Midterm Review Integrated Algebra 1

Algebra 1 Name______Midterm- Review- Part 1 Date:______Test Format: Part I : 20 Multiple Choice (omit 2) 2 points each – No work shown - NO PARTIAL CREDIT Part II: 5 Short Response (choose 4) 2 points each – Show all work - PARTIAL CREDIT Part III : 10 Extended Response (choose 8) 4 points each – Show all work - PARTIAL CREDIT

Test Content: Holt Algebra 1—Chapters 1 – 6

Numbers and Operations 1. Which interval notation represents the set of all numbers from 2 through 7, inclusive? a. b. c. d.

2. Which interval notation represents the set of all numbers greater than or equal to 5 and less than 12? a. b. c. d.

3. The set is equivalent to a. b. c. d.

4. The set is equivalent to a. b. c. d.

5. Which set-builder notation describes ? a. b. c. d.

6. Evaluate x2 – 3xy – z when x = -1, y = 2 and z = -2 a. -5 b. 9 c. 11 d. 5

7. What is the multiplicative inverse of –3x + 2?

1 1 a. 3x –2 b. c. d.  3x  2 8. What is the multiplicative inverse of 7y – 2? 1 a. -7y + 2 b. 7y  2 1 c. - d. 7y - 2 7y  2

9. What’s the additive inverse of -56r+45 1 a. -56r-45 b. 56r-45 c. 56r+45 d. 56r  45

10. Which interval notation represents -2 < y < 18? a. [-2, 18] b. [-2, 18)

c. (-2, 18) d. (-2, 18]

11. For which of the following is the set {-1,0,1} closed? a. Multiplication b. Subtraction c. Division (for the non-zero element) d. Both choices A) and C)

Use the following information to answer questions #12-14 Universal Set ={-5,-3,-1,0,3,5} Set A = {-3, -1, 3, 5} Set B = {-5, 0, 1, 3, 5} Set C = {2, 4, 6} 12. What is A B ? a. {-5, -3, -1, 0, 1, 3, 5} b. {3, 5} c. {3,0} d. {0}

13. What is A B ? a. {-5, -3, -1, 0} b. {3, 5} c. {3,0} d. {0}

14. What is B  C ? a. {-5, -3, -1, 0} b. {3, 5} c. {3,0} d. { }

15. Which number is irrational? 2 a. 2.3 b. 10 c. d. 25 3 16. Which number is rational? a. b. 0.9 c.  d. 7.131131113…

17. The set {0, 1, 2} is closed under which operation? a. Addition b. Subtraction c. Multiplication d. Division

18. Evaluate 7x – 3(5-5x) when x = 1

19. What is the additive inverse of -5x+8? 2 20. Aaron claims that if a=-3 then a4 = -81. Is he correct? Explain why or why not. 21. What is the additive inverse of -4d – 5?

22. Evaluate 5(5a + 2b - 2c) – c when a = 1, b = -2, and c = 3

23. Complete this chart: Number Operation Closed/Not Closed? Set Integers Subtraction Integers Division Whole Numbers Subtraction {…,2,4,6,…} Squaring

24. Set U contains all integers greater than -10 and less than 10. Using proper set notation, list the members of the subset of Set U containing negative odd integers.

25. Evaluate the expression when a = -2 and b = -3, a 2  5ab  b

26. What is -72 equal to?

27. What interval notation represents 3

28. Express the following in scientific notation. 0.0000026

Solving Equations 1. Solve for x in terms of a and b. ax + b = 5b

2. Solve this equation for x in terms of y and z: 5x + 2y = 6z

3. Solve for y: 0.05y + 0.2 = 1.25

4. Solve for x: 4x+24=640

5. Solve for a: a – 14 = 4

6. Solve for x: 5.29 + 0.8x = 6.65

3 7. Solve the equation 5a – 3b = c for b 5x x 8. Solve for x:   19 6 5

9. In the equation A = p + prt, t is equivalent to:

10. Solve for x: 3.3 – x = 3(x – 1.7)

11. Solve for x: 14x + 3x - 65 = 600 – 2x

2 1 12. Solve for x:  x  20 x  9

13. Solve the equation for p in terms of m and t: 3p + 7m = t

14. Solve for x: 1.9 + 0.25x = 0.15

Inequalities

1. Solve for x and graph: -7x + 2 >51?

2. What is the smallest integer that makes the inequality -5x + 13 < 28 true?

3. What is the largest integer that makes this inequality a true statement: 17 – 4x  100

4. Draw the graph of y  5 y  2

5. Solve and graph on a number line and express your answer using interval notation: -11 < x – 4 < 8

6. What is the smallest integer that would make 5x-6>34 a true statement?

7. Solve and graph on a number line and express your answer using interval notation: x  2 x  3

8. Graph on a number line and write in interval notation: -5 < x < 2

4 Linear Functions

Graph the following linear equations:

(1) y = 2x – 1 (2) y = -½x + 2

(3) y = 5 (4) x = -3

(5) 3x – 4y = -4

(6) Is the point (-1, 3) on the line 2x + y = 7? Justify your answer algebraically.

