Free Printable Alg 1💐Spring Final Exam

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Alg 1💐Spring Final Exam

Total questions: 67

Worksheet time: 3hrs 21mins

Name

Class

Date

During a summer beach party, you found a seashell with a length of √80 cm. Which expression correctly simplifies the length of the seashell?

2√20

4√5

20√5

5√4

During a summer festival, the path of a firework is modeled by the equation f(x) = x². The path was adjusted to avoid a tree, resulting in the new equation f(x) = (x - 2.5)² + 1. Which of these describes this adjustment?

A horizontal shift 2.5 units right and a vertical shift 1 unit up

A horizontal shift 2.5 units left and a vertical shift 1 unit up

A vertical shift 2.5 units down and a horizontal shift 1 unit right

A vertical shift 2.5 units up and a horizontal shift 1 unit right

During a summer fair, a parabolic water slide is set up. The height of the slide at different points is represented by a quadratic function. Which function best represents the height of the slide?

f(x) = 2x² + 10x - 2

f(x) = x² - 5x + 2

f(x) = x² + 5x - 2

f(x) = -x² + 10x - 8

Which graph best represents the solution set of the inequality where the temperature difference between two summer days, x - 2y ≤ - 4?

During a summer sale, the price of a beach ball is given by the equation 3x + (2 – x) = 5x – (2x + 5) + 11. What is the value of x that makes this equation true?

– 4

– 1/4

1/4

If the temperature in degrees Celsius on a summer day is given by the function T(x) = 3x² - 4x + 2, what is the temperature when T(–3)?

During a summer festival, a game booth offers a prize for solving a puzzle. The puzzle is to find the negative solution to the equation 0 = 2x² – 18. Can you solve it?

(a)

Which system of equations best represents the paths of two ice cream trucks on a summer day?

2x + 3y = 6

4x – y = 8

6x – 4y = 8

3x – y = 2

3x + 2y = 8

y + 4x = 6

x – 4y = 8

2x – 3y = 6

During a summer fair, a vendor is selling lemonade. The vendor's profit can be modeled by the expression 12x² + 8x – 15. Which expression is a factor of this profit model?

(3x + 1)

(6x – 5)

(x + 3)

(2x – 3)

10.

Which representation does not show the number of ice creams sold as a function of temperature?

11.

Which inequality best represents the domain of temperatures during a summer day?

-5 ≤ g(x) < 1

-5 ≤ g(x) ≤ 1

-7 < x ≤ 6

-7 ≤ x < 6

12.

Which inequality best represents the range of temperatures during a summer day?

-5 ≤ g(x) < 1

-5 < g(x) ≤ 1

-7 < x ≤ 6

-7 ≤ x < 6

13.

During a summer fair, a parabolic water fountain has its highest point at (2, 5) and passes through the point (–3, 15). Which quadratic function in vertex form represents the path of the water?

y = (2/5)(x – 2)² + 5

y = -(2/5)(x – 2)² + 5

y = (2/5)(x + 2)² - 5

y = -(2/5)(x + 2)² - 5

14.

The value of a new surfboard decreases at a rate of 16% annually. The surfboard was initially purchased for $35,280. Which function models the value of the surfboard after t years?

f(t) = 1.16(35,280)^t

f(t) = 0.84(35,280)^t

f(t) = 35,280(1.16)^t

f(t) = 35,280(0.84)^t

15.

During a summer fair, a graph is displayed showing the number of ice creams sold over time. Which ordered pair best represents the location of the y-intercept?

(0, 2)

(2, 0)

(0, 3)

(3, 0)

16.

The number of ice creams sold is directly proportional to the temperature. If 24 ice creams are sold when the temperature is 120°F, how many ice creams are sold when the temperature is 360°F?

(a)

17.

The summer festival is hosting a lemonade and ice cream sale as a fundraiser. They will choose any combination of lemonade cups and ice cream cones to sell and want to earn at least $2,000 from this sale. If lemonade cups cost $8.99 each and ice cream cones cost $6.99 each, which inequality represents all possible combinations of x lemonade cups and y ice cream cones?

8.99x + 6.99y ≥ 2,000

8.99x + 6.99y > 2,000

6.99x + 8.99y ≥ 2,000

6.99x + 8.99y > 2,000

18.

During a summer beach party, a lifeguard station is set up at the point (7, – 5) on a coordinate grid representing the beach. What is the equation of the line that passes through the lifeguard station and runs parallel to the y-axis?

x = – 5

x = 7

y = – 5

y = 7

19.

During a summer festival, a vendor sets up a rectangular booth with an area of a² – 4a – 21 square meters. Which expression represents the dimensions of the booth?

