. A total of 221 students were surveyed. c. Less than 50% of the grade 8 students surveyed exercised 5 or more hours last week. d. More than 50% of the students surveyed exercised less than 5 hours last week. e. A total of 107 grade 7 students were surveyed. 59. Which equation has both 4 and -4 as possible values of y? a. y! = 8 b. y! = 8 c. y! = 16 d. y! = Eric planted a seedling in his garden and recorded its height each week. The equation, h =! w +!, can be used to estimate the height, h, in inches, of the seedling after w, weeks since!! Eric planted the seedling. a. What does the slope of the graph of the equation h =!! w +!! represent? i. the height, in inches, of the seedling after w weeks ii. the height, in inches, of the seedling when Eric first planted it iii. the increase in the height, in inches, of the seedling each week iv. the total increase in the height, in inches, of the seedling after w weeks b. The equation h =! w +!!! many weeks? estimates the height of the seedling t be 8.25 inches after how

11 Interpreting Rates of Change Line t and ΔECA and ΔFDB are shown on the coordinate grid. Which statements are true? Select ALL that apply. A. The slope of AC is equal to the slope of BC. B. The slope of AC is equal to the slope of BD. C. The slope of AC is equal to the slope of line t. D. The slope of line t is equal to EC AC. E. The slope of line t is equal to FB FD. F. The slope of line t is equal to AE FD. 62. The functions A, B, and C are linear functions. Some values of function A are shown in the table. The graph of function B has a y-intercept of (0,3) and an x-intercept of (-5,0). Function C is defined by the equation y = 3x+1. Order the linear functions based on the rate of change, from least to greatest.

12 Systems of linear equations a) Solve the system algebraically: y = 3x + 1 y = 4 b) What does your solution(s) represent? c) How many solutions does the system have (one solution, no solution, or infinitely many solutions)? How could you have known this answer just by looking at the equations in the system? 64. a) Solve the system algebraically: y = x y = x 4 b) What does your solution(s) represent? c) How many solutions does the system have (one solution, no solution, or infinitely many solutions)? How could you have known this answer just by looking at the equations in the system? 65. a) Solve the system algebraically: y = x 8y = 8x b) What does your solution(s) represent? c) How many solutions does the system have (one solution, no solution, or infinitely many solutions)? How could you have known this answer just by looking at the equations in the system?

13 66. A school is selling t-shirts and sweatshirts for a fundraiser. The table shows the number of t- shirts and the number of sweatshirts in each of three recent orders. The total cost of orders A and B are given. Each t-shirt has the same cost and each sweatshirt has the same cost. The system of equations shown can be used to represent this situation. 2x + 2y = 38 3x + y = 35 a) What is the total cost of one t- shirt and one sweatshirt? b) In the system above, x represents and y represents c) If the system of equations is graphed in a coordinate plane, what are the coordinates (x, y) of the intersection of the two lines? d) What is the total cost in dollars of order C?