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Name: Period: Algebra I Midterm Review Packet Mr. Pernerstorfer & Mrs. DiPaolo

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Algebra 1: Midterm Multiple Choice Practice

1. Which of the following is an irrational number?

(1) 2.5 (2) √25 (3) 2. 33̅̅̅̅ (4) √5

2. Evaluate the function 𝑓(𝑥) = −3𝑥 + 𝑥2when 𝑥 = −2.

(1) 2 (2) 10 (3) -2 (4) -10

3. Describe the transformation that was applied to f(x) to g(x).

𝑓(𝑥) = 𝑥 + 3; 𝑔(𝑥) = 𝑓(𝑥 − 4)

(1) Translation 4 units right (3) Translation 4 units left

(2) Translation 4 units up (4) Translation 4 units down

4. What is the slope of a line whose equation is −4𝑥 + 3𝑦 = 8?

(1) 4

3 (2) -

4

3 (3)

3

4 (4) -

3

4

5. If 𝐴 =1

3𝐵ℎ, then h is equal to

(1) 𝐴

3𝐵 (2) 3𝐴𝐵 (3)

3𝐴

𝐵 (4)

𝐵

3𝐴

6. The expression 14𝑥2𝑦

4𝑥𝑦3 is equivalent to

(1) 7𝑥

2𝑦2 (2)

2𝑦2

7𝑥 (3)

7𝑦2

2𝑥 (4)

2𝑥

7𝑦2

7. Which of the following shows the associative property of addition?

(1) 3 + 7 = 7 + 3 (3) 4(3 + 2) = 4(3) + 4(2)

(2) 4 + (5 + 6) = (5 + 6) + 4 (4) 3 + (2 + 4) = (3 + 2) + 4


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8. If the domain of the function 𝑦 = −2𝑥 + 9 is −1 ≤ 𝑥 ≤ 5, what is range of the function?

(1) −1 ≤ 𝑦 ≤ 11 (3) 11 ≤ 𝑦 ≤ −1

(2) 19 ≤ 𝑦 ≤ 7 (4) 7 ≤ 𝑦 ≤ 19

9. The cost of airing a commercial on television is modeled by the function C(n) 110n 900, where n is the

number of times the commercial is aired. Based on this model, which statement is true?

(1) The commercial costs $0 to produce and $110 per airing up to $900.

(2) The commercial costs $110 to produce and $900 each time it is aired.

(3) The commercial costs $900 to produce and $110 each time it is aired.

(4) The commercial costs $1010 to produce and can air an unlimited number of times.

10. Which equation is represented by the graph below?

(1) (2) (3) (4)

11. If f(1) 3 and f(n) 2f(n 1) 1, then f(5)

(1) 5 (2) 11 (3) 21 (4) 43

12. Jack bought 3 slices of cheese pizza and 4 slices of mushroom pizza for a total cost of $12.50. Grace bought

3 slices of cheese pizza and 2 slices of mushroom pizza for a total cost of $8.50. What is the cost of one slice of

mushroom pizza?

(1) $1.50 (2) $2.00 (3) $3.00 (4) $3.50

13. Daniel’s Print Shop purchased a new printer for $35,000. Each year it depreciates at a rate of 5%. What will

its approximate value be at the end of the fourth year?

(1) $33,250.00 (2) $30,008.13 (3) $28,507.72 (4) $27,082.33


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14. What is the solution of 3(2m− 1) ≤ 4m+ 7?