(a + 3)(a + 7)

(a – 7)(a – 3)

(a + 3)(a – 7)

(a + 7)(a – 3)

20.

During a summer festival, the height of a water fountain's spray is modeled by f(x) = 2x² – 6x – 5. What is the range of the fountain's height?

–6.8 ≤ y ≤ 3.68

all real numbers

y ≥ 1.5

y ≥ –9.5

21.

Which ordered pair is in the solution set of 4x – 3y > 2 during a summer beach volleyball game?

(2, 2)

(–1, –3)

(1, 3)

(–6, 4)

22.

During a summer sale, the price of a beach umbrella decreases exponentially according to the function y = 25,000(0.33)^x. Which statement about the price graph is true?

The equation of the asymptote is x = 0

The coordinates of the x-intercept are (0.33, 0)

The coordinates of the y-intercept are (0, 25,000)

The graph represents exponential growth

23.

During a summer festival, a vendor is selling refreshing drinks. Each drink is made using a special recipe that involves mixing ingredients in a specific ratio. Which expression is equivalent to the simplified form of the recipe $\left(36m^8p^{14}\right)^{\frac{1}{2}}$ for all positive values of m and p?

6m⁴p⁷

18m⁴p⁷

36m⁴p⁷

6m⁸p¹⁴

24.

The graph shows the height in feet of a beach ball above the sand t seconds after it was thrown.

h(t) = –16t² + 65t

h(t) = –16t² – 65t

h(t) = –16t² + 90t – 65

h(t) = –16t² – 90t + 65

25.

During a summer camp, the number of participants on the 2nd day was 9, on the 3rd day was 14, on the 4th day was 19, and on the 6th day was 29. Based on this information, which equation can be used to find the number of participants on the nth day, a_n?

a_n = n + 7

a_n = –5n – 1

a_n = n + 5

a_n = 5n – 1

26.

The school soccer teams went to the local ice cream shop to get ice creams after practice. Each large ice cream costs the same amount, and each small ice cream costs the same amount.

- The girls soccer team paid $65 total for 10 large ice creams and 5 small ice creams

- The boys soccer team paid $77 total for 14 large ice creams and 3 small ice creams

Which system of equations would be used to find x the cost of a small ice cream and y the cost of a large ice cream?

10x – 5y = 65

14x – 3y = 77

5x + 10y =65

3x + 14y = 77

65x – 77y = 10

x + y = 20

5x + 10y = 77

3x + 14y = 65

27.

The school soccer teams went to the local ice cream shop to get ice creams after practice. Each large ice cream costs the same amount, and each small ice cream costs the same amount.

- The girls soccer team paid $65 total for 10 large ice creams and 5 small ice creams

- The boys soccer team paid $77 total for 14 large ice creams and 3 small ice creams

What was the cost in dollars for each large summer smoothie?

$5.25

$3.50

$4.75

$7.00

28.

A model rocket was launched from the top of a lifeguard tower on the beach. The height, in feet, of the rocket above the sand can be found using the function y = – 16x² + 80x + 40, where x is the time in seconds the rocket has been in the air. How many seconds did it take the model rocket to reach the sand? Round your answer to the nearest hundredth. Record your answer and fill in the bubbles on your answer document.

(a)

29.

The table shows the height in inches and weight in pounds of 6 players on the local beach volleyball team.

What is the best prediction of the weight of a player that is 69 inches tall?

154 pounds

171 pounds

150 pounds

205 pounds

30.

The table shows the height in inches and weight in pounds of 6 players on the local volleyball team.

What is the best prediction of the weight of a player that is 67 inches tall during a summer beach volleyball game?

154 pounds

241 pounds

150 pounds

205 pounds

31.

During a summer sale, a store offers a discount such that the total cost of 3x items plus 8 dollars is less than or equal to the cost of 2x items minus the cost of 3x items plus 4 dollars.

$-3x+8\le2x-\left(3x+4\right)$

What is the solution set for x?

x ≤ −6

x ≤ 6

x ≥ −10

x ≥ 6

32.

During a summer beach party, a lifeguard needs to set up a flagpole that is perpendicular to a line of beach chairs arranged along the line represented by y = 3/4x + 5. If the flagpole must pass through the point (−3, −4), what is the equation in slope-intercept form of the line where the flagpole should be placed?

y = −3/4x + 5

y = 4/3x

y = 3/4x − 7/4

y = −4/3x − 8

33.

During a summer camp, the distance between two tents is (x − 8)² = 49 meters. What are the possible distances between the tents?

