Friday, April 21, 2023

Unit 4Practice TestAnswer Key

1 The number of students who watch less than 1 hour or more than 7 hours of television is approximately what percent of the number of students who watch television each night? 2

3

9

7

students ofnumber Total

hours 7 than more hour 1 than less

3792

32

21

5 = 0.24 = 24%

Percent

≈ 25%

Students watch Students watch

2 The graph shows the number of people in the family of each student enrolled at the local high school. About how many students live in a family of fewer than 4 people?

Total Percentage = 11.7% + 13.3% = 25%

Number of students = 25% of 1,500

= 0.25 1,500= 375

Harrison has grades of 87, 83, 74, and 89. What grade must he get on his fifth test so that his average will be 85?

Method #1Let x = Fifth test score

Sum of Five Scores

Number of scoresAverage

87 83 74 8985

5

x

33385

5

x

85 333

1 5

x

(1)(333+x) = (85)(5)

333 + x = 425

x = 92

3

Harrison has grades of 87, 83, 74, and 89. What grade must he get on his fifth test so that his average will be 85?

Method #2 Test each answer

Sum of Five Scores

Number of scoresAverage A. 85

B. 88

C. 90

D. 92

E. 93

?

87 83 74 89

5

85

418

5 = 83.6 ≠ 85

NO

3

421

5

87 83 74 89

5

88

Harrison has grades of 87, 83, 74, and 89. What grade must he get on his fifth test so that his average will be 85?

Method #2 Test each answer

Sum of Five Scores

Number of scoresAverage A. 85

B. 88

C. 90

D. 92

E. 93

?

= 84.2 ≠ 85

NO

? NO

3

423

5

87 83 74 89

5

90

Harrison has grades of 87, 83, 74, and 89. What grade must he get on his fifth test so that his average will be 85?

Method #2 Test each answer

Sum of Five Scores

Number of scoresAverage A. 85

B. 88

C. 90

D. 92

E. 93

?

= 84.6 ≠ 85

NO

? NO

? NO

3

425

5

87 83 74 89

5

92

Harrison has grades of 87, 83, 74, and 89. What grade must he get on his fifth test so that his average will be 85?

Method #2 Test each answer

Sum of Five Scores

Number of scoresAverage A. 85

B. 88

C. 90

D. 92

E. 93

?

= 85

NO

? NO

? NO

? YES

3

4 Tom and Karen ate lunch at the ballpark. Tom ordered a frankfurter, fries, and a soda. Karen ordered a hamburger and a soda. They divided the total bill evenly. What was the difference between what Karen paid and what she should have paid?

4

Total Bill = $4.50 + $3.50 = $8.00

Tom

Frankfurter $2.00

Fries $1.50

Soda $1.00

Total $4.50

Karen

Hamburger $2.50

Soda $1.00

Total $3.50

Bill divided evenly = $8.00 2 = $4.00

What Karen paid – What Karen should have paid

$4.00 – $3.50 = $0.50

5 The graph shows students in the twelth-grade honor roll from 1992 to 1996. What was the percent increase in the number of students who made honor roll from 1993 to 1995?

Increase amount

125

135= 135 – 125= 10

Percent Increase

Amount Starting

Amount Increase

125

10 = 0.08 = 8%

The average grade on a class test taken by 11 students is 85. When James (who was absent) took the test, his score raised the class average by 1 point. What was James’ score?

Sum of 11 tests

Number of testsAverage

of 11 tests

Sum of 11 tests85

11

85 Sum of 11 tests

1 11

(1)(Sum of 11 tests) = (85)(11)

Sum of 11 tests = 935

6

The average grade on a class test taken by 11 students is 85. When James (who was absent) took the test, his score raised the class average by 1 point. What was James’ score?

85 + 1 = 86Let x = Jame’s test score

Sum of 11 tests = 935

Average with Jame’s test

Sum of 11 tests +

Jame’stest

Number of tests=

Average with Jame’s test

93586

12

x

6

The average grade on a class test taken by 11 students is 85. When James (who was absent) took the test, his score raised the class average by 1 point. What was James’ score?

85 + 1 = 86Let x = Jame’s test score

Sum of 11 tests = 935 Average with Jame’s test

93586

12

x

86 935

1 12

x

1(935 + x) = (86)(12)

935 + x = 1032–935 –935

x = 97

6

7 The circle graphs shows how David’s monthly expenses are divided. If David spends $450 per month for food, how much does he spend per month on his car?

