FSA Practice Test (6th Grade: Math) 1 — Questions and Answers

Question 1: The perimeter of the following shape is? (It's in the shape of a right triangle)

32 cm
14 cm
18 cm
24 cm (Correct answer)

Correct answer: 24 cm

The perimeter of any polygon is the total distance around its exterior. To find the perimeter of the right triangle, you simply add the lengths of all its sides. Assuming the sides are 6 cm, 8 cm, and 10 cm (a common Pythagorean triple), the sum is 6 + 8 + 10 = 24 cm.

Question 2: Watermelons are currently on sale for $1.25 for two. What is the cost per unit?

62.5¢/watermelon (Correct answer)
61.5¢/watermelon
64.5¢/watermelon
63.5¢/watermelon

Correct answer: 62.5¢/watermelon

To find the cost per unit, divide the total cost by the number of units. Here, $1.25 for two watermelons means $1.25 ÷ 2 = $0.625 per watermelon. Converting this to cents, we multiply by 100, resulting in 62.5¢ per watermelon.

Question 3: Anthony has three blue and eight red balls. What is the ratio of blue to red balls?

3:11
3:8 (Correct answer)
3:3
3:5

Correct answer: 3:8

A ratio expresses the relationship between two quantities in a specific order. When asked for the ratio of blue to red balls, you list the number of blue balls first, followed by the number of red balls. Since Anthony has three blue balls and eight red balls, the ratio is 3:8.

Question 4: What is the equivalent expression to 4(6x + 11)?

24x + 11
68x
24x + 44 (Correct answer)
68

Correct answer: 24x + 44

To find an equivalent expression, apply the distributive property. This means multiplying the number outside the parentheses by each term inside. So, 4 multiplied by 6x is 24x, and 4 multiplied by 11 is 44, resulting in the expression 24x + 44.

Question 5: Ralph received a quotient of 26 with a remainder of 13 when he divided 403 by a number. What was the number Ralph divided by?

16
15 (Correct answer)
14
13

Correct answer: 15

The division algorithm states that Dividend = Divisor × Quotient + Remainder. We have 403 = Divisor × 26 + 13. First, subtract the remainder from the dividend: 403 - 13 = 390. Then, divide this result by the quotient: 390 ÷ 26 = 15. Therefore, the number Ralph divided by was 15.

Question 6: There are 55 blue and 143 red balls. We want to put these balls in certain boxes so that there are the same amount of red balls in each box and there are same number of blue balls in each box. How many boxes will we require?

9
10
11 (Correct answer)
8

Correct answer: 11

To ensure the same number of red balls in each box and the same number of blue balls in each box, the number of boxes must be a common divisor of both 55 and 143. To find the maximum number of such boxes, we determine the Greatest Common Divisor (GCD) of 55 and 143. The factors of 55 are 1, 5, 11, 55, and the factors of 143 are 1, 11, 13, 143, making 11 the GCD. Thus, 11 boxes are required.

Question 7: Which is the better deal: 5 for $1.00, 4 for 85¢, 2 for 25¢, or 6 for $1.10?

4 for 85¢
5 for $1.00
6 for $1.10
2 for 25¢ (Correct answer)

Correct answer: 2 for 25¢

To find the better deal, calculate the unit price for each option. 5 for $1.00 is $0.20/item, 4 for 85¢ is $0.2125/item, 2 for 25¢ is $0.125/item, and 6 for $1.10 is approximately $0.1833/item. The lowest unit price of $0.125 per item makes '2 for 25¢' the best deal.

Question 8: Which of the following statements best describes unit rate?

Dave is driving 16 miles.
Dave ate 3 cookies and 1 orange.
Dave ate 1 hotcake.
Dave is driving 30 miles per 1 hour. (Correct answer)

Correct answer: Dave is driving 30 miles per 1 hour.

A unit rate describes how many units of the first quantity correspond to one unit of the second quantity. It is a ratio where the denominator is 1. 'Dave is driving 30 miles per 1 hour' clearly expresses a rate with '1 hour' as the single unit of time, making it the best description of a unit rate.

Question 9: Choose the x value that answer the equation or inequality. 2x + 5 = 9

x = 1.1
x = 2 (Correct answer)
x = 1
x = 3

Correct answer: x = 2

To solve the equation 2x + 5 = 9, first subtract 5 from both sides to isolate the term with x: 2x = 9 - 5, which simplifies to 2x = 4. Next, divide both sides by 2 to solve for x: x = 4 ÷ 2. Therefore, x = 2.

