Algebra 1 ECA Remediation Diagnostic Homework Review #2

Transcription

1 Lesson 1 1. Simplify the expression. (r 6) +10r A Algebra 1 ECA Remediation Diagnostic Homework Review # Lesson. Solve the equation. 5x + 4x = 10 +6x + x A1..1 Lesson 3. Solve the equation n = n A1..1 Lesson A Solve the equation. a 8 7a 1 5 Lesson A The equation below was solved incorrectly. Study the work below. 8(k + 1) = k Step 1: 16k + 1 = k Step : Step 3: Step 4: 1 = k 16 = 5k 16 k 5 Describe the mistake in the work shown above. What is the solution to the equation, 8(k + 1) = k?

2 Lesson 3 A Solve the proportion. b 1 b 5 Lesson 3 7. The formula C r represents the circumference of a circle where C represents the A1.. circumference, and r is the radius of the circle. Solve this formula for r. Lesson 4 8. Solve the inequality. 6v 1 < 5(v + 4) A1..4 Lesson 4 9. Solve the compound inequality. 10 < 6x 8 < 5 A1..5 Lesson 5 A Tommy works at a dress store. Tommy earns $750 every week plus $350 for every dress that he sells. Write an inequality that can be used to determine the number of dresses (d) Tommy must sell in one week if he wants to earn a minimum of $1800 for that week. What is the minimum number of dresses Tommy must sell in one week to earn a weekly salary of $1800?

3 Distance (miles) Lesson 7 A1.3.3 A What is the domain and range of the relation shown in the table shown? x y Domain Range Is the relation in the table above a function? Lesson 7 A Cyndi ran from her grandmother s house at a constant speed. She immediately turned around and ran back to her grandmother s house, but at a faster constant speed. Cyndi ran along a straight path to and from her grandmother s house. Draw a graph that best represents Cyndi s distance from her grandmother s house over time? Cyndi s Distance from Grandma s Time (minutes)

4 Broken Pencil Led Distance from Home (miles) Lesson 8 A Penny rode her horse from the stables to the meadow. The graph below shows Penny s distance from the stables over time. 30 Penny s Horseback Ride Time (minutes) Describe Penny s horseback ride home with respect to time and distance. Be sure to include any change in speed during the horseback ride. Lesson 8 A The graph below represents the total number of times pencil led breaks in a mechanical pencil over a five day period. A Number of Days

5 What is the slope of this line segment and what does it represent in terms of this situation? Write an equation that represents the total number of times pencil led breaks, L, after d days. If this trend continues, how many times will the led break in 14 days? Lesson 9 A Sketch the graph of the line. 4 y x 3

6 Lesson Sketch the graph of the line. x y = A1.4.1 Lesson Which equation has a graph with no x intercept? A1.4. A. y = 6 B. x = C. y = x D. y = x Lesson What is the slope, x-intercept, and y-intercept of the graph of 3x + y = 0? A1.4.3 Slope = x-intercept = y-intercept = Lesson Write the slope-intercept form of the equation of the line through the given point with the A1.4.4 given slope. (1, ) and m = Lesson Write the slope intercept form of the equation of the line through the given points. A1.4.4 (4, 1) and (0, )

7 Lesson Sketch the graph of the linear inequality. y < x + 4 A1.4.6 Lesson 13. Sketch the graph of the linear inequality. x y < 4 A1.4.6 Lesson 14 A Candy earns $3 for each DVD she sells and $4.5 for each Blue ray she sells. Candy earned $71.5 last week selling DVDs and Blue rays. Write an equation to represent the number of DVDs (d) and Blue rays (b) Candy sold last week given that she earned $71.5. If Candy sold 11 DVDs last week, how many Blue rays did she sell?

