ALGEBRA 1 MID-TERM REVIEW STUDY GUIDE

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1 Name: Class: _ Date: _ ALGEBRA 1 MID-TERM REVIEW STUDY GUIDE Simplify: ( 3 + 4) 3 A B C D Evaluate qr q + r when q = 8 and r = 13. F. 1 G H I If the pattern shown is continued, what would be the total number of triangles in the ninth stage of the pattern? A. 36 B. 144 C. 180 D It is known that a cyclist can travel 41.4 miles in 3 hours. At that rate, how far can the same cyclist travel in 7 hours? F miles G miles H miles I miles 5 At Dr. Carrey's clinic, 42% more patients are treated for flu symptoms in the winter than in the summer. Which is an algebraic expression for the number of flu cases in the winter? A. w ( 0.58)w C. ( 0.58)w B. s + ( 0.42)s D. ( 0.42)s 6 Alicia runs for exercise. If Alicia runs 30 miles in six days, how many feet does she run per day? F. 8,800 ft H. 26,400 ft G. 22,629 ft I. 158,400 ft 7 A shipping service charges $0.43 for the first ounce and $0.29 for each additional ounce of package weight. Write an equation to represent the price P of shipping a package that weighs x ounces, for any whole number of ounces greater than or equal to 1. A. P = ( x 1) C. P = ( x 1) B. P = x D. P = x 1

2 Name: 8 The cost of renting a canoe is $5.25, plus $0.50 per hour for the time that the canoe is out. Which equation could be used to find C, the cost in dollars for using the canoe for H hours? F. C = H H. C = H G. C = ( )H I. C H = A store that sells gift baskets is having a promotional sale. Customers can make their own fruit baskets to use as gifts. Customers pay $3.00 for a basket and add $0.20 per pound for all types of fruit. The cost for a basket containing p pounds of fruit is $4.30. Which equation could be used to find p, the number of pounds of fruit in this basket? A p =4.30 C. 3.00Ê ËÁ pˆ = 3.00 B. ( ) p = 3.00 D p = A jumbo jet carries 330 passengers, 32 in first class, and the remainder in coach. If the average first class ticket is $860 and the average coach ticket is $360, how much will the airline gross if the plane is full? F. $267,800 G. $201,300 H. $137,780 I. $134, Roberto drove from Miami to Jacksonville along Interstate 95. He left Miami at 6:30 A.M. and stopped in West Palm Beach from 8:00 A.M. to 8:45 A.M. for breakfast. The only other stop he made was for 1 2 hour when he got off the highway to get gasoline and to stretch his legs. His average speed while driving on the highway was 50 miles per hour. If he reached Jacksonville at 2:30 P.M., how far did he drive, to the nearest 10 miles? A. 340 miles B. 370 miles C. 310 miles D. 400 miles 12 A used-book store sells paperback books for $1.30, with a $0.25 discount for each book more than 5 that a customer buys. A customer bought some books last week for $ The store has a sale this week. The price for each book is $1.15, with the same discount on each book over 5 purchased. How much would the customer save if the same books were bought this week? F. $12.05 G. $1.80 H. $0.05 I. $ The total height of a building and the flagpole on the roof is 208 feet. The building is 7 times as tall as the flagpole. How tall is the building? A. 234 feet B. 182 feet C. 156 feet D. 26 feet 14 Bartholomew's pet snake was 1.3 meters long one week ago. In 7 days it grew 22 centimeters. How long is the snake? F m G cm H cm I m 2

3 Name: 15 When Alexis works overtime (any hours over 40 hours a week), she is paid 1.5 times her regular hourly rate. In one week, she worked 51 hours. If her regular hourly rate is $7.05, how much did she earn that week? A. $ B. $ C. $ D. $ There are 64 teams in a soccer tournament. Each team plays until it loses one game. There are no ties. How many games are played? You may want to draw a diagram to look for a pattern. F. 63 games G. 64 games H. 62 games I. 65 games 17 A school soccer team has a game at 4:00 P.M. The team bus takes 30 minutes to travel from school to the field where the game is being played. After arriving at the field, the team needs to warm up for 45 minutes before the start of the game. Which is the best first step to take in order to find the time that the team should depart from the school? A. Add the time it takes to travel to the game to 4:00 P.M. B. Add the time needed to warm up to 4:00 P.M. C. Add the travel time and the warm up time together. D. Subtract the warm up time from the travel time. 18 Which function rule matches the input-output table? Input, x Output, y F. y = 3 + 5x G. y = 3 + 4x H. y = 4 + 3x I. y = 2 + 4x 19 A bag of chips costs $2.33. Your total grocery bill, b, is a function of the number of bags of chips, n, you purchase. Write an equation to represent this function. A. n = 2.33b C. B. b = 2.33 n b 2.33 = n D. b = 2.33n 20 Which equation corresponds to the values in the table below? Input, x Output, y F. y = 8x + 9 G. y = 9x + 7 H. y = 9x + 8 I. y = 10x For which value of x is the relation not a function? {(0, 1), (x, 0), (3, 5), (2, 6)} A. 1 B. 3 C. 4 D. 6 3