Question 10: Which of the following expressions is equivalent to the one below? 7h + 1

(5h + 2) + 1
h + 7
(5 + 2)h + 1 (Correct answer)
7(h + 1)

Correct answer: (5 + 2)h + 1

To find an equivalent expression, we need one that simplifies to 7h + 1. In option C, (5 + 2)h + 1, the terms inside the parentheses (5 and 2) can be added first, resulting in 7h + 1. This matches the original expression exactly, demonstrating equivalence.

Question 11: What is the value of the expression below? 2,205÷315

7 (Correct answer)
8
5
6

Correct answer: 7

To find the value of the expression, perform the division: 2,205 divided by 315. By multiplying 315 by 7, we get 2205 (7 * 300 = 2100, 7 * 15 = 105, and 2100 + 105 = 2205). Therefore, the value is 7.

Question 12: A box of three bracelets costs $2.22. What is the price per unit?

98¢ per bracelet
74¢ per bracelet (Correct answer)
$1.11 per bracelet
$2.22 per bracelet

Correct answer: 74¢ per bracelet

To find the price per unit, divide the total cost by the number of items. A box of three bracelets costs $2.22, so $2.22 ÷ 3 = $0.74 per bracelet. Converting this to cents, we get 74¢ per bracelet.

Question 13: What is the value of the expression below? 4/5 ÷ 8/7

7/10 (Correct answer)
10/7
20/40
40/28

Correct answer: 7/10

To divide fractions, you multiply the first fraction by the reciprocal of the second fraction. So, 4/5 ÷ 8/7 becomes 4/5 × 7/8. Multiplying the numerators gives 28 and the denominators gives 40, resulting in 28/40. This fraction simplifies by dividing both numerator and denominator by 4, yielding 7/10.

Question 14: The temperature in Cleveland is -10 degrees Fahrenheit. In Kansas City, it is cooler than in Cleveland. Select the value that could be used to represent Kansas City's temperature.

-12 (Correct answer)
8
-8
12

Correct answer: -12

On a temperature scale, 'cooler' means a lower temperature. Since Cleveland is -10 degrees Fahrenheit, Kansas City's temperature must be a value less than -10. Of the given options, -12 degrees Fahrenheit is the only value that is numerically smaller (further to the left on a number line) than -10 degrees Fahrenheit.

Question 15: Two portions of fruits are served with each meal in a school cafeteria. In the school cafeteria, what is the ratio of meals served to fruit portions?

2 : 1
3 : 1
1 : 3
1 : 2 (Correct answer)

Correct answer: 1 : 2

The question asks for the ratio of meals served to fruit portions. For every one meal served, two portions of fruit are provided. Therefore, the ratio of meals to fruit portions is 1:2.

Question 16: Solve the equation below. 112=22+𝑥

𝑥=90 (Correct answer)
𝑥=−90
𝑥=134
𝑥=−134

Correct answer: 𝑥=90

To solve the equation 112 = 22 + x, you need to isolate x. Subtract 22 from both sides of the equation: 112 - 22 = x. Performing the subtraction gives 90 = x. Therefore, x = 90.

Question 17: In 23 meters, how many millimeters are there?

2,300 mm
23,000 mm (Correct answer)
230 mm
2.3 mm

Correct answer: 23,000 mm

To convert meters to millimeters, you need to know that 1 meter is equivalent to 1,000 millimeters. Therefore, to find how many millimeters are in 23 meters, multiply 23 by 1,000. This calculation yields 23,000 millimeters.

Question 18: Find the value of X. x + 9 = 14

x =6
x = 5 (Correct answer)
x = 23
x = 9

Correct answer: x = 5

To solve the equation x + 9 = 14, you need to isolate x. Subtract 9 from both sides of the equation: x = 14 - 9. Performing the subtraction gives x = 5.

Question 19: What is the expression's value? 1608 ÷ 268

6 (Correct answer)
5
12
16

Correct answer: 6

To find the value of the expression, perform the division: 1608 divided by 268. By multiplying 268 by 6, we get 1608 (6 * 200 = 1200, 6 * 60 = 360, 6 * 8 = 48, and 1200 + 360 + 48 = 1608). Therefore, the value is 6.

Question 20: In a park, all of the trash cans are red or blue. The park has a 3:4 ratio of red to blue trash cans. Which of the following statements is true based on this information?

For every 3 red trash cans in the park, there are 4 blue trash cans. (Correct answer)
For every 3 red trash cans in the park, there are 7 blue trash cans.
For every 4 trash cans in the park, 3 are red.
For every 7 trash cans in the park, 4 are red.

Correct answer: For every 3 red trash cans in the park, there are 4 blue trash cans.

A ratio of 3:4 for red to blue trash cans directly means that for every 3 red trash cans, there are 4 blue trash cans. The order of the numbers in the ratio corresponds to the order of the items being compared.

Question 21: At a given period, truck A travels 221.5 kilometers, while truck B travels 1.2 times the distance traveled by truck A at the same time. During that time, how far does truck B travel?

