alg 1a midterm review - coachpate - home 1a mt... · · 2016-12-01alg 1a midterm review ... the...

Alg 1A MidTerm Review

Multiple Choice

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

____ 1. Find the solution of the equation if the replacement set is .

a. 63 c. 81

b. 35 d. 51

Express each relation as a graph and a table. Then determine the domain and range.

____ 2. {(0, –1), (3, 4), (–4, –3), (0, –3), (–4, –2)}

a.

x

y

D = {–4, 0, 3}; R = {–3, –2, –1, 4}

c.

x

y

D = {–4, 0, 3}; R = {–3, –2, –1, 4}

b.

x

y

d.

x

y

D = {–4, 0, 3}; R = {–3, –1, 4}

D = {–4, 0, 3}; R = {–3, –2, –1, 4}

The following table shows car sales at a local car dealership for the first seven days of October.

Day 1 2 3 4 5 6 7

Sales 3 4 6 7 9 10 12

____ 3. Write the ordered pairs that represent the car sales for the first week of October.

a. (1, 3), (2, 4), (3, 6), (4, 7), (5, 9), (6, 10), (7, 12)

b. (3, 1), (4, 2), (6, 3), (7, 4), (9, 5), (10, 6), (12, 7)

c. (1, 3), (2, 4), (3, 6), (4, 7), (6, 10), (7, 12)

d. (1, 4), (2, 4), (3, 6), (4, 6), (5, 9), (6, 10), (7, 12)

The following table shows the monthly charges for subscribing to the local newspaper.

Number of Months 1 2 3 4 5

Total Cost ($) 15.25 30.50 45.75 61.00 76.25

____ 4. Use the data in the newspaper subscription table to find the cost of the subscription for one year.

a. $167.75 c. $152.50

b. $183 d. $182.90

Identify the hypothesis and conclusion of the statement.

____ 5. If you live in Tampa, then you are near a beach.

a. H: you have been to Tampa

C: you live near a beach

c. H: you live in Tampa

C: you are near a beach

b. H: you are near a beach

C: you live in Tampa

d. H: you live in Tampa

C: you have a swimming pool

Find a counterexample for the statement.

____ 6. If x is an odd composite number, then x is divisible by 3.

a. c. b. d.

____ 7. If , then .

a. c. b. d.

Translate the sentence into an equation.

____ 8. Eighty-five minus five times x is equal to ten.

a. c. b. d.

____ 9. The number x divided by the number y is the same as six less than three times the difference of x and y.

a. c.

b. d.

Translate the equation into a verbal sentence.

____ 10.

a. Three times c plus the difference of c and four is 127.

b. Three times c plus the sum of c and four is 127.

c. Three plus c plus the sum of c and four is 127.

d. Three times c plus the product of c and four is 127.

Solve the equation. Then check your solution.

____ 11.

a. –2.7 c. 7.9

b. 2.7 d. 13.78

____ 12.

a. 3.9 c. 8.1

b. –3.9 d. –6.9

____ 13.

a. 14 c. 24

b. –14 d. –13

____ 14.

a. 9.88 c. 6.12

b. 15.04 d. –6.12

____ 15.

a. 35 c. 140

b. 70 d. 116

____ 16. 6p = 3

a. 2 c. ½

b.-2 d. -½

____ 17. –8p = 31

4

a. 43

4 c. 13

32

b. 13

32 d. 26

Write an equation and solve each problem.

____ 18. Find four consecutive odd integers with a sum of –32.

a. ; –11, –13, –15, –17

b. ; –10, –9, –7, –6

c. ; –5, –3, –1, 1

d. ; –11, –9, –7, –5

Solve the equation. Then check your solution.

____ 19. 4

5k – 5 = –7

2

5k

a. 5 c. 12

3

b. 5 d. 30

____ 20. 4 – 3

5(3a + 4) = 7

a. 7.4 c. 3

b. –6 d. –3

____ 21. 1

2(15 + 7d) =

a. 3 c. –4

b. 2 d. –2

State whether the percent of change is a percent of increase or a percent of decrease. Then find the percent of

change. Round to the nearest whole percent.

____ 22. original: 11

new: 33

a. increase; 200% c. decrease; 200%

b. increase; 67% d. decrease; 67%

Find the total price of the item.

____ 23. groceries: $87.23

tax: 6.5%

a. $5.67 c. $92.90

b. $81.56 d. $92.46

Find the discounted price of the item.

