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Name:Date:

Algebra I Final Review Sheet

You must show all work to receive full credit.

Chapter 1-3

Solve for each variable.

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1)y – 7 = 12

2)x + 12 = 19

3)-5 + z = 8

4)9x = 72

5)

6)

7)15 = 3 – 4x

8)

9)8 – (b – 2) = 11

10)-2x + 4 = 5 – 3x

11)3(q – 2) + 2 = 5q – 7 – 2q

12)5z = -3(z + 7)

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Solve each inequality and graph on the number line

13)2k – 6 > 3k + 2

14)2(5 – f) ≤ f + 12

15)

16)Dion needs to rent a moving van for the day. Company A charges $75 plu $0.25 for every mile driven. Company B charges $50 plus $0.75 for each mile. For how many miles is company B less expensive than company A?

17)-1 ≤ x – 3 < 3

18) t + 7 < 3 OR t – 1 > 4

19) d – 2 < 5 AND d + 1 ≥ 7

20)The driving school instructor has asked Lina to stay within 2 miles of the posted speed limits. The current road has a speed limit of 45 mi/h. Write a compound inequality to show Lina’s acceptable speed s.

Chapter 4: Functions

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21)Graph: y = x – 5

22)Graph: y = x2 – 5

23)Graph

24)The function y = 30x describes the amount of interest y earned in a savings account in x years. Graph the function. Use the graph to estimate the total amount of interest earned in 7 years.

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25)Make a scatter plot on graph paper of the given population data for the state of Indiana.

Year / Population
(in millions)
1900 / 2.5
1910 / 2.7
1920 / 2.9
1930 / 3.2
1950 / 3.9
1960 / 4.7
1970 / 5.2
1980 / 5.3
  1. Determine your best fit line.

Which points did you use (______, ______) and (______, ______)?

  1. Use linear interpolation to estimate the population in the year 1935 and 1945.
  1. Use your calculator to obtain the equation of the least squares line that will estimate the population if the year is known. (Use option 4 under the STAT CALC menu). Write the equation andr in the space below. Round the slope and the y-intercept to the nearest hundredth.

Y = ______r = ______

  1. Use the equation from part c to estimate the population in the following years:

2000______1940 ______1880 ______

  1. Choose an appropriate year for which you would use the least squares line to interpolate, backwards extrapolation and forwards extrapolation in order to obtain a population estimate. Explain why you chose that year.

26)Choose the graph that best represents each situtation.

  1. A person walks leisurely, stops, and then continues walking.
  2. A person jogs, then runs, and then jogs again.

27)Give the domain and range for each relation. Tell wheter the relation is a function. Explain.

28)Bowling costs $3 per game plus $2.50 for shoe rental. Identify the independent and dependent variable. Write a rule in function notation for the situtation.

29)Evaluate each function for the given input values.

  1. For f(x) = -3x + 4, find f(x) when x = -2.
  1. For g(x) = 2x2, find f(x) when x = -3.

30)An engraver charges a $10 fee plus $6 for each line of engraving. Write a function to describe the situtation. Find a reasonable domain and range for the function for up to 8 lines.

31)Graph each function and its given domain.

32)Graph each function and its given domain.

33)Graph each function and its given domain.

34)Sketch a graph for each situation and tell if it is continuous or discrete.

  1. Simon is selling candles to raise money for the school dance. For each candle he sells, the school will get $2.50. He has 10 candles that he can sell.
  1. Angelia’s heart rate is being monitored while she exercises on a treadmill. While walking, her heart rate remains the same. As she increases her pace, her heart rate rises at a steady rate. When she begins to run, her heart rate increases more rapidly and then remains high while she runs. As she decreases her pace, her heart rate slows down and returns to her normal rate.

35)In the winter, more electricity is used when the temperature goes down, and less is used when the temperature rises.

Dependent:

Independent:

36)The cost of shipping a package is based on its weight.

D:I:

Chapter 5: Linear Functions

37) Tell whether the given ordered pairs satisfy a linear function. Explain.

