Midterm Review

Midterm Review Part I

Multiple Choice

Identify the choice that best completes the statement or answers the question.

____ 1. Salvador reads 12 books from the library each month for n months in a row. Write an expression to show how

many books Salvador read in all. Then, find the number of books Salvador read if he read for 7 months.

a. 12 – n; 19 books c. 12 + n; 19 books

b. ; 84 books d. 12n; 84 books

____ 2. The temperature on the ground during a plane’s takeoff was 4ºF. At 38,000 feet in the air, the temperature

outside the plane was –38ºF. Find the difference between these two temperatures.

a. –34ºF c. 34ºF

b. 42ºF d. –42ºF

____ 3. Divide.

0 5.928

a. –5.928 c. undefined

b. 5.928 d. 0

____ 4. Carina hiked at Yosemite National Park for 1.75 hours. Her average speed was 3.5 mi/h. How many miles did

she hike?

a. 2 mi c. 61.25 mi

b. 20 mi d. 6.125 mi

____ 5. Simplify .

a. 27 c. 729

b. 93 d. 12

____ 6. The area of a square garden is 202 square feet. Estimate the side length of the garden.

a. 16 ft c. 17 ft

b. 12 ft d. 14 ft

____ 7. Translate the word phrase, the product of 8.5 and the difference of –4 and –8, into a numerical expression.

a. c.

b. d.

____ 8. A toy company's total payment for salaries for the first two months of 2005 is $21,894. Write and solve an

equation to find the salaries for the second month if the first month’s salaries are $10,205.

a.

The salaries for the second month are $11,689.

b.


c.


d.


____ 9. The time between a flash of lightning and the sound of its thunder can be used to estimate the distance from a

lightning strike. The distance from the strike is the number of seconds between seeing the flash and hearing

the thunder divided by 5. Suppose you are 17 miles from a lightning strike. Write and solve an equation to

find how many seconds there would be between the flash and thunder.

a. , so t is about 85 seconds.

b. , so t is about 3.4 seconds.

c. , so t is about 22 seconds.

d. , so t is about 0.3 seconds.

____ 10. If , find the value of .

a. 3 c. 5

b. –5 d. –3

____ 11. Solve . Tell whether the equation has infinitely many solutions or no solutions.

a. Two solutions c. Infinitely many solutions

b. No solutions d. Only one solution

____ 12. A video store charges a monthly membership fee of $7.50, but the charge to rent each movie is only $1.00 per

movie. Another store has no membership fee, but it costs $2.50 to rent each movie. How many movies need

to be rented each month for the total fees to be the same from either company?

a. 3 movies c. 7 movies

b. 5 movies d. 9 movies

____ 13. Solve for y.

a. c.

b. d.

____ 14. 66 is 56% of what number? If necessary, round your answer to the nearest hundredth.

a. 0.85 c. 1.18

b. 117.86 d. 36.96

____ 15. Solve .

a. x = 1 c. No solution

b. x = 11

6 d. x =

8

3

____ 16. Denise has $365 in her saving account. She wants to save at least $635. Write and solve an inequality to

determine how much more money Denise must save to reach her goal. Let d represent the amount of money

in dollars Denise must save to reach her goal.

a. ; c. ;

b. ; d. ;

____ 17. Solve the inequality 3 and graph the solutions.

a. x 24

0 5 10 15 20 25 30 35 40 45 500

b. x 24

0 5 10 15 20 25 30 35 40 45 500

c. x 3

8

0 1 2 3 4 5 6 7 8 9 10 11 120

d. x 24

0 5 10 15 20 25 30 35 40 45 500

____ 18. Solve the inequality 2m 18 and graph the solutions.

a. m 9

0 1 2 3 4 5 6 7 8 9 10 110–1

b. m 36

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 950

c. m 36

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 950

d. m 9

0 1 2 3 4 5 6 7 8 9 10 110–1

____ 19. Write a possible situation for the graph.

Time

Wate

r le

vel

a. A pool is filled with water using one valve. Then, immediately after the pool is filled to its

capacity, the pool needs to be emptied because of some problems. The pool is refilled right

after it is completely empty, using two valves this time.

b. A pool is filled with water using one valve. A little time after the pool is filled to its

capacity, the pool needs to be emptied because of some problems. Then, the pool is

refilled immediately, using two valves this time.

c. A pool is filled with water, and people are having fun swimming and jumping in and out

of the pool.

d. A pool is filled with water. A little time after the pool is filled to its capacity, the pool

needs to be emptied because of some problems. Then, the pool is refilled immediately at

the same rate as before.