____ 24. DVD: $19.95

discount: 20%

a. $3.99 c. $15.96

b. $23.94 d. $20.15

Two trains leave Chicago at the same time, one traveling east and the other traveling west. The eastbound

train travels at 50 miles per hour, and the westbound train travels at 40 miles per hour. Let t represent the

amount of time since their departure.

____ 25. Complete the table representing the situation.

a.

b.

c.

d.

____ 26. Write an equation that could be used to determine when the trains will be 405 miles apart.

a. c. b. d.

Find the solution set for the equation, given the replacement set.

____ 27. –x + 5y = –2; {(7, 1.6), (5, 0.6), (6, 3.6), (4, –1.4)}

a. {(5, 0.6)} c. {(6, 3.6)}

b. {(4, –1.4)} d. {(7, 1.6)}

____ 28. In 1994, school lunch at Rockwell High School was $1.20. In 1999, the cost increased to $2.25. Find the

annual rate of change in the price for school lunch from 1994 to 1999.

a. $0.18 per year c. $0.20 per year

b. $0.21 per year d. $1.05 per year

Source: www.cityoforlando.net/public_works/stormwater/rain/rainfall.htm

____ 29. For which one month period was the rate of change in rainfall amounts in Orlando the greatest?

a. May - June c. June - July

b. Aug. - Sept. d. Feb. - March

Write a direct variation equation that relates the variables. Then graph the equation.

____ 30. Roasted cashews are $5.98 per pound. The total cost of p pounds is C.

a.

1 2 3 4 5 6 7 8 9 10 p

1

2

3

4

5

6

7

8

9

10

C

c.

1 2 3 4 5 6 7 8 9 10 p

1

2

3

4

5

6

7

8

9

10

C

b.

1 2 3 4 5 6 7 8 9 10 C

1

2

3

4

5

6

7

8

9

10

p

d.

1 2 3 4 5 6 7 8 9 10 p

1

2

3

4

5

6

7

8

9

10

C

____ 31. The total cost is C for n packages of popcorn priced at $1.50 per package.

a.

1 2 3 4 5 6 7 8 9 10 C

1

2

3

4

5

6

7

8

9

10

n

c.

1 2 3 4 5 6 7 8 9 10 n

1

2

3

4

5

6

7

8

9

10

C

b. d.

1 2 3 4 5 6 7 8 9 10 n

1

2

3

4

5

6

7

8

9

10

C

1 2 3 4 5 6 7 8 9 10 n

1

2

3

4

5

6

7

8

9

10

C

Find the next three terms of the arithmetic sequence.

____ 32. 55, 47, 39, 31, . . .

a. 36, 41, 46 c. 29, 27, 25

b. 23, 15, 7 d. 26, 21, 16

Write an equation of the line with the given slope and y-intercept

____ 33. slope: 0.8, y-intercept: 10

a. y = –0.8x + 10 c. y = 0.8x + 10

b. y = 0.8x – 10 d. y = 5

7x + 10

Beach Bike Rentals charges $5.00 plus $0.20 per mile to rent a bicycle.

____ 34. Write an equation for the total cost C of renting a bicycle and riding for m miles.

a. c. b. d.

Write an equation of the line that passes through each point with the given slope.

____ 35.

a. c.

b. d.

Write the point-slope form of an equation for a line that passes through the point with the given slope.

____ 36. (–6, –6), m = 4

7

a. y – 6 = 4

7(x + 6) c. y + 6 =

4

7(x + 6)

b. y + 6 = 4

7(x – 6) d. y + 6 =

4

7(x + 6)

Determine whether the graph shows a positive correlation, a negative correlation, or no correlation. If there

is a positive or negative correlation, describe its meaning in the situation.

____ 37.

Average Cycling Speed

Miles

Per

Hour

Minutes5 10 15 20 25 30 35

2

4

6

8

10

12

14

16

18

a. no correlation

b. negative; as time passes, speed decreases

c. positive; as time passes, speed increases

d. positive; as time passes, speed decreases

____ 38.

Consumer Price Index, 1950-2002

1950 1960 1970 1980 1990 2000

100

200

300

400

500

600

700

Year Source: Bureau of Labor Statistics, U.S. Dept. of Labor

a. no correlation

b. positive correlation; as time passes, the CPI increases.

c. positive correlation; as time passes, the CPI decreases.

d. negative correlation; as time passes, the CPI decreases.

____ 39.

Sport Utility Vehicle Sales in the U.S.,

1991-2001

1990 1992 1994 1996 1998 2000 2002

1

2

3

4

5

6

7

Year Source: The World Almanac, 2003

a. negative correlation; as time passes, SUV sales decrease.

b. no correlation

c. positive correlation; as time passes, the SUV sales decrease.

d. positive correlation; as time passes, the SUV sales increase.