Let x = Total Monthly Expenses

25% of total monthly expenses is food cost

25% of x = 450

.25x = 450

x = 1800

.25.25x 450.25 =

7 The circle graphs shows how David’s monthly expenses are divided. If David spends $450 per month for food, how much does he spend per month on his car?

Let x = Total Monthly Expenses

x = 1800

20% of 1800

= 0.20 1800

= 360

Car Expense

8 The average of 7 test scores is 86. Four of the scores are 80, 83, 86, and 92. Which of the following could NOT be the other scores?

Total Points = 7 Average = 7 86 = 602

Four scores total = 80 + 83 + 86 + 92 = 341

Total Points – Four scores total = Other scores total

602 – 341 = 261

Test A 80 + 90 + 91 = 261 YES

Test B 75 + 88 + 98 = 261 YES

Test C 85 + 84 + 93 = 262 NO

9Based on the chart, which best approximates the total number of video rentals by premium members at Store B during the years 2000–2002?

Premium MembersStore B / 2000 – 2002

Total Video RentalsStore B / 2000 – 2002

12(500)+15(1000) +20(1250) = 46,000

10

The average of a and b is 5, and the average of c, d, and 10 is 24. What is the average of a, b, c, and d?

52

a b

Average of a and b is 5Average of c, d, and 10 is 24

1024

3

c d

2 52

2a b

10a b

–10

10

33 3 24

c d

10 72c d –10

62c d Average of a, b, c, and d

10 62 7218

4 4 4

a b c d

11

Salespeople at Victory Motors give discounts based on the retail price of the car to repeat customers, such as Todd and Alyse. If Todd buys a car with a retail price of $22,000 and Alyse buys a car for $14,500, what is the difference in the discounted prices of the cars?

Todd $22,000Discount

Alyse $14,500Discount

= 8% of $22,000= 0.08 22,000 = $1760

= 5% of $14,500= 0.05 14,500 = $725

11

Salespeople at Victory Motors give discounts based on the retail price of the car to repeat customers, such as Todd and Alyse. If Todd buys a car with a retail price of $22,000 and Alyse buys a car for $14,500, what is the difference in the discounted prices of the cars?

Todd $22,000Discount = $1760

Alyse $14,500Discount = $725

Discount Price

Discount Price

= $22000 – $1760= $20240

= $14500 – $725 = $13775

11

Salespeople at Victory Motors give discounts based on the retail price of the car to repeat customers, such as Todd and Alyse. If Todd buys a car with a retail price of $22,000 and Alyse buys a car for $14,500, what is the difference in the discounted prices of the cars?

Todd $22,000Discount = $1760

Alyse $14,500Discount = $725

Discount Price = $20240

Discount Price = $13775Difference in Discounted Prices

$20240 – $13775 = $6465

12

If x = 2 and y = 3, what is the value of the median of the following set?

2x + y , 2y – x , 2(x + y) , 3x + y

2(2) + 34 + 3

7

2(3) – 26 – 2

4

2(2 + 3)2(5)10

3(2) + 36 + 3

9

4 , 7 , 9 , 10Write numbers in order:

Median = 7 + 92

= 162

= 8

13

What was the average (arithmetic mean) amount of money, rounded to the nearest dollar, raised by all the clubs in 1996?

600 400

1996Average

400 350 250 200

600 400 400 350 250 200 2200367

6 6

14 If a = 2b and b = 3c and the average of a, b, and c is 40, what is the value of a?

a = 2b b = 3c

a = 2(3c)

a = 6c

Average3

a b c

6 340

3

c c c

40 10

1 3

c

(1)(10c) = (40)(3)

10c = 120c = 12

If a = 2b and b = 3c and the average of a, b, and c is 40, what is the value of a?

a = 2b b = 3c

a = 2(36)

Substitute c = 12

b = 3(12)

b = 36 a = 2b

a = 72

14

15 The table shows the total number of copies of Book B that were sold by the end of each of the first 5 weeks of its publication. How many copies of the book were sold during the 3rd week of its publication?

TotalCopies Sold

End of 1st week 3200End of 2nd week 5500End of 3rd week 6800End of 4th week 7400End of 5th week 7700

Copies Sold Each Week(Total Copies Sold present week

minus total copies sold previous week)

1st week 32002nd week 5500 – 3200 = 23003rd week 6800 – 5500 = 1300

16

A doll’s wardrobe consists of 40 possible outfits consisting of a shirt, pants, and a pair of shoes. If there are 5 shirts and 2 pairs of shoes, how many pairs of pants are in the doll’s wardrobe?