____ 20. Give the domain and range of the relation. Tell whether the relation is a function.

x y

0 –5

1 –1

1 3

1 6

a. D: {0, 1}; R: {–5, –1, 3, 6}

The relation is a function.

c. D: {0, 1}; R: {–5, –1, 3, 6}

The relation is not a function.

b. D: {–5, –1, 3, 6}; R: {0, 1}

The relation is a function.

d. D: {–5, –1, 3, 6}; R: {0, 1}

The relation is not a function.

____ 21. Determine a relationship between the x- and y-values. Write an equation.

x 1 2 3 4

y 4 5 6 7

a. y = x + 4 c. y = x + 3

b. y = 3x + 1 d. y = –x + 3

____ 22. Brian has 64 flowers for a big party decoration. In addition, he is planning to buy some flower arrangements

that have 18 flowers each. All of the arrangements cost the same. Brian is not sure yet about the number of

flower arrangements he wants to buy, but he has enough money to buy up to 5 of them. Write a function rule

to describe how many flowers Brian can buy. Let x represents the number of flower arrangements Brian buys.

Find a reasonable range for the function.

a. ; {64, 82, 100, 118, 136}

b. ; {154}

c. ; {82, 100, 118, 136, 154}

d. ; {64, 82, 100, 118, 136, 154}

____ 23. Data was collected on the average winter temperature and the number of days with snow of a random group

of cities in the United States. Identify the correlation you would expect to see between the average winter

temperature and the number of days with snow.

a. constant correlation c. positive correlation

b. no correlation d. negative correlation

____ 24. This table shows the number of swimmers in the ocean at a given time. Find the rate of change for each time

period. During which period did the number of swimmers increase at the fastest rate?

Time 10:30 am 12:30 pm 1:30 pm 3:30 pm 5:30 pm

Number of swimmers 41 55 64 70 80

a. Between 12:30 and 1:30 c. Between 10:30 and 12:30

b. Between 3:30 and 5:30 d. Between 1:30 and 3:30

____ 25. Write the equation in slope-intercept form. Then graph the line described by the equation.

a.

2 4 6 8–2–4–6–8 x

2

4

6

8

10

–2

–4

–6

–8

–10

y

c.

2 4 6 8–2–4–6–8 x

2

4

6

8

10

–2

–4

–6

–8

–10

y

b.

2 4 6 8–2–4–6–8 x

2

4

6

8

10

–2

–4

–6

–8

–10

y d.

2 4 6 8–2–4–6–8 x

2

4

6

8

10

–2

–4

–6

–8

–10

y

____ 26. Show that ABCD is a parallelogram.

A

B

C

D

1 2 3 4 5 6 7 x

1

2

3

4

5

6y

a.

ABCD is a parallelogram because both pairs of opposite sides are parallel.

b.


c.


d.


____ 27. Identify the lines that are perpendicular:

; ; ;

a. and are perpendicular.

b. None of the lines are perpendicular.

c. and are perpendicular.

d. and are perpendicular; and are

perpendicular.

____ 28. Show that LMN is a right triangle.

M (9, 8)

N (4, -2)

L (5, 10)

2 4 6 8 10 x

2

4

6

8

10

–2

y

a. Slope of and slope of . is perpendicular to because

. LMN is not a right triangle because it does not contain a right angle.

b. Slope of and slope of . is not perpendicular to because

. LMN is not a right triangle because it does not contain a right angle.

c. Slope of and slope of . is perpendicular to because

. LMN is a right triangle because it contains a right angle.

d. Slope of and slope of . is perpendicular to because

. LMN is a right triangle because it contains a right angle.

____ 29. Describe the transformation from the graph of to the graph of .

a. The graph is the result of translating the graph of up 5 units.

b. The graph is the result of translating the graph of down 3 units.

c. The graph is the result of translating the graph of up 3 units.

d. The graph is the result of translating the graph of down 5 units.

____ 30. Solve .

a. a = –29 c. a = 15

b. a = 29 d. a = –15

____ 31. Solve .

a. c.

b. d.

____ 32. If 8y – 8 = 24, find the value of 2y.

a. 8 c. 2

b. 11 d. 24

____ 33. Solve .

a. n = 11

2 c. n = 3

1

2

b. n = 41

2 d. n = 1

1

6

____ 34. The formula for the resistance of a conductor with voltage V and current I is . Solve for V.

a. I = Vr c. V = Ir

b. d.

____ 35. Solve for x.

a.

c.

b.

d.

____ 36. Solve the proportion .

a. x = 36 c. x = 0.03

b. x = 26 d. x = 25

____ 37. Solve .

a. x = 55 c. x = 55 or x = –43

b. x = 13 d. x = 13 or x = –1

Short Answer

38. Solve –14 + s = 32.

39. Solve .

40. The formula gives the profit p when a number of items n are each sold at a cost c and expenses e

are subtracted. If , , and , what is the value of c?