____ 40.

Cars Passing School

Num

ber

of

Car

s

Hours1 2 3 4 5 6 7 8 9 10

10

20

30

40

50

60

70

80

90

100

a. negative; as time passes, the number of cars increases.

b. negative; as time passes, the number of cars decreases.

c. no correlation

d. positive; as time passes, the number of cars decreases.

Domestic Traveler Spending in the U.S., 1987-1999

1986 1988 1990 1992 1994 1996 1998 2000

225

250

275

300

325

350

375

400

425

450

Year Source: The World Almanac, 2003

____ 41. Use the scatter plot that shows the domestic traveler spending. Use the points (1987, 235) and (1999, 446) to

write the slope-intercept form of an equation for the line of fit shown in the scatter plot.

a. c.

b. d.

Strawberries Picked

Quar

ts P

icked

Time (hours)1 2 3 4 5 6 7 8 9 10

10

20

30

40

50

60

70

80

90

100

____ 42. Use the scatter plot that shows the number of quarts of strawberries picked each hour. Use the points (1, 73)

and (8, 41) to write the slope-intercept form of an equation for the line of fit shown in the scatter plot.

a. c.

b. d.

Sport Utility Vehicle Sales in the U.S., 1991-2001

Year 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001

Sales

(millions)

0.9

1.2

1.4

1.6

1.8

2.2

2.5

2.8

3.0

3.4

3.8 Source: The World Almanac, 2003

____ 43. Let x represent the number of years since 1990. Let y represent the sport utility vehicle sales in millions. Write

the slope-intercept form of the equation for the line of fit using the points representing 1992 and 2000.

a. c.

b. d.

Solve the inequality. Graph the solution on a number line.

____ 44.

a.

0 3 6 9 120–3–6–9

b.

0 3 6 9 120–3–6–9

c.

0 3 6 9 120–3–6–9

d.

0 3 6 9 120–3–6–9

Solve the inequality.

____ 45.

a. c. b. d.

____ 46.

a. (all real numbers) c.

b. d. (the empty set)

Solve the compound inequality and graph the solution set.

____ 47. and

a.

0 2 4 6 8 100–2–4–6–8–10

b.

0 2 4 6 8 100–2–4–6–8–10

c.

0 2 4 6 8 100–2–4–6–8–10

d.

0 2 4 6 8 100–2–4–6–8–10

____ 48. or

a.

0 2 4 6 8 100–2–4–6–8–10

b.

0 2 4 6 8 100–2–4–6–8–10

c.

0 2 4 6 8 100–2–4–6–8–10

d. (all real numbers)

0 2 4 6 8 100–2–4–6–8–10

____ 49. |x-76| < 6

a. {x | 70 x 82} c. {x | 70 x}

b. {x | x 70 or x 82} d. {x | x 82}

Alg 1 MidTerm Review

Answer Section

MULTIPLE CHOICE

1. ANS: A

The solution set of an open-sentence is the set of elements from the replacement set that make the

open-sentence true.

Feedback

A Correct! B Did you add or subtract after replacing the variable? C Does that replacement make the equation true? D Be careful with division.

PTS: 1 DIF: Basic REF: Lesson 1-5

OBJ: 1-5.1 Solve open-sentence equations. NAT: NA 1 | NA 6 | NA 8 | NA 9 | NA 2

STA: AL 1.a | AL 1 TOP: Solve open-sentence equations

KEY: Equations | Solve Equations

2. ANS: D

A relation is a set of ordered pairs. A relation can also be represented by a table, a graph, or a mapping.

Feedback

A Did you plot all the points correctly? B Did you plot all the points correctly? C Check your table again. D Correct!

PTS: 1 DIF: Average REF: Lesson 1-6

OBJ: 1-6.1 Represent relations of sets of ordered pairs, tables, mappings, and graphs.

NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 3

TOP: Represent relations as sets of ordered pairs, tables, mappings, and graphs

KEY: Relations | Ordered Pairs | Tables | Mappings | Graphs

3. ANS: A

An ordered pair is a set of numbers, or coordinates, written in the form (x, y).

Feedback

A Correct! B Which variable is the independent variable? C Did you include all of the ordered pairs? D Be careful pairing the variables.

PTS: 1 DIF: Basic REF: Lesson 1-6 OBJ: 1-6.3 Draw graphs of relations.

NAT: NA 1 | NA 6 | NA 8 | NA 10 | NA 2 TOP: Draw graphs of functions

KEY: Graphs | Functions

4. ANS: B

Use the table to find the relationship between the independent and dependent variables. Use this relationship

to find the cost for one year.