(1) m ≤ 5 (2) m ≥ 5 (3) m ≤ 4 (4) m ≥ 4

15. Which ordered pair is in the solution set for the following system of linear inequalities?

y > x − 4

y + x ≥ 2

(1) (3, -1) (2) (2, 2) (3) (6, 0) (4) (1, -4)

16. The expression (−2𝑎2𝑏3)(4𝑎𝑏5)(6𝑎3𝑏2) is equivalent to

(1) 8𝑎6𝑏30 (2) 48𝑎5𝑏10 (3)−48𝑎6𝑏10 (4) −48𝑎5𝑏10

17. What is an equation of the line that passes through the points (2, 1) and (6, 5)?

(1) 𝑦 = −3

2𝑥 − 2 (2) 𝑦 = −

3

2𝑥 + 4 (3) 𝑦 = −

2

3𝑥 − 1 (4) 𝑦 = −

2

3𝑥 +

7

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18. Connor wants to attend the town carnival. The price of admission to the carnival is $4.50, and each ride

costs an additional 79 cents. If he can spend at most $16.00 at the carnival, what is the maximum number of

rides he can go on?

(1) 3 rides (2) 4 rides (3) 14 rides (4) 15 rides

19. A sequence has the following terms: 𝑎1 = 4, 𝑎2 = 10, 𝑎3 = 25, 𝑎4 = 62.5. Which formula represents the

nth term in the sequence?

(1) 𝑎𝑛 = 4 + 2.5𝑛 (2) 𝑎𝑛 = 4 + 2.5(𝑛 − 1) (3) 𝑎𝑛 = 4(2.5)𝑛 (4) 𝑎𝑛 = 4(2.5)𝑛−1


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20. What is the slope of a line passing through the points (2, -3) and (5, 1)?

(1) 4

3 (2) −

4

3 (3)

3

4 (4) −

3

4

21. The equations 5x 2y 48 and 3x 2y 32 represent the money collected from school concert ticket sales

during two class periods. If x represents the cost for each adult ticket and y represents the cost for each student

ticket, what is the cost for each adult ticket?

(1) $20 (2) $10 (3) $8 (4) $4

22. Which equation represents a line that is parallel to the x-axis?

(1) 𝑦 = 𝑥 (2) 𝑦 = −𝑥 (3) 𝑦 = −1 (4) 𝑥 = −1

23. The expression 𝑥𝑦7

𝑥3𝑦4 is equivalent to

(1) 𝑥2

𝑦3 (2)

𝑦3

𝑥2 (3) 𝑥4𝑦11 (4)

𝑥3

𝑦3

24. Describe the transformation that maps f(x) to h(x).

𝑓(𝑥) =1

2𝑥 + 5; ℎ(𝑥) = −𝑓(𝑥)

(1) a vertical stretch of -1 was applied to f(x)

(2) a vertical shrink of -1 was applied to f(x)

(3) f(x) was reflected over the y-axis

(4) f(x) was reflected over the x-axis


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25. A pattern of blocks is shown below.

If the pattern continues, which formula(s) could be used to determine the number of blocks in the nth term?

(1) I and II (2) I and III (3) II and III (4) III, only

26. The diagram below shows the graph of .

Which diagram shows the graph of ?

(1) (2) (3) (4)

27. What is an equation of the line that passes through the points (2,0) and (0,3)?

(1) 𝑦 − 2 = −3

2𝑥 (3) 𝑦 = −

3

2(𝑥 + 3)

(2) 𝑦 = −3

2(𝑥 − 2) (4) 𝑦 + 3 = −

3

2𝑥


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28. Identify the function that represents the sequence below:

15, 9, 3, -3, …

(1) 𝑎𝑛 = 21 − 6𝑛 (3) 𝑎𝑛 = 9 − 6𝑛

(2) 𝑎𝑛 = 12 − 6𝑛 (4) 𝑎𝑛 = 9 + 6𝑛

29. What is the solution to the system of linear equations 4𝑥 − 𝑦 = −26 and 3𝑥 + 𝑦 = −30?

(1) (–2, –7) (2) (–6, –8) (3) (–7, –2) (4) (–8, –6)

