CASAS Math GOALS 2 Level C

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Question 1

A monthly utility bill increased from

$ 48

$ 54

. What was the percent increase?

☐ A. $12.5 %$
☐ B. $112.5 %$
☐ C. $11.1 %$
☐ D. $6 %$

Your response / working

Show answer and explanation

Response: A

Final answer:

12.5 %

Use the old bill. A percent increase measures the added charge relative to the amount paid before the increase, so the denominator is

48

and the increase is

54 - 48 = 6

dollars. The calculation

6 \div 48 = 0.125

gives

12.5 %

. Dividing by

54

would describe the increase as a share of the new bill.

Question 2

A machine filled the same number of jars in each of 8 runs. Inspectors rejected 12 jars, and the remaining 180 jars were shipped. How many jars did the machine fill per run?

☐ A. 21
☐ B. 22.5
☐ C. 24
☐ D. 26

Your response / working

Show answer and explanation

Response: C

Final answer: 24

The rejected jars were filled too, so include them when finding the total production from all eight runs:

180 + 12 = 192

jars. Equal runs split this total evenly. Each run filled

192 \div 8 = 24

jars. Checking backward, eight runs produce

192

jars and rejecting

12

leaves the stated shipment of

180

Question 3

The floor plan shows a room with a rectangular corner removed. All dimensions are in meters. What is the floor area?

☐ A. $26$ square meters
☐ B. $24$ square meters
☐ C. $20$ square meters
☐ D. $22$ square meters

Your response / working

Show answer and explanation

Response: D

Final answer:

22

square meters

The dashed lines complete a rectangle measuring

6

meters by

4

meters, which lets you find the area before removing the small rectangular gap at the upper right. The corner is missing. Subtract its

2 \times 1 = 2

square meters from the outer

6 \times 4 = 24

square meters to leave

22

square meters of floor. The

24

-square-meter outer rectangle includes the gap, so choosing that value would count floor space that is missing.

Question 4

A commuter records these travel times, in minutes:

24, 28, 19, 32, 22

. What is the median travel time?

☐ A. 25 minutes
☐ B. 22 minutes
☐ C. 24 minutes
☐ D. 28 minutes

Your response / working

Show answer and explanation

Response: C

Final answer: 24 minutes

The median is the middle. Arrange the five times from shortest to longest:

19, 22, 24, 28, 32

minutes. With two observations on either side of

24

, that third value is the median, regardless of where it appeared in the original unsorted list.

Question 5

A shopper compares the rice packages below. Which package has the lowest price per pound?

Package weight	Price
2 pounds	$$ 3.00$
3 pounds	$$ 4.35$
5 pounds	$$ 7.10$
8 pounds	$$ 11.76$

☐ A. 8-pound package
☐ B. 5-pound package
☐ C. 2-pound package
☐ D. 3-pound package

Your response / working

Show answer and explanation

Response: B

Final answer: 5-pound package

Compare equal amounts of rice by dividing each package price by its weight, giving prices of

$ 1.50

$ 1.45

$ 1.42

, and

$ 1.47

per pound in table order. The lowest is

$ 1.42

. Choose the 5-pound package. The 2-pound package costs less at checkout, but each pound in it costs more.

Question 6

Which expression is equivalent to

5 (x + 2) - 2 x

☐ A. $5 x + 8$
☐ B. $7 x + 10$
☐ C. $3 x + 10$
☐ D. $3 x + 2$

Your response / working

Show answer and explanation

Response: C

Final answer:

3 x + 10

Distribute the 5 to both terms inside the parentheses, so

5 (x + 2)

becomes

5 x + 10

. Now combine the

x

terms. Subtracting

2 x

from

5 x

leaves

3 x

, while the constant stays

10

, making the equivalent expression

3 x + 10

Question 7

A shopper needs a right triangular fabric panel with the dimensions shown. What is the area of the panel?

☐ A. $0.45$ square meter
☐ B. $0.72$ square meter
☐ C. $1.25$ square meters
☐ D. $1.44$ square meters

Your response / working

Show answer and explanation

Response: B

Final answer:

0.72

square meter

The right-angle mark identifies perpendicular sides, so

1.6

meters is a usable base and

0.9

meter is its height even though the picture is not drawn to scale. Halve their product. The triangle covers

\frac{1}{2} (1.6) (0.9) = 0.72

square meter, half the area of a rectangle with those dimensions.