Feedback

A How many months are in one year? B Correct! C How many months did you use? D Did you multiply correctly?

PTS: 1 DIF: Average REF: Lesson 1-6 OBJ: 1-6.3 Draw graphs of relations.

NAT: NA 1 | NA 6 | NA 8 | NA 10 | NA 2 TOP: Draw graphs of functions

KEY: Graphs | Functions

5. ANS: C

The hypothesis is the part of the conditional following the word if, and the conclusion is the part of the

conditional following the word then.

Feedback

A Read the conditional again. Is that what it says? B Is the part after the word if the hypothesis? C Correct! D Is the conclusion correct?


OBJ: 1-8.1 Identify the hypothesis and conclusion in a conditional statement.

NAT: NA 1 | NA 8 | NA 9 | NA 10 | NA 2 STA: AL 1

TOP: Identify the hypothesis and conclusion in a conditional statement

KEY: Conditional Statements | Hypothesis | Conclusion

6. ANS: A

A counterexample is a specific case in which a statement is false. It takes only one counterexample to show

that a statement is false.

Feedback

A Correct! B Are the hypothesis and conclusion both true? C Is the hypothesis true? D Is the hypothesis true?


OBJ: 1-8.2 Use a counterexample to show that an assertion is false.

NAT: NA 6 | NA 8 | NA 9 | NA 10 | NA 7

TOP: Use a counterexample to show that an assertion is false

KEY: Counterexample | Deductive Reasoning

7. ANS: C

A counterexample is a specific case in which a statement is false. It takes only one counterexample to show

that a statement is false.

Feedback

A Are the hypothesis and conclusion both true? B Are the hypothesis and conclusion both true? C Correct! D Is the hypothesis true?


OBJ: 1-8.2 Use a counterexample to show that an assertion is false.

NAT: NA 6 | NA 8 | NA 9 | NA 10 | NA 7

TOP: Use a counterexample to show that an assertion is false

KEY: Counterexample | Deductive Reasoning

8. ANS: B

Translate verbal sentences into equations by using key words and phrases you have learned to replace words

with symbols.

Feedback

A Is addition indicated by the sentence? B Correct! C What is being subtracted? D Are the parentheses needed?


OBJ: 2-1.1 Translate verbal sentences into equations. NAT: NA 6

TOP: Translate verbal sentences into equations KEY: Verbal Sentences | Equations

9. ANS: B

Translate verbal sentences into equations by using key words and phrases you have learned to replace words

with symbols.

Feedback

A How do you translate less than? B Correct! C Be careful in translating divided by. D Do you need parentheses in your equation?


OBJ: 2-1.1 Translate verbal sentences into equations. NAT: NA 6

TOP: Translate verbal sentences into equations KEY: Verbal Sentences | Equations

10. ANS: B

Using key words for operations, translate the equation into a number sentence.

Feedback

A What did you translate as the difference? B Correct! C Are there three additions in the equation? D Are there two products in the equation?


OBJ: 2-1.2 Translate equations into verbal sentences. NAT: NA 1 | NA 8 | NA 9 | NA 10 | NA 2

STA: AL 7 TOP: Translate equations into verbal sentences

KEY: Equations | Verbal Sentences

11. ANS: C

To solve an equation means to find all the values of the variable that make the equation a true statement. One

way to do this is to isolate the variable on one side of the equation. You can sometimes do this by adding the

same number to both sides of the equation.

Feedback

A Did you subtract from both sides? B Did you use the Addition Property of Equality? C Correct! D Did you add the same number to both sides?


OBJ: 2-2.3 Solve equations with decimals by using addition. NAT: NA 1 | NA 8 | NA 9 | NA 10 | NA 2

STA: AL 7 TOP: Solve equations with decimals by using addition

KEY: Solve Equations | Addition | Decimals

12. ANS: B


way to do this is to isolate the variable on one side of the equation. You can sometimes do this by adding the

same number to both sides of the equation.

Feedback

A Did you use the Addition Property of Equality? B Correct! C Did you add the same number to both sides? D Did you subtract from both sides?


OBJ: 2-2.3 Solve equations with decimals by using addition. NAT: NA 1 | NA 8 | NA 9 | NA 10 | NA 2

STA: AL 7 TOP: Solve equations with decimals by using addition

KEY: Solve Equations | Addition | Decimals

13. ANS: B


way to do this is to isolate the variable on one side of the equation. You can sometimes do this by subtracting

the same number from both sides of the equation.

