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ALGEBRA – STUDY GUIDE TRIMESTER 1 (Holt Chapters 1-4) CHAPTER 1 1. If n is a real number, then 2n would never be part of which number set? (A) a real number (B) an irrational number (C) a rational number (D) an imaginary number (E) an integer 2. If 3n – 1 is an odd integer, what is true about 3n + 1? (A) It is an odd integer. (B) It is an even integer. (C) It can be an odd or even integer. (D) It is a prime number. (E) It is a perfect square. 3. If 3x 4 4 x y and x = 3, what is x y ? (A) -5 (B) -4 (C) 2 (D) 4 (E) 5 4. Which one of the following is false? (A) If m and n are odd, then m + n is even. (B) If m and n are even, then mn is even. (C) If m and n are odd, then mn is odd. (D) If m and n are even, then m - n is even. (E) If m and n are odd, then (m – 1)(n + 1) is odd. 5. Which property is shown by the equation? 3 2 3 2 (9 15) 6 9 (15 6 ) 5 9 5 9 A. Associative Property of Addition B. Distributive Property C. Commutative Property of Addition D. Identity Property of Addition E. Inverse Property 6. Which set of numbers contains the fewest number of elements? (A) whole numbers (B) natural numbers (C) integers (D) real numbers (E) rational numbers 7. If y x 2 x 4 2 x 1 and x 3 , then 1 y (A) (D) 1 9 1 11 1 21 1 (E) 7 (B) (C) 1 11 8. If m is a positive odd integer and n is a negative even integer, what MUST be true about the sum of m and n? (A) The sum is a negative even integer. (B) The sum is a positive even integer. (C) The sum is a negative odd integer. (D) The sum is a positive odd integer. (E) The sum cannot be equal to zero. 9. If 2n 2 is an even integer, what is true about n + 1? (A) It is an even integer. (B) It is an odd integer. (C) It can be an odd or even integer. (D) It is a prime number. (E) It is a perfect square. 10. The equation 3(4a 5b) (4a 5b)3 demonstrates which property? (A) Distributive Property (B) Associative Property of Addition (C) Associative Property of Multiplication (D) Commutative Property of Addition (E) Commutative Property of Multiplication 11. If the lengths of the sides of a square are integers, which of the following could be the area of the square in square units? (A) 1 (B) 2 (C) 6 (D) 8 (E) All of the above 12. Which expression is equivalent to 3(2 x y 2 ) ? A. 3xy2 B. 9xy 2 C. 6 x 3 y 2 D. 5 x 6 y E. 6 x 3 y 2 13. Evaluate x 3 2 x 2 5 x 10 for x = -3. (A) -80 (B) -75 (C) -70 (D) -69 (E) -65 14. Which operation is NOT CLOSED under the set of integers? A. addition B. subtraction C. multiplication D. division E. none of these 15. Which of these sets of numbers is a subset of rational numbers? A. imaginary B. whole C. irrational D. real E. none of these 16. Simplify 2(6x + 7) - 5(x + 3). A. 7x – 1 B. 7x + 1 C. 7x + 19 D. 17x – 1 E. 17x + 19 21. Which property is used in this equation: (5 x 7 y )1 5 x 7 y ? A. Associative Property of Addition B. Associative Property of Multiplication C. Identity Property of Addition D. Identity Property of Multiplication E. Inverse Property of Multiplication 22. If x =-3 and y 2 x 4 6 3x , then what does y equal? A. -13 B. -5 C. 5 D. 13 E. 17 17. What is the first step in simplifying 2 3(2 x 1) ? A. add -2 and -3 B. add 2x and -1 C. multiply -2 by -3 D. multiply -3 by 2x E. add 2 to both sides 23. Which of these values is not an integer? A. -2 B. 0 C. 36 16 1 D. E. 4 2 18. 24. -1 T 0 Which of the following values could NOT be the value of T on the number line above? 