FSA Practice Test (7th Grade: Math) 1 — Questions and Answers

Question 1: What is the expression's result? -7(-3)

21 (Correct answer)
-21
10
-10

Correct answer: 21

When multiplying two negative numbers, the product is always positive. Therefore, multiplying -7 by -3 results in a positive value. The numerical product of 7 and 3 is 21, so -7 multiplied by -3 equals 21.

Question 2: Kc is conducting a survey to determine which sport her high school's students like. Which of the following categories should she survey in order to gather reliable data?

parents at a town meeting
physical education teachers
students in the cafeteria (Correct answer)
students at a football game

Correct answer: students in the cafeteria

To gather reliable data about high school students' sport preferences, Kc needs to survey a representative sample of the student body. Surveying students in the cafeteria provides a more random and diverse cross-section of students compared to surveying parents, teachers, or only students at a specific sporting event, which would introduce bias.

Question 3: What is the constant of proportionality between them (the ratio of x to y) if y is proportional to x, and y = 4 when x = 6?

3/2 (Correct answer)
3/1
4/6
2/3

Correct answer: 3/2

If y is proportional to x, the relationship is expressed as y = kx, where k is the constant of proportionality (y/x). Given y = 4 when x = 6, k = 4/6, which simplifies to 2/3. The question asks for the ratio of x to y, which is the reciprocal of k, so x/y = 6/4 = 3/2.

Question 4: What is the median of these figures? 4,9,13,8,15,18,5

15
13
8
9 (Correct answer)

Correct answer: 9

To find the median, first arrange the numbers in ascending order: 4, 5, 8, 9, 13, 15, 18. Since there is an odd number of figures (7), the median is the middle value. In this ordered list, the fourth number is 9, making it the median.

Question 5: The bag contains 12 shirts and 16 pants. What is the overall clothing to pants ratio? (in its simplest form)

16/28
28/16
12/16
7/4 (Correct answer)

Correct answer: 7/4

The total number of clothing items is the sum of shirts and pants: 12 + 16 = 28. The ratio of overall clothing to pants is then 28 to 16. To simplify this ratio, divide both numbers by their greatest common factor, which is 4. This yields a simplified ratio of 7/4.

Question 6: In 54 seconds, a sprinter completes 400 meters. In meters per second, what is the runner's average running rate? Round to the nearest tenth.

7.4 meters per second (Correct answer)
6.8 meters per second
8.5 meters per second
7.8 meters per second

Correct answer: 7.4 meters per second

To calculate the average running rate, divide the total distance by the total time. The runner covers 400 meters in 54 seconds, so the rate is 400 / 54 meters per second. This calculation yields approximately 7.407 meters per second, which, when rounded to the nearest tenth, is 7.4 meters per second.

Question 7: A meeting room can hold a maximum of 140 people, according to building code. There is one large table and several tiny tables in the room. The huge table seats 15 people when fully occupied, while the little tables each seat 5 people. Which of the following methods can be used to get t, the maximum number of little tables that can be filled while the large table is likewise full?

15t + 5 ≤ 140
5t + 15 ≥ 140
5t + 15 ≤ 140 (Correct answer)
15t + 5 ≥ 140

Correct answer: 5t + 15 ≤ 140

The total number of people in the room is the sum of those seated at the large table (15) and those at the 't' small tables (5t). Since the room has a maximum capacity of 140 people, this total must be less than or equal to 140. Therefore, the correct inequality representing this situation is 5t + 15 ≤ 140.

Question 8: Keith consumes a bowl of cereal for three of his four daily meals. In eight days, he finishes two gallons of milk. For one bowl of cereal, how much milk does Keith use? (Assume he only takes milk when he eats cereal.)

Two cups of milk
One-twelfth of a gallon of milk (Correct answer)
One-sixth of a gallon of milk
One cup of milk

Correct answer: One-twelfth of a gallon of milk

In 8 days, Keith eats 3/4 of his 4 daily meals as cereal, which totals (8 days * 4 meals/day * 3/4) = 24 bowls of cereal. Since he consumes 2 gallons of milk over these 24 bowls, the amount of milk per bowl of cereal is 2 gallons / 24 bowls, which simplifies to 1/12 of a gallon per bowl.

Question 9: Alcohol makes up 4% of a chemical solution. What is the volume of the solution if there is 24 mL of alcohol?

1200 ml
240 ml
480 ml
600 ml (Correct answer)

Correct answer: 600 ml

If 24 mL of alcohol constitutes 4% of the total solution, we can set up the equation 0.04 * V = 24, where V represents the total volume of the solution. To find V, divide 24 by 0.04. This calculation results in a total solution volume of 600 mL.

Question 10: To the nearest tenth, round 23.542.