Feedback

A Be careful with sign rules. B Correct! C Did you subtract a number from both sides? D Did you perform the subtraction correctly?


OBJ: 2-2.4 Solve equations with integers by using subtraction. NAT: NA 1 | NA 8 | NA 9 | NA 10 | NA 2

STA: AL 7 TOP: Solve equations with integers by using subtraction

KEY: Solve Equations | Subtraction | Integers

14. ANS: C


way to do this is to isolate the variable on one side of the equation. You can sometimes do this by subtracting

the same number from both sides of the equation.

Feedback

A Did you subtract from both sides? B Did you subtract the same number from both sides? C Correct! D Did you use the Subtraction Property of Equality?


OBJ: 2-2.6 Solve equations with decimals by using subtraction.


TOP: Solve equations with decimals by using subtraction

KEY: Solve Equations | Subtraction | Decimals

15. ANS: B

If an equation is true and each side is multiplied by the same number, the resulting equation is true.

Feedback

A What did you multiply both sides by? B Correct! C Did you isolate the variable? D Did you multiply both sides by the correct number?


OBJ: 2-2.7 Solve equations with integers by using multiplication.


TOP: Solve equations with integers by using multiplication

KEY: Solve Equations | Multiplication | Integers

16. ANS: A

If an equation is true and each side is multiplied by the same number, the resulting equation is true. Rewrite

each mixed number as an improper fraction and multiply each side by the reciprocal of the factor that is

multiplied by the variable.

Feedback

A Correct! B Did you change to improper fractions and multiply by the reciprocal? C Be careful with sign rules. D Did you multiply by the reciprocal?


OBJ: 2-2.10 Solve equations with mixed numbers using multiplication and division.


TOP: Solve equations with mixed numbers by using multiplication and division

KEY: Solve Equations | Multiplication | Division | Mixed Numbers

17. ANS: C

If an equation is true and each side is multiplied by the same number, the resulting equation is true. Rewrite

each mixed number as an improper fraction and multiply each side by the reciprocal of the factor that is

multiplied by the variable.

Feedback

A Did you subtract from both sides? B Be careful with sign rules. C Correct! D Did you multiply by the reciprocal?


OBJ: 2-2.10 Solve equations with mixed numbers using multiplication and division.


TOP: Solve equations with mixed numbers by using multiplication and division

KEY: Solve Equations | Multiplication | Division | Mixed Numbers

18. ANS: D

First translate the verbal sentences into equations by using key words and phrases you have learned to replace

words with symbols. Then to solve an equation with more than one operation, undo operations by working

backward.

Feedback

A Did you do the correct operation? B Are these consecutive odd integers? C Check your calculation again. D Correct!


OBJ: 2-3.2 Solve consecutive integer problems. NAT: NA 1 | NA 2 | NA 6 | NA 8

STA: AL 5 | AL 7 TOP: Solve consecutive integer problems.

KEY: Solve Equations | Integers

19. ANS: A

To solve equations with variables on each side, first use the Addition or Subtraction Property of Equality to

write an equivalent equation that has all of the variables on one side. Simplify both sides of the equation, and

use the Multiplication or Division Property of Equality to solve for the variable.

Feedback

A Correct! B Be careful with sign rules. C Did you combine the variable fractions correctly? D Did you use the Addition or Subtraction Property correctly?


OBJ: 2-4.2 Solve equations with fractions with the variable on each side.


TOP: Solve equations with fractions with the variable on each side

KEY: Solve Equations | Variables | Fractions

20. ANS: D

Use the Distributive Property to remove the grouping symbols. Simplify the expressions on each side of the

equals sign. Use the Addition and/or Subtraction Properties of Equality to get the variables on one side of the

equals sign and the numbers without variables on the other side of the equals sign. Simplify the expressions

on each side of the equals sign. Use the Multiplication or Division Property of Equality to solve.

Feedback

A Be careful with the Addition and Subtraction Properties. B Be careful with the Division Property. C Be careful with sign rules. D Correct!


OBJ: 2-4.5 Solve equations with fractions involving grouping symbols.


TOP: Solve equations with fractions involving grouping symbols

KEY: Solve Equations | Grouping Symbols | Fractions

21. ANS: D

Use the Distributive Property to remove the grouping symbols. Simplify the expressions on each side of the

equals sign. Use the Addition and/or Subtraction Properties of Equality to get the variables on one side of the

equals sign and the numbers without variables on the other side of the equals sign. Simplify the expressions

on each side of the equals sign. Use the Multiplication or Division Property of Equality to solve.