3 A. 5 D. B. 0.6 2 3 19. If x = A. -18 D. 6 5 C. 7 3 3 and form a pair of 4 4 A. multiplicative inverses B. identities C. reciprocals D. additive inverses E. none of these 2 E. NONE OF THESE 1 and y = -6, then xy2 2 B. -12 C. -6 E. 18 20. Martin changed the expression a a b into 0 b by using which property? A. Inverse Property of Addition B. Distributive Property C. Associative Property of Multiplication D. Identity Property of Addition E. Identity Property of Multiplication CHAPTER 2 1. When a number n is subtracted from 18 and the difference is divided by n, the result is 2. What is the value of n? (A) 4 (B) 6 (C) 8 (D) 10 (E) 14 2. Christoph has 9 more baseball trading cards than Miguel. The number of cards that they have combined is 45. If c represents the number of cards Miguel has, which equation correctly represents the situation? (A) 2c + 9 = 45 (B) c + 9 = 45 (C) c = 45 (D) 3c + 9 = 45 (E) 2c + 9 = 45 - c 3. Bill and Ross are twins. Their brother Mark was born on the same day as the twins, but is three years older. If Mark was born in 1990, in what year did the three boys’ ages total 21? (A) 1995 (B) 1996 (C) 1997 (D) 1998 (E) 1999 4. Solve the equation for x: y = mx + b. y b (A) x = y - m – b (B) x = m (C) x = my + b (D) x = y + m + b y b (E) x = m 5. The perimeter of a rectangle is 54 in. The length is 3 in. more than the width. What is the length of the rectangle? (A) 13 in. (B) 15 in. (C) 25.5 in. (D) 28.5 in. (E) 31 in. 6. Mr. Lawrence stops at a gas station. He has enough cash in his pocket to buy nine gallons of gas. If the cost of each gallon of gas was 20 cents less, Mr. Lawrence could buy one more gallon. How much cash does Mr. Lawrence have? (A) $18.00 (B) $19.00 (C) $20.00 (D) $22.00 (E) $25.00 7. Leroy travels often for his job. He has figured that he must pay $650 per month for rent, $2 per day for water for every day he is in his apartment, and $4 per day for electricity for every day he is in his apartment. If x represents the number of days Leroy is in his apartment, which of the following represents the amount Leroy pays each month for rent, water, and electricity? (A) x + 656 (B) x + 830 (C) 6x + 650 (D) 650x (E) 830x 8. Kelly’s class is collecting box tops. Kelly has collected 75 and plans to collect an additional 4 box tops each week. The equation y = 75 + 4x can be used to represent this situation. How many weeks will it take her to collect 119 box tops? (A) 8 (B) 11 (C) 15 (D) 44 (E) 48 9. If x = -3 and x 2 xy 15 , what is the value of y ? (A) -2 (B) -1 (C) 2 (D) 3 (E) 5 10. (0,y) y x (5,0) If the area of the triangle shown is 30 square units, what is the value of y ? (A) 5 (B) 6 (C) 8 (D) 10 (E) 12 11. The equation y = 3x + 7 is equivalent to which of the following? 3x y 7 A. 3x y 7 B. 3 3x 7 C. 3x y 7 D. y 1 E. x y 7 3 12. If 3x - 2 = y, which of the following is equal to y - 2? (A) 3x (B) 3x – 4 (C) 3x + 2 (D) 3x + 4 (E) 3x + 8 13. If 5x 8 a 2 , which of the following is equal to a? (A) 5x (B) 5x – 6 (C) 5x - 2 (D) 5x + 2 (E) 5x + 6 14. The lengths of the sides of a rectangle are consecutive even integers. If the perimeter of the rectangle is 28 units, what is the area of the rectangle in square units? (A) 14 (B) 24 (C) 28 (D) 32 (E) 48 15. If 4y = 3x - 1, then 3x = 4 A. 4y + 1 B. y 1 3 4y 1 4y 1 D. E. 3 3 C. 4 y 1 3 16. Solve for y: 2a z x 2a z C. y x E. y 2ax zx xy z a ? 