−41 and 57 meters

1 and 15 meters

−57 and 41 meters

−15 and −1 meters

34.

During a summer festival, a vendor is selling potted plants. The number of plants he has is represented by $\frac{\left(p^6\right)^{\frac{1}{2}}}{p^4}$ . Which expression is equivalent to this for all values of p where the expression is defined?

p⁵

1/p

p⁷

1/p⁴

35.

During a summer fair, a vendor sets up a lemonade stand. The graph of the vendor's profit over time is shown on the grid. Which equation is best represented by this graph?

$y-2=\frac{2}{3}\left(x-6\right)$

$y+2=\frac{2}{3}\left(x+6\right)$

$y-3=-\frac{2}{3}\left(x-4\right)$

$y-4=\frac{2}{3}\left(x-3\right)$

36.

During a summer picnic, Sandy took ibuprofen for pain relief after a long hike. The function $f\left(x\right)=600\left(0.72\right)^x$ gives the number of milligrams of ibuprofen in her system at the end of x hours. Which statement is the best interpretation of one of the values in this function?

The initial amount of ibuprofen in her system is 0.72 milligrams.

The amount of ibuprofen in her system increases at a rate of 0.72 milligrams per hour.

The initial amount of ibuprofen in her system is 600 milligrams.

The amount of ibuprofen in her system decreases at a rate of 0.72 milligrams per hour.

37.

Which graph best represents the solution set of the temperature difference between day and night being less than -4 degrees?

$x-2y<-4$

38.

If a summer ice cream truck sells g(x) = 3x² - 4x + 2 ice creams on a given day, what is the number of ice creams sold when g(–1)?

39.

During a summer festival, a game booth offers a prize for solving a puzzle. The puzzle is to find the positive solution to the equation 0 = 2x² – 18. Can you solve it to win the prize?

(a)

40.

Which system of equations best represents the paths of two ice cream trucks on a summer day?

Select the TWO correct answers.

4x – y = 8

3x + 2y = 8

6x – 4y = 8

2x + 3y = 6

3x + 2y = 8

41.

During a summer fair, a vendor is selling lemonade. The vendor's profit can be modeled by the expression 12x² + 8x – 15. Which expression is a factor of this profit model?

(3x + 1)

(6x + 5)

(x + 3)

(2x + 3)

42.

Which representation does show the number of ice creams sold as a function of the temperature?

Select ALL correct tables.

43.

Which inequality best represents the range of temperatures at the beach?

-5 ≤ g(x) < 1

-5 < g(x) ≤ 1

-7 < x ≤ 6

-7 ≤ x < 6

44.

Which inequality best represents the domain of temperatures during a summer day?

A. -5 ≤ g(x) < 1

B. -5 ≤ g(x) ≤ 1

C. -7 < x ≤ 6

D. -7 ≤ x < 6

45.

The value of a new surfboard increases at a rate of 16% annually. The surfboard was initially purchased for $35,280. Which function models the value of the surfboard after t years?

f(t) = 1.16(35,280)^t

f(t) = 0.84(35,280)^t

f(t) = 35,280(0.84)^t

f(t) = 35,280(1.16)^t

46.

The graph of a function is shown on the grid. Which ordered pair best represents the location of the x-intercept?

(0, 2)

(2, 0)

(0, 3)

(3, 0)

47.

The value of y is directly proportional to the value of x. If y = 85 when x = 52, what is the value of y when the value of x = 208?

(a)

48.

The school booster club is hosting a dinner plate sale as a fundraiser. They will choose any combination of barbeque plates and vegetarian plates to sell and want to earn more than $2,000 from this sale. If barbeque plates cost $8.99 each and vegetarian plates cost $6.99 each, which inequality represents all possible combinations of x barbeque plates and y vegetarian plates?

8.99x + 6.99y > 2,000

8.99x + 6.99y ≥ 2,000

6.99x + 8.99y ≥ 2,000

6.99x + 8.99y > 2,000

49.

x = – 5

x = 7

y = – 5

y = 7

50.

Which expression is equivalent to a² + 4a – 21?

(a + 3)(a + 7)

(a – 7)(a – 3)

(a – 3)(a + 7)

(a – 7)(a + 3)

51.

What is the domain of f(x) = 2x² – 6x – 5?

−6.8 ≤ y ≤ 3.68

all real numbers

y ≥ −9.5

y ≥ 1.5

52.

Which ordered pair is in the solution set of 4x – 3y ≥ 2?

(2, 2)

(−1, −1)

(1, 3)

(−6, 4)

53.

Which statement about the graph of y = 25,000(0.33)^x is true?