Feedback

A Did you use the Addition or Subtraction Property of Equality correctly? B Be careful with sign rules. C Be careful with the Division Property of Equality. D Correct!


OBJ: 2-4.5 Solve equations with fractions involving grouping symbols.


TOP: Solve equations with fractions involving grouping symbols

KEY: Solve Equations | Grouping Symbols | Fractions

22. ANS: A

First find the amount of change. Then find the percent of change by using the original number as the base.

Feedback

A Correct! B Did you use the original number as the base? C Which is the greater number, the new or the original? D Which number is greater?


OBJ: 2-7.1 Find percents of increase and decrease. NAT: NA 2 | NA 6 | NA 8 | NA 9 | NA 3

TOP: Find percents of increase and decrease

KEY: Percent of Increase | Percent of Decrease

23. ANS: C

Find the amount of tax by multiplying the tax rate as a decimal. Add the tax to the original price.

Feedback

A That is the amount of tax. B Did you subtract the tax? C Correct! D Did you use the correct tax rate?


OBJ: 2-7.2 Solve problems involving percents of change. NAT: NA 1 | NA 8 | NA 9 | NA 10 | NA 2

TOP: Solve problems involving percents of change KEY: Percent of Change | Solve Problems

24. ANS: C

Find the amount of discount by multiplying the discount rate converted to a decimal. Subtract the amount of

discount from the original price.

Feedback

A That is the amount of discount. B Did you add the amount of discount? C Correct!

D Did you add the percent as a decimal?


OBJ: 2-7.2 Solve problems involving percents of change. NAT: NA 1 | NA 8 | NA 9 | NA 10 | NA 2

TOP: Solve problems involving percents of change KEY: Percent of Change | Solve Problems

25. ANS: A

Uniform motion problems are problems where an object moves at a certain speed, or rate. Use the formula

d = rt to solve these problems, where d is the distance, r is the rate, and t is the time. Complete the table using

the given information.

Feedback

A Correct! B How fast were the trains traveling? C Did the eastbound train travel longer? D Were the trains traveling at the same rate of speed?


OBJ: 2-9.1 Solve uniform motion problems. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6

STA: AL 12 TOP: Solve uniform motion problems KEY: Uniform Motion | Solve Problems

26. ANS: B

Uniform motion problems are problems where an object moves at a certain speed, or rate. Use the formula

d = rt to solve these problems, where d is the distance, r is the rate, and t is the time. Complete the table using

the given information. The sum of the distances the two trains travel is equal to the total distance.

Feedback

A Would the left side be equal to the total distance the trains are apart? B Correct! C Would the right side be equal to the total distance the trains are apart? D Would the left side be equal to the total distance the trains are apart?


OBJ: 2-9.1 Solve uniform motion problems. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6

STA: AL 12 TOP: Solve uniform motion problems KEY: Uniform Motion | Solve Problems

27. ANS: A

A solution of an equation in two variables is an ordered pair that results in a true statement when substituted

into the equation.

Feedback

A Correct! B Does substituting for x and y result in a true equation? C Does the ordered pair make the equation true? D Is the equation true?


OBJ: 3-1.1 Identify linear equations, intercepts, and zeros. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 3

STA: AL 4 | AL 3 TOP: Use an equation to determine the range for a given domain

KEY: Domain | Range

28. ANS: B

Slope can be used to describe a rate of change. The rate of change tells, on average, how a quantity is

changing over time.

Feedback

A How many years did you divide by? B Correct! C Did you subtract carefully? D Did you divide by the number of years?


OBJ: 3-3.1 Use rate of change to solve problems. NAT: NA 2 | NA 4 | NA 7 | NA 10 | NA 3

STA: AL 2.a | AL 2 TOP: Use rate of change to solve problems

KEY: Rate of Change | Solve Problems

29. ANS: A

Slope can be used to describe a rate of change. The rate of change tells, on average, how a quantity is

changing over time.

Feedback

A Correct! B What is the difference in rainfall amounts for that period? C Is that the largest rate of change? D What is the rate of change for that period?


OBJ: 3-3.1 Use rate of change to solve problems. NAT: NA 2 | NA 4 | NA 7 | NA 10 | NA 3

STA: AL 2.a | AL 2 TOP: Use rate of change to solve problems

KEY: Rate of Change | Solve Problems

30. ANS: C

Direct variation equations are of the form y = kx, where k 0. The graph of y = kx always passes through the

origin.

Feedback

A Does the graph match the equation? B Which variable is the independent variable? C Correct! D Do points on the graph make the equation true?