38)Lily plans to volunteer at the tutoring center for 45 hours. She can tutor 3 hours per week. The function f(x) = 45 – 3x gives the number of hours she will have left to tutor after x weeks. Graph the function and find its intercepts. What does each intercept represent?

For # 39:

39)Use the intercepts to graph the line described by 2x – 3y = 6.

40)Find the slope of each line. Then tell what the slope represents.

41)Tell whether each relationship is direct variation. If so, identify the constant of variation.

42)Write the equation 2x – 2y = 4 in slope – intercept form, and then graph.

For # 43:

43)Graph the line with slope that contains the point (-4, -3).

44)Write an equation in slope-intercept form for the line through (-1, 1) and (0, 3).

45)Identify which lines are parallel:

46)Identify which lines are perpendicular:

47)Write an equation in slope-intercept form for the line that passes through (0, 6) and is parallel to the line described by y = 2x + 3.

48)Write the equation in slope-intercept form for the line that passes throught (4, 6) and is perpendicular to the line described by y = x – 3.

49)Given the slope and an ordered pair write an equation in point-slope form. (y – y1) = m(x – x1)

  1. m = -5; (-2,-3)
  2. m = ¾; (2, -7)

50)Given an equation convert to standard form. Ax + By = C

  1. 2y = 5x + 3
  2. y = 8x – 1
  3. 5y + 3 = 2x
  4. 2x + 6y + 7 = 0

51)While on his way to school Matt saw that the costs of peaches were on sale for $1.50 per gallon. Write a direct varation equation to describe the cost of y of x pounds of peaches. Graph it.

Chapter 6: Systems of Equations

52)Tell whether the ordered pair is a solution of the given system.

53)Solve each sytem by graphing.

54)Solve each system by substitution.

55)The costs for services at two kennels are shown in the table. Brenna plans to board her dog and have him bathed once during his stay. For what number of days will the cost for boarding and bathing her dog at each kennel be the same? What will the cost be? If Brenna plans a week long vacation, which is the cheaper service? Explain.

56)Solve each system by elimination.

57)Classify each system. Give the number of solutions.

58)Graph the solutions of each linear inequality. Given two possible solutions.

59)Graph each system of linear inequalities. Give two ordered pairs that are solutions and two that are not soltuions.

60)Eva and Tom sold at least 150 coupons. Eva sold at most 30 more books than twice the number that Tom sold. Show and describe all possible combination of the numbers of coupon books Eva and Tom sold. List two possible combinations.

Chapter 7: Polynomials

61)Evaluate each expression for the given value(s) of the variable(s).

62)Use the laws of exponents to simplify each of these examples. Do not leave any answers with negative exponents.

(-4)-2

(3x2y5)2(7x5) · (14x)-1

63)Write each number in scientific notation form.

0.00000002310,000,000,0000.00004567

64)Write each expression in standard form.

65)(6.2 x 104) (5 x 106)(6 x 105) (2 x 107)

66)

67)Add or Subtract:

68)Multiply:

Chapter 10: Probability

69)An equal sectioned spinner contains the numbers 1 to 5. Find each probability.

  1. P(5)P(even)P(odd)P(6)

70)A box contains cards numbered from 1 to 10. Find each probability.

  1. P (even number)P(number less than 4)P(not 5)

71)Use the letters M, A, T, H, E, M, A, T, I, C and S. Find each probability.

  1. P(M)P(not vowel)P(not E)

72)A number is selected at random from the numbers 1 to 50. Find each probability.

  1. P(multiple of 3) P(a factor of 50)P(not a factor of 50)

73)Moesha has 6 pairs of socks and 2 pairs of sneakers. She chooses 1 pair of socks and 1 pair of sneakers. How many possible combinations are there?

74)Ralph wants to have soup and salad for lunch. There are 5 kinds of soup and 3 kinds or salad on the menu. He picks one of each. From how many possible combinations can he choose?