41. Solve the inequality n – 4 3 and graph the solutions.

0 2 4 6 8 10 12 140–2–4–6–8–10–12–14

42. Solve and graph .

0 2 4 6 8 10 12 140–2–4–6–8–10–12–14

43. Solve the inequality and graph the solution.

0 2 4 6 8 10 12 140–2–4–6–8–10–12–14

44. Solve the inequality .

45. Give the domain and range of the relation.

x y

5 11

6 13

0 0

–8 –15

46. Use the graph of the function 2x + 2 to find the value of y when .

1 2 3 4 5 6–1–2–3–4–5–6 x

1

2

3

4

5

6

–1

–2

–3

–4

–5

–6

y

47. Tell whether the slope of the line is positive, negative, zero, or undefined.

1 2 3 4 5–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y

48. Write the equation that describes the line with slope = 2 and y-intercept = 3

2 in slope-intercept form.

Midterm Review Part I

Answer Section

MULTIPLE CHOICE

1. ANS: D

The expression 12n models the number books Salvador read in all.

Evaluate 12n for n = 7.

12(7) = 84

If Salvador read for 7 months, then that means Salvador read 84 books.

Feedback

A Use a different operation. B Use a different operation. C Use a different operation. D Correct!

PTS: 1 DIF: Average REF: Page 8 OBJ: 1-1.4 Application

NAT: 12.5.2.a STA: A.3.A TOP: 1-1 Variables and Expressions

KEY: algebraic expression | word problem | operation

2. ANS: B

Subtract the lower temperature from the higher temperature to calculate the difference in the two readings.

Feedback

A Subtract the lower temperature from the higher temperature. B Correct! C Subtract the lower temperature from the higher temperature. D Check the signs.


NAT: 12.1.3.a TOP: 1-2 Adding and Subtracting Real Numbers

KEY: integers | subtraction | word problem

3. ANS: D

The quotient of 0 and any nonzero number is 0.

Feedback

A Multiply or divide by 0. B Multiply or divide by 0. C Only division by 0 is undefined. D Correct!

PTS: 1 DIF: Basic REF: Page 22

OBJ: 1-3.3 Multiplying and Dividing with Zero NAT: 12.1.3.a

TOP: 1-3 Multiplying and Dividing Real Numbers

4. ANS: D

Distance = rate time Substitute 3.5 for rate and 1.75 for time.

Distance = Multiply to find the distance.

Feedback

A To find distance, multiply rate by time. B To find distance, multiply rate by time. Then estimate to check if your answer is

reasonable. C The decimal point is not in the correct place. Use estimation to check if your answer is

reasonable. D Correct!


NAT: 12.1.3.a TOP: 1-3 Multiplying and Dividing Real Numbers

5. ANS: C

The exponent tells the number of times to multiply the base number by itself.

Multiply 9 by itself 3 times.

Feedback

A Multiply the base number by itself as many times as the exponent tells you. B Multiply using the base. The exponent just tells how many times to multiply the base by

itself. C Correct! D Multiply the number by itself rather than adding two different numbers.

PTS: 1 DIF: Basic REF: Page 27 OBJ: 1-4.2 Evaluating Powers

NAT: 12.1.3.a TOP: 1-4 Powers and Exponents KEY: evaluate | exponent | power

6. ANS: D

202 is between 196 and 225. Since 202 is closer to 196, the best estimate for the side length is 14 ft.

Feedback

A Find the two perfect squares that the area is between. B Find the two perfect squares that the area is between. C Of the two perfect squares that the area is between, which is closer to the area? D Correct!

PTS: 1 DIF: Average REF: Page 33 OBJ: 1-5.2 Problem-Solving Application

NAT: 12.2.1.h TOP: 1-5 Square Roots and Real Numbers

KEY: square roots | squares | area | irrational numbers | mental math | real world applications

7. ANS: D

Use parentheses so that the difference is evaluated first.

Product means multiplication.

Feedback

A "Product" indicates multiplication. B Use parentheses so the difference is evaluated first. C When finding a difference, subtract the second number from the first. D Correct!


OBJ: 1-6.4 Translating from Words to Math NAT: 12.5.2.b

TOP: 1-6 Order of Operations

8. ANS: A

First month

salaries

Added

to

Second month

salaries is 21,894

b + x = 21,894

b + x = 21,894 Write an equation to represent the relationship.

10,205 + x = 21,894

–10,205 –10,205

Substitute 10,205 for b. Since 10,205 is added to x, subtract

10,205 from both sides to undo the addition.


Feedback

A Correct! B Subtract the same number from both sides of the equation. C Check your answer. D Use the same operation on both sides of the equation.