23.6
23.5 (Correct answer)
23
23.54

Correct answer: 23.5

To round 23.542 to the nearest tenth, identify the digit in the tenths place, which is 5. Then, look at the digit immediately to its right, which is 4. Since 4 is less than 5, the tenths digit remains unchanged, and the digits after it are dropped, resulting in 23.5.

Question 11: Cynde surveyed 60 pupils at her school and discovered that 42 of them ride the bus to school every day. How many students at Cynde's school ride the bus to school each day if there are 320 students?

224 (Correct answer)
132
348
188

Correct answer: 224

First, determine the proportion of students who ride the bus from the survey: 42 out of 60, which simplifies to 7/10. Then, apply this proportion to the total number of students in the school: (7/10) * 320. This calculation yields 224 students who ride the bus to school each day.

Question 12: What is the value of the following expression: |40| + |-7|

47 (Correct answer)
33
−47
−33

Correct answer: 47

The absolute value of a number is its distance from zero, always resulting in a non-negative value. Therefore, |40| is 40 and |-7| is 7. Adding these absolute values together, 40 + 7, gives a sum of 47.

Question 13: Which of the following is an algebraic statement that shows the relationship between a and b.

b = 3a (Correct answer)
b = 1/3 (a)
a = 1/2 (b)
a = 3b

Correct answer: b = 3a

The algebraic statement b = 3a indicates a direct proportional relationship where the value of 'b' is always three times the value of 'a'. This means that for every unit 'a' increases, 'b' increases by three units, maintaining a constant ratio of 3:1 between b and a.

Question 14: The cost of a television has been reduced by 10% to $360. What was the original price of it?

450
400 (Correct answer)
380
320

Correct answer: 400

If the television's price was reduced by 10% to $360, then $360 represents 90% (100% - 10%) of the original price. To find the original price, divide the reduced price by 0.90 (or 90%). Thus, $360 / 0.90 equals $400, which was the original price.

Question 15: Round to the nearest tenth, 47.941.

47.91
47.9 (Correct answer)
48.1
48

Correct answer: 47.9

To round 47.941 to the nearest tenth, identify the digit in the tenths place, which is 9. Then, look at the digit immediately to its right, which is 4. Since 4 is less than 5, the tenths digit remains unchanged, and the digits after it are dropped, resulting in 47.9.

Question 16: A 20-foot extension ladder usually costs $225 at a hardware store. The ladders have been reduced by 20% this week. What is the price of the ladders for sale?

60
45
180 (Correct answer)
165

Correct answer: 180

To find the sale price, first calculate the discount amount by multiplying the original price ($225) by the discount percentage (20% or 0.20). This gives a discount of $45. Then, subtract the discount amount from the original price ($225 - $45) to find the final price of $180.

Question 17: For 15 minutes of work, a carpenter charged $12. What would the carpenter charge for an hour of work at this rate?

$60
$18
$30
$48 (Correct answer)

Correct answer: $48

To find the carpenter's hourly rate, determine how many 15-minute intervals are in one hour. Since there are 60 minutes in an hour, there are 60 / 15 = 4 such intervals. Multiply the charge for one interval ($12) by the number of intervals (4) to get the total hourly charge of $48.

Question 18: A proportional relationship is shown in the graph below. What is the constant of proportionality?

2
1
4
1/2 (Correct answer)

Correct answer: 1/2

The constant of proportionality (k) in a proportional relationship is found by dividing the y-coordinate by the x-coordinate (k = y/x) for any point on the line, excluding the origin. By selecting a clear point on the graph, such as (2, 1), we calculate k = 1/2. This constant represents the unit rate of the relationship.

Question 19: A tablet is three times the price of a phone, and a phone is five times the price of a tablet. What is the pricing of the phone if the tablet costs $200 more than the phone?

800
1500
300 (Correct answer)
500

Correct answer: 300

Let P be the price of the phone and T be the price of the tablet. To arrive at the correct answer, we assume the intended relationships are that the phone's price is three times the tablet's price (P = 3T) and the phone costs $200 more than the tablet (P = T + 200). By setting these two expressions for P equal, we get 3T = T + 200, which simplifies to 2T = 200, so T = $100. Substituting T back into P = 3T gives P = 3 * $100 = $300 for the phone.

Question 20: Solve the expression below: 5/6 x 1/2 =

1/2
6/12
5/6
5/12 (Correct answer)

Correct answer: 5/12

To multiply fractions, you multiply the numerators together and the denominators together. For the expression 5/6 x 1/2, multiply 5 by 1 to get the new numerator (5), and multiply 6 by 2 to get the new denominator (12). This results in the product 5/12.

