High School Algebra I for Middle Grades Students SY14-15

High School Algebra I for Middle Grades Students

SY14-15 Algebra Exit Exam Practice #2

Practice Exit Exam_05/2015 1

Student Name: ______________________________

Directions: Solve each problem. You have a total of 90 minutes.

Choose the best answer and fill in your answer document accordingly. For questions requiring a written response, write your answers neatly in the space provided in the test booklet.

Do not use too much time on any one question. Solve as many as you can; then return to the others in the time you have left for this assessment.

You may use a calculator for any problems you choose, but some of the problems may best be done without using a calculator.

Note: Unless otherwise stated, all of the following should be assumed. 1. Illustrative figures are NOT necessarily drawn to scale. 2. Geometric figures lie in a plane. 3. The word line indicates a straight line. 4. The word average indicates arithmetic mean.

DO YOUR FIGURING HERE

1.

Maria is selling cupcakes for $1.65 each. Let 𝑐 be the number of cupcakes Maria sells. Let 𝑠 be her sales in dollars.

Which equation represents the relationship between 𝑐 and 𝑠?

a. 𝑠 = 1.65𝑐

b. 𝑐 = 1.65𝑠

c. 𝑠 = 𝑐 + 1.65

d. 𝑐 = 𝑠 + 1.65





2.

For several weeks, Teddy really focused his time on studying and saw his math quiz scores slowly improve. As he began to understand the concepts, his scores improved more rapidly. He then stopped studying and his quiz scores no longer improved. Which of the following graphs represents Teddy’s quiz scores as a function of time in weeks? a.

b.

c.

d.





3.

If 𝐴 = −4𝑡2 + 5𝑡 + 4 and 𝐵 = 9𝑡2 − 3𝑡 + 5, what is 𝐵 − 𝐴? a. 5𝑡2 − 8𝑡 + 1

b. 13𝑡2 − 8𝑡 + 1

c. 13𝑡2 + 2𝑡 + 9

d. −13𝑡2 + 8𝑡 − 1

4.

Which of the following is NOT a true statement about the graph of the linear equation 3𝑥 + 5𝑦 = 20? a. The 𝑦-intercept of the line is (0,4).

b. The slope of the line is −3

5.

c. As the values of 𝑥 increase, the values of 𝑦 increase.

d. The line intersects the 𝑥-axis at a positive value.

5.

Jelani made a mistake solving an equation. His work is shown below.

5𝑥 − 3(2𝑥 − 4) = 2𝑥 step 1

−3(2𝑥 − 4) = −3𝑥 step 2

−6𝑥 − 12 = −3𝑥 step 3

−12 = 3𝑥 step 4

−4 = 𝑥 step 5 Where did Jelani make a mathematical mistake?

a. Going from step 1 to step 2.

b. Going from step 2 to step 3.

c. Going from step 3 to step 4.

d. Going from step 4 to step 5.





6.

The table below shows the total cost of parking a car in a downtown parking garage for different lengths of time.

Time (parked hours)

Total cost ($)

1 $22

3 $30

4 $34

6 $42

Which of the following statements represents the rate of change of the line containing the data in the table?

a. The cost of parking per hour

b. The cost of parking for 6 hours

c. The total cost of parking for any number of hours

d. The difference between the cost of parking for 1 and 6 hours

7.

The zeros of the function 𝑓(𝑥) = −7(𝑥 + 2)(5𝑥 − 15) are:

a. – 2 and – 3

b. – 2 and 3

c. 2 and – 3

d. 2 and – 3

8.

In the expansion of (2𝑥2 − 3𝑥 − 1)(𝑥 + 5), what is the coefficient of 𝑥2? a. 2

b. 7

c. 10

d. 13





9.

Find all values of 𝑥 that satisfy the equation below. Write your solution(s) in the shaded box below.

(𝑥 + 1)2 −25

9= 0

10.

If Sam works ℎ hours per week, then his weekly income from his car repair business is 15ℎ − 100. Which of the following best describes the meaning of 15 in this expression? a. The number of hours he works per week

b. The amount of money he makes after he accounts for the cost to run his business

c. The amount he earns each hour

d. The amount of money he makes before he accounts for the cost to run his business

11.