2 A. y B. y 24. Twice the sum of two consecutive integers is 10 fewer than 5 times the smaller integer. Find the greater integer? A. 12 B. 14 C. 13 D. -6 E. -8 2( a z ) x 25. Which expression represents the verbal phrase “the sum of three times a number and five”? A. 3(n + 5) B. 3 + n (5) C. 3(5) + n D. 3 + (n +5) E. 3n + 5 D. y 2ax zx 17. Find x -5 if 2( x 1) 16 ? A. 9 B. 14 C. 7 D. 4 E. 28 18. If x represents an odd integer, which would represent the previous consecutive odd integer ? A. x B. x 1 C. x 2 D. x 1 E. x 2 19. If 4x + 3 = 2x + y, then 2x = A. y – 6 B. y – 3 C. y + 3 D. 2y – 3 E. 2y + 3 20. The value of Mrs. Jones’ car decreases by $1000 each year. If she paid $18,000 for her car in 2000, which expression tells how much the car was worth in 2003? A. 18000-1000 B. 1800 0+2000 C. 18000+3000 D. 18000-2000 E. 18000-3000 21. Which of the following is an identity? A. x + 0 = 3x B. 1 2( x 1) x 1 C. 5 x 6 y D. ( x 2) x 2 E. 3 x 6 3( x 2) 22. Solve for p in the equation q 1 A. p 100q 1 100 q E. p 100(q 1) C. p 1 q 1 B. p 100 q D. p 1 100 23. Solve for x: 2 x p . 100 B. x = -26 D. x = 26 E. x = 54 C. x = 27. Which value of h makes the equation true? 3 (24 8h) 2(5h 1) 4 11 A. h = 1 B. h = C. h = 3 4 17 D. h = E. h = 4 4 28. Which operation is used on both sides of the equation to solve it: A. Add 3 4 D. Multiply by 3 x 24 4 B. Subtract 3 3 C. Multiply by 4 4 4 3 B. w 3 2 C. w 5 D. w 7 2 E. w 1 5 18 5 E. Divide by 3. 29. The number line below represents the solution to which equation? A. w 1 8 x 40 7 A. x = -54 26. Hector has 6 times as many coins as Wilma. If Hector has 126 coins, which equation would you use to find out how many coins Wilma has? A. c + 6 = 126 B. 6c = 126 C. 6(126) = c 126 6 D. c E. 126c = 6 6 CHAPTER 3 1. Maxine graphed an absolute value inequality and found that the solution set was all the numbers between -4 and 6. This solution is an example of which? (A) injunction (B) identity (C) contradiction (D) disjunction (E) conjunction 2. Your soccer team averages between 1 and 5 goals per game. Which absolute value inequality describes the average number x of goals per game? (A) x 2 5 (B) x 3 5 (C) x 3 2 (D) x 2 5 (E) x 2 5 4. For what values of x is 2 x 1 3 8 ? (A) x < 2 (B) -2 < x < 3 (C) -3 < x < 2 (D) x < -2 or x >3 (E) x <-3 or x > 2 5. Which of the following is equivalent to 3 x (2 6 x) 28 ? A. x 10 B. 3x 30 C. 3x 2 32 D. 3x 2 6x 28 E. 6 x (4 12 x) 14 6. Which of the following is the graph of the solution set of -2x - 2 x + 10? B. C. D. A. B. C. D. E. 9. Which statement is false? 3. What is the smallest integer that satisfies the inequality 4x + 5 > 2x - 3? (A) -5 (B) -4 (C) -3 (D) 4 (E) 5 A. 8. Which of the following is the graph of the solution set of x 3 3x 5 ? 6 3 2 A. 3.02 3.2 B. C. 2 4 4 2 D. 13 2 13 13 13 2 E. 53 (5) 3 10. Solve: x 1 x 2 2 4 1 2 D. x > 3 B. x < 2 A. x < C. x > 2 E. x < 3 11. Which graph represents the solution of 6 x 3 1 ? A. B. C. -4 4 -4 4 -4 4 -4 4 -4 4 E. 7. If x 2 5 x 14 0 , then which of the following can NOT equal x? A. -21 B. -19 C. 1 D. 3 E. 19 D. E. CHAPTER 4 1. What is the equation of the function that matches the table? 2 2 A. y x B. y 2 x 9 C. y x 2 5 5 3 D. y x 2 E. y 3x 11 4 2. What is the range of the function graphed? A. all real numbers B. all real number less than or equal to -3 C. all real numbers less than or equal to 2 D. all real numbers greater than or equal to 2 E. all real numbers greater than or equal to -3 3. A technology consultant charges her clients a $50 estimation fee plus $65 per hour. Which function best represents how she figures her total bill? A. f (x ) = 65x B. f (x ) = -65x + 50 C. f (x ) = 65x – 50 D. f (x ) = 50x + 65 E. f (x ) = 65x + 50 4. The sum of three consecutive odd numbers is 327. This can be represented by the equation, n + (n - 2) + (n - 4) = 327. What does n represent? A. The least integer B. The