Name: Period: Date: Algebra 1 1st Semester Review Which best describes the solution(s) for this equation? 3 ( 8x 12) = 33 2x

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1 Name: Period: ate: lgebra 1 1st Semester Review Which algebraic expression could NOT match the pictorial representation below? 5 Which best describes the solution(s) for this equation? 3 ( 8x 12) = 33 2x 4 ( ) 3( x 4) 3( x) 34 () 3()+ x 34 () 3( x + 4) 2 Write the equation modeled with the lgebra Tiles? x = 3 x = 6 There is no solution. There are infinitely many solutions. 6 ompare the values of x in olumn and olumn. Which statement is true? olumn olumn 3 What is the solution of the equation below? 17 = 2 3 n + 3 Record your answer and fill in the bubbles below. The values are equal. The value of x in olumn is greater. The value of x in olumn is greater. The relationship cannot be determined from the information given. 7 Regina and Tomas both worked the same problem. Their steps are shown below. Who did not solve it correctly and what mistake was made? Regina Tomas 4 What is the solution(s) for this equation? Regina did not solve it correctly. She distributed the negative 3 to one and got positive 3. Regina did not solve it correctly. She subtracted 3 from both sides when she should have divided by negative 4. Tomas did not solve it correctly. He did not distribute the negative 3 to the negative 1. Tomas did not solve it correctly. He did not simplify correctly. 1

2 8 Find the measure of. 12 The perimeter of a rectangle is equal to the perimeter of a regular pentagon. Find the value of k. 9 is complementary to. Find m given that m = ( 2x 5) and m = ( 3x 10). Record your answer and fill in the bubbles below. 10 The three angles of a triangle include: m J = ( x 18), m K = ( x + 5), and m L = ( 2x 35). Find the measure of each angle. 13 Write and solve an equation to find three consecutive integers with a sum of rectangular desktop has a length of units and a width of units. Write a simplified expression for the perimeter of the desktop. 14 Vicki is filling up her car with gas that costs $3.27 per gallon. She also buys a soda for $1.19 and a candy bar for $0.75 bringing her total to $41.18 before tax. Write and solve an equation to find the number of gallons of gas Vicki bought. 2

3 15 Graph the solution set of 3 2x Write a possible situation for the given graph. e sure to analyze each section of the graph as it relates to the situation you create. Include rates of change, maximums, minimums, and time periods for each section. Squirrel s istance from the Ground 16 Which is NOT a solution of the inequality 5 2x 3? In order to lose weight, ob must eat no less than 2600 calories per day and no more than 3400 calories per day. Write and graph a compound inequality to represent this situation. 18 Write the expression for the n th term of this arithmetic sequence. -9, -5, -1, 3, 7, If you were to sketch a graph for each situation below, tell whether the data would be continuous or discrete. 19 Write a rule that could be used to find the number of squares in the nth term of the pattern below: I. Simon is selling candles to raise money for the school dance. For each candle he sells, the school will get $2.50. He has 10 candles that he can sell. II. truck driver enters a street, drives at a constant speed of 20 mph, slows down to stop at a light, and then gradually accelerates to continue at 20 mph. II. For his iology class, Jorge plans to monitor the growth of a bean plan throughout a two week period. IV. small bookstore sold between 5 and 8 books each day for 7 days. 3

4 22 When the bell rang to dismiss his class at the end of the day, Simon left school to begin his walk home. On the way home, he stopped at his grandmother s house for a snack before continuing home. Which of the following graphs fits this description? 23 etermine which relation is NOT a function. {( 1, 3), (0, 2), (1, 5), (1, 7) } 24 What is the domain and range of the function graphed below? 4