5 (7) The point (3, k) is on the line whose equation is -3x – 2y = 5. Find the value of k.

Find the slope and y-intercept for each of the following linear equations:

(8) y = 3x + 5 (9) y = -x

(10) 2y = 4x + 5 (11) –y = -3x + 1

(12) x = 9 (13) y = -2

(14) 3x + 2y = 6 (15) 3y – 5x = 9

(16) What is the equation of the x-axis?

(17) What is the equation of the y-axis?

(18) Write an equation of a line whose slope is -⅝ and y-intercept is -7.

(19) Write an equation of a line whose slope is -⅓ and passes through the point (-6, 0).

6 (20) Write an equation of a line that passes through the points (3, 4) and (-3, 0).

(21) Write an equation of a line that is parallel to the line 2y – 4x = 9 and passes through the point (-2, 1).

(22) Write an equation of a line that is perpendicular to the line 3y + 2x = 6 and passes through the point (2, 4).

(23) What is the standard form of a linear equation?

(24) What is the process for determining if the graph of a relation represents a function?

(25) Given: Miles Driven 0 60 150 170 230 260 Gas Used (Gal) 0 2 5 6 9 11 Determine: a. if the data models direct variation. Justify your answer. b. the correlation coefficient (r). c. the line of best fit (a.k.a. linear regression equation) d. if miles driven is a good predictor of gas used. Explain. e. the amount of gas used if there were 1,000 miles driven.

7 Systems of Equations

1. Solve the following system of equations 2. Graph the solution set of each system below. graphically and check: a. 2x + y > - 4 2x + y = 8 x – y  1 y – x = 2

3. Solve the following system of equations by the addition method 5x – 2y = 20 2x + 3y = 27

4. Solve the following system of equations by the substitution method 3x – 2y = 4 y = 2x – 1

8 Mixed Word Problems

1. The width of a rectangle is 2cm less than the length. The perimeter is 200 cm. Find the length and width. Write an equation to express the dimensions of the rectangle.

2. The championship basketball game at North High School was this past Friday night. The school raised $600 in ticket sales. The tickets sold for $5.50 in advance and $8.00 at the door. If 100 tickets were sold, what was the number of tickets sold at the door? Only and algebraic solution will be accepted.

3. Two cars leave a gas station at noon traveling in opposite directions. One travels at 50 mph and the other at 60 mph. At what time will they be 220 miles apart?

4. Two trains leave the same station at the same time and travel in opposite directions. One train travels at 80 kilometers per hour and the other at 100 kilometers per hour. In how many hours will they be 900 kilometers apart?

5. Two trains leave the same station at noon traveling in opposite directions. One train travels 100 mph and the other 120 mph. AT WHAT TIME will the trains be 880 miles apart?

6. A coin bank contains nickels and dimes. The number of nickels is 6 more than three times the number of dimes. If the total value of the coins is less than $7.50. What is the greatest possible number of dimes in the bank?

7. Sal keeps quarters, nickels, and dimes in his change jar. He has a total of 52 coins. He has three more quarters than dimes and five fewer nickels than dimes. How many dimes does Sal have?

8. The sum of 2 consecutive integers is –15. What is the smaller integer?

9. The length of a rectangle is 6m more than the width. The perimeter is 20m. Find the length, width and area.

10. The owner of a movie theater was counting the money from 1 day’s ticket sales. She knew the total number of tickets sold was 150. Adult tickets cost $7.50 and each child’s ticket is $4.75. If $891.25 was collected that day how many of each kind were sold? (Only an algebraic solution will be accepted)

11. Sharon has $2.35 in nickels and in dimes. If she has a total of thirty-two coins, how many of each coin does she have?

12. Find three even consecutive integers such that three times the middle integer is ten more than the greatest. Find the integers. (Only an algebraic solution will be accepted)

13. Hertz Rent-a-car charges $75 per week to rent a car plus $3.75 per mile. Alamo charges $100 per week and $2.95 for each mile. For what number of miles are the companies’ prices the same?

14. Rental A charges $25.25 to rent a car plus $0.13 per mile. Rental B charges $31.45 plus $0.09 per mile. For what number of miles will Rental A and Rental B cost the same?

15. Kim has a cellular phone that costs $16.50 per month plus $0.45 per minute for each call. Bob’s plan costs $18.95 per month plus $0.25 per minute for each call. What is the minimum number of COMPLETE minutes for which Bob’s plan is more economical?

16. Jay has twice the number of dimes as he has quarters. He has five more nickels than quarters. Write an expression to represent the total number of coins that Jay has.