OBJ: 3-4.2 Solve problems involving direct variation. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 4

STA: AL 2.b | AL 2 TOP: Solve problems involving direct variation

KEY: Direct Variation | Solve Problems

31. ANS: B

Direct variation equations are of the form y = kx, where k 0. The graph of y = kx always passes through the

origin.

Feedback

A Which variable is the independent variable? B Correct! C Do the equation and graph match?

D Do points on the graph make the equation true?


OBJ: 3-4.2 Solve problems involving direct variation. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 4

STA: AL 2.b | AL 2 TOP: Solve problems involving direct variation

KEY: Direct Variation | Solve Problems

32. ANS: B

Each term of an arithmetic sequence after the first term can be found by adding the common difference to the

preceding term.

Feedback

A Is the fifth term the result of adding the common difference to the fourth term? B Correct! C What is the common difference? D What is the common difference?


OBJ: 3-5.2 Extend and write formulas for arithmetic sequences.

NAT: NA 1 | NA 8 | NA 9 | NA 10 | NA 2

TOP: Extend and write formulas for arithmetic sequences KEY: Sequences | Arithmetic Sequences

33. ANS: C

The linear equation y = mx + b is written in slope-intercept form, where m is the slope and b is the y-intercept.

Feedback

A What is the slope? B What is the y-intercept? C Correct! D What is the slope of the line?


OBJ: 4-1.1 Write and graph linear equations in slope-intercept form.

NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 4 STA: AL 2.c | AL 2

TOP: Write and graph linear equations in slope-intercept form

KEY: Slope-Intercept Form | Linear Equations | Graphs

34. ANS: A

If a quantity changes at a constant rate over time, it can be modeled by a linear equation. The y-intercept

represents a starting point, and the slope represents the rate of change.

Feedback

A Correct! B Which number would be the y-intercept in the linear equation? C Which variable should be the independent variable? D What is the rate of change?


OBJ: 4-1.2 Model real-world data with an equation in slope-intercept form.

NAT: NA 2 | NA 4 | NA 9 | NA 10 | NA 3 STA: AL 2.a | AL 2

TOP: Model real-world data with an equation in slope-intercept form

KEY: Slope-Intercept Form | Equations | Real-World Problems

35. ANS: D

Find the y-intercept by replacing x and y with the given point and m with the given slope in the slope-intercept

form. Solve for b. Write the equation in slope-intercept form using the given m and the calculated b.

Feedback

A What is the y-intercept? B What is the y-intercept? C What is the slope of the line? D Correct!


OBJ: 4-2.1 Write an equation of a line given the slope and one point on the line.

NAT: NA 2 | NA 4 | NA 9 | NA 10 | NA 3 STA: AL 2.a | AL 2

TOP: Write an equation of a line given the slope and one point on a line

KEY: Slope | Equations | Lines

36. ANS: D

The linear equation is written in point-slope form, where is a given point on a

nonvertical line and m is the slope of the line.

Feedback

A What is the y-coordinate of the given point? B Did you subtract the x-coordinate from x? C What is the slope of the line? D Correct!


OBJ: 4-3.1 Write the equation of a line in point-slope form. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6

STA: AL 2.a | AL 2 TOP: Write the equation of a line in point-slope form

KEY: Point-Slope Form | Equations | Lines

37. ANS: B

A scatter plot is a graph in which two sets of data are plotted as ordered pairs in a coordinate plane. There is a

positive correlation when as x increases, y increases. There is a negative correlation when as x increases, y

decreases. There is no correlation when x and y are not related.

Feedback

A Are the variables related? B Correct! C Is the speed increasing? D What is meant by positive correlation?


OBJ: 4-5.1 Interpret points on a scatter plot. NAT: NA 2 | NA 6 | NA 7 | NA 9 | NA 3

STA: AL 2.b | AL 2 TOP: Interpret points on a scatter plot

KEY: Scatter Plot | Interpret Data

38. ANS: B




Feedback

A Are the variables not related? B Correct! C What is meant by positive correlation? D Is the CPI decreasing?





39. ANS: D




Feedback

A Are sales decreasing? B Are the variables not related? C What is meant by positive correlation? D Correct!





40. ANS: C




Feedback

A What is meant by negative correlation? B Is the number of cars decreasing with the passage of time? C Correct! D What is meant by positive correlation?





41. ANS: C

Use the two points to calculate the slope of the line. Then find the slope intercept form of the equation of the

line using the slope and one of the points.

Feedback

A Is the slope of the line of fit negative? B Which variable is the independent variable? C Correct! D How did you determine the slope of the line?