5 25 Give the domain and range for each representation below. I. 27 The height of a bean plant can be found using the equation y = 2x + 5, where y is the height in centimeters and x is the number of weeks since the experiment began. Which is the most reasonable domain for the linear function that represents this situation? ll real numbers ll real numbers greater than or equal to 0 ll integers greater than or equal to 0 ll integers greater than or equal to 2 II. 28 Marta has been scuba diving for 15 years. When she dives in seawater, the water pressure increases by 0.44psi (pounds per square inch) for every foot deeper she dives. What is the independent quantity in this relationship? The number of years Marta has been a diver The water pressure Marta s depth below sea level The volume of her oxygen tank 29 Which of the following shows the equation y= 2x in function notation? f(x)= 2x f(x)= 2x III. pet store is selling 8 puppies for $50 each. f(x)= x 2 f(x)= 2 x 26 What is the range of the function graphed below? The set of all real numbers -1 < y < 1-2 < y < 2 y > helicopter takes off from the roof of a building and rises steadily. The roof is 140 feet high. This table shows the helicopter s height above the ground, h(x),after it has been in flight for x minutes. Time in Minutes Height in Feet h(x) (x) Which equation represents the functional relationship shown in the table? h(x) = x h(x) = x h(x) = x h(x) = x 5

6 31 Which table represents a linear function? 32 The equation F = ( 9 )+ 32 represents the 5 linear function that can be used to convert temperatures in degrees elsius,, to degrees Fahrenheit, F. Which table could also represent this function? 33 The function y = 4 x + 3 represents a linear 5 function. omplete the table below so that it also represents this function. 6

7 34 The cost of parking in a garage in the city includes a $5 flat fee plus an additional $2.50 for each hour the garage is used. Which graph best represents this problem? 36 worm is 11 millimeters long when it hatches and is growing at a rate of 2 millimeters per day. Which equation best represents the functional relationship between l, the current length of the worm in millimeters, and d, the number of days that have passed since the worm has hatched? d = 10l d = l l= 10d l= d 37 What is the slope of a line that passes through the points (-1, 1) and (1, -15)? Record your answer and fill in the bubbles below. 38 The graph below represents the water level in Paul s glass after his workout. 35 n electrician charges $100 for each house call plus an additional $65 for each hour worked. Which best represents the functional relationship between the total charge, (h), and the total number of hours worked, h? (h) = 165h (h) = 100h + 65 (h) = h (h) = h Find the rate of change of the water level in Paul s glass and explain what the rate of change means. 7

8 39 Which representation does NOT have the same slope as the line graphed below? 41 taxi charges a flat fee for each ride plus an additional charge for each mile traveled. The graph below shows how the total charge for a ride changes depending on m, the number of miles traveled. line passing through ordered pairs (6, 0) and (3, -1) What does the slope of the graph represent? The flat fee, $0.50 The flat fee, $3.00 The additional charge per mile, $0.50 The additional charge per mile, $1.00 y = 1 3 x What is the y-intercept of the linear function graphed below? The height of the paper airplane is increasing one feet for every three second. 40 Graph a line with an x-intercept of 8 and a y-intercept of -6. Record your answer and fill in the bubbles below. 8

9 43 Find the slope of the linear relations represented by each table below. I. II. III. IV. 44 etermine the x and y-intercepts for each representation below. I. II. III. 45 The liner of an above-ground swimming pool is leaking a certain amount of water each day. The graph below shows how the total height of water in the pool has changed after the leak began. What does the x-intercept of the graph represent? The height of the water in the pool when the leak began, 28 inches The number of days it will take before the height of the water in the pool is 0 inches, 14 days The rate at which the water is flowing out of the pool, 14 inches per day The total number of days, 28. 9

10 46 The graph below represents a linear function. 49 How does the graph of y = 2x + 1 compare to the graph of y = x + 1? Which function represents the line above? The graph of y = 2x + 1 is the result of a shift of the graph of y = x + 1 down 2 units. The graph of y = 2x + 1 is a reflection of the graph of y = x + 1 across the x-axis. The graph of y = 2x + 1 is less steep than the graph of y = x + 1. The graph of y = 2x + 1 is steeper than the graph of y = x + 1. f(x) = 1 4 x + 1 f(x) = 1 4 x 1 f(x) = 4x 1 f(x) = 4x Give the equation of the linear parent function. Then graph the linear parent function. 47 The graph of the linear equation y = 1 2 x + 1 is shown below. 51 If m > 1, how does the graph of y = mx compare to the graph of y = x? What is the value for x when y=13? The graph of y = mx is less steep than the graph of y = x. The graph of y = mx is steeper than the graph of y = x. 48 If c is a positive integer, how does the graph of y = x + c compare to the graph of y = x? The graph of y = x + c is steeper than the graph of y = x. The graph of y = x + c is less steep than the graph of y = x. The graph of y = x + c is the result of a shift of the graph of y = x upward. The graph of y = x + c is the result of a shift of the graph of y = x downward. The graph of y = mx is the result of a shift of the graph of y = x upward. The graph of y = mx is the result of a shift of the graph of y = x downward. 52 What is the equation of the line that passes through the point (-2, 1) and has a slope of 4? y= 4x + 9 y= 4x 7 y= 4x 2 y= 1 4 x