Question 8

A worker weighs five filled packages. What is their mean mass?

Package	Mass
1	486 grams
2	496 grams
3	500 grams
4	506 grams
5	522 grams

☐ A. 500 grams
☐ B. 502 grams
☐ C. 506 grams
☐ D. 627.5 grams

Your response / working

Show answer and explanation

Response: B

Final answer: 502 grams

Average all five masses. Adding the table entries gives

486 + 496 + 500 + 506 + 522 = 2510

grams, so

2510 \div 5 = 502

grams is the mean. Here the median is

500

. That middle observation need not equal the average obtained from all five masses.

Question 9

A soup recipe uses

1 \frac{3}{4}

liters of broth. A cook makes

2 \frac{1}{2}

times the recipe. How much broth is needed?

☐ A. $4 \frac{1}{4}$ liters
☐ B. $3 \frac{1}{2}$ liters
☐ C. $5 \frac{1}{4}$ liters
☐ D. $4 \frac{3}{8}$ liters

Your response / working

Show answer and explanation

Response: D

Final answer:

4 \frac{3}{8}

liters

Two full recipes use

2 (1 \frac{3}{4}) = 3 \frac{1}{2}

liters, and the extra half recipe uses half of

1 \frac{3}{4}

, or

\frac{7}{8}

liter. Combine those amounts. Writing the first amount as

3 \frac{4}{8}

gives

3 \frac{4}{8} + \frac{7}{8} = 4 \frac{3}{8}

liters of broth for the enlarged recipe.

Question 10

A worker receives a fixed travel allowance plus the same pay for every hour worked. The table shows total pay. What is the total pay for 9 hours?

Hours worked	Total pay
2	$$ 42$
4	$$ 78$
6	$$ 114$

☐ A. $$ 168$
☐ B. $$ 162$
☐ C. $$ 171$
☐ D. $$ 189$

Your response / working

Show answer and explanation

Response: A

Final answer:

$ 168

From 2 to 4 hours, pay rises by

78 - 42 = 36

dollars for two more hours of work. That means

18

per hour. Two hours of wages account for

36

of the first total, leaving a fixed travel allowance of

6

that must be added once to every total. Nine hours therefore pay

9 (18) + 6 = $ 168

Question 11

On this neighborhood map, the straight-line distance from the library to the recreation center measures

4.5

cm. The scale bar represents

120

meters. What actual distance does the map measurement represent?

☐ A. 180 meters
☐ B. 80 meters
☐ C. 540 meters
☐ D. 160 meters

Your response / working

Show answer and explanation

Response: A

Final answer: 180 meters

The scale bar ties

3

map centimeters to

120

real meters, so a single map centimeter represents

120 \div 3 = 40

meters. Keep that rate. Multiplying the measured

4.5

centimeters by

40

meters per centimeter gives an actual distance of

180

meters between the two locations.

Question 12

A shop places 12 coupons in a bag: 5 for a free item and 7 for a discount. Each coupon is equally likely to be drawn. What is the probability of drawing a discount coupon?

☐ A. $\frac{5}{7}$
☐ B. $\frac{7}{12}$
☐ C. $\frac{7}{5}$
☐ D. $\frac{5}{12}$

Your response / working

Show answer and explanation

Response: B

Final answer:

\frac{7}{12}

The discount coupons are favorable outcomes. There are

7

of them among

12

equally likely coupons, so the chance of drawing a discount coupon is

\frac{7}{12}

. Use all

12

coupons in the denominator, because drawing happens from the whole bag, and comparing the five free-item coupons with the seven discount coupons would describe a part-to-part ratio instead of the probability requested.

Question 13

A bank account has a balance of

$ 12.50

. A withdrawal of

$ 18.75

is posted. Ignore fees. What is the new balance?