30. What piecewise function best represents the graph below?

(1) 𝑓(𝑥) = {−1, 𝑥 ≥ −1

3

2𝑥 +

9

2, 𝑥 < −1

(3) 𝑓(𝑥) = {−1, 𝑥 > −1

3

2𝑥 +

9

2, 𝑥 ≤ −1

(2) 𝑓(𝑥) = {−1, 𝑥 ≤ −1

3

2𝑥 +

9

2, 𝑥 > −1

(4) 𝑓(𝑥) = {−1, 𝑥 < −1

3

2𝑥 +

9

2, 𝑥 ≥ −1

31. If 𝑥 = −2 and 𝑦 = −3, what is the value of 𝑥2𝑦 + 3𝑦?

(1) 3 (2) 21 (3) −21 (4) −3


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32. The domain for f(x) 3x 2 is 3 x 2. The greatest value in the range of f(x) is

(1) 7 (2) 2 (3) 8 (4) 11

33. Tamara has a cell phone plan that charges $0.07 per minute plus a monthly fee of $19.00. She budgets

$29.50 per month for total cell phone expenses without taxes. What is the maximum number of minutes Tamara

could use her phone each month in order to stay within her budget?

(1) 150 (2) 271 (3) 421 (4) 692

34. Julia went to the movies and bought one jumbo popcorn and two chocolate chip cookies for $5.00. Marvin

went to the same movie and bought one jumbo popcorn and four chocolate chip cookies for $6.00. How much

does one chocolate chip cookie cost?

(1) $0.50 (2) $0.75 (3) $1.00 (4) $2.00

35. Cassandra bought an antique dresser for $500. If the value of her dresser increases 6% annually, what will

be the value of Cassandra's dresser at the end of 3 years to the nearest dollar?

(1) $415 (2) $590 (3) $596 (4) $770


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Algebra 1: Midterm Short Answer Practice

I. Scatterplot line of best fit, residuals

Make a scatter plot of the data. Let x be the actual temperature and let y be the

temperature on a thermometer.

a) Tell whether x and y show a positive, a negative, or no correlation.

b) Find the line of best fit

c) Find the correlation coefficient

d) Interpret the slope

e) Interpret the y-intercept

f) Find the residual when x=1

II. Writing the equation of a line

Rewrite in the form y = mx + b and state the slope, y-intercept and x-intercept.

1. 2x + 6y = 12

2. 5y – 7x = -6

Write the equation in slope-intercept form of the line that meets the given requirements.

3. Passes through (4, -3) and has slope -5.

4. Passes through (2, 7) and (-4, -5)

5. Is perpendicular to 2x + 4y = 8 and passes through (-7, 12)

6. Is parallel to the y-axis and passes through (6, -20)

Write the equation in point-slope form of the line that meets the given requirements.

7. Is parallel to y = -5x – 9 and passes through the origin.

8. Has slope of 8 and passes through (0, -2.5)

9. Is perpendicular to y = -3x + 7and passes through (-6, 1)

x 2 2 1 1 0 1 2

y 3 1 2 1 0 1 2


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III. Arithmetic, Geometric, recursive sequences, piece-wise

Graph the arithmetic sequence.

1. 4, 0, 4, 8,

Determine whether the sequence is arithmetic. If so, find the common difference.

2. 2, 4, 7, 11, 16, 24, 3. 7, 13, 19, 25,

Graph the function. Describe the domain and range.

4. 2 1, if 1

3 1, if 1 4

x xy

x x

Identify the initial amount a and the rate of growth r (as a percent) of the exponential function.

Evaluate the function when t 4. Round your answer to the nearest tenth.

5. 250 1 0.05t

y 6. 3tp t

Write a function that represents the situation.

7. A $20,000 car decreases in value by 15% every year.

8. A newborn baby weighs 8 pounds and increases its weight by 5% every week.

Determine whether the sequence is arithmetic, geometric, or neither.

9. 180, 90, 45, 10. 1, 4, 16, 64, 11. 17, 23, 29, 35,

Write the next three terms of the geometric sequence.

12. 486, 162, 54,

Write the first six terms of the sequence.

13. 1 11, 3n na a a 14. 1 13, 2n na a a

15. Write a recursive rule for the number of bacteria at time t, if after 1 minute, there is

1 bacterium. After 2 minutes, there are 3 bacteria. After 3 minutes, there are 9 bacteria. After

4 minutes, there are 27 bacteria.