greatest integer C. The sum of the integers D. The integer in the middle E. The number of integers 5. If f (x ) = x 2 2 x 3 then f (-3) = (A) -18 (B) -12 (C) -6 (D) 6 (E) 18 6. If f (a) = 11, then use the table tofind f (a - 2). (A) 4 (B) 7 (C) 9 8. The graph of f (x) is shown. What is the value of f ( 0) ? (A) -3 (B) -2 (C) 0 (D) 2 (E) 3 9. Which of the following best describes the correlation between the variables x and y in the scatter plot? A. B. C. D. E. strong positive correlation weak positive correlation strong negative correlation weak negative correlation no correlation 10. What is the difference between the price for a 300-page novel on the trend line and the actual price of a 300-page novel? (D) 16 (E) 21 7. The table of values given can be derived from which one of the following functions? A. f (x) = 2x + 10 C. f (x) = 2x 2 E. f (x) = x – 6 B. f (x) = x + 2 D. f (x)= 4 - x A. $0 B. $1 C. $3 D. $6 E. $8 11. Which is the most reasonable predicted annual average dial-up modem sales for a store in Year 6? 15. Which pair of variables could be supported by this scatter plot? 12. The graph below shows the horsepower needed as the revolutions per minute of an agitator increases. What is the most valid statement about this function? A. x = the price per gallon of gasoline y = number of miles driven B. x = hours worked y = amount of free time C. x = capacity of gas tanks in cars y = amount of miles driven on one tank of gas D. x= monthly rainfall amount for a community y = amount of watering done by a resident in the community E. x = amount of time a person spends at baseball games y =amount of time a person spends on his woodworking hobby A. The domain includes both positive and negative values. B. The range includes both positive and negative values. C. For at least one x-value there is more than one y-value. D. For at least one y-value there is more than one x-value. E. The domain includes the set of all real numbers. 16. Which situation would require the use of a piecewise function? A. The Lions Club earns 15% of total sales if they sell 100 or fewer candy bars and 20% if they sell more than 100. B. Sarah charges $6 per hour to babysit on weekdays and $8 per hour on Friday and Saturday. C. Al’s Plumbing charges a service call of $25 plus $40 per hour for plumbing issues. D. Roberto has taken three quizzes so far and wants to have an average of at least 90 percent. E. The population of a particular city increased for two years and then decreased for the next three. A. 500 B. 100 C. 50 D. 5 E. 1 13. The bus company in town sells a bus pass each year for $8.50, and then charges $0.25 a ride. Using the function f (b ) = 0.25b + 8.5, how much will it cost someone to ride the bus 38 times? A. $9.50 B. $18.00 C. $20.00 D. $9.50 E. $118.00 14. Let f (x) = 0.4 + .85x be the equation of the line-of-best-fit used to approximate the data on a scatter plot. What would be the approximate value of f (5)? A. 4.65 B. 5.41 C. 6.25 D. 8.25 E. 24.25 17. When you graph the function y x 1 for x=-3, -2, -1, 0, 1, what type of shape is made? A. line B. C-shape C. U-shape D. V-shape E. none of these Answer Key—Trimester 1 Final Exam Study Guide CHAPTER 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 D A C E A B E E C E A E C D B A D E E A D A E D CHAPTER 2 1 B 2 A 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 E E B A C B A E A B E E A A D C B E E E E C E B A D B CHAPTER 3 1 E 2 3 4 5 6 7 8 9 10 11 C C C B B C C D B A CHAPTER 4 1 C 2 D 3 E 4 B 5 B 6 B 7 D 8 B 9 C 10 C 11 C 12 D 13 B 14 A 15 C 16 A 17 D