The equation of the asymptote is x = 0.

The graph represents an exponential growth of 33%.

The coordinates of the x-intercept are (0.33, 0).

The graph represents exponential decay.

54.

Which expression is equivalent to $\left(36m^{16}p^{28}\right)^{\frac{1}{2}}$ for all positive values of m and p?

6m⁴p⁷

18m⁸p¹⁴

36m⁴p⁷

6m⁸p¹⁴

55.

In a sequence of numbers, a₂ = 9, a₃ = 15, a₄ = 21, and a₆ = 33. Based on this information, which equation can be used to find the nth term in the sequence, a_n?

a_n = 6n – 3

a_n = –6n – 3

a_n = n + 6

a_n = n – 3

56.

The school soccer teams went to the local smoothie shop to get smoothies after practice. Each large

smoothie costs the same amount, and each small smoothie costs the same amount.

• The girls soccer team paid $65 total for 10 large smoothies and 5 small smoothies

• The boys soccer team paid $77 total for 14 large smoothies and 3 small smoothies

Which system of equations would be used to find x the cost of a small smoothie and y the cost of a large smoothie?

3x + 14y = 77

10x – 5y = 65

5x + 10y = 65

5x + 10y = 77

3x + 14y = 65

57.

The school soccer teams went to the local smoothie shop to get smoothies after practice. Each large

smoothie costs the same amount, and each small smoothie costs the same amount.

• The girls soccer team paid $65 total for 10 large smoothies and 5 small smoothies

• The boys soccer team paid $77 total for 14 large smoothies and 3 small smoothies

What was the cost in dollars for each small smoothie?

$5.25

$3.50

$4.75

$7.00

58.

A model rocket was launched from the roof of a 4-story building. The height, in feet, of the rocket above the ground can be found using the function y = – 16x² + 80x + 40, where x is the time in seconds the rocket has been in the air. How many seconds did it take for the model rocket to reach its maximum height?

(a)

59.

During a summer sale, a store offers a discount such that the total cost of 3x items plus 8 dollars is less than or equal to the cost of 2x items minus the cost of 3x items plus 4 dollars.

$-3x+8\ge2x-\left(3x+4\right)$

What is the solution set for x?

x ≤ −6

x ≤ 6

x ≥ −10

x ≥ 6

60.

During a summer beach party, a lifeguard needs to set up a flagpole that is parallel to a line of beach chairs arranged along the line represented by y = 3/4x + 5. If the flagpole must pass through the point (−3, −4), what is the equation in slope-intercept form of the line where the flagpole should be placed?

y = −3/4x + 5

y = 4/3x

y = 3/4x − 7/4

y = −4/3x − 8

61.

The value of a new surfboard decreases at a rate of 20% annually. The surfboard was initially purchased for $40,000. Which function models the value of the surfboard after t years?

f(t) = 1.20(40,000)^t

f(t) = 0.80(40,000)^t

f(t) = 40,000(1.20)^t

f(t) = 40,000(0.80)^t

62.

During a summer festival, a vendor is selling refreshing drinks. Each drink is made using a special recipe that involves mixing ingredients in a specific ratio. Which expression is equivalent to the simplified form of the recipe $\left(49m^6p^{12}\right)^{\frac{1}{2}}$ for all positive values of m and p?

7m³p⁶

14m³p⁶

49m³p⁶

7m⁶p¹²

63.

Graph $y=\left(x-3\right)^2-4$

64.

A ball is hit from the ground. When the ball has traveled a horizontal distance of x meters, it can be modeled by the function;

$h\left(x\right)=-\frac{1}{4}x^2+2x$

The ball traveled (a) meters before it hit the ground. The ball reached a (b) height of (c) meters.

Choose from the below words

maximum

feet

minumum

65.

A quadratic is defined as $y=\left(x+3\right)^2-6$

What is the equation for this function in standard form?

Your answer needs to be in the form of:

$y=ax^2+bx+c$

Enter your answer in the space provided.

66.

Which expression is equivalent to $\frac{\left(p^6\right)^{\frac{1}{2}}}{p^{-4}}$ for all values of p where the expression is defined?

p⁵

1/p

p⁷

1/p⁴

67.

The initial amount of ibuprofen in her system is 0.72 milligrams.

The amount of ibuprofen in her system increases at a rate of 72% milligrams per hour.

The initial amount of ibuprofen in her system is 600 milligrams.

The amount of ibuprofen in her system decreases at a rate of 28% milligrams per hour.

100 %

Alg 1💐Spring Final Exam

Total questions: 67

Worksheet time: 3hrs 21mins

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