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IV. Solve for the variable____________________________________________

1. x – 3(1 – x) = 47 – x

2. 2 1

11 4(16 )3 3

t t t

3. 1

(27 18) 12 6( 4)3

x x

4. 1 3

4 9 444 4

c c

5. 5 – 3(a + 6) = a – 1 + 8a

6. Solve for a: 2S = n(a + l)

7. Solve for g: 1

2s gt

8. 2 1 5

3 6 6

x

9. Solve for b1: 1 2

1

2A h b b

V. Inequalities _______________________________________________________

1. Solve algebraically for x:

2. Solve the inequality algebraically for x.

3. The manufacturer of Ron's car recommends that the tire pressure be at least 26 pounds per square inch

and less than 35 pounds per square inch. On the accompanying number line, graph the inequality that

represents the recommended tire pressure.

4. Which inequality is represented in the accompanying graph?


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5. Given 2x + ax – 7 > -12, determine the largest integer value of a when x = -1.

6. Solve and graph: 2 7 27 or 3 3 30t t

VI. Functions

Determine whether the table represents a linear or nonlinear function. Explain.

1. 2.

Determine whether the equation represents a linear or nonlinear function. Explain.

3. 4 2y x 4. 2 3 5x y 5. 2 2y x x

Evaluate the function when 3, 0, and 4.x

6. 5f x x

Find the value of x so that the function has the given value.

7. 13

2; 4r x x r x 8. 2 1; 17q x x q x

Graph the linear function.

9. 13

2w x x 10. 4 7h x x

x 0 1 2 3

y 7 11 15 19

Input 2 4 6 8

Output 1 2 8 16


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VII. Solve the system of equations and inequalities

Solve the system of equations graphically.

1. x = 9

y = -3

2. 3x – 2y = 6

x – 4y = -8

3. A company is hiring a truck driver to deliver the company’s product. Truck driver A

charges an initial fee of $50 plus $7 per mile. Truck driver B charges an initial fee of $175

plus $2 per mile.

a. Write a linear equation the represents each truck driver’s total cost y (in dollars)

as a function of miles driven x.

b. Solve the system of linear equations by graphing. Interpret your solution.

4. Solve the system of linear equations by substitution. Check your solution.

6 11

2 3 7

y x

x y

5. Solve the system of linear equations by elimination. Check your solution.

5 4 30

3 9 18

x y

x y

6. School A and school B have taken a field trip to a professional baseball game. School A took 8

vans and 8 buses to get its 240 students to the game. School B took 4 vans and

1 bus to get its 54 students to the game. Find the number of students that were in each van

and bus.

7. Your work truck can haul at most 1000 pounds. The inequality 10 50 1000x y represents

the number x of bags of potting soil and the number y of bags of mulch your truck can haul.

Can you haul 20 bags of potting soil and 20 bags of mulch? Explain.

Graph the system of linear inequalities.

8. 4 2

2

x y

y

9. 23

43

3

3

y x

y x


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IX. Transformation of functions

Use the graphs of f and g to describe the transformation from the graph of f to the graph

of g.

1. 3 1;f x x 13

1g x x 2. 2 4;f x x 2 4g x x

Write a function g in terms of f so that the statement is true.

3. The graph of g is a vertical stretch by a factor of 3 of the graph of .f

4. The graph of g is a horizontal translation 4 units right of the graph of .f

Graph the function. Compare the graph to the graph of f x x . Describe the domain

and range.

5. 1t x x 6. 3r x x 7. 14

h x x

Graph and compare the two functions.

8. 2 ;f x x 2 2g x x 9. 1 2h x x ; 3 1 2t x x

X. Consecutive Integers

1. Find 3 consecutive integers such that the greatest integer is four less than

three times the smallest integer.

2. Find 3 consecutive odd integers such one less than three times the greatest

integer equals double the sum of the lesser two integers.

3. Find 3 consecutive even integers such that 2 less than 3 times the least integer

equals the sum of the greater two.

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