The temperature 𝑇 (in Fahrenheit) as a function of altitude 𝑎 (in feet) is modeled by the linear function

𝑇 = −35

10000𝑎 + 60.

Which of the following statements is a correct interpretation of the slope of the linear model?

a. For each increase of 10000 feet in elevation, the

temperature increases by 35

10000 degrees Fahrenheit.

b. For each increase of 10000 feet in elevation, the

temperature decreases by 35


c. For each increase of 1 foot in elevation, the

temperature increases by 35


d. For each increase of 1 foot in elevation, the

temperature decreases by 35






12.

If (𝑥 − 7) is one of the factors of 2𝑥2 − 11𝑥 + 𝑘, what is the other factor? a. (2𝑥 − 21)

b. (2𝑥 − 17)

c. (2𝑥 + 3)

d. (2𝑥 + 7)

13.

Given ℎ(𝑥) = 2𝑥3 + 𝑥2 + 7, what is the value of ℎ(−3)? Write your final answer in the shaded box below.

14.

Naoki has 50 CDs. She joins a club that sends her 3 CDs each month. Which of the following equations

expresses the number of CDs, 𝑛, in Naoki’s collection as a function of the number of months, 𝑡, after she joins the club? a. 𝑛 = 3𝑡

b. 𝑛 = 50𝑡

c. 𝑛 = 3 + 𝑡

d. 𝑛 = 50 + 3𝑡





15.

The graph of linear function 𝑓(𝑥) is shown below.

Another function 𝑔(𝑥) has equation 𝑔(𝑥) = −3

2𝑥 + 13.

For what value of 𝑥 does 𝑓(𝑥) = 𝑔(𝑥)?

a. 4

b. 6

c. 7

d. 13

16.

A line passes through the two points (0, −2) and (9,1). What is the 𝑦-coordinate of the point on this line whose 𝑥-coordinate is 12? a. −6

b. 0

c. 2

d. 4





17.

Find all solutions of 𝑥2 + 2𝑥 − 3 = 0. a. 𝑥 = −1 and 𝑥 = −3

b. 𝑥 = +1 and 𝑥 = −3

c. 𝑥 = −1 and 𝑥 = 3

d. 𝑥 = +1 and 𝑥 = 3

18.

Tickets for a high school play sell for $5. Seven hundred tickets were sold in advance. The theater has 1000 seats. Let 𝐴 be the total amount of ticket sales, in dollars, including tickets sold at the door. Which statement best describes 𝐴? a. 𝐴 ≥ 700

b. 𝐴 ≥ 3500

c. 3500 ≤ 𝐴 ≤ 5000

d. 𝐴 ≤ 5000





19.

Given the graph below, which of the following gives the number of values of 𝑥 where 𝑓(𝑥)= 𝑔(𝑥)?

a. 0

b. 2

c. 3

d. 6





20.

A soccer ball is kicked upward from the ground with a speed of 96 feet per second. Its height ℎ, in feet, after 𝑡 seconds is given by the equation ℎ(𝑡) = −16𝑡2 + 96𝑡. a. How long will it take for the soccer ball to return to the ground?

b. How long will it take the soccer ball to reach its maximum height?

c. What is the maximum height of the soccer ball?

a.

b.

c.





21.

How many solutions does the following system of equations have?

3𝑎 + 𝑏 = 12 12𝑎 + 4𝑏 = 48

a. 0

b. 1

c. 2

d. infinitely many

22.

If 𝑎 = 𝑏𝑐 − 2 and 𝑏 ≠ 0, which of the following equations expresses 𝑐 in terms of 𝑏 and 𝑎?

a. 𝑐 =𝑎

𝑏+2

b. 𝑐 =𝑏

𝑎+2

c. 𝑐 =𝑏−2

𝑎

d. 𝑐 =𝑎+2

𝑏





23.

