Algebra 1 ECA Remediation Diagnostic Homework Review #1

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1 Algebra 1 ECA Remediation Diagnostic Homework Review #1 Lesson 1 1. Simplify the expression. 8 5(7 r) A Lesson. Solve the equation. 4x 1 = 9 x A1..1 Lesson 3. Solve the equation. 1.6n 5.95 = n n A1..1 Lesson 4. Solve the equation. 3 x 8 x 7 A1..1 Lesson A The equation below was solved incorrectly. Study the work below. 7(n + 1) = 7 + 4n Step 1: 7n 7 = 7 + 4n Step : Step 3: Step 4: 7 = n 14 = 11n 14 n 11 Describe the mistake in the work shown above. What is the solution to the equation, 7(n + 1) = 7 + 4n?

2 Lesson 3 A Solve the proportion. x1 x 4 5 Lesson 3 7. The formula A hb b 1 1 represents the area of a trapezoid where A represents the A1.. area, h is the height of the trapezoid, and b 1 and b are the bases of the trapezoid. Solve this formula for h. Lesson 4 8. Solve the inequality. v 33 > 6(6 + 4v) A1..4 Lesson 4 9. Solve the compound inequality. 5 < 6 4 < 8 A1..5 Lesson 5 A Sally works at a bike store. Sally earns $800 every week plus $300 for every bike that she sells. Write an inequality that can be used to determine the number of bikes (b) Sally must sell in one week if he wants if he wants to earn a minimum of $000 for that week. What is the minimum number of bikes Sally must sell in one week to earn a weekly salary of $000?

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 Brett ran from his school at a constant speed. He immediately turned around and ran back to school, but at a slower constant speed. Joe ran along a straight path to and from school. Draw a graph that best represents Brett s distance from his school over time? Brett s Distance from School Time (minutes)

4 Puddings Eaten Distance from Home (miles) Lesson 8 A Peter rode his motorcycle home from work. The graph below shows Peter s distance from work over time. 30 Peter s Motorcycle Ride Home Time (minutes) Describe Peter s motorcycle ride home with respect to time and distance. Be sure to include any change in speed during the bike ride. Lesson 8 A The graph below represents the total number of times a certain pudding is eaten at an elementary school 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 pudding is eaten, P, after d days. If this trend continues, how many times will pudding get eaten in 1 days? Lesson 9 A Sketch the graph of the line. 1 y x 3 3

6 Lesson Sketch the graph of the line. x + y = A1.4.1 Lesson Which equation has a graph with no y 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 x y =? 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, 1) and m = 4 Lesson Write the slope intercept form of the equation of the line through the given points. A1.4.4 (0, 4) and ( 4, )

7 Lesson Sketch the graph of the linear inequality. y > x + 4 A1.4.6 Lesson 13. Sketch the graph of the linear inequality. 5x + y > 5 A1.4.6 Lesson 14 A Ginger earns $3 for each DVD she sells and $5.50 for each Blue ray she sells. Ginger earned $170 last week selling DVDs and Blue rays. Write an equation to represent the number of DVDs (d) and Blue rays (b) Ginger sold last week given that she earned $170. If Ginger sold 0 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 no solution, what do the two equations in the system have in common? Lesson 16 A Use elimination to find the x-coordinate of the solution to each system. 3x 8y 19 x 4y 13 Lesson 16 A Solve each system by elimination. 5x 9y x 8y 18 Lesson 17 A Solve each system by substitution. y x1 6x5y 1 Lesson 19 A Sam bought 3 shirts and pairs of jeans for $ Kim bought shirts and 4 pairs of jeans for $ 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 Steven bought a medium pizza with 3 toppings for $ Tina bought a medium 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. 1 y x y x 3 Lesson 31. Simplify the sum. (4 + 4r + 3r) + (8 3r + 6r ) A1.6.1 Lesson 3. Simplify the difference. ( 8m 3 + 4m) (m 4 6m 3 ) A1.6.1 Lesson Find the product. (3a 6)(5a + 6) A1.6.4 Lesson Find the product. (4v 5) A1.6.4 Lesson Simplify. x 4 3x 3 A1.6..1

10 Lesson Simplify. (4ab 3 ) A Lesson 5 A Simplify. 3xy xy 4 4 Lesson Factor the common factor out of the expression. 54n 3 + 9n 4 m + 7n 4 A1.6.5 Lesson 6 A Divide. 4 3 (n 8 n n ) (4 n) Lesson 7 A Factor completely. x 8x 1 Lesson 7 A Factor completely. 4n 1 Lesson 8 A Factor completely. 3n n 14 Lesson Simplify. 196 A1.1. Lesson 9 A Simplify v

11 Lesson 31 A Solve the equation by factoring. k 48 k Lesson 31 A Solve the equation by factoring. n n 30 Lesson Solve. x 3 5 A1.8.3 Lesson 33 A Solve the equation with the quadratic formula. p 3p 9 0 Lesson 34 A Consider the square below. (x ) 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 ( 3, 0) and (9, 0). A1.6.8 Lesson 35 A What are the zeros of the function, 6k k 1 0?

12 Lesson 37 A Sketch the graph of the function. y x x Lesson 37 A Sketch the graph of the function. y x x 4 4 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. Lesson Solve the equation. Remember to check for extraneous solutions. r 70 17r A1.8.8

13 Key to Algebra 1 ECA Review # r. {} 3. {3.5} 4. {4} 5. In step to step 3 we were supposed to add 7 to both sides, not subtract 7. The correct answer is {3} 7. A ( b b ) h 1 8. v < 3 9. < x < < 300b + 800, 4 bikes minimum 11. Domain {-3, 1, 5, 9}, Range {-4, -3, -1, 3}, Yes, it is a function Peter travels 10 miles in 0 minutes. He then stops for 10 minutes. Peter then travels faster at a rate of 0 miles in 5 minutes. 14. The slope is about 15 puddings in one day. This represents how many puddings are eaten each day, P = 15d, P(1) = 180 puddings B 18. m = ½, x int = -, y int = Y = -4x y x d + 5.5b = 170, 0 Blue ray 4. The slopes of both equations are the same. Parallel lines do not intersect and they have the same slope (-5, 4) 7. (-3, -6) 8. $ $.50

14 r m m a 1a v 40v x a b 37. 3xy n (6 m n 3 n) 39. n n 4 3 n 40. (x )(x 6) 41. (n + 1)(n 1) 4. (3n 7)(n + ) v v 45. {6, -8} 46. {6, -5} 47. {7, -3} , y = (x + 3)(x 9) or y x x , seconds 55. {7, 10}

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