8 Lesson 15 A If you are trying to solve a system of equations and there is one solution, what do you know about their slopes? Lesson 16 A Use elimination to find the x-coordinate of the solution to each system. 7x y 17 3x 3y 1 Lesson 16 A Solve each system by elimination. 6x 5y 1 8x 10 y 18 Lesson 17 A Solve each system by substitution. y 5x 15 7x y 1 Lesson 19 A Katie bought shirts and 3 pairs of jeans for $ Lenny bought 4 shirts and 5 pairs of jeans for $61.5. Each shirt costs the same amount. Each pair of jeans costs the same amount. What is the cost, in dollars, for 1 pair of jeans? Lesson 0 A Lynn bought a large pizza with 5 toppings for $ Daniel bought a large pizza with toppings for $ Each topping cost the same amount. The base price for each medium pizza is also the same. What is the price of one topping on the pizza.

9 Lesson 1 A Sketch the solution to each system of inequalities. y x 1 1 y x Lesson 31. Simplify the sum. 5x 8x 5 7x 6x 1 A1.6.1 Lesson 3. Simplify the difference. 5k 5k 3 5k 3k 5 4k 3 A1.6.1 Lesson Find the product. (7n )(3n 1) A1.6.4 Lesson Find the product. (b 5) A1.6.4 Lesson Simplify. 3v 4v A1.6..1

10 4 Lesson Simplify. xy A Lesson 5 A Simplify. 3xy xy 4 3 Lesson 6 A Factor the common factor out of the expression. 6x y 15x y 4x Lesson 6 A Divide. 4 3 ( k k k ) (8 k) Lesson 7 A Factor completely. b 7b 30 Lesson 7 A Factor completely. 5x 16 Lesson 8 A Factor completely. 3x 17x 6 Lesson Simplify. 600 A1.1.

11 Lesson 9 A Simplify r Lesson 31 A Solve the equation by factoring. n 4n 3 Lesson 31 A Solve the equation by factoring. x 1 7x Lesson Solve. x 5 81 A1.8.3 Lesson 33 A Solve the equation with the quadratic formula. b 5b 14 0 Lesson 34 A Consider the square below. (x + 7) units What is the value of x if the area of the square is square units? Lesson Write the equation of a function whose graph has x-intercepts at ( 7, 0) and (5, 0). A1.6.8

12 Lesson 35 A What are the zeros of the function, 3p 5p 0? Lesson 37 A Sketch the graph of the function. y x x 4 3 Lesson 37 A Sketch the graph of the function. y x x 4 3 Lesson 38 A The height (h) of a stone, in meters, thrown into the air can be modeled by the equation, h t t , where t represents time in seconds. How many seconds will it take for the stone to hit the ground (h = 0) after it is thrown into the air? Round your answer to the tenths place.

13 Lesson Solve the equation. Remember to check for extraneous solutions. k k A1.8.8 Key to Algebra 1 ECA Review # 1. 9r + 6. {5} 3. {.5} 4. {-1} 5. In step 1 the distributive property is not done correctly. The -8 should be multiplied by both terms in the parenthesis. The correct answer is {-4} 7. C r 8. v > < x < < 350d + 750, 3 dresses minimum 11. Domain {, 5, 8}, Range {-, 0, 4, 7}, No, it is not a function Penny travels 10 miles in 30 minutes. She then stops for 15 minutes. Penny then travels faster at a rate of 0 miles in 5 minutes. 14. The slope is about 30 breaks in one day. This represents how many times the pencil led breaks each day, L = 30d, L(14) = 40 breaks A 18. m = 1, x int = 0, y int = y = x y x 4

14 d + 4.5b = 71.5, 9 Blue ray 4. The slopes of both equations are the different. Lines with different slopes intersect exactly one time (-1, -1) 7. (-3, 0) 8. $ $ x x k k 5k n 13n 34. b 10b v xy 37. 3y x x (x y 5y 8 x ) k k k 40. (b + 3)(b 10) 41. (5x + 4)(5x 4) 4. (3x + 1)(x 6) r {8, -4} 46. {3, 4} 47. {4, -14} 48. {7, -} y = (x + 7)(x 5) or y x x , seconds 55. k = 1, k cannot be -. If you plug - back in, the equation is incorrect -.