Which of the following tables represent functions?

a. Table I and Table II

b. Table II and Table III

c. Table III and Table IV

d. Table IV and Table V

Table I

𝒙 𝒚

0 5

1 −3 2 8

0 −3

Table II

𝒙 𝒚

1 5

6 −1 0 5

6 −2

Table III

𝒙 𝒚

7 1

3 1 8 1

−5 1

Table IV

𝒙 𝒚

18 5

7 13 6 2

9 2

Table V

𝒙 𝒚

0 0

1 0 2 0

2 1





24.

A bike shop owner bought eighteen bicycles and sixteen tricycles for $4100.10. He found he had under-ordered, so he placed another order for twelve bicycles and eight tricycles for $2591.40. Find the price for an individual bicycle and an individual tricycle. Define any variables you use and show all your work.

b. Show your work:

a. Define your variables:

c. Answer:





25.

Solve for 𝑥: −3(𝑥 − 4) ≤ 9 + 𝑥

a. 𝑥 ≤ 3

4

b. 𝑥 ≥ 3

4

c. 𝑥 ≤ −13

4

d. 𝑥 ≥ −13

4

26.

The table shows 𝑥 and 𝑦 values for a quadratic function. Based on the table, which of the following statements is NOT true? a. The parabola opens upward.

b. The graph of the function crosses the 𝑥-axis between 0 and 1.

c. The graph of the function has more than one 𝑥-intercept.

d. The maximum 𝑦-value of the function is 1.

𝒙 𝒚

−1 −7 0 −1

1 1 2 −1

3 −7





27.

The surface area, S, of a right circular cylinder with height ℎ and radius 𝑟 is given by the formula

𝑆 = 2𝜋𝑟2 + 2𝜋𝑟ℎ. Which of the following equations gives ℎ for a right circular cylinder with a surface area of 54? a. ℎ = 27 − 𝑟

b. ℎ = 54 − 2𝑟

c. ℎ =27−𝜋𝑟2

𝜋𝑟

d. ℎ =54−𝜋𝑟2

𝜋𝑟

28.

Ben is studying how the number of bacteria in a dish changes over time. He determines the initial number of bacteria in the dish is 640 and that the number of bacteria doubles at the end of each hour. Which function, 𝑓(𝑡), can Ben use to determine the number of bacteria in the dish after 𝑡 hours? a. 𝑓(𝑡) = 640 + 2𝑡

b. 𝑓(𝑡) = 640 × 2𝑡

c. 𝑓(𝑡) = 640 × 1

2𝑡

d. 𝑓(𝑡) = 640 × 2𝑡





29.

Sandra buys 3 notebooks and 5 pens for $10.47. Hector buys 2 of the same notebooks and 6 of the same pens for $9.58. Which system of equations can be used to find 𝑥, the cost of a single notebook and 𝑦, the cost of a single pen?

a. {𝑥 + 𝑦 = 10.47𝑥 + 𝑦 = 9.58

b. {10.47𝑥 + 9.58𝑦 = 20.05

𝑥 + 𝑦 = 16

c. {3𝑥 + 5𝑦 = 10.472𝑥 + 6𝑦 = 9.58

d. {3𝑥 + 2𝑦 = 10.475𝑥 + 6𝑦 = 9.58

30.

Suppose a baseball player hits a ball in the air. After 𝑡 seconds, the height ℎ(𝑡) in meters of the ball is modeled by ℎ(𝑡) = −4.9𝑡2 + 30𝑡 + 1.4.

Which of the following is the best interpretation of ℎ(2) within this context? a. After 2 seconds, the ball is 41.8 meters high.

b. After 41.8 seconds, the ball is 2 meters high.

c. The ball reaches its maximum height at 2 seconds.

d. The ball travels at 41.8 meters/second.





31.

Toni deposited $100 into a bank, and the amount in her bank account increases by 5% each year. Enter a number from the box below onto each of the blanks in the formula for 𝑓(𝑥) so that the resulting function correctly represents Toni’s situation.

𝑓(𝑥) = _________ × ________ 𝑡

Part I Part II

Fill in the bubble next to the value in the appropriate space on your answer sheet.

0.95 1.00 1.05 95 100 105





32.