PossibleOutfits = Shirts Pants Shoes

40 = 5 Pants 2

40 = 10 Pants4 = Pants

17

The diagram shows the Washington, D.C. attractions visited by a social studies class. If 22 students visited the Capitol, how many students visited the Smithsonian?

Capitol = x + 2 + 9 + 622 = x + 2 + 9 + 622 = x + 175 = x Smithsonian = 5 + 2 + 3 + 10

Smithsonian = 20

18

A bag contains 3 round blue pegs, 2 round red pegs, 5 square red pegs, 4 square yellow pegs, and 6 square blue pegs. One peg dropped out of the bag. What is the probability that it was red or round?

P(red OR round)

P(red) OR P(round)

7

20

5

20+ =

12

20=

3

5

redred

19

A circular target is inscribed in a square base. The radius of the circle is 3. Assuming that a dart randomly strikes the figure, what is the probability that it lands in the circle?

6

A = s2

A = 62

A = 36

A = r2

A = 32

d = 6

A = 9A = 9

P(circle)square of area

circle of area

Circle area Square area

P(circle)36

9

4

Students studying neither = 30 – 22 = 8

20 There are 30 students in Mary’s homeroom. Of these students, 15 are studying Spanish, 10 are studying Latin, and 3 are studying both languages. How many students are studying neither language?

Spanish Latin

12 73

Students studying languages = 12 + 7 + 3 = 22

Each sector in the spinner is of equal size and there is no overlap. The spinner is equally likely to stop on any sector. What is the probability that the spinner will land on a sector labeled with a prime number?

P(landing on prime number)

21

sectors with prime number

total number of sectors

5

6

22

In a class of 24 students, there are twice as many male students as female students. Twelve students have a driver’s license. One quarter of the male students have a driver’s license. How many females in the class do not have a driver’s license?

Students = Males Females+

Males = 2xFemales = x

24 = 2x x+24 = 3x8 = x

82(8) = 16

In a class of 24 students, there are twice as many male students as female students. Twelve students have a driver’s license. One quarter of the male students have a driver’s license. How many females in the class do not have a driver’s license?

Males with D.L. = ¼ Males Males = 16Females = 8

Males with D.L. = ¼ 16Males with D.L. = 4

Females D.L. = Males D.L.–Students D.L.Females D.L. = 4–12Females D.L. = 8

FemalesWithoutD.L. = 0

22

23

A class roster lists 15 boys and 12 girls. Two students are randomly selected to speak at a school assembly. If one of the students selected is a boy, what is the probability that the other student selected is a girl?

There are 15 boys.One boy is selected.

There are now 14 boys.

P(selecting girl)# girls

# girls + #boys 12

12 14

1226

6 13

A box contains colored jellybeans. There are 14 red, 6 yellow, and x blue jellybeans in the bag. If the probability of drawing a yellow jellybean is ,

what is the value of x?

P(yellow)

24

number of yellow

total number of jellybeans

14

1

4

6 1

14 6 4x

6 1

20 4x

(1)(x + 20) = (6)(4)

x + 20 = 24–20 –20

x = 4

If a die is rolled twice, what is the probability that is lands on 5 both times?

P(#5 on 1st roll AND #5 on 2nd roll)

25

P(#5 on 1st roll) AND P(#5 on 2nd roll)

1

6

1

6 =

1

36

26

A box contains 50 marbles. Twenty-five are red, 15 are white, and 10 are blue. Steve took a marble without looking. What is the probability that the marble is not blue?

P(not blue)

P(red OR white)

P(red) OR P(white)

25

50

15

50+ =

40

50=

4

5

27

A target is made up of concentric circles as shown in the figure. Assuming that a dart randomly strikes the target, what is the probability that it will strike the shaded region?

A = 32A = 9

= 9

P(shaded)Big area Small area

Big area

A = r2

Big area

P(shaded)9 4

9

5

9

A = 22A = 4

= 4

A = r2

Small area

5 9

28

The Venn Diagram illustrates a relationship between cake, cookie, and pie orders at a bakery.

Cake Pie

4

Cookies

3

5

1

6 2

0

28a

How many people ordered

pies and cookies?