11 53 Write the equation of a line in point-slope form with a slope of 1 that passes through 2 the point ( 8,3). 57 Which graph represents a direct variation? 54 Mr. Joyner is at a hotel 240 miles from his home. The graph below shows how long it will take him to reach his home if he drives at a constant rate of 40 miles per hour. How would the graph change if Mr. Joyner chose to drive at a constant speed of 60 miles per hour instead? The x-intercept would increase. The x-intercept would decrease. The y-intercept would increase. The y-intercept would decrease. 55 Tell whether the lines representing the equations below are parallel, perpendicular, or neither. 7x 4y = 4 x 4y = 3 perpendicular parallel neither 56 Given the graph below. Show that PQRS is a rectangle. (Hint: In a rectangle, all four angles are right angles.) 11

12 58 Traveling at an average speed of 40 miles per hour, a limousine drive made the trip from his headquarters to the airport in 3 hours. If the return trip back to headquarters took 2.5 hours, what was the driver s average speed, in miles per hour, on the return trip? Record your answer and fill in the bubbles below. 60 Mel works as a waiter. He calculates his hourly earnings in dollars, y, based on the number of tables, x, that he serves. He determined that he earns $4 for each table he serves plus his hourly rate of $5. What is the fewest number of tables he must serve per hour in order to earn more than $25 per hour? 4 tables 5 tables 6 tables 7 tables 61 Graph the inequality 2x 3y Which inequality is represented by this graph? 62 Which point is not part of the solution set of the inequality represented by this graph? y < 1 3 x 2 y > 1 3 x 2 y < 3x 2 y > 3x 2 (-3, 2) (0, 0) (1, 1) (4, -2) 12

13 63 Steve purchased x Vs at $20 each and y s priced $10 each. He spent less than $90, not including tax. The inequality 20x + 10y < 90 can be used to represent his purchase. Which point represents a reasonable number of Vs and s that Steve purchased? 66 Which scatterplot shows no correlation? (5, 1) (1, 8) (2, 3) (4, 4) 64 Justin borrowed $200 from his father. Each week, he pays back $15. If he currently owes his father fewer than d dollars, which inequality could be used to represent the amount Justin still owes if he has been paying back the loan for w weeks? w > d w < d w > d w < d 65 The scatterplot below shows the number of hours each of 12 students spent working on their science fair projects and the grades earned. What is the closest equation to a line of best fit for this scatterplot? y = 7 2 x + 67 y = 7 2 x + 53 y = 2 7 x + 67 y = 2 7 x

14 67 The scatterplot below shows the daily high temperature at the beach and the number of beach passes sold that day for a sample of 13 days. 69 Neal kept track of the number of minutes it took him to assemble sandwiches at his restaurant. Number of sandwiches Minutes What is the best prediction of the number of passes that would be sold on a day with a daily high temperature of 72 F? 68 The price of a cup of soup at Sam s Soup Stand varies according to the type of soup. On the grid below, Sam recorded the price of each type of soup and the number he sold in one day. I. Graph a scatterplot of the data. II. raw a trend line. III. escribe the correlation. IV. ase on the trend line you drew, predict the amount of time it will take Neal to assemble 12 sandwiches. Which best describes the trend, if any, shown by the scatterplot? s the price of a container of soup increases, the number sold increases. s the price of a container of soup increases, the number sold decreases. s the price of a container of soup increases, the number sold remains constant. The scatterplot shows no trend. 14

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