Review - Algebra I Week 24 DCA 2012

Transcription

1 Name: Period: Date: Review - Algebra I Week 24 DCA What is the area of the shaded region? Write the area in standard form. 3. A square has sides measuring 3x-1 cm. Find the perimeter and area of the square. Be sure to use standard form. 4. Evaluate the polynomial expression, 2x 2 x + 5, if x= Simplify: (2x 5)(3x 2 + x 4). 2. Write a polynomial expression to represent the sentence below. 5x 2 8x 7 is subtracted from 2x 2 + x 5. Simplify the polynomial expression. Be sure to use standard form. 6. Find the area and perimeter of a rectangle with a length of 7x-3 and a width of 2x-5. 1

2 7. Of the four expressions below, all except one are considered equivalent. Identify the expression that is not equivalent to the other three. 10. The area of a rectangle is 48x 7 y 6 z square cm. Find the width of the rectangle if the length is 16x 4 y 2 cm. A (5m 3 n 2 ) 2 ( 2mn 6 ) 2 B (10m 4 n 4 ) 2 C 400 4m 8 n 8 D ( 2m 3 n 3 p 0 ) 2 ( 5mn) 2 8. Otto mistakenly thinks that a 3 Ê = a ˆ 3 b Ë Á b. Sabrina reminds Otto that this is not true. Which pair of values for a and b shows that Otto s theory is incorrect? A a = 5 and b = 1 B a = 0 and b = Angelina is 23.5 years younger than her mother. The sum of their ages is 34.3 years. Write a system of equations that could be used to determine, a, Angela s age in years and m, her mother s age in years. Solve the system of equations. Equation 1: Equation 2: Solution: C a = 1 and b = 5 9. Find the area of the square below: 2

3 12. Mr. Nadir wants to put a flagstone border around his rectangular flowerbed so he determines at the perimeters of the flowerbed is 76 feet. The length of the flowerbed is 2 feet less than four times the width. Write a system of equations which could be used to find the length, l, and the width, w, of the flowerbed. Solve the system of equations. Equation 1: Equation 2: Solution: 13. Gary visits the NASA Ballunar Festival, the local hot air ballooning event held at the Houston space center. When he arrives, he first views the Wells Fargo balloon which is 400 feet above the ground and descending at a constant rate of 20 feet per minute. On the ground, he sees the balloon sponsored by REMAX launch and watches it slowly ascend at a constant rate of 10 feet per minute. The flights of the two balloons are represented on the coordinate grid below. Two Hot-Air Balloons Passing in the Night How far had the Wells Fargo ballon descended when it reached the same height as the REMAX ballon? 3

4 14. Use graphing to solve the system of equations below. Write both equations in slope-intercept form before graphing. Ôx + 3y = 15 2x 2y = Which equation is the result of using elimination to solve the system of equations? Ô4x + 10y = 48 6x 10y = 28 A B 10x=-20 2x=-20 C 10x=76 D 10x= Write the system of equations represented by the graph below. Then give the solution to the system. 17. Without actually solving, label each system of equations as having no solution, one solution, or infinitely many solutions. Hint: think about what happens to the variables if you use the elimination method to solve each system. 4x + 5y = 10 I. Ô 4x + 5y = 30 4x + 5y = 10 II. Ô 8x + 10y = 20 x + 5y = 30 III. Ô 4x + 5y = 10 4

5 18. Jeanette solved a system of equations by graphing the equations on her TI-Nspire and checking the table that went with her graph. What was the solution to the system of equations that she located on the calculator screen? 19. Taylor and Josie bike each week as they train for the MS150 bike ride to Austin. The table below shows how their training schedule changes over time. Weekly Distances Biked # of weeks (w) Taylor - Miles biked Josie- Miles biked If the distance biked each week continues to change in the same way, after what number of weeks will the distances biked by Taylor and Josie be the same? 20. Mrs. Travis wants to have a clown deliver balloons to her secretary s office. Clowns R Fun charges a fee per balloon and $6 for delivery. Singing Balloons charges a fee per balloon and $2 for delivery. How many balloons does Mrs. Travis needs to purchase in order for Clowns R Fun to have the same price as Singing Balloons? # of balloon s Cost at Clowns R Fun Cost at Singing Balloons 0 $6 $2 1 $7.25 $ $8.50 $ $9.75 $7.25 5

6 21. While reviewing for a test, Marco looks at his notes about solving systems of equations. His notes include the sentence, The solution to a system of equations will belong to one of three categories: no solution, one solution, or infinitely many solutions. Marco realizes that he needs to understand how each of these will look when he is solving by graphing, elimination, and substitution. Each statement below describes work Mario is reviewing. Label each statement as an example of a system with no solution, one solution, or infinitely many solutions. I. Mario graphs both lines in the system and they intersect. II. Mario s first equation is already in slope-intercept form and it is easy for him to graph. As he solves the second equation for y, he notices that the slope is the same as the slope of the first equation, but the y-intercepts are different. III. Mario s first equation is already in slope-intercept form and it is easy for him to graph. As he solves the second equation for y, he notices that the two equations are identical. IV. In the process of solving by elimination, Mario notices that both variables cancel and he ends up with 0=10. V. In the process of solving by substitution, Mario notices that both variables cancel and he ends up with 5=5. VI. In the process of solving by elimination, Mario has gotten the y s to cancel. The sum of the two equations at that point is 2x=10. 6

7 22. Solve each system of equations below. Each equation can be solved most efficiently using a particular method. Identify the most appropriate method and complete the work within that area of the table. Systems of Equations 5x - y = 3 y = 3x + 1 Graphing x - 2y = 10 2x + y = 10 Substitution y = -x + 1 y = ½x - 2 Elimination Solution: Solution: Solution: 7