4 Name: 22 The table below shows the height of a plant over time. Bamboo Height Time (Week) Height Find the graph that shows the relationship between time and the height of the plant. F. The height of the plant increases over time. H. The height of the plant increases over time. G. The height of the plant decreases over time. I. The height of the plant decreases over time. 4

5 Name: 23 Employees earn $5 per hour plus $0.75 for every unit they produce per hour. Which of the following shows both an equation in which y represents the employee's wages for producing x units per hour, and the graph of the wages earned for producing 2, 5, 8, and 10 units per hour? A. y = x C. y = 5x B. y = 5x D. y = x 5

6 Name: 24 Use the vertical-line test to determine whether the graph represents a function. If not, identify two points a vertical line would pass through. F. Yes, the relation is a function. G. No, the relation is not a function. (0, 4) and (0, 4) 6

7 Name: 25 Which graph represents a function? A. C. B. D. 26 Select the description that matches the graph. F. integers greater than or equal to 5 G. integers less than or equal to 6 H. integers less than or equal to 7 I. integers greater than or equal to 6 27 Which of the following illustrates the associative property of addition? A. 7 + (2 + 3) = 7 + (2 + 3) C = B. ( ) + 3 = 11 + (12 + 3) D =

8 Name: 28 Which of the following illustrates the associative property of addition? F. (11 + 8) + 5 = 11 + (8 + 5) H = G. 3 + (3 + 1) = 3 + (3 + 1) I = On Monday, Kevin wrote a check for $575 to pay his rent. On Tuesday, he deposited a tax refund check for $638. On Friday, he wrote checks for $75 for groceries and $266 for a car repair. Which integer represents the overall change in his checking account balance for the week, in dollars? A. 278 C B. 916 D Identify the product that will be negative. F. ( 2) ( 3) ( 4) ( 5) H. ( 2) ( 3) ( 4) ( 5) G. ( 2) ( 3) ( 4) ( 5) I. ( 2) ( 3) ( 4) ( 5) Use the distributive property to write an equivalent expression. 31 4(x 4) A. 4x 4 B. 4x + 16 C. 4x 16 D. 4x Bill wants to simplify the following expression. 5Ê ËÁ 3x 2yˆ + 2Ê ËÁ x + 2yˆ 3Ê ËÁ 3x 2yˆ Which of the following expressions is equivalent to the expression above? F. 8x G. 8x 12y H. 8xy I. 8x 8y Ê 33 Find the quotient ˆ ËÁ 9 A B. 3 9 C. 9 4 D Estimate the square root to the nearest integer. 7 F. 3 G. 3 H. 49 I Which of the following is an irrational number? A. 9 C B. D

9 Name: 36 Complete the statement using < or >. 9 2? 9 4 F. 9 2 < 9 4 G. 9 2 > A gardener building a wooden garden gate wants to brace it as shown in the picture below. The gardener used the Pythagorean Theorem to determine that the brace must be 8 41 inches long. Which of the following numbers is closest to 8 41? A. 48 B. 320 C. 56 D A cube-shaped audio speaker has a volume of 112,000 cubic centimeters. Find the length of a side of the speaker to the nearest centimeter. F. 48 cm G. 45 cm H. 335 cm I. 46 cm Solve the equation = m 6 A. 22 B. 108 C. 12 D x + 12 = 26 F. 37 G. 38 H. 15 I A college student has budgeted $240 to use the coin-operated laundry facility in his dormitory. Each time he uses the machines, it costs $8.00. Choose the equation he can use to find x, the number of times he can do laundry. Then solve the equation. A. 240 = x 8; 248 times C. 240 = x + 8; 232 times B. 240 = 8x; 30 times D. 240 = x ; 30 times 8 9