OBJ: 4-5.2 Use lines of fit to make and evaluate predictions. NAT: NA 2 | NA 6 | NA 7 | NA 9 | NA 5

STA: AL 2.c | AL 2.b TOP: Write equations for lines of fit

KEY: Best Fit Line | Equations

42. ANS: D

Use the two points to calculate the slope of the line. Then find the slope intercept form of the equation of the

line using the slope and one of the points.

Feedback

A Is the slope of the line of fit positive? B Which variable is the independent variable? C How did you determine the slope of the line? D Correct!





43. ANS: A

If the data points do not all lie on a line, but are close to a line, you can draw a line of fit. This line describes

the trend of the data. Once you have a line of fit, you can find an equation of the line using 2 points to find the

slope and y-intercept.

Feedback

A Correct! B Is there a negative correlation? C Did you add when you should have subtracted? D Which variable is the independent variable?





44. ANS: C

Solve the inequality by subtracting the constant term on the left side of the inequality from both sides of the

inequality.

Feedback

A Check the inequality sign. B Use subtraction to solve this inequality. C Correct! D Use subtraction to solve this inequality.


OBJ: 5-1.2 Solve linear inequalities by using subtraction. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6

STA: AL 7 | AL 2.c TOP: Solve linear inequalities by using subtraction

KEY: Linear Inequalities | Subtraction

45. ANS: A

First add the two variable terms in the numerator. Secondly, multiply both sides by the denominator. Next,

add the constant term on the left to both sides. Finally, divide both sides by the coefficient of the variable.

Feedback

A Correct! B There is no need to flip the inequality sign since you are multiplying and dividing by

positive numbers. C Check the order of your steps. You must add the constant to both sides before you

divide by the coefficient of the variable. D Check the order of your steps. You must multiply both sides by the denominator before

you add the constant to both sides.


OBJ: 5-3.2 Solve linear inequalities with fractions involving more than one operation.

NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6 STA: AL 7 | AL 2.c

TOP: Solve linear inequalities with fractions involving more than one operation

KEY: Linear Inequalities | Fractions

46. ANS: C

Using the Distributive Property, multiply to eliminate the parentheses. Combine like terms and then solve the

inequality for g.

Feedback

A Double-check your calculations. The set of real numbers means that the inequality

resulted in a statement that is always true. B Double-check your calculations on the right side of the inequality. Remember that the

product of two negative numbers is a positive number. C Correct! D Double-check your calculations. The empty set means that the inequality resulted in a

false statement.


OBJ: 5-3.4 Solve linear inequalities with integers involving the Distributive Property.


TOP: Solve linear inequalities with integers involving the Distributive Property

KEY: Linear Inequalities | Integers | Distributive Property

47. ANS: A

Solve each of the inequalities for u. Combine the two resulting inequalities into one sentence and graph it on

the number line. Be careful to include the endpoint on the left but not the value on the right.

Feedback

A Correct! B Double-check your calculations and your graph. C Remember that an open circle on a graph means the endpoint is not included and a solid

circle means it is included. D Did you use subtraction to solve the first equation and addition to solve the second?


OBJ: 5-4.1 Solve compound inequalities containing the word and and graph their solution sets.


TOP: Solve compound inequalities containing the word 'and' and graph their solution sets

KEY: Compound Inequalities | Graphs | Solution Set

48. ANS: D

Solve each of the inequalities for v. The union of the two inequalities will be the set of all real numbers.

Feedback

A Is this the union of the two inequalities? B This is only the solution to the first inequality. C This is only the solution to the second inequality. D Correct!


OBJ: 5-4.2 Solve compound inequalities containing the word or and graph their solution sets.


TOP: Solve compound inequalities containing the word 'or' and graph their solution sets

KEY: Compound Inequalities | Graphs | Solution Set

49. ANS: A

The difference between the height of the record jump and the height of John’s jump is less than or equal to 6

inches. Let x be the height of John’s jump. Write an absolute value inequality and solve.

Feedback

A Correct! B Be careful with your greater than and less than symbols. C Did you consider the case that the expression inside the absolute value symbol is

positive? D Did you consider the case that the expression inside the absolute value symbol is

negative?


OBJ: 5-5.2 Apply absolute value inequalities in real-world problems.

NAT: NA 2 | NA 8 STA: AL 4 | AL 7.b

TOP: Apply absolute value inequalities in real-world problems.

KEY: Absolute Value | Inequalities | Real-World Problems

alg 1a midterm review - coachpate - home 1a mt... · · 2016-12-01alg 1a midterm review ... the...

Documents