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Algebra I: 1st Semester Exam Review

Chapter 1

1. Label the appropriate set of numbers. Write two examples for each set of numbers.

2. Write algebraic expressions.

a. 8 less than the product of a number and 4

b. The quotient of 14 and a number squared

3. Write verbal expressions.

a.

b.

c.

4. Evaluate if and .

a. b.

5. Simplify.

a. b.

6. Express the relation {(1, 1), (0, 2), (3, –2)} as a table, a graph, and a mapping. Determine the domain

and range.

7. Determine if each relation is a function.

a. b. {(–3, –3), (–3, 4), (–2, 4)} c.

8. If – and – , find each value.

a. f(4) b. g(2) c. f(–5)

9. Identify the graph as linear or nonlinear. Then explain what the graph represents.

a. b. c.

Identify the property that justifies each of the equality expressions below.

10. – –

11.

12.

13.

14.

15.

Chapter 2

Translate each sentence into an equation or formula.

1. Three times a number t minus twelve equals forty.

2. One–half of the difference of a and b is 54.

3. Three times the sum of d and 4 is 32.

4. The area A of a circle is the product of π and the radius r squared.

Translate each equation into a sentence.

5. 4a – 5 = 23

6. 10 + k = 4k

7. V =

Bh

8. 3(g + h) = 12

Solve each equation. Check your solution.

9. h – 3 = –2 10. w + 2 = –13 11.

w = -9

12. 5 =

13. 5x + 3 = 23 14. 4 = 3a – 14

15. 5 +

= 1 16.

= 2 17. 2m + 12 = 3m – 31

18. 6(–3v + 1) = 5(–2v – 2) 19. 3(8 – 3t) = 5(2 + t) 20.

v – 6 = 6 –

v

Write an equation and solve each problem.

21. Twice a number plus four equals 6. What is the number?

22. Sixteen is seven plus three times a number. Find the number.

23. Find two consecutive even integers whose sum is 36.

Evaluate each expression if t = 3.

24. 25.

Solve each equation. Then graph the solution set.

26. 27.

Determine whether each pair of ratios are equivalent ratios. Write yes or no. Show your work below each question.

28.

,

29.

,

30.

,

Solve each proportion. If necessary, round to the nearest hundredth.

31.

=

32.

=

33.

=

Find the total price of each item.

34. basketball: $17.00 35. concert tickets: $48.00

tax: 6% tax: 7.5%

Find the discounted price of each item.

36. CD: $15.99 37. shirt: $25.50

discount: 20% discount: 40%

Chapter 3

Determine whether each equation is a linear equation. Write yes or no. If yes, write the equation in standard form.

1. 4x – 2y = –1 2. 3xy + 8 = 4y 3.

= 12 – 4x 4. y = + 7

Determine the x– and y-intercepts of the following linear equations.

5. 2x + y = –2 6. 3x – 6y = –3 7. –2x + y = –2

Find the slope of the line that passes through each pair of points.

8. 9. 10. (2, 5), (3, 6) 11. (6, 2), (–6, 1)

Suppose y varies directly as x. Write a direct variation equation that relates x to y. Then solve.

12. If y = 4 when x = 2, find y when x = 16. 13. If y = 9 when x = –3, find x when y = 6.

Determine whether each sequence is an arithmetic sequence. Write yes or no. Explain.

14. 1, 5, 9, 13, 17, . . . 15. 1, 3, 9, 27, 81, . . .

Write an equation for the nth term of each arithmetic sequence. Then graph the first five terms of the sequence.

16. 1, 3, 5, 7, . . . 17. –4, –9, –14, –19, . . .

Write an equation in function notation for the relation shown in the table. Then complete the table.

18. x –1 0 1 2 3 4

y –2 2 6

19. x –2 –1 0 1 2 3

y 10 7 4

Chapter 4

Write an equation of a line in slope-intercept form with the given slope and y-intercept.

1. slope: 8, y-intercept –3 2. slope: –2, y-intercept –1 3.

Graph each equation using a table, intercepts, or slope and y-intercept.

4. 5 6. –

Write an equation in point-slope form for the line that passes through each point with the given slope.

7. 8 (2, 1), m = 4 9. (–7, 2), m = 6

Write each equation in standard form.

10. y + 3 = –(x – 5) 11. y – 4 =

(x + 3)

Write each equation in slope-intercept form.

12. y + 4 = 4(x – 2) 13. y – 5 =

(x – 6)

Find the inverse of each relation.

14. f (x) = 4x – 3 15. f (x) = –3x + 7 16. –

Write the equation of the line in slope intercept form given the following descriptions. You may use either slope-

intercept form or point-slope form to write your equations.

17. (8, 2); slope

18. (–1, –3); slope 5

19. – 20.

21. goes through the point (–2, 2) and is parallel to the line y = 4x – 2.

22. goes throught the point (4, 2) and is perpendicular to the line y =

x + 1.

Determine whether each graph shows a positive correlation, a negative correlation, or no correlation. If there is a

positive or negative correlation, describe its meaning in the situation.

23. 24. 25.

4.

26. The table shows the number of students per computer in Easton High School for certain school years from

1996 to 2008.

Year 1996 1998 2000 2002 2004 2006 2008

Students per Computer 22 18 14 10 6.1 5.4 4.9

a. Determine what relationship exists, if any. Explain.

b. Use the points and to write the

slope-intercept form of an equation for the line of fit.

Chapter 5

Solve each inequality.

1. t – 12 ≥ 16 2. n – 12 < 6 3. 6 ≤ g – 3

4.

≤ 2 5.

≥ –3 6.

< –6

7. 25 ≥ –2m 8. 6n + 12 < 8 + 8n 9. –12 – d > –12 + 4d

10. 5r – 6 > 8r – 18 11. 3(2y – 4) – 2(y + 1) > 10 12. 8 – 2(b + 1) < 12 – 3b

Write an inequality and solve.

13. Twice the sum of a number and 4 is less than 12.

14. Three times the sum of a number and six is greater than four times the number decreased by two.

15. Twice the difference of a number and four is less than the sum of the number and five.

Solve each compound inequality. Then graph the solution set.

16. –4 < x + 2 ≤ –2 17. y – 1 < 2 and y + 2 ≥ 1

18. 3 < 3w or 3w ≥ 9 19. –3p + 1 ≤ –11 or p < 2

Graph each inequality.

20. y < 4 21. x ≥ 1 22. y ≤ 3x 23. y < –

x – 3

Chapter 6

Use the graph at the right to determine whether

each system is consistent or inconsistent and if it is

independent or dependent. Then determine the number of solutions that

each system has, if any.

1. y = x – 1 2. y = –x + 1 3. y = x – 1

x – y = –4 y = x + 4 2x – 2y = 2

Graph each system and determine the number of solutions that it has. If it has one solution, name it.

4. 2x – y = 1 5. x = 1

y = –3 2x + y = 4

Determine the best method to solve each system of equations. Then solve the system.

6. 3x – 5y = 7 7. 4x – 2y = -14 8. 2x + y = 0

5x + 3y = 16 3x – y = -8 5x + 2y = 2

9. Two times a number plus three times another number equals 13. The sum of the two numbers is 7. What are the

numbers?

Solve each system of inequalities by graphing.

10. 2x + y ≥ 1 11. y ≤ 2x + 3 12. 5x – 2y < 6

x – y ≥ –2 y ≥ –1 + 2x y > –x + 1