75)Carla has 4 hats and 4 scarves for winter weather. She picks one of each to wear. How many hat and scarf combinations are there?

76)In how many ways can all the letters of the word SUMMER be arranged?

77)In how many ways can you arrange eight friends in a row for a photo?

78)At a track meet, 50 students entered the 100-m race. In how many ways can first, second, and third places be awarded?

79)A bicycle rack outside a classroom has room for six bicycles. In the class, 10 students sometimes ride their bicycles to school. How many different arrangements of bicycles are possibel for any given day?

80)Ten students from a class have volunteered to be on a committee to organize a dance. In how many ways can six be chosen for the comitee?

81)Twenty-three people try out for extra parts in a play. In how many ways can eight be chosen to be extra?

82)A team of eight players are to be chosen from 15 avalable players. In how many ways can this be done?

83)In a talent show, five semi-finalists are chosen from 46 enteries. In how many ways can the semi-finalists be chosen?

84)June is creating a beaded necklace with 5 different beads. How many ways can arrange the beads on the necklace?

85)A shelf holds 3 novels, 2 biographies, and 1 history book. Two students in turn choose a book at random. What is the probability that the studetn chooses each of the following?

  1. 1st pick a novel & 2nd pick is a novel
  2. 1st pick is a Biographies & 2nd pick is a Biograph
  3. 1st pick is a history and 2nd pick is a novel
  4. 1st pick is a history book and 2nd pick is also a history book

86)Meg flipped a penny the given number of times. What is the probability the results were as follows?

  1. Flipped 2 times and got two heads
  2. Flipped 3 times and got three tails
  3. Flipped 2 times & got a tail & then a head
  4. Flipped 5 times and got 5 tails

87)Two puppies are choosen at random from a box at the mall. What is the probability of the following outcomes?

  1. 1st puppy is black & 2nd puppy is black
  1. 1st puppy is brown & 2nd puppy is brown
  1. 1st puppy is a setter and 2nd puppy is a retriever
  1. 1st puppy is a setter and 2nd pupy is a setter

88)You have cards with the words M-A-T-H-I-S-F-U-N, written on them. You put them in a bag and randomly pick one at a time. What is the probability?

  1. You pick the letter M, replace it and then pick the letter N.
  1. You pick a vowel, replace it and then pick a consonant.

89)A manufacturer inspects 500 watches and finds that 498 have no defects.

  1. What is the experimental probability that a watch chosen at random has no defects?
  1. There are 30,000 watches in the wearhouse. Predict the number of watches that are likely to have no defect.

90)An experiment consists of pulling one card out of a bag that has 12 cards, each with a different month of the year printed on it. What is the probability that the month begins with the letter A?

91)The odds of spinning red on a spinner are 2:7. What is the probability of not spinning red?

92)The odds of winning a contest are 1:4. What is the probability of winning the contest?

93)The probability of choosing a green marble is 3/5. What are the odds of choosing a green?

94)The probability the temperature being over 90°F tomorrow is 80%. What are the odds of the temperature being over 90°F.?

Chapter 8 & 11

95)Annual sales for a clothing store are $270,000 are increasing at a rate of 7% a year. Write an exponential growth function to model the situation. Then find the annual sales after 3 years. Use the formula: y = a(1 + r)t

96)Chelsea invested $5600 at a rate of 3.6% compounded quarterly. Write a compound interest function to model the situtation. Then find the balance after 6 years. Use the formula:

97)The number of trees in a forest is decreasing at a rate of 5% per year. The forest had 24,000 trees 15years ago. Write an exponential decay function to model the situation. The find the number of trees now. y = a(1 – r)t

98)The half-life of strntium-90 is approximately 28 years. Find the amount of strontium-90 left from a 10 gram sample after 56 years. A = P(0.5)t

99)Factor each trinomial

x2 + 6x + 5x2 – 4x – 21 x2 – 8x + 15

100) Factor: x2 + 7x + 12 x2 – 15x + 50x2 – 1x – 6

B-Level Only

101)Simplify:

102)Factor: