Semester 1 Exam Review Name __________________________________ Date ___________ Solve each equation. 𝑦 1) −2 = 2 + 4

2) 5 − 7 = 10

3) 15 = 𝑥 + 21

4) 2𝑥 − 6 = 11

5) −𝑥 + 5 = −17

6) 4(𝑥 − 12) = 16

7) 4𝑥 + 2 − 6𝑥 = 24

8) 7(𝑥 − 2) + 4 = 32

𝑦

7

9) 3 = 2

𝑏

2

10) 3 =

10 𝑑

11)

13) Name each function: Linear, Quadratic or Exponential a) 𝑦 = 𝑥 + 2 b) 𝑦 = 2𝑥 2 c) 𝑦 = 4𝑥

𝑟−3 3

1

7

𝑥−1 2

=2

12) 5 =

d) 𝑦 = 2𝑥 + 6

e) 𝑦 = −3𝑥 − 1

14) Hector knows there is a relationship between the number of cars he washes and the time it takes him to wash those cars. Identify the independent quantity and the dependent quantity in the problem situation.

15) David rode his bike to the park. After staying at the park for a few minutes, he then continued his ride to the grocery store. The graph shows this relationship. In the graph, what is the independent quantity and what is the dependent quantity?

16) Rachel paints landscapes. She sells each painting for $15. She writes the equation y = 15x to determine how much she will earn for her paintings. What does the independent variable represent in this situation?

17) Robin bought new eyeshadows for her make-up collection. She spent $12 per eye shadow. The expression y = 12x represents how much she spent on new make-up. What does the dependent variable represent in this situation?

18) Tickets to a movie cost $7.50 for children and $9.50 for adults. Write a function that shows the total cost for s student tickets and a adult tickets.

19) Emily is training for a half marathon. She runs the first seven miles at a constant speed. Write a function to represent the distance Emily runs, d, in terms of her speed, s.

20) An elevator in a high-rise building moves upward at a constant rate. The table shows the height of the elevator above the ground floor after various times. a. What are the dependent and independent quantities in this problem situation? Explain your reasoning.

Time

Height

Seconds

Feet

0

0

1

12

c. Complete the table.

2

24

d. Write an expression that represents the height for an arbitrary time t seconds in the last row.

3

Units b. Determine the unit rate of change for the problem situation.

4.5 5 Expression

t

21) Joy has $200 to spend at the shopping mall. She decides to buy sweaters and pants with her money. Sweaters cost $35 each and pants cost $20 each. a. Write an equation to represent this problem situation. Use s to represent the number of sweaters and p to represent the number of pants.

b. If Joy buys 3 sweaters, what is the greatest number of pants she can buy? Show your work and explain your reasoning.

c. If Joy buys no pants, what is the greatest number of sweaters she can buy? Show your work and explain your reasoning.

22) Determine the unit rate of change: a. (105, 1) and (702, 3)

b. (1100, 6) and (900, 8)

23) Find the value of 𝑓(𝑥) = −4.50𝑥 + 12.4 for the following values of x: a. x = -2 b. x = 4.1

c. x = -12.8

24) Tell whether each graph represents a function. a.

b.

c.

d.

25) Create an equation and sketch a graph for each set of given characteristics. a. • is a function

b. • is a function

• is linear

• is exponential

• is discrete

• is continuous

• is increasing

• is decreasing

26) Solve and graph each inequality. a. 8(4 − 𝑦) ≥ 24

b. 85 ≤ 17𝑥 ≤ 136

c. 𝑥 + 3 < −5 𝑜𝑟 − 5𝑥 ≤ −15

27) Ashley saved $75. She has already spent $15. She plans to spend $9.50 on tickets each month. Write an inequality representing the number of tickets she can buy?

28) Which compound inequality has no solution? a. 𝑥 < 5 𝑎𝑛𝑑 𝑥 < −2 b. 𝑥 > 5 𝑎𝑛𝑑 𝑥 < −4

c. 𝑥 > 5 𝑜𝑟 𝑥 < −4

d. 𝑥 < 5 𝑜𝑟 𝑥 < −2

c. |3𝑥 − 4| = −10

d. |𝑥 + 5| − 8 = 12

29) Simplify each absolute value expression. −12+5 a. |−10| − |5 − 6| b. | | 2

30) Solve each absolute value equation. a. |𝑦 + 2| = 5 b. 50 = 10|𝑥 + 1|

31) Find the x and y intercepts of each equation. a. 2𝑥 − 3𝑦 = −18

1

b. 𝑦 = 2 𝑥 + 6

32) A local high school is selling tickets to a play. Adult tickets cost $10 and student tickets cost $5. For one play, the amount earned on ticket sales was $1,430. Let x represent the number of student tickets sold and y represent the number of adult tickets sold. Determine the x and y intercepts. Graph using those intercepts.

33) Write each equation in standard form. 2 a. 𝑦 = − 3 𝑥 + 3

1

b. 𝑦 = − 2 𝑥 − 2

34) Write each equation in slope intercept form. a. 2𝑥 − 8𝑦 = −16 b. 3𝑥 + 2𝑦 = −12

35) Write an equation in point slope form (start by finding the slope) then translate the equation into slope intercept form. (3, -6); (6, -4)

35) The equation 𝑑 = 𝑟𝑡 gives the distance d for rate r and time t. Solve the equation for time.

36) Solve 𝑐 = 2(𝑎 − 3) for a

Graph each of the following equations. 1 37) 𝑦 = 2 𝑥 + 3

-9 -8 -7 -6 -5 -4

-3 -2 -1

38) 2𝑥 + 3𝑦 = 6

9

9

8

8

7

7

6

6

5

5

4

4

3

3

2

2

1

1

0

1

2

3

4

5

6

7

8

9

0

-2

-2

-3 -4

-3 -4

-5

-5

-6

-6

-7

-7

-8

-8

-9

-9

2

-3 -2 -1

-3 -2 -1

-1

39) 𝑦 = − 3 𝑥 + 1

-9 -8 -7 -6 -5 -4

-9 -8 -7 -6 -5 -4

-1

1

2

3

4

5

6

7

8

9

1

2

3

4

5

6

7

8

9

40) 4𝑥 − 5𝑦 = 20 9

9

8

8

7

7

6

6

5

5

4

4

3

3

2

2

1

1

0

1

2

3

4

5

6

7

8

9

-9 -8 -7 -6 -5 -4

-3 -2 -1

0

-1

-1

-2

-2

-3 -4

-3 -4

-5

-5

-6

-6

-7

-7

-8

-8

-9

-9

Graph each line. 41) x = 4

-9 -8 -7 -6 -5 -4

-3 -2 -1

42) y = -2 9

9

8

8

7

7

6

6

5

5

4

4

3

3

2

2

1

1

0

1

2

3

4

5

6

7

8

9

-9 -8 -7 -6 -5 -4

-3 -2 -1

0

1

-1

-1

-2

-2

-3 -4

-3 -4

-5

-5

-6

-6

-7

-7

-8

-8

-9

-9

2

3

4

5

6

7

8

9

41) Describe each pattern shown.

a.

b.

42) Identify each sequence as arithmetic or geometric. Then determine the common difference or common ratio for each sequence. 1 1 1 1 a. 2, 5, 8, 11, 14, 17 b. -6, 12, -24, 48, -96 c. 1, 4 , 16 , 64 , 256

d. 0.13, 0.38, 0.63, 0.88, 1.13

43) Identify the next tern in each sequence. a. 0.2, 1, 5, 25…..

e. 8, -1, -10, -19, -28

b. -432, -444, -456, -468….

f. 200, 20, 2, .02, 0.02

44) For each sequence, determine whether it is arithmetic or geometric. Then use the appropriate formula to determine the 15th term in the sequence.

an  a1  d (n  1)

g n  g1 r n 1

a. 5, 10, 20, 40, 80, 160…

b. -0.25, 0.5, 1.25, 2, 2.75…

c. 4, 2, 1, 0.5, 0.25…

d. -7, -2, 3, 8…

45) Determine the 50th term in the sequence defined by 𝑎𝑛 = −11 + 5(𝑛 − 1)

1 𝑛−1

46) Determine the 7th term in the sequence defined by 𝑔𝑛 = 2 ∙ (2)

47) Shelby’s printer had 500 sheets of paper in it. After Monday, there were 466 sheets of paper. After Tuesday, there were 432 sheets of paper. After Wednesday, there were 398 sheets of paper. If this pattern continues, how many sheets of paper will be left after Friday?

48) Greg is filling his sink to wash dishes. After one minute, there are 2.75 gallons of water in the sink. After two minutes there are 5.5 gallons of water in the sink. After three minutes, there are 8.25 gallons of water in the sink. If this pattern continues, how any gallons of water will be in the sink after five minutes?

49) Identify each of the following for the function f ( x)  4  2 x . Then graph the function.

a. x-intercept(s) b. y-intercept c. asymptote d. domain e. range f.

interval(s) of increase/decrease

50) The revenue for a company this year was $750,000. Each year the revenue increases at a rate of 1.75% per year. Write a function that represents the company’s revenue as a function of time in years.

51) The formula for an account that earns simple interest is 𝑃𝑡 = 𝑃0 + (𝑃0 ∙ 𝑟)𝑡. John deposited $2,500 into an account that earned 3.5% simple interest annually. How much was in his account after one year?

52) The formula for an account that earns compound interest is 𝑃𝑡 = 𝑃0 ∙ (1 + 𝑟)𝑡 . John deposited $3,000 into an account that earned 2.5% compound interest annually. How much was in his account after 3 years?

53) The average rate of attendance at a local college this year was 3,420. Each year the attendance decreases at a rate of 2.5% per year. What will the average attendance be in 4 years?

54) Write the equation of each function after the translation described. a. f ( x)  10 x after a translation 5 units to the right b. f ( x)  3x after a translation 4 units up

c. 𝑓(𝑥) = 7𝑥 after a translation 2 units left d. 𝑓(𝑥) = −3𝑥 after a reflection over y = 0 e. 𝑓(𝑥) = 2𝑥 3 after a translation 2 units left f. 𝑓(𝑥) = 5𝑥 after a reflections over x = 0

55) Describe each graph in relation to its basic function. a. Compare f ( x)  ( x  3) 2 to the basic function h( x)  x 2 . b. Compare 𝑓(𝑥) = −(𝑏 𝑥 ) to the basic function h( x)  b x . c. Compare f ( x)  b  x to the basic function h( x)  b x . d. Compare f ( x)  x3  9 to the basic function h( x)  x3 . e. Write a function that is a reflection of the function about the y-axis. 56) Sketch a function 𝑓(𝑥) = 𝑥 3 after a reflection about y = 0.

58) Write an equation and sketch a graph that:  is an exponential function  is continuous  is increasing  is translated 5 units up from 𝑓(𝑥) = 2𝑥 Equation: g(x) = __________

57) Sketch a function 𝑓(𝑥) = 2𝑥 after a reflection about x = 0.