NAT: 12.5.3.b STA: A.7.A TOP: 2-1 Solving Equations by Adding or Subtracting

9. ANS: A

Seconds divided by 5 equals distance.

Write an equation. Let d = distance from the lightning strike in miles

and t = number of seconds between flash and thunder.

Substitute 17 for d, the distance from the lightning strike.

Multiply both sides of the equation by 5 to undo the division.

The number of seconds between flash and thunder is about 85

seconds.

Feedback

A Correct! B Divide the distance from the lightning strike by 5. C Divide the distance from the lightning strike by 5. D Divide the distance from the lightning strike by 5.


NAT: 12.5.3.b STA: A.7.A TOP: 2-2 Solving Equations by Multiplying or Dividing

10. ANS: B

Solve the equation.

Substitute 8 for x and simplify.

Feedback

A Find the value of x by solving the equation. Then substitute it for x in the given

expression and simplify. B Correct! C Subtract the terms in the right order. D Find the value of x by solving the equation. Then substitute it for x in the given

expression and simplify.

PTS: 1 DIF: Advanced NAT: 12.5.4.a STA: A.4.A

TOP: 2-2 Solving Equations by Multiplying or Dividing

11. ANS: C

Combine like terms on each side of the equation before collecting variable terms on one side.

If you get an equation that is always true, the original equation is an identity, and it has infinitely many

solutions.

If you get a false equation, the original equation is a contradiction, and it has no solutions.

Feedback

A First, combine like terms on each side of the equation. Then collect variable terms on

one side. Now, if you get an equation that is always true, it means that the original

equation has infinitely many solutions. If you get a false equation, the original equation

has no solutions. B If you get an equation that is always true, the original equation is an identity, and it has

infinitely many solutions. If you get a false equation, the original equation is a

contradiction and it has no solutions. C Correct! D If you get an equation that is always true, the original equation is an identity, and it has

infinitely many solutions. If you get a false equation, the original equation is a

contradiction and it has no solutions.

PTS: 1 DIF: Average REF: Page 102

OBJ: 2-4.3 Infinitely Many Solutions or No Solutions NAT: 12.5.4.a

STA: A.7.C TOP: 2-4 Solving Equations with Variables on Both Sides

12. ANS: B

Let m represent the number of movies rented each month.

Here are the costs for each company (in dollars).

7.5 + m = 2.5m

To collect the variable terms on one side, subtract m from both sides.

7.5 – m = 2.5m – m

7.5 = 1.5 m

Divide both sides by 1.5.

= m

5 = m

Feedback

A You divided $7.50 by $2.50. Before dividing by 2.50, subtract the $1.00 charge from

the $2.50. B Correct! C You divided $7.50 by $1.00. Subtract the $1.00 charge from the $2.50 and then divide.

D Set up this equation 7.5 + m = 2.5m, where m is the number of movies.


NAT: 12.5.4.a STA: A.7.A TOP: 2-4 Solving Equations with Variables on Both Sides

13. ANS: B

Subtract 2 from both sides.

Subtract the term from both sides.

Rewrite 3.8 as .

Multiply by .

Distribute.

Simplify.

Feedback

A Divide all terms by 3.8. B Correct! C Multiply by the reciprocal of 3.8. D Keep the x term in the equation.


TOP: 2-5 Solving for a Variable

14. ANS: B

Method 1 Use a proportion.

Use the percent proportion.

Let x represent the whole.

Find the cross products.

Since x is multiplied by 56, divide both sides by 56 to undo

the multiplication.

_56% of 66 is

117.86.

Method 2 Use an equation.

Write an equation. Let x represent the whole.

Write the percent as a decimal.

Since x is multiplied by 0.56, divide both sides by 0.56 to

undo the multiplication.

_56% of 66 is 117.86.

Feedback

A Use the percent proportion: part is to whole as percent is to 100. Then, find the cross

products. B Correct! C Set up an equation where the percent is a variable, "of" means to multiply, and "is"

means "=". Then, solve for the variable. D Set up an equation where the percent is a variable, "of" means to multiply, and "is"

means "=". Then, solve for the variable.

PTS: 1 DIF: Average REF: Page 128 OBJ: 2-8.3 Finding the Whole

NAT: 12.1.4.d STA: A.4.A TOP: 2-8 Percents KEY: percent

15. ANS: C

First, isolate the absolute value expression.

Subtract 8 from both sides.

The absolute value expression is equal to a negative number, which is impossible. The equation has no

solution.

Feedback

A An absolute value must be greater than or equal to 0. B Isolate the absolute value by subtracting the term outside absolute value bars. C Correct! D Subtract the term outside the absolute value bars.


OBJ: 2-Ext.2 Special Cases of Absolute-Value Equations

TOP: 2-Ext Solving Absolute-Value Equations

16. ANS: A

Let d represent the amount of money in dollars Denise must save to reach her goal.

