FSA Practice Test (8th Grade: Math) 1 — Questions and Answers

Question 1: For the first 44 hours of labor in a week, King is paid $616, and for any further hours, he is paid 1.5 times his regular hourly rate. King requires $826 this week to cover his rent, bills, and other expenses. How many hours must he work this week to make enough money?

54 (Correct answer)
40
48
53

Correct answer: 54

First, calculate King's regular hourly rate: $616 / 44 hours = $14/hour. He needs an additional $826 - $616 = $210. His overtime rate is 1.5 * $14 = $21/hour. To earn the extra $210, he must work $210 / $21 = 10 overtime hours. Therefore, King must work a total of 44 (regular) + 10 (overtime) = 54 hours this week.

Question 2: Richard designed a triangle-shaped flag with the measurements indicated below. Which of the following is the most closest to X's value?

11.5
9.5
13
10.4 (Correct answer)

Correct answer: 10.4

To find the value of X in a right-angled triangle, the Pythagorean theorem (a² + b² = c²) is used. Assuming the image shows a right triangle with legs of 6 and X, and a hypotenuse of 12 (a common scenario for such problems), the equation is 6² + X² = 12². This simplifies to 36 + X² = 144, so X² = 108. Taking the square root, X ≈ 10.39, which rounds to 10.4.

Question 3: Which of the following is a number that is an integer?

-12.5
0.454545...
-3 (Correct answer)
1/4

Correct answer: -3

An integer is a whole number that can be positive, negative, or zero, without any fractional or decimal parts. Among the given options, -3 is the only number that fits this definition. Options like -12.5, 0.454545..., and 1/4 are decimals or fractions, and thus are not integers.

Question 4: Customers can rent a small cargo truck from a hardware store to transport any large items they buy. To rent the truck, the shop charges a rental fee of $20 plus $7.50 per hour. Which equation is the most accurate representation of the situation?

y=20x + 7.5
y=7.5x + 20 (Correct answer)
y=7.5x - 20
y=20x - 7.5

Correct answer: y=7.5x + 20

This situation describes a linear relationship where the total cost (y) depends on the number of hours (x). The $20 rental fee is a fixed cost, acting as the y-intercept (b). The $7.50 per hour charge is the variable cost, representing the slope (m). Therefore, the equation follows the slope-intercept form y = mx + b, resulting in y = 7.5x + 20.

Question 5: A scatter plot is displayed. Which of the following statements about the scatter plot is correct?

The data show a positive correlation. (Correct answer)
The data show a negative correlation.
The data show a nonlinear association.
The data show no association.

Correct answer: The data show a positive correlation.

A positive correlation in a scatter plot indicates that as the values of one variable increase, the values of the other variable also tend to increase. This relationship is visually represented by data points generally trending upwards from the bottom-left to the top-right of the plot. This suggests a direct relationship between the two variables being measured.

Question 6: Rica earns $15 per week in addition to $.50 per customer on her paper route. She wants to make at least $25 every week. What formula can she use to calculate x, the number of clients she'll need to make exactly $25?

50x + 15 = 25
2x + 15 = 25
0.50x + 15 = 25 (Correct answer)
x + 15 = 25

Correct answer: 0.50x + 15 = 25

Rica's total earnings are composed of a fixed weekly amount and a variable amount based on customers. The fixed amount is $15, and the variable amount is $0.50 multiplied by the number of customers (x), or 0.50x. To find the number of clients needed to make exactly $25, we set the sum of these earnings equal to $25, resulting in the equation 0.50x + 15 = 25.

Question 7: Faye was three times as old as Eddie five years ago. How old is Faye today, if Eddie is ten years old?

8
4
20 (Correct answer)
12

Correct answer: 20

First, determine Eddie's age five years ago by subtracting 5 from his current age: 10 - 5 = 5 years old. Faye was three times as old as Eddie at that time, so Faye was 3 * 5 = 15 years old five years ago. To find Faye's age today, add 5 years to her age from five years ago: 15 + 5 = 20 years old.

Question 8: On the coordinate grid below, a function is graphed. Which of the following statements is the most accurate description of the function?

As the value of x increases, the value of y decreases for all values of x.
As the value of x increases, the value of y decreases for positive values of x only. (Correct answer)
As the value of x increases, the value of y increases for all values of x.
As the value of x increases, the value of y increases for positive values of x only.

Correct answer: As the value of x increases, the value of y decreases for positive values of x only.

To describe a function's behavior, we observe how the y-value changes as the x-value increases. The statement 'As the value of x increases, the value of y decreases for positive values of x only' means that the graph slopes downwards from left to right specifically in the region where x is greater than zero. This accurately describes a function that is decreasing only for its positive domain.

Question 9: Which of the statements below is correct?

Every rational number is a whole number.
Every rational number is an integer.
Every whole number is a rational number. (Correct answer)
Every irrational number is a natural number.

Correct answer: Every whole number is a rational number.

Whole numbers include 0, 1, 2, 3, and so on. A rational number is any number that can be expressed as a fraction p/q, where p and q are integers and q is not zero. Since any whole number 'n' can be written as n/1, every whole number fits the definition of a rational number.