Cake Pie

4

Cookies

3

5

1

6 2

0

3 + 1 = 4

28b

Cake Pie

4

Cookies

3

5

1

6 2

0

How many people ordered pies or cookies?5 + 2 + 3 + 1 + 0 + 4 = 15

28c

How many people orderedcookies and no cake?

Cake Pie

4

Cookies

3

5

1

6 2

0

4 + 1 = 5

29

Find the number of ways you can arrange

two letters in the word MATH.

___ ___

1st

letter2nd

letter

4

Number of choices

3 = 12

Answer: 12 arrangements

30

There are four black cats and five grey cats in a cage, and none of them want to be in there. The cage door opens briefly and two cats escape. What is the probability that both escaped cats are black?

9

4

P(1st black AND 2nd black)P(1st black) P(2nd black)AND

8

3

1

3

1

2 =

6

1

Each cat leaves the cage without replacement.

4

8

1

2

3

9

1

3

Find the 10th term of the sequence.31

19 25 31 37

+6 +6 +6

19, 25, 31, 37, …

Term 1st 2nd 3rd 4th 5th

+6

43

Term 6th 7th 8th 9th 10th

6th

+6

49

49

+6

55

+6

61

+6

67

+6

73

Method #1

Find the 10th term of the sequence.

19, 25, 31, 37, …

an = a1 + d(n – 1)

a1 = 19 d =

an = 19 + 6(n – 1)

an = 19 + 6n – 6

an = 6n + 13

First: Find formula Next: Find 10th term

an = 6n + 13

a10 = 6(10) + 13

= 60 + 13

= 73

+6 +6 +6

6

31

Method #2

Find the 12th term of the sequence.32

4 9 14 19

+5 +5 +5

4, 9, 14, 19, …

Term 1st 2nd 3rd 4th 5th

+5

246th

+5

29

29

+5

34

+5

39

+5

44

+5

49

Method #1

Term 6th 7th 8th 9th 10th 11th 12th

+5

54

+5

59

Find the 12th term of the sequence.

4, 9, 14, 19, …

an = a1 + d(n – 1)

a1 = 4 d =

an = 4 + 5(n – 1)

an = 4 + 5n – 5

an = 5n – 1

First: Find formula Next: Find 12th term

an = 5n – 1

a12 = 5(12) – 1

= 60 – 1

= 59

+5 +5 +5

5

32

Method #2

What term of the sequence is 25?33 1, 4, 7, 10, …

an = a1 + d(n – 1)

a1 = 1 d =

an = 1 + 3(n – 1)

an = 1 + 3n – 3

an = 3n – 2

First: Find formula Next: Let an = 25

an = 3n – 2

25 = 3n – 2+2 +2

+3 +3 +3

3

27 = 3n

9 = n

Which set is not a geometric sequence?34

A. {48, 24, 12, 6, …}

× ½ × ½ × ½

Geometric

B. {2, –6, 18, –54, …} Geometric

× –3 × –3 × –3

Which set is not a geometric sequence?34

C. Geometric1 1 1 1

, , , , ...32 16 8 4

ì üï ïï ïí ýï ïï ïî þ×2 ×2 ×2

D. {4, 2, 0, –2, …} NotGeometric

–2 –2 –2

The 8th term of the geometric sequence {243, 81, 27, 9, …} is

35

243

× ⅓ × ⅓ × ⅓

81 27 9Term 1st 2nd 3rd 4th

9

× ⅓ × ⅓ × ⅓

Term 4th

3 1

× ⅓

7th 8th5th 6th1

31

9

19

What is the tenth term of the geometric sequence

36 1 1

, , 1, ...4 2

ì üï ïï ï- -í ýï ïï ïî þ

× -2 × -2 × -2

Term 1st 2nd 3rd

–1 2

× -2

–4

4th 5th1

4-

1

2

6th

× -2

8

8

× -2 × -2 × -2

Term 6th

–16 32

× -2

9th 10th7th 8th

–64 128

If {1, –2, 4, …} is a geometric sequence, what is the sum of the first seven terms?

37

1

× -2 × -2 × -2

Term 1st 2nd 3rd

–2 4 –8

× -2

164th 5th

16

× -2 × -2

Term 5th

–32 646th 7th

Sum = 1 + (–2) + 4 + (-8) + 16 + (-32) +64

Sum = 85 +(-42) = 43