10 Name: Solve the equation y 65 = 0 F. 520 G H. 520 I The perimeter of a rectangular garden is 860 ft. The two short sides of the garden are each 30 ft long. You are asked to find the length of the other sides. Which equation models this situation? A x = 860 C. 30( x 2) = 860 B. 2( 30) + 2x = 860 D x = Donny decides to manufacture and sell his band s CD. It requires an investment of $3349 for computer hardware and it will cost $3.65 for materials for each disk. If each CD sells for $13.50, how many must he sell to break even? F. 196 G. 340 H. 195 I For $46, Joel can rent a machine to make novelty buttons to sell at the county fair. The materials cost $0.39 per button. How many buttons must he sell at $1.40 each in order to make a profit? Identify the graph that shows all the possible answers. A. B. C. D. 46 Michelle wants to earn $900 selling 22 knit scarves. She wants to sell each scarf for $4 less than her competitor. If x is the price charged by her competitor, which equation models the situation? F. 2( 22) + 2x = 900 H. 22( x 4) = 900 G. 22x = 900 I x = The perimeter of a rectangular garden is 690 ft. The two long sides of the garden are each 270 ft long. You are asked to find the length of the other sides. Which equation models this situation? A x = 690 C x = 690 B. 2( 270) + 2x = 690 D. 270( x 2) =

11 Name: 48 Tommy has 600 pennies in his collection. He plans to give 50 to his little brother and split the rest between himself and his two sisters. He wants to know how many pennies to keep for himself. Which equation models this situation? F x = 600 H. 3( 50) + 2x = 600 G. 50( x + 3) = 600 I x = A group of 94 students is taking a field trip to the planetarium. The buses used to take the students carry 13 students each. How many buses will be needed to take all of the students to the planetarium? Check to be sure your answer is reasonable. A. 8 C. 7.2 B. 6 D Two machines can complete 5 tasks every 4 days. Let t represent the number of tasks these machines can complete in a 31-day month. Which proportion can you use to find the value of t? F. G = t = t 5 H. I. 5 4 = t = t At a concert, people s hands were stamped as they walked in. To estimate the attendance, the staff randomly stamped 120 people's hands with a red stamp instead of blue. A random sample of 250 people in the crowd found 4 people with a red stamp. What is the best estimate for the size of the crowd? A people C people B people D. 11,250 people Solve the proportion. Check your solution. 52 y 2 = 6 24 F. 2 G. 1 4 H. 1 2 I In 2 hours a candymaker can produce 80 boxes that each contain 10 pieces of candy. How many pieces of candy does the candymaker produce in 6 hours? A. 480 pieces C pieces B pieces D. 600 pieces 11

12 Name: 54 The figure below represents a building in the shape of a pentagon. Using the scale 1 inch = 94 feet, what is the perimeter of the building? F. 376 feet H feet G. 470 feet I feet 55 Estimate the grade received on a test when 24 questions are answered correctly out of 40. A. 60% B. 76% C. 16% D. 24% 56 Mae answered 40 of 45 questions on a test. Of those she answered, Mae answered 6 incorrectly. Approximately what percent of all the questions on the test did she answer incorrectly or not answer? F. 25% G. 24% H. 89% I. 76% 57 Last month, a poll of 300 voters found that 123 of them approved of the job the senator was doing. This month, a new poll of 300 voters found that 156 of them were happy with the senator's performance. What is the percent of increase of the number of voters who approved of the senator? A. 26.8% B. 11.0% C. 52% D. 33% 12

13 Name: 58 Three candidates are running for mayor of Grenville. The results of the latest poll of registered voters are shown. Which of the following statements can be made based on the results of the poll? F. At least one candidate has the support of less than 15% of the registered voters in the poll. G. No candidate has the support of greater than 40% of the registered voters in the poll. H. Every candidate has the support of at least 25% of the registered voters in the poll. I. The difference between the percentage of support of the candidates with the greatest and the least support is over 20%. 13

14 Name: 59 A high school is choosing a color scheme for an upcoming dance. Students were given the opportunity to vote on the color. The results are shown in the table. Which of the following statements can be made based on the results? A. Less than 45% of the votes for purple came from sophomores and seniors. B. The percent of juniors who chose purple was greater than the percent of freshmen who chose green. C. The number of votes is highest in the junior class because the juniors are planning the dance. D. Green is the only color that was chosen by at least 25% of all of the voters. 60 The coefficient of friction, µ, is a ratio that compares the friction acting on a dragged object to its weight, w. The relationships between the mass m and the acceleration a of an object that is being dragged across a flat surface, such as a table top, by a force F, is given by the equation ma = F µw. What formula can you use to find the coefficient of friction? F. µ = ma F w G. µ = ma F H. µ = F ma w + w I. µ = F ma w 14

15 Name: 61 When x pounds of force is applied to one end of a lever that is L feet long, the resulting force y on the other end is determined by the distance between the fulcrum (the lever's pivot) and the end of the lever on which the x pounds of force is exerted. The formula relating the forces is xd = y( L d). What formula can you use to find the length of the lever? A. L = xd y B. L = xd + d y + d C. L = xd yd y 62 Name the coordinates of the points A, B, C, and D. D. L = yd x + d F. A (3, 3), B (4, 2), C ( 2, 1), D ( 5, 4) G. A ( 3, 3), B (4, 2), C (1, 2), D ( 5, 4) H. A (3, 3), B (2, 4), C ( 2, 1), D ( 4, 5) I. A ( 3, 3), B (2, 4), C (1, 2), D ( 4, 5) 15

16 Name: Make a table of values for the equation when x = 1, x = 0, and x = 1. Then graph the equation in a coordinate plane. 63 y = 5x A. x y C. x y B. x y D. x y What is the y-intercept of the line with the equation 4x + 9y = 108? F. 12 G. 12 H. 27 I

17 Name: 65 Which graph below would match the situation described? A car travelling at 23 mi/h accelerates to 45 mi/h in 5 seconds. It maintains that speed for the next 5 seconds, and then slows to a stop during the next 5 seconds. A. C. B. D. 66 Find the slope and y-intercept of the line with the equation 9x + 3y = 54. F. m = 3, b = 18 H. m = 3, b = 18 G. m = 18, b = 3 I. m = 18, b = 3 17

18 Name: 67 The equation y = 2 x + 3 is graphed below. Which graph shows the result of changing the 3 in the 5 equation to 1? A. C. B. D. Consider lines whose equations have the form y = m x Find the difference of the x-intercepts of lines l 1 and l 2 if their slopes are m 1 and m 2, respectively. 68 Which statement is always a correct conclusion about the values of x and y in the function y = x 3? F. The value of x is always 3 less than the value of y. G. The value of y is always less than the value of x. H. When the value of x is positive, the value of y is also positive. I. As the value of x increases, the value of y decreases. 69 Solve 2(32 + 8z) = 64 graphically. Check your solution algebraically. A. z = 12 C. z = 8 B. z = 16 D. z = 0 18

19 Name: 70 The number of gallons of paint needed to cover a wall varies directly with the area of the wall. The Robertsons find that they have used 1 2 gallon of paint to cover 540 square feet of wall. Which of the following equations shows the number of gallons of paint they will need, G, to cover s square feet of wall? F. G = s 540 G. G = 270s H. G = s 1080 I. G = s Choose an equation, in slope-intercept form, of a line with a slope 7 and a y-intercept of 9. A. y = 7x 9 C. x = 7y 9 B. y = 7x + 9 D. y = 1 7 x 9 72 Write an equation in slope-intercept form of the graph. F. y = 8 3 x 4 H. y = 3 8 x 4 G. y = 8 3 x 4 I. y = 3 8 x 4 73 Erik pays $225 in advance on his account at the athletic club. Each time he uses the club, $9 is deducted from the account. Write an equation that represents the value remaining in his account after x visits to the club. Find the value remaining in the account after 7 visits. A. V = 225 9x; $162 C. V = 225 9x; $2032 B. V = 9 225x; $162 D. V = 225 9x; $

20 Name: Which is the equation for the linear function f in the form f( x) = mx + b that has the given values? 74 f( 1) = 2, f( 6) = 17 F. f( x) = 3x 1 H. f( x) = 3x + 1 G. f( x) = 3x 1 I. f( x) = 3x f( 2) = 9, f( 0) = 3 A. f( x) = 3x 3 C. f( x) = 3x + 9 B. f( x) = 3x 3 D. f( x) = 3x The function f( x) = ( x 1) represents the cost (in dollars) of ordering x t-shirts printed with a specialty logo. Which description best fits the function? F. The cost includes a $15 fee plus $10 for each t-shirt. G. The cost is $10 for each t-shirt. H. The cost is $15 for the first t-shirt and $10 for each additional t-shirt. I. The cost is $15 for each t-shirt. 77 Determine whether the sequence 1, 7, 15, 23, 31,... appears to be an arithmetic sequence. If so, find the common difference and the next three terms in the sequence. A. Yes; common difference 8; next three terms are 23, 15, 7 B. Yes; common difference 7; next three terms are 38, 45, 52 C. Not an arithmetic sequence D. Yes; common difference 8; next 3 terms are 39, 47, Write an equation of the line that passes through Ê ËÁ 5, 1ˆ and is parallel to the line y = 4x 6. F. y = 4x + 19 H. y = 5x + 19 G. y = 4x 6 I. y = 5x 6 20