265.8 km (Correct answer)
241.5 km
222.7 km
233.5 km

Correct answer: 265.8 km

To find the distance Truck B travels, multiply the distance Truck A traveled by 1.2. So, 221.5 kilometers × 1.2 = 265.8 kilometers. This calculation determines that Truck B travels 265.8 km.

Question 22: In a tablespoon, how many teaspoons are there?

5 teaspoons
4 teaspoons
2 teaspoons
3 teaspoons (Correct answer)

Correct answer: 3 teaspoons

This is a standard culinary conversion. There are exactly 3 teaspoons in 1 tablespoon. This is a common measurement equivalence used in cooking and baking.

Question 23: Randolf's scooter can travel 128 miles on a single tank of gas. How far can Randolf go on one gallon of gas if the scooter has a 4-gallon gas tank?

32 miles per gallon (Correct answer)
64 miles per gallon
20 miles per gallon
512 miles per gallon

Correct answer: 32 miles per gallon

To find how far Randolf can go on one gallon of gas, you need to calculate the scooter's fuel efficiency, which is a unit rate. Divide the total distance traveled (128 miles) by the total amount of gas used (4 gallons): 128 miles ÷ 4 gallons = 32 miles per gallon.

Question 24: Kevin is shipping a rectangular prism-shaped cardboard box. Kevin's box net is shown. In square inches, what is the area of cardboard required for Kevin's box?

40
24
60
248 (Correct answer)

Correct answer: 248

The area of cardboard required for the box is its total surface area. For a rectangular prism with dimensions, for example, 10 inches by 6 inches by 4 inches, the surface area is calculated as 2(length × width + length × height + width × height). This results in 2(10×6 + 10×4 + 6×4) = 2(60 + 40 + 24) = 2(124) = 248 square inches.

Question 25: Pj stands at a height of 1.8 meters. How tall is Pj in centimeters?

18 centimeters
180 centimeters (Correct answer)
0.18 centimeter
0.018 centimeter

Correct answer: 180 centimeters

To convert meters to centimeters, you need to know that 1 meter is equivalent to 100 centimeters. Therefore, to find Pj's height in centimeters, multiply 1.8 meters by 100. This calculation yields 180 centimeters.

Question 26: The trapezoid below has a perimeter of 38. What is the size of the area?

162 cm²
198 cm²
81 cm² (Correct answer)
99 cm²

Correct answer: 81 cm²

A square is a special type of trapezoid because it has at least one pair of parallel sides. If the perimeter of a square were 36 cm, each of its four equal sides would be 9 cm (36 / 4 = 9). The area of a square is calculated by squaring the side length (side * side). Therefore, the area would be 9 cm * 9 cm = 81 cm². This suggests a likely scenario where the given perimeter of 38 might be a typo, or the image would have provided specific dimensions that lead to 81.

Question 27: In a gallon, how many pints are there?

5 pt.
9 pt.
4 pt.
8 pt. (Correct answer)

Correct answer: 8 pt.

This question asks for a standard unit conversion within the imperial system. There are 2 pints in 1 quart, and 4 quarts in 1 gallon. To find the number of pints in a gallon, you multiply the number of quarts by the number of pints per quart: 4 quarts * 2 pints/quart = 8 pints. Therefore, there are 8 pints in a gallon.

Question 28: What is the value of the given expression? 2312.2 + 3.4

243.6
2315.6 (Correct answer)
231.56
2321

Correct answer: 2315.6

To add decimal numbers, you must align the decimal points vertically and then add each column from right to left, just like with whole numbers. Adding 2312.2 and 3.4 means adding the tenths (2 + 4 = 6) and then the whole numbers (2312 + 3 = 2315). Combining these results in 2315.6.

Question 29: What is the value of the given expression? (5)³

15
115
5/3
125 (Correct answer)

Correct answer: 125

The expression (5)³ represents exponentiation, where the base number (5) is multiplied by itself the number of times indicated by the exponent (3). So, (5)³ means 5 * 5 * 5. First, 5 * 5 equals 25, and then 25 * 5 equals 125. Thus, the value of the expression is 125.

Question 30: The price of a 12-pack of milk pouches is $6.00. What is the price of one milk pouch?

$0.50 (Correct answer)
$0.72
$0.02
$0.20

Correct answer: $0.50

To find the price of one item when you know the total price of a pack, you need to divide the total cost by the number of items. In this case, the total price is $6.00 for 12 milk pouches. Dividing $6.00 by 12 gives you $0.50. Therefore, one milk pouch costs 50 cents.

FSA Practice Test (6th Grade: Math) 1

The perimeter of the following shape is? (It's in the shape of a right triangle)