The function ℎ(𝑥) = 25𝑥 represents the cost of a dinner at a restaurant for a group of 𝑥 people. The dinner can only be held if at least 10 people show up. The restaurant can seat a maximum of 40 people. What is a realistic domain for this function? a. The set of real numbers 𝑥 such that

10 ≤ 𝑥 ≤ 40

b. The set of integers 𝑥 such that 10 ≤ 𝑥 ≤ 40

c. The set of real numbers 𝑥 such that 250 ≤ 𝑥 ≤ 1000

d. The set of integers 𝑥 such that 250 ≤ 𝑥 ≤ 1000





33.

Examine the two quadratic functions shown below.

1

𝑔(𝑥) = 𝑥2 − 2𝑥 − 24

2

𝑓(𝑥)

Which statement is true about 𝑓(𝑥) and 𝑔(𝑥)?

a. The minimum value of 𝑓(𝑥) is less than the minimum value of 𝑔(𝑥).

b. The minimum value of 𝑓(𝑥) is equal to the minimum value of 𝑔(𝑥).

c. The minimum value of 𝑓(𝑥) is greater than the minimum value of 𝑔(𝑥).

d. There is no way to determine a comparison between the minimum value of 𝑓(𝑥) and the minimum value of 𝑔(𝑥).

34.

Which of the following points is NOT a solution of the system?

{𝑥 < 3𝑦 − 3

5𝑥 − 2𝑦 ≥ 11

a. (4,3)

b. (4,4)

c. (3,4)

d. (5,3)





35.

The population of a city is modeled by the function below, where 𝑡 is time in years. Based on the model, which is true about the city’s population?

𝑃(𝑡) = 106(1.08)𝑡

a. The population is increasing by 0.08% each year.

b. The population is increasing by 8% each year.

c. The population is increasing by 1.08% each year.

d. The population is increasing by 108% each year.

36.

What is the 𝑦-intercept of the line that passes through the point (−8,7) and is perpendicular to the line

𝑦 = 2𝑥 + 5? Write and bubble in your answer in the appropriate space on your answer sheet. Make sure to start in the first, farthest left box for each part on the answer sheet for your response. Make sure to fill in the appropriate bubble below each box you write in.





37.

The length of the shortest side of a right triangle is 11 inches. The lengths of the other two sides are represented by consecutive integers. Which equation could be used to find the lengths of the other sides of the triangle? a. 𝑥2 + (𝑥 + 1)2 = 112

b. 112 + 122 = 132

c. 112 + (𝑥 + 1)2 = 𝑥2

d. 112 + (𝑥 − 1)2 = 𝑥2

38.

Which function describes the recursive relationship shown in the table?

𝒏 𝒇(𝒏) 0 4

1 10

2 28

3 82

a. 𝑓(𝑛 + 1) = 𝑓(𝑛) + 6

b. 𝑓(𝑛 + 1) = 3𝑓(𝑛) − 2

c. 𝑓(𝑛 + 1) = 2𝑓(𝑛) + 8

d. 𝑓(𝑛 + 1) = 3𝑛+1 + 1

39.

Suppose 𝑥 and 𝑦 are real numbers and 𝑥 + 𝑦 = 2. Which of the following statements must be true about 𝑥 and 𝑦? a. Both 𝑥 and 𝑦 must be rational.

b. Both 𝑥 and 𝑦 must be irrational.

c. One of the numbers can be irrational but not both.

d. If one of the numbers is irrational then both are irrational.





40.

The function 𝑔(𝑥) = 4(𝑥 + 5)2 + 3 is a transformation of 𝑓(𝑥) = 𝑥2 + 3. Which of the following best describes the relationship between the graphs of 𝑓(𝑥) and 𝑔(𝑥)? a. The graph of 𝑔(𝑥) is narrower and shifted 5 units to

the left.

b. The graph of 𝑔(𝑥) is narrower and shifted 5 units to the right.

c. The graph of 𝑔(𝑥) is wider and shifted 5 units to the left.

d. The graph of 𝑔(𝑥) is wider and shifted 5 units to the right.

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High School Algebra I for Middle Grades Students SY14-15