21 Name: 79 Find the equation of the line that passes through point A and is perpendicular to the line shown in the graph below. A. y = 2x + 9 C. y = 1 2 x + 9 B. y = 1 x 9 D. y = 2x Which of the following lines is NOT parallel to the line shown in the graph? F. 3x + y = 3 H. 12x + 4y = 9 G. y 3x = 9 I. 3x y = 3 81 Which pair of lines would be perpendicular when graphed? A. y = 3, x = 5 C. y = 2x, y = 1 2 x B. x = 4, y = x D. y = 3, y = x 21

22 Name: 82 The line y = 2x + 3 is graphed below. Are the lines y = 2x + 3 and 2y 4x = 6 parallel, perpendicular, neither parallel nor perpendicular, or the same line? F. the same line H. perpendicular G. neither parallel nor perpendicular I. parallel 83 Which equation matches the scatter plot? A. y = 2x + 1 C. y = 2 2x B. y = 2x 1 D. y = 1 2x 22

23 Name: 84 Presley is learning a foreign language. The scatter plot shows the total number of vocabulary words Presley has learned at the end of each of his first eight days in class. Assuming the trend shown by the scatter plot continues, which is the best prediction of the number of words Presley will have learned by his 10th day in class? F. 50 G. 20 H. 45 I Lev earns $5.65 per hour working after school. He needs at least $245 for a stereo system. Write and solve an inequality that describes how many hours he must work to reach his goal. A. x x 44 hours B x 245 x 44 hours C. 245 x 5.65 x 43 hours D x 245 x 45 hours 86 Which problem could be solved using the inequality 2c < 70? F. The product of 2 and a number is equal to 70. G. Two students split a restaurant bill that came to $70. H. Two equal-priced shirts came to at least $70. I. Marty earned under $70 for 2 hours of work. Solve. 87 5x + 5 > 25 A. x > 25 B. x < 4 C. x > 4 D. x < 25 23

24 Name: 88 On a road in the city of Rochester, the maximum speed is 50 miles per hour and the minimum speed is 20 miles per hour. If x represents speed, which sentence best expresses this condition? F. 50 x 20 H. 50 x 20 G. 50 x 20 I. 50 x Your veterinarian tells you that a healthy weight for your dog is between 70 and 80 pounds. Write an inequality to represent your dog's healthy weight w in kilograms. A. w 36.4 C w 36.4 B. 154 w 176 D. w 154 Solve. 90 4x + 2 = 3 F. 1 4, 5 4 G. 1 4, 5 4 H. 1 4, 3 4 I. 2,

25 Name: 91 Let g( x) be a shift of f( x) = x 3 units right. Write the rule for g( x) and graph the function. A. g( x) = x 3 C. g( x) = x + 3 B. g( x) = x 3 D. g( x) = x

26 Name: 92 Let g( x) be a shift of f( x) = x 4 units up. Write the rule for g( x) and graph the function. F. g( x) = x 4 H. g( x) = x 4 G. g( x) = x + 4 I. g( x) = x

27 Name: 93 Make a table of values for g( x) = x Use the following values for x: 1, 2, 3, 4, 5. Then graph the function and compare the graph with the graph of f( x) = x. A. The graph is 5 units to the left and 3 units below the graph of y = x. C. The graph is 3 units to the left and 5 units below the graph of y = x. B. The graph is 5 units to the right and 3 units above the graph of y = x. D. The graph is 3 units to the right and 5 units above the graph of y = x. 27

28 Name: 94 4x 2 < 3 Solve. Graph your solution. F. 1 4 < x < 5 4 G. x 1 4 or x 5 4 H. 1 4 x 5 4 I. x < 1 4 or x > Solve x and graph your solution. A. B. C. D. 96 x + 1 > 2 is equivalent to which of the following? F. 3 < x < 1 H. x > 1 G. x > 1 and x < 3 I. x < 1 28

29 Name: 97 x 1 > 4 is equivalent to which of the following? A. 3 < x < 5 C. x > 5 and x < 3 B. x > 5 D. x < x 2 3 is equivalent to which of the following? Ê F. 7 6 x 1 ˆ ËÁ 6 G. x 1 6 H. x 1 6 Ê I. 1 6 x 7 ˆ ËÁ 6 Graph. 99 y x 1 A. C. B. D. 29

30 Name: 100 y 7x 9 F. H. G. I. 30