$365 plus additional amount of money

in dollars

is at least $635

365 + d 635

Since 365 is added to d, subtract 365 from both sides to undo the

addition.

365

365

Check the endpoint 270 and a number that is greater than the endpoint.

Feedback

A Correct! B You should be solving an inequality, not an equation. C Subtract from both sides of the inequality. D Check the endpoint to see if you get a true statement.


NAT: 12.5.4.c STA: A.7.B TOP: 3-2 Solving Inequalities by Adding and Subtracting

17. ANS: A

3

3(8) Multiply both sides by 8 to isolate x.

x 24

0 5 10 15 20 25 30 35 40 45 500

Use a solid circle when the value is included in the graph, such as with or Use an empty circle when the

value is not included, such as with > or <.

Feedback

A Correct! B Use a solid circle when the value is included in the graph. Use an empty circle when the

value is not included. C To solve the inequality, use multiplication to undo the division. D Check that the arrow is pointing in the correct direction.


OBJ: 3-3.1 Multiplying or Dividing by a Positive Number NAT: 12.5.4.c

STA: A.7.B TOP: 3-3 Solving Inequalities by Multiplying and Dividing

KEY: solving | inequality | graph MSC: solving | inequality | graph

18. ANS: D

2m 18

Divide both sides by 2 to isolate m.

m 9



0 1 2 3 4 5 6 7 8 9 10 110–1

Feedback

A Check that the arrow is pointing in the correct direction. B To solve the inequality, use division to undo the multiplication. C Use a solid circle when the value is included in the graph. Use an empty circle when the

value is not included. D Correct!


OBJ: 3-3.1 Multiplying or Dividing by a Positive Number NAT: 12.5.4.c

STA: A.7.B TOP: 3-3 Solving Inequalities by Multiplying and Dividing

KEY: solving | inequality | graph MSC: solving | inequality | graph

19. ANS: B

First, identify the labels. The x-axis is the time, and the y-axis is the water level. Then, analyze the sections of

the graph. Over time, the water level increased steadily, then remained unchanged, next decreased steadily,

then increased steadily, and finally remained unchanged.

Feedback

A Look at the graph from left to right. Is the pool refilled with water immediately, or does

the pool have the same level of water for a certain amount of time? B Correct! C No doubt that people could be having fun in the pool, but you should use all the

information the graph tells about the level of water as time passes. D Look at the two segments on the graph that show the pool is filled with water. Does it

take the same amount of time to fill the pool in both instances?

PTS: 1 DIF: Average REF: Page 232 OBJ: 4-1.3 Writing Situations for Graphs

NAT: 12.5.2.b STA: A.2.C TOP: 4-1 Graphing Relationships

20. ANS: C

A function is a special type of relation that pairs each x-value with exactly one y-value. If the same x-value

has more than one y-value, then the relation is not a function.

Feedback

A A function has a unique y-value for each x-value. B A function has a unique y-value for each x-value. C Correct! D Check the domain and the range. The domain is the set of all x-values; the range is the

set of all y-values.

PTS: 1 DIF: Basic REF: Page 237 OBJ: 4-2.3 Identifying Functions

NAT: 12.5.1.e STA: A.2.B TOP: 4-2 Relations and Functions

KEY: function | relation | input | output

21. ANS: C

The correct equation is y = x + 3.

x 1 2 3 4

x + 3 4 5 6 7

Feedback

A Substitute the x-values into your equation to make sure they give the correct y-values. B Substitute the x-values into your equation to make sure they give the correct y-values. C Correct! D Substitute the x-values into your equation to make sure they give the correct y-values.


OBJ: 4-3.1 Using a Table to Write an Equation NAT: 12.5.2.b

STA: A.1.D TOP: 4-3 Writing Function Rules KEY: table | equation | function

22. ANS: D

Total flowers is 18 per arrangement plus the 64 flowers already bought

f(x) = 18 • x + 64

If Brian buys x flower arrangements, he will have flowers.

Brian has enough money to buy only up to 5 flower arrangements, so he can buy 0, 1, 2, 3, 4, or 5 flower

arrangements. These are the only reasonable values for the domain.

Substitute these values into the function rule to find the range values.

x

0 1 2 3 4 5

The range for this situation is {64, 82, 100, 118, 136, 154}.

Feedback

A "Up to 5" means 5 is included. B Is 5 the only number in the domain of the function? Is it possible that fewer items were

bought? C The number 0 also belongs to the domain of the function. It is possible that no item was

bought. D Correct!


OBJ: 4-3.5 Finding Reasonable Domain and Range of a Function

NAT: 12.5.1.g STA: A.2.B TOP: 4-3 Writing Function Rules

23. ANS: D

Positive correlation: both data sets increase or decrease together.

Taller students tend to have larger shoe sizes, so these data sets would probably have a positive correlation.

Negative correlation: as one data set increases the other decreases.

In general, the higher the average temperature, the fewer snow days there will be. You would expect a

negative correlation between these data sets.

No correlation: changes in one data set do not affect the other data set.

Your height has nothing to do with the number of pets you have, so you would expect no correlation between

these data sets.

Feedback

A The term "constant correlation" isn't used in statistics. B If one value tends to increase/decrease when the other increases, there is a

positive/negative correlation. Otherwise, there is no correlation. C In a positive correlation, both sets of data values increase. In a negative correlation, one

set of data values increases as the other set decreases. If there is no relationship between

the data sets, then there is no correlation. D Correct!

PTS: 1 DIF: Average REF: Page 264 OBJ: 4-5.3 Identifying Correlations

NAT: 12.4.1.a STA: A.2.D TOP: 4-5 Scatter Plots and Trend Lines

KEY: positive correlation | negative correlation | scatter plot

24. ANS: A

To find the rate of change in the number of swimmers in each time period, divide the change in the number of

swimmers by the change in the number of hours.

10:30 to 12:30

12:30 to 1:30

1:30 to 3:30

3:30 to 5:30

The number of swimmers increased at the fastest rate from 12:30 to 1:30.

Feedback

A Correct! B The rate of change between 3:30 and 5:30 is 5 swimmers per hour. One of the other

periods has a greater rate. C The rate of change between 10:30 and 12:30 is 7 swimmers per hour. One of the other

periods has a greater rate. D The rate of change between 1:30 and 3:30 is 3 swimmers per hour. One of the other

periods has a greater rate.


NAT: 12.5.2.b STA: A.6.B TOP: 5-3 Rate of Change and Slope

25. ANS: D

,

Plot . Count 1 down and 2 right, and plot another point. Draw a line connecting the two points.

(0, –3)(2, –4)

2 4 6 8 10–2–4–6–8–10 x

2

4

6

8

10

–2

–4

–6

–8

–10

y

Feedback

A Check the sign of the slope. B The slope is the change in y divided by change in x. The numerator tells how many units

to move up or down. The denominator tells how many units to move to the right. C Check the sign of the y-intercept. D Correct!


OBJ: 5-6.3 Using Slope-Intercept Form to Graph NAT: 12.5.3.d

STA: A.6.D TOP: 5-6 Slope-Intercept Form

26. ANS: C

Use the ordered pairs and the slope formula to find the slopes of the four line segments formed by the four

points given. If the points given create two sets of parallel segments, then the quadrilateral formed by the four

points is a parallelogram.

A

B

C

D

1 2 3 4 5 6 7 x

1

2

3

4

5

6y

The formula for the slope between two points

(x1, y1) and (x2, y2) is

Feedback

A Use the slope formula to find the slopes of the sides of the figure. B Use the correct ordered pairs. C Correct! D Use the slope formula to find the slopes of the sides of the figure.


NAT: 12.3.3.g STA: A.6.B TOP: 5-8 Slopes of Parallel and Perpendicular Lines

27. ANS: D

is horizontal, and is vertical. These lines are perpendicular.

Check if the product of the slopes of the other two lines is .

has slope . has slope .

The product of the slopes is , so these two lines are also perpendicular.

Feedback

A Check to see whether the other lines are perpendicular. B Vertical lines are perpendicular to horizontal lines. Also, if the product of the slopes of

two lines is -1, then the lines are perpendicular. C Check to see whether the other lines are perpendicular. D Correct!


OBJ: 5-8.3 Identifying Perpendicular Lines NAT: 12.3.3.g

STA: A.6.B TOP: 5-8 Slopes of Parallel and Perpendicular Lines

28. ANS: D

A right triangle contains one right angle. L and N are not right angles, so the only possibility is M. If

LMN is a right triangle, will be perpendicular to .

slope of

slope of

, so is perpendicular to .

LMN is a right triangle because it contains a right angle.

Feedback

A Since the product of the slopes is -1, the lines are perpendicular. LMN is a right triangle

because it contains a right angle. B Subtract -2 from 8 when calculating the second slope. C To find the slope, divide the change in y by the change in x. D Correct!


NAT: 12.3.3.g STA: A.6.B TOP: 5-8 Slopes of Parallel and Perpendicular Lines

29. ANS: D

and are parallel lines with slopes equal to 1.

The y-intercept of f(x) is 4, and the y-intercept of g(x) is –1.

