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Algebra I (PH) Name: __________________ 1 Midterm Review Hour: __________

Midterm Review 1

Unit 0

Evaluate the expression

1.) u + xy, for u = 18, x = 10, and y = 8. 2.) f(g) – h , for f = 11, g = 7, and h = 3.

3.) ( )2ab for a = 4 and b = 3. 4.) ( )ba −72 , for a = 2 and b = 6

Simplify the expression, write out all steps. Only do one operation at a time.

5.) 6.) 4123232 ÷+•

7.) 5 + 2• 8 – 4² 8.) ( )53058 ÷+

Evaluate each expression for m = -3, n = 4, p = 2

9.) pnm+

8 10.) ( )3mp

11.) ( ) nmp +−5 12.) pnm 3+−−


13.) For every real number x, y, and z, the statement is __________________ true. a. always b. sometimes c. never

Simplify each expression

14.) 7m + -2m 15.) 22 126 xx + 16.) ( )84 +x 17.) ( )723 −− y

18.) ( )m+− 8 19.) ( ) dd 445 +−

Unit 1 (Chapters 3 & 4) Solve the equation.

20.) x – 9 = 3 21.) 4g + 44 – 17 + 3g = 111

22.) 4(y + 4) = 40 23.) 24.) 25.) 7x – 4 -3x = 6x – 6

34


0 1 2 3 4 5 6 7 80–1–2–3–4–5–6–7–8 0 1 2 3 4 5 6 7 80–1–2–3–4–5–6–7–8

26.) 7d – d – 2d + 8 = 3d 27.) 28.) A customer went to a garden shop and bought some potting soil for $17.50 and 4 shrubs. The total bill was $53.50. Write and solve an equation to find the price of each shrub. 29.) Steven wants to buy a $565 bicycle. Steven has no money saved, but will be able to deposit $30 into a savings account when he receives his paycheck each Friday. However, before Steven can buy the bike, he must give his sister $65 that he owes her. For how many weeks will Steven need to deposit money into his savings account before he can pay back his sister and buy the bike? Write and solve an equation. Solve the inequality. Graph the solution on a number line. 30.) 𝟏𝟖 ≤ 𝒙

!𝟑+ 𝟏𝟔 31.)


0 1 2 3 4 5 6 7 80–1–2–3–4–5–6–7–80 1 2 3 4 5 6 7 80–1–2–3–4–5–6–7–8

32.) 2 + 2k ≤ 8 33.) 2(4y – 5) > –10

34.) −2 ≤ 3y+ 8 < 41 35.) −2 < 2𝑦 − 6 < 4

36.) Write 5 solutions for the inequality. x < 𝟑

𝟏𝟕 ________________________

37.) Write an inequality for the graph _________________________ In 38 & 39, Write an inequality to model the situation. 38.) Thomas earned no more than $40. 39.) You must be at least 18 to vote. _________________________ ______________________

0 1 2 3 4 5 6 7 80–1–2–3–4–5–6–7–8

0 1 2 3 4 5 6 7 80–1–2–3–4–5–6–7–8 0 1 2 3 4 5 6 7 80–1–2–3–4–5–6–7–8


Unit 2 & 3 (Chapters 5 & 6) 40. Lena makes home deliveries of groceries for a supermarket. Her only stops after she leaves the supermarket are at traffic lights and the homes where she makes the deliveries. The graph shows her distance from the store on her first trip for the day.

a) What is the greatest possible number of stops she made at traffic lights? b) Label each part of the graph.

41. Look at the grah to the right and then answer the following questions. a) What do the flat parts of the graph represent?

b) Circle the sections of the graph that show the speed decreasing.

42. Sketch the height of an airplane above the ground flying from Dallas to Atlanta. It is a non-stop flight there & makes 3 intermediate stops on the way back. Put time on the horizontal axis and altitude on the vertical axis.

43. Evaluate for x = 3.

44. Evaluate for x = 4.

Time

Distance


45. Use a mapping diagram to determine whether the relation is a function.

Is the relation a function? _______ Explain _______________________

_____________________________ _____________________________

46. A taxi company charges passengers $2.00 for a ride, no matter how long the ride is, and an

additional $0.20 for each mile traveled. a.Write a function rule to describe the amount you will be charged for a number of miles. c = money charged m = number of miles ________________________________ b. What is the charge for a 1-mile ride? ________________________________ c. What is the charge for a 2.7-mile ride? ________________________________

47. A snail travels at a rate of 2.37 feet per minute.

a. Write a rule to describe the function. _________________________ b. How far will the snail travel in 6 minutes? _________________________

In 48 – 49, Write a function rule for the table. 48._____________________ 49. ________________________

x f(x) 2 –8 3 –12 4 –16 5 –20

x f(x) 3 7 4 8 5 9 6 10


In 50 – 53 , Graph the function by making a chart with the domain –𝟐,−𝟏,𝟎,𝟏,𝟐 and find the range. Also describe the shape of the graph.

50. y = −2x+ 3 ______________

51. 𝑦 = 3𝑥 − 1 ______________

x y -2

-1

0

1

2

x y -2

-1

0

1

2


52. y = −2x²+ 3 ______________

53. y = x²− 2 ______________

54. What would the graph, 𝑦 = −3 𝑥 − 1, look like? 55. What are the x- & y- intercepts of the graph in # 50

Determine whether the relation is a function. Also write the domain and range for both.

56. ___________

57. _______________

x y -2

-1

0

1

2

x y -2

-1

0

1

2

Algebra I (PH) Name: __________________ 9 Midterm Review Hour: __________ For 58 & 59, find the slope of the line.

58. ________ 59. ________

For 60 & 61, write an equation in slope- intercept form. 60. Point: (4, -7) Slope: !

! 61. Two points: (–5, 6), (–2, 3)

62. 63.

Slope= _________________ Slope = _________________ Equation: _______________ Equation: ________________

1 2 3 4 5–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y

1 2 3 4 5–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y

1 2 3 4 5–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y

1 2 3 4 5–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y

Algebra I (PH) Name: __________________ 10 Midterm Review Hour: __________ In 64-65, find the slope of the given line. Then find the slope of the line parallel and the slope of the line perpendicular.

64. 65.

Slope of line: ___________ Slope of line: ___________

Slope of parallel line: __________ Slope of parallel line: __________

Slope of perpendicular line: _________ Slope of perpendicular line: _______ 66. Write an equation that is perpendicular to 𝑦 = − !

! 𝑥 + 7 and is through the point (-9, -4)

67. Write the equation in slope-intercept. -3x + 9y = -54 68. Determine if the lines are parallel, perpendicular or neither. EXPLAIN.

Line 1: (7, 11) & (0, 5) Line 2: (15, – 3) & (9, 4)

Slope: Slope:

Parallel, Perpendicular, Neither? ____________________________________ Explain.

1 2 3 4 5–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y

1 2 3 4 5–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y


In 69-70, use inductive reasoning to describe the pattern. Then find the next two numbers in the pattern.

69. 8, 13, 18, 23, . . .

70. –3, 6, –12, 24, . . .

In 71-72 find the common difference of the arithmetic sequence.

71. 22, 12, 2, –8, . . .

72. –8, –6.1, –4.2, –2.3, . . .

In 73 - 74 find the first, fourth, and tenth terms of the arithmetic sequence described by the given rule.

73.

74.

Chapters 7

In 75-76 solve the system of equations by graphing

75.) 𝑦 = 𝑥 − 3𝑦 = !

!𝑥 − 2 ________ 76.) 𝑦 = 2𝑥 + 6

4𝑥 − 2𝑦 = 8 _________

Algebra I (PH) Name: __________________ 12 Midterm Review Hour: __________ In 77- 80 solve the system of equations.

77.) 𝑦 = 2𝑥 − 10𝑦 = 4𝑥 − 8 78.) −4𝑥 + 3𝑦 = −12

−2𝑥 + 3𝑦 = −18

79.) 3𝑥 + 2𝑦 = 7

𝑦 = −3𝑥 + 11 80.) 3𝑥 + 5𝑦 = 105𝑥 + 7𝑦 = 10

In 80 - 81, how can you solve these systems by elimination? 80.) 5𝑥 + 2𝑦 = −22

3𝑥 + 10𝑦 = 22 ________________________________________________

81.) 3𝑎 + 2𝑏 = −1

−6𝑎 − 3𝑏 = 6 ______________________________________________ In 82 write a system of equations & Solve 82.) The sum of two numbers is 82. Their difference is 24. Find the two numbers by writing a system of equations. a.) Define 2 variables:_______________________________ _____________________________

b.) Write a System:

c.) Solve the system.

d.) Final Answer in words:

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