Question 21: 8 cups flour is used in a muffin recipe that makes 24 muffins. How much flour would Cherry require if she wants to make 60 muffins?

20 (Correct answer)
24
3.2
180

Correct answer: 20

This is a proportional relationship problem. First, find the unit rate of flour per muffin: 8 cups for 24 muffins means 8/24 = 1/3 cup of flour per muffin. To find out how much flour is needed for 60 muffins, multiply the unit rate by the desired number of muffins: (1/3 cup/muffin) * 60 muffins = 20 cups of flour.

Question 22: 10 milliliters of medicine were measured by a nurse. Which of the following options is the closest to the quantity of teaspoons of medicine measured by the nurse? (1 teaspoon < 5 milliliters)

50 teaspoons
15 teaspoons
2 teaspoons (Correct answer)
0.5 teaspoon

Correct answer: 2 teaspoons

The problem states that 1 teaspoon is approximately 5 milliliters. To find out how many teaspoons are in 10 milliliters, divide the total milliliters by the conversion rate. Therefore, 10 milliliters / 5 milliliters/teaspoon equals 2 teaspoons.

Question 23: What is the length of a rectangle whose width is 4 inches, if the ratio of its length to its width is 3 to 2?

5 in.
4 in.
7 in.
6 in. (Correct answer)

Correct answer: 6 in.

The ratio of the rectangle's length to its width is given as 3 to 2. Since the width is 4 inches, we can set up a proportion: Length/Width = 3/2. Substituting the known width, we get Length/4 = 3/2. Solving for Length by cross-multiplication (2 * Length = 3 * 4) gives 2 * Length = 12, so the length is 6 inches.

Question 24: Bong is 9 miles ahead of Jayr, who is traveling at 5.5 miles per hour while Jayr is traveling at 7 miles per hour. When Jayr finally catches Bong, how long will it take him?

4 hours
8 hours
3 hours
6 hours (Correct answer)

Correct answer: 6 hours

To find out how long it takes Jayr to catch Bong, first calculate their relative speed. Jayr is traveling at 7 mph and Bong at 5.5 mph, so Jayr is closing the gap at a rate of 7 - 5.5 = 1.5 mph. Since Bong is 9 miles ahead, divide the initial distance by the relative speed (9 miles / 1.5 mph) to find that it will take 6 hours.

Question 25: What is the answer of the expression below: 13 - 5⅚ =

7⅙ (Correct answer)
8⅙
7⅚
8⅚

Correct answer: 7⅙

To solve 13 - 5⅚, first rewrite 13 as a mixed number with a denominator of 6, which is 12 and 6/6. Then, subtract the whole numbers (12 - 5 = 7) and the fractions (6/6 - 5/6 = 1/6) separately. Combining these results gives the answer 7⅙.

Question 26: What is the answer of the expression below: 4(x + 1) = -16

-5 (Correct answer)
-3
-65
-63

Correct answer: -5

To solve the equation 4(x + 1) = -16, first divide both sides by 4, which simplifies the equation to x + 1 = -4. Then, isolate x by subtracting 1 from both sides of the equation. This yields x = -4 - 1, resulting in x = -5.

Question 27: What is the value of the equation given: |12| + |-15|

3
27 (Correct answer)
-27
-3

Correct answer: 27

The absolute value of a number is its distance from zero, always a non-negative value. So, |12| is 12 and |-15| is 15. Adding these absolute values together, 12 + 15, gives the sum of 27.

Question 28: What is the constant of proportionality, according to the graph?

1/3
3
3/5 (Correct answer)
5

Correct answer: 3/5

The constant of proportionality (k) for a proportional relationship represented by a graph is found by taking any point (x, y) on the line (excluding the origin) and calculating the ratio y/x. From the graph, a clear point is (5, 3), so the constant of proportionality is 3/5.

Question 29: A total of 55 students took the exam, and 11 of them failed. What percentage of students passed the exam?

40%
60%
80% (Correct answer)
20%

Correct answer: 80%

First, determine the number of students who passed the exam by subtracting the number of failed students (11) from the total number of students (55), which is 44 students. Then, calculate the percentage of students who passed by dividing the number of passed students (44) by the total number of students (55) and multiplying by 100%. This results in (44/55) * 100% = 80%.

Question 30: What does a pound of seed cost per unit?

$7.25
$17.50
$1.75 (Correct answer)
$3.50

Correct answer: $1.75

To find the cost per unit (per pound) of seed, divide the total cost by the total quantity. Assuming the missing information indicates that 5 pounds of seed cost $8.75, dividing $8.75 by 5 pounds yields a unit cost of $1.75 per pound.

FSA Practice Test (7th Grade: Math) 1

What is the expression's result?
-7(-3)