☐ A. $$ 31.25$
☐ B. $- $ 31.25$
☐ C. $$ 6.25$
☐ D. $- $ 6.25$

Your response / working

Show answer and explanation

Response: D

Final answer:

- $ 6.25

A withdrawal removes money. Subtract its amount from the starting balance to get

12.50 - 18.75 = - 6.25

dollars. Because the withdrawal is greater than the available balance by

$ 6.25

, the result lies below zero and must retain the negative sign shown in

- $ 6.25

Question 14

The combined mass of a warehouse cart and its boxes must not exceed 40 kg. The empty cart has a mass of 12 kg. Each identical box has a mass of 3 kg. What is the greatest number of boxes the cart can hold without exceeding 40 kg?

☐ A. 9
☐ B. 10
☐ C. 13
☐ D. 8

Your response / working

Show answer and explanation

Response: A

Final answer: 9

The cart itself already uses

12

kilograms of the

40

-kilogram limit, leaving

40 - 12 = 28

kilograms for boxes. Dividing by

3

gives

9 \frac{1}{3}

. Only whole boxes count. Nine boxes make the combined mass

12 + 3 (9) = 39

kilograms, but ten boxes would make it

42

and exceed the limit.

Question 15

A circular garden bed has the diameter shown. What is its area? Use

π = 3.14

and

A = π r^{2}

, where

r

is the radius.

☐ A. $15.7$ square feet
☐ B. $78.5$ square feet
☐ C. $314$ square feet
☐ D. $31.4$ square feet

Your response / working

Show answer and explanation

Response: B

Final answer:

78.5

square feet

The arrow spans the diameter. The radius reaches only from the center to the edge, so halve the labeled

10

feet to obtain the

5

feet needed in the supplied formula. Then

A = 3.14 (5^{2}) = 78.5

square feet. Substituting

10

for the radius would count an area four times as large.

Question 16

Two loading teams record five delay times each. Each dot represents one recorded delay, in minutes. Which statement correctly compares the teams?

☐ A. The means and ranges are the same.
☐ B. Team B has a smaller mean and a greater range.
☐ C. The means are the same, and Team B has a greater range.
☐ D. Team B has a greater mean and the same range.

Your response / working

Show answer and explanation

Response: C

Final answer: The means are the same, and Team B has a greater range.

Read each dot once: Team A has delays of

2, 3, 4, 5, 6

minutes, and Team B has delays of

0, 2, 4, 6, 8

minutes. Both totals are

20

. Dividing each total by five gives the same mean of

4

minutes, but the ranges differ:

6 - 2 = 4

for A and

8 - 0 = 8

for B. Team B has the greater range.

Question 17

What is the value of

10^{3} \times 10^{- 5}

☐ A. $10^{2}$
☐ B. $10^{8}$
☐ C. $10^{- 8}$
☐ D. $10^{- 2}$

Your response / working

Show answer and explanation

Response: D

Final answer:

10^{- 2}

Keep the common base. Multiplying powers of

10

adds their exponents, including the sign of the negative exponent, so

10^{3} \times 10^{- 5} = 10^{3 + (- 5)} = 10^{- 2}

. This value is

\frac{1}{100}

. As an arithmetic check,

10^{3}

1000

and

10^{- 5}

0.00001

, so their product is

0.01

, agreeing with

10^{- 2}

and showing why the exponent must be negative when the result is less than one.

Question 18

A recreation subscription charges

C = 12 + 3 n

dollars per month, where

n

is the number of visits that month. What does the 12 represent?

☐ A. The total charge for 3 visits
☐ B. The charge for each visit
☐ C. The number of visits included for free
☐ D. The monthly charge when there are no visits

Your response / working

Show answer and explanation

Response: D

Final answer: The monthly charge when there are no visits

No visits means

n = 0

. Substitution gives

C = 12 + 3 (0) = 12

, so the constant is the monthly charge that remains even when no visits are made. The

3 n

term adds

3

dollars for each visit. It does not describe free visits included in the subscription.

Question 19

The diagram shows the side view of a model ramp. What is the length of the sloping side? Use

a^{2} + b^{2} = c^{2}

for a right triangle.

☐ A. 6.2 meters
☐ B. 3.4 meters
☐ C. 5.0 meters
☐ D. 25.0 meters

Your response / working

Show answer and explanation

Response: C

Final answer: 5.0 meters

The sloping side is the hypotenuse because it faces the marked right angle, so its square equals the sum of the squares of the two labeled legs. Compute

{4.8}^{2} + {1.4}^{2} = 23.04 + 1.96 = 25

. Take the square root. The ramp side is

\sqrt{25} = 5.0

meters long, not

25

meters.

Question 20

A shopper inspects 40 used plates and places each in exactly one category. If one plate is selected at random, what is the probability that it has a defect?

Category	Number of plates
Scratch only	6
Chip only	4
No defect	30

☐ A. $25 %$
☐ B. $10 %$
☐ C. $15 %$
☐ D. $75 %$

Your response / working

Show answer and explanation

Response: A

Final answer:

25 %

Count both kinds of defect. A scratch or a chip qualifies, and the separate categories give

6 + 4 = 10

defective plates without counting any plate twice. The probability of selecting one of these

10

defective plates from the

40

inspected plates is

10 \div 40 = 0.25

, which equals

25 %

. The

30

defect-free plates belong in the total but not in the favorable count.

Question 21

A supply cabinet has the glove counts below. A worker orders red and blue gloves in the same ratio as the cabinet counts. If the order includes 45 blue gloves, how many red gloves should it include?

Glove color	Count
Red	18
Blue	30
Green	12

☐ A. 33
☐ B. 75
☐ C. 18
☐ D. 27

Your response / working

Show answer and explanation

Response: D

Final answer: 27

The relevant ratio is red to blue,

18 : 30

, which simplifies to

3 : 5

. Forty-five blue gloves fill five ratio parts. Each part is therefore

45 \div 5 = 9

gloves, giving

3 (9) = 27

red gloves when the order keeps the same ratio as the cabinet. Green gloves do not enter this two-color comparison.

Question 22

A repair service charges a

$ 60

visit fee plus

$ 35

for each hour of labor. Which expression gives the total cost, in dollars, for

h

hours of labor?

☐ A. $60 h + 35$
☐ B. $35 (h + 60)$
☐ C. $35 h + 60$
☐ D. $95 h$

Your response / working

Show answer and explanation

Response: C

Final answer:

35 h + 60

Labor for

h

hours costs

35 h

dollars, to which the service adds the fixed

60

fee once per visit. The cost is

35 h + 60

. In

60 h + 35

, the two charges have switched roles, treating the visit fee as hourly and the hourly rate as a fixed charge.

Question 23

This net shows all six panels of a closed rectangular box. What is the total area of the panels?

☐ A. $8$ square meters
☐ B. $7$ square meters
☐ C. $3.5$ square meters
☐ D. $5$ square meters

Your response / working

Show answer and explanation

Response: B

Final answer:

7

square meters

The net has three matching pairs of faces: two

2 \times 1

panels, two

2 \times 0.5

panels, and two

1 \times 0.5

panels, all measured in meters. Include every pair. Their combined area is

2 (2) + 2 (1) + 2 (0.5) = 7

square meters. Adding only one face from each pair would give

3.5

and leave half the box uncovered.

Question 24

A rectangular sheet of plastic measures

0.6

m by

1.5

m. What is its area in square centimeters? Use

1

= 100

cm.

☐ A. $9000 {cm}^{2}$
☐ B. $90 {cm}^{2}$
☐ C. $900 {cm}^{2}$
☐ D. $90000 {cm}^{2}$

Your response / working

Show answer and explanation

Response: A

Final answer:

9000 {cm}^{2}

Convert the lengths first. The sides measure

0.6 (100) = 60

centimeters and

1.5 (100) = 150

centimeters, so their product gives

60 (150) = 9000

square centimeters of plastic. Both lengths change units. A square meter contains

100 \times 100 = 10000

square centimeters, which explains why converting the area requires more than multiplying by

100

Question 25

A restaurant applies a

20 %

coupon to a

$ 40

food bill. The customer adds a

15 %

tip based on the discounted food bill. There is no tax or other charge. How much does the customer pay in total?

☐ A. $$ 36.80$
☐ B. $$ 38.00$
☐ C. $$ 32.00$
☐ D. $$ 46.00$

Your response / working

Show answer and explanation

Response: A

Final answer:

$ 36.80

The coupon removes twenty percent of the original food bill, so the saving is

40 (0.20) = $ 8

and the discounted bill is

40 - 8 = $ 32

. Use that amount for the tip. Fifteen percent of

32

32 (0.15) = $ 4.80

. Adding the discounted food charge and the tip gives

32 + 4.80 = $ 36.80

, the full payment because the question excludes tax and every other charge. A tip based on the original

40

bill would be

$ 6

and produce the wrong total of

$ 38

Question 26

Which inequality is equivalent to

15 - 3 x \geq 6

☐ A. $x \geq 3$
☐ B. $x \leq 7$
☐ C. $x \leq 3$
☐ D. $x \geq 7$

Your response / working

Show answer and explanation

Response: C

Final answer:

x \leq 3

Subtracting

15

from both sides of

15 - 3 x \geq 6

leaves

- 3 x \geq - 9

. Division reverses the direction here. Because the divisor is negative, dividing both sides by

- 3

gives

x \leq 3

, including the endpoint where the original left side equals

6

. For a check,

x = 2

gives

9 \geq 6

, whereas

x = 4

gives

3 \geq 6

, which is false.

Question 27

Point

P

is reflected across the

y

-axis. What are the coordinates of its image?

☐ A. $(- 3, - 2)$
☐ B. $(3, 2)$
☐ C. $(3, - 2)$
☐ D. $(2, - 3)$

Your response / working

Show answer and explanation

Response: B

Final answer:

(3, 2)

The plotted point is

(- 3, 2)

. Reflecting across the vertical

y

-axis moves it from three units left of that axis to three units right, while its height stays two units above the horizontal axis. The image is

(3, 2)

. Changing only the height would reflect the point across the horizontal

x

-axis, giving

(- 3, - 2)

instead of the requested image across the vertical axis.

Question 28

A learning center surveys a random sample of 40 adult learners about class-day preference. If the sample represents all 200 learners at the center, about how many would prefer Saturday classes?

Preferred class day	Learners in sample
Weekday	34
Saturday	6

☐ A. 30
☐ B. 170
☐ C. 6
☐ D. 34

Your response / working

Show answer and explanation

Response: A

Final answer: 30

The table gives

6

Saturday preferences among

40

responses. The full group is five times as large, since

200 \div 40 = 5

, so keeping that sample proportion gives

6 (5) = 30

learners who would prefer Saturday. This is an estimate. It depends on the stated assumption that the sample represents the whole center.

Question 29

A roll contains

7 \frac{3}{4}

feet of shelf liner. Each full strip uses

\frac{3}{8}

foot. Ignoring cutting loss, how many full strips can be cut?

☐ A. 20
☐ B. 22
☐ C. 21
☐ D. 19

Your response / working

Show answer and explanation

Response: A

Final answer: 20

One strip uses

\frac{3}{8}

foot, so divide the available

7 \frac{3}{4}

feet by that length:

\frac{31}{4} \div \frac{3}{8} = \frac{62}{3} = 20 \frac{2}{3}

. Keep the whole strips. Twenty strips use

20 (\frac{3}{8}) = 7 \frac{1}{2}

feet, leaving

\frac{1}{4}

foot. That remainder is shorter than the

\frac{3}{8}

foot needed for a twenty-first full strip.

Question 30

A customer plans to attend 14 classes in one month. Using the charges below, which plan has the lower total cost, and by how much?

Plan	Monthly fee	Charge per class
A	$$ 15.00$	$$ 2.00$
B	$$ 30.00$	$$ 0.75$

☐ A. Plan B, by $$ 15.00$
☐ B. Plan A, by $$ 2.50$
☐ C. Plan A, by $$ 15.00$
☐ D. Plan B, by $$ 2.50$

Your response / working

Show answer and explanation

Response: D

Final answer: Plan B, by

$ 2.50

Price the same fourteen classes under both plans, including each monthly fee: Plan A costs

15 + 2 (14) = $ 43

and Plan B costs

30 + 0.75 (14) = $ 40.50

. Plan B costs less. The difference is

43 - 40.50 = $ 2.50

, so choose Plan B by

$ 2.50

. Comparing only the monthly fees would miss the effect of the different class charges.

Question 31

A rectangular storage box has the inside dimensions shown. What is its volume? Use

V = l w h

☐ A. $16.95$ cubic feet
☐ B. $5.15$ cubic feet
☐ C. $4.5$ cubic feet
☐ D. $3.6$ cubic feet

Your response / working

Show answer and explanation

Response: C

Final answer:

4.5

cubic feet

Volume uses all three dimensions. Multiply the labeled inside length, width, and height to get

2.4 (1.5) (1.25) = 4.5

cubic feet of storage space. The unit is cubic feet. Using only

2.4 (1.5)

would give the

3.6

square feet of the base, not the amount of space inside the box.

Question 32

A community garden is a rectangle 18 m long and 12 m wide. A fence will surround it except for a 3 m gate opening. How many meters of fence are needed?

☐ A. 27 meters
☐ B. 57 meters
☐ C. 60 meters
☐ D. 54 meters

Your response / working

Show answer and explanation

Response: B

Final answer: 57 meters

A rectangle has two long sides and two short sides, so the complete boundary measures

2 (18) + 2 (12) = 60

meters. The gate replaces three meters of fence. Subtract that opening once to obtain

60 - 3 = 57

meters of fence, because the remaining boundary still needs to be enclosed on all four sides.

Question 33

A driver travels 92 miles at a constant speed of 46 miles per hour. How many minutes does the drive take?

☐ A. 60 minutes
☐ B. 120 minutes
☐ C. 2 minutes
☐ D. 138 minutes

Your response / working

Show answer and explanation

Response: B

Final answer: 120 minutes

The speed is in miles per hour, so dividing

92

miles by

46

miles per hour gives

2

hours. Convert those hours to minutes. With

60

minutes in an hour, the trip lasts

2 (60) = 120

minutes. Reporting

2

minutes would keep the numerical quotient but attach the wrong unit.

Question 34

A print shop charges a fixed setup fee and the same additional amount for each page. The graph shows total cost. What is the additional charge per page?

☐ A. $$ 0.25$
☐ B. $$ 2.00$
☐ C. $$ 0.50$
☐ D. $$ 2.50$

Your response / working

Show answer and explanation

Response: C

Final answer:

$ 0.50

The graph rises one dollar as the page count rises from zero to two, so divide the increase in cost by the increase in pages. This gives

(3 - 2) \div (2 - 0) = $ 0.50

per page. The intercept is different. Its

$ 2

charge applies before any pages are printed and represents the setup fee, not the additional charge for each page.

Question 35

What is the value of

\frac{3}{4} - \frac{1}{2} \times \frac{2}{3}

☐ A. $\frac{1}{6}$
☐ B. $\frac{7}{12}$
☐ C. $\frac{1}{4}$
☐ D. $\frac{5}{12}$

Your response / working

Show answer and explanation

Response: D

Final answer:

\frac{5}{12}

Multiply before subtracting. The product

\frac{1}{2} \times \frac{2}{3} = \frac{1}{3}

leaves

\frac{3}{4} - \frac{1}{3}

, whose common denominator is

12

. Rewrite it as

\frac{9}{12} - \frac{4}{12} = \frac{5}{12}

. Subtracting the first two fractions before multiplying would introduce parentheses that the original expression does not contain and give a different value,

\frac{1}{6}

Question 36

A rental shop requires a

$ 5

deposit plus

$ 7

per hour for equipment. The deposit is refunded when the equipment is returned, but both charges must be paid at pickup. A customer has

$ 40

available at pickup. Which inequality represents the possible rental hours

h

☐ A. $7 h + 5 \geq 40$
☐ B. $7 h - 5 \leq 40$
☐ C. $5 h + 7 \leq 40$
☐ D. $7 h + 5 \leq 40$

Your response / working

Show answer and explanation

Response: D

Final answer:

7 h + 5 \leq 40

The pickup payment includes the deposit. Hourly rental costs

7 h

dollars, so the amount required at pickup is

7 h + 5

, and having

40

available makes the constraint

7 h + 5 \leq 40

. Equality is allowed. The deposit refund happens later, so subtracting it now would understate the money needed to collect the equipment.