The y-intercept has decreased by |4 – (–1)| = 5, so the translation from f(x) to g(x) is 5 units downwards.

f(x)

g(x)2 4 6 8 10–2–4–6–8–10 x

2

4

6

8

10

–2

–4

–6

–8

–10

y

The graph is the result of translating the graph of down 5 units.

Feedback

A The direction of translation from f(x) to g(x) is downward when the y-intercept

decreases. B The distance between two numbers is the absolute value of their difference. C The translation is upward only if the y-intercept increases. D Correct!

PTS: 1 DIF: Basic REF: Page 358 OBJ: 5-9.1 Translating Linear Functions

NAT: 12.5.2.d STA: A.6.C TOP: 5-9 Transforming Linear Functions

30. ANS: D

First x is multiplied by –2. Then 14 is added.

Work backward: Subtract 14 from both sides.

Since x is multiplied by –2, divide both sides by –2 to undo the

multiplication.

Feedback

A To solve for the variable, work backward. B Substitute the solution in the original equation to check your answer. C Check the signs. D Correct!

PTS: 1 DIF: Basic REF: Page 92 OBJ: 2-3.1 Solving Two-Step Equations

NAT: 12.5.4.a STA: A.4.A TOP: 2-3 Solving Two-Step and Multi-Step Equations

31. ANS: C

Since is subtracted from , add to both sides to undo

the subtraction.

Since f is divided by 45, multiply both sides by 45 to undo the

division.

Simplify.

Feedback

A First, add to undo the subtraction. Then, multiply to undo the division. B Check your signs. C Correct! D First, add to undo the subtraction. Then, multiply to undo the division.


OBJ: 2-3.2 Solving Two-Step Equations That Contain Fractions

NAT: 12.5.4.a STA: A.4.A TOP: 2-3 Solving Two-Step and Multi-Step Equations

32. ANS: A

8y – 8 = 24 Add 8 to both sides of the equation.

+ 8 + 8

8y =

32

8y = 32 Divide both sides by 8.

8 8

y = 4

2(4) = 8 Apply 4 to 2y.

Feedback

A Correct! B Add before multiplying. C To undo subtraction, add to both sides. D To undo multiplication, divide.


OBJ: 2-3.5 Solving Equations to Find an Indicated Value STA: A.4.A

TOP: 2-3 Solving Two-Step and Multi-Step Equations

33. ANS: A

Combine like terms.

Add to undo the subtraction. Or subtract to undo the addition.

Then, divide to undo the multiplication.

n = 11

2

Feedback

A Correct! B Add to undo the subtraction. Or subtract to undo the addition. Then, divide to undo the

multiplication. C Add to undo the subtraction. Or subtract to undo the addition. Then, divide to undo the

multiplication. D Combine like terms, and then solve.


OBJ: 2-4.2 Simplifying Each Side Before Solving Equations NAT: 12.5.3.c

STA: A.4.A TOP: 2-4 Solving Equations with Variables on Both Sides

KEY: equations | equivalent equations | terms

34. ANS: C

Locate V in the equation.

Since V is divided by I, multiply both sides by I to undo the division.

Feedback

A Multiply both sides by I to isolate r. B Multiply both sides by I to isolate r. C Correct! D Multiply both sides by I to isolate r.


OBJ: 2-5.2 Solving Formulas for a Variable NAT: 12.5.4.f

STA: A.4.A TOP: 2-5 Solving for a Variable KEY: literal equation | solving | variables

35. ANS: D

Add z to both sides.

Divide both sides by 4.

Feedback

A To undo subtraction, add to both sides. B Both terms need to be divided by the coefficient of x. C To undo multiplication, divide. D Correct!


OBJ: 2-5.3 Solving Literal Equations for a Variable NAT: 12.5.4.f

STA: A.4.A TOP: 2-5 Solving for a Variable

36. ANS: D

Use cross products.


Feedback

A Use cross products to solve. B Cross multiply. C Multiply the numerator of one fraction by the denominator of the other fraction. D Correct!

PTS: 1 DIF: Basic REF: Page 116 OBJ: 2-6.4 Solving Proportions

NAT: 12.1.4.c STA: A.6.G TOP: 2-6 Rates Ratios and Proportions

KEY: proportion | cross products

37. ANS: D


What numbers are 7 units from 0?

Case 1: Case 2: Rewrite the equation as two cases.

x – 6 = 7 x – 6 = –7 The solutions are x = 13 or x = –1.

Feedback

A Divide before you add or subtract. There are two cases to solve. B Absolute value means distance from zero. Solve the second case when the number

inside the absolute value is negative.

C Divide before you add or subtract. D Correct!


OBJ: 2-Ext.1 Solving Absolute-Value Equations

TOP: 2-Ext Solving Absolute-Value Equations

SHORT ANSWER

38. ANS:

s = 46

When something is added to the variable, add its opposite to both sides of the equation to isolate the variable.

Here, –14 is added to the variable, so add 14 to both sides of the equation to isolate s.


OBJ: 2-1.3 Solving Equations by Adding the Opposite NAT: 12.5.4.a

STA: A.4.A TOP: 2-1 Solving Equations by Adding or Subtracting

39. ANS:

Use the Commutative Property of Addition.

Combine like terms.

Since 10 is added to 17a, subtract 10 from both sides to undo

the addition.

Since a is multiplied by 17, divide both sides by 17 to undo the

multiplication.


OBJ: 2-3.3 Simplifying Before Solving Equations NAT: 12.5.3.c

STA: A.4.A TOP: 2-3 Solving Two-Step and Multi-Step Equations

40. ANS:

1.55

Substitute 3750 for p, 3000 for n, and 900 for e.

Add 900 to both sides of the equation.



TOP: 2-3 Solving Two-Step and Multi-Step Equations

41. ANS:

n –7

0 2 4 6 8 100–2–4–6–8–10

Use inverse operations to undo the operations in the inequality one at a time.

n – 4 3

n –7

0 2 4 6 8 100–2–4–6–8–10




OBJ: 3-4.1 Solving Multi-Step Inequalities NAT: 12.5.4.a

STA: A.7.B TOP: 3-4 Solving Two-Step and Multi-Step Inequalities

KEY: solving | two-step inequality MSC: solving | two-step inequality

42. ANS:

x < 5

0 1 2 3 4 5 6 7 8 9 10 11 12 130–1–2–3–4–5–6–7–8–9–10–11–12–13

3x < 15 Subtract 3x from both sides to collect the x terms on one side of the

inequality symbol.

x < 5 Divide both sides by 3.

0 1 2 3 4 5 6 7 8 9 10 11 12 130–1–2–3–4–5–6–7–8–9–10–11–12–13


OBJ: 3-5.1 Solving Inequalities with Variables on Both Sides NAT: 12.5.4.c

STA: A.1.C TOP: 3-5 Solving Inequalities with Variables on Both Sides

MSC: multistep inequality | solving | word problem

43. ANS:

0 1 2 3 4 5 6 7 8 9 100–1–2–3–4–5–6–7–8–9–10

On the left side, combine the two terms. On the right side, distribute 1.5.

Subtract the 1.5x from both sides of the inequality.

6

Divide both sides of the inequality by . Reverse the inequality symbol.

3


OBJ: 3-5.3 Simplifying Each Side Before Solving NAT: 12.5.4.c

STA: A.1.C TOP: 3-5 Solving Inequalities with Variables on Both Sides

44. ANS:

all real numbers

When the inequality is simplified, if the result is a statement that is always true, then the solution set includes

all real numbers. If the result is a statement that is always false, then there are no solutions to the inequality.

PTS: 1 DIF: Average REF: Page 196 OBJ: 3-5.4 Identities and Contradictions

NAT: 12.5.3.c STA: A.7.B TOP: 3-5 Solving Inequalities with Variables on Both Sides

45. ANS:

D: {–8, 0, 5, 6}; R: {–15, 0, 11, 13}

The domain is the set of all x-values. The range is the set of all y-values.


OBJ: 4-2.2 Finding the Domain and Range of a Relation NAT: 12.5.1.g

STA: A.2.B TOP: 4-2 Relations and Functions KEY: domain | range | function | relation

46. ANS:

6

Locate 2 on the x-axis. Move up or down to the graph of the function. Then, move right or left to the y-axis to

find the corresponding value of y.

y = 6

1 2 3 4 5 6–1–2–3–4–5–6 x

1

2

3

4

5

6

–1

–2

–3

–4

–5

–6

y

PTS: 1 DIF: Average REF: Page 254 OBJ: 4-4.3 Finding Values Using Graphs

NAT: 12.5.2.b STA: A.1.D TOP: 4-4 Graphing Functions

KEY: graph | solution | equation

47. ANS:

undefined

A line has positive slope if it rises from left to right.

A line has negative slope if it falls from left to right.

A line has zero slope if it is a horizontal line.

A line has undefined slope if it is a vertical line.

PTS: 1 DIF: Average REF: Page 312 OBJ: 5-3.5 Describing Slope

NAT: 12.5.2.b STA: A.6.B TOP: 5-3 Rate of Change and Slope

48. ANS:

y = 2x + 3

2

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. Substituting 2 for the

slope and 3

2 for the y-intercept gives y = 2x +

3

2.


OBJ: 5-6.2 Writing Linear Equations in Slope-Intercept Form NAT: 12.5.3.d

STA: A.6.D TOP: 5-6 Slope-Intercept Form

KEY: slope | y-intercept | slope-intercept form

Midterm Review

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