Question 10: In scientific notation, how would you write 564,000,000?

5.64 x 10⁶
5.64 x 10⁻⁷
56.4 x 10⁷
5.64 x 10⁸ (Correct answer)

Correct answer: 5.64 x 10⁸

To write 564,000,000 in scientific notation, move the decimal point to the left until it is after the first non-zero digit, which is 5. This requires moving the decimal point 8 places. Since the original number is greater than 1, the exponent of 10 is positive and equal to the number of places moved, resulting in 5.64 x 10⁸.

Question 11: The total amount of money, y, saved over x weeks is represented by the function y = 3.50x + 2. What is the function's fact?

It is nonlinear because it is always increasing.
It is nonlinear because it increases at a constant rate.
It is linear because it is always increasing.
It is linear because it increases at a constant rate. (Correct answer)

Correct answer: It is linear because it increases at a constant rate.

The function y = 3.50x + 2 is in the form y = mx + b, which is the standard equation for a linear function. In this equation, 'm' (3.50) represents the constant rate of change, or slope. This means the amount of money saved increases by $3.50 for every additional week, indicating a constant rate of increase, which is the defining characteristic of a linear function.

Question 12: What value of x is required for this equation to be true? 4x – 10 = 18

8
7 (Correct answer)
2
4

Correct answer: 7

To solve the equation 4x – 10 = 18 for x, first add 10 to both sides: 4x = 18 + 10, which simplifies to 4x = 28. Next, divide both sides by 4: x = 28 / 4. This yields x = 7.

Question 13: If AE=4, CD=6, and AC=12, what is the length of AB in the following diagram?

4.8 (Correct answer)
7.2
24
3.8

Correct answer: 4.8

This problem involves similar triangles, typically where triangle ABE is similar to triangle ACD (assuming B is on AC, E is on AD, and BE is parallel to CD). In similar triangles, the ratio of corresponding sides is constant: AB/AC = AE/AD = BE/CD. Given AC=12 and AE=4, and by testing the answer choices, if AB=4.8, the ratio AB/AC is 4.8/12 = 0.4. This ratio is consistent with similar triangles where AE/AD = 0.4, implying AD=10, and BE/CD = 0.4, implying BE=2.4 for CD=6.

Question 14: What is the number of calories Marvin will burn after walking at a constant rate of 42 minutes, based on the graph?

210
168 (Correct answer)
162
132

Correct answer: 168

To determine the calories burned, first find the constant rate of calorie burning from the graph (e.g., calories per minute). For instance, if the graph shows 40 calories burned in 10 minutes, the rate is 4 calories per minute. Then, multiply this rate by the desired time: 4 calories/minute * 42 minutes = 168 calories.

Question 15: Which of the following statements about the square root of 10 is correct?

It is irrational. (Correct answer)
It is rational.
It is a whole number.
It is an integer.

Correct answer: It is irrational.

An irrational number cannot be expressed as a simple fraction of two integers and has a non-repeating, non-terminating decimal expansion. Since 10 is not a perfect square, its square root (approximately 3.162...) is a non-terminating and non-repeating decimal. Therefore, the square root of 10 is an irrational number.

Question 16: In scientific notation, what is.0002?

2.0 x 10⁻⁴ (Correct answer)
2.0 x 10⁻⁵
2.0 x 10⁻²
2.0 x 10⁻³

Correct answer: 2.0 x 10⁻⁴

To write 0.0002 in scientific notation, move the decimal point to the right until it is after the first non-zero digit, which is 2. This requires moving the decimal point 4 places. Since the original number is less than 1, the exponent of 10 is negative, so it is 10⁻⁴. Thus, 0.0002 is written as 2.0 x 10⁻⁴.

Question 17: Which of the following equations could be used to represent the data in the table?

y = 3x + 1
y = x + 2
y = x + 4
y = 2x + 3 (Correct answer)

Correct answer: y = 2x + 3

To find the correct equation, substitute the x-values from the table into each option and check if they produce the corresponding y-values. For the equation y = 2x + 3, if x=1, y=2(1)+3=5; if x=2, y=2(2)+3=7; if x=3, y=2(3)+3=9. This equation consistently matches the data pairs in the table.

Question 18: How many gallons does a gas tank contain when it is 2/5 full if it can store 25 gallons?

62.5
50
10 (Correct answer)
125

Correct answer: 10

To calculate how many gallons are in the tank when it is 2/5 full, multiply the total capacity by the given fraction. So, (2/5) * 25 gallons = (2 * 25) / 5 gallons. This simplifies to 50 / 5 gallons, which equals 10 gallons.

Question 19: What is the value of the following expression? 8 – 3√16

2
20
-40
-4 (Correct answer)

Correct answer: -4

To evaluate the expression 8 – 3√16, follow the order of operations (PEMDAS/BODMAS). First, calculate the square root: √16 = 4. Next, perform the multiplication: 3 * 4 = 12. Finally, perform the subtraction: 8 - 12 = -4.

Question 20: On the number line, where does √5 lie between two whole numbers?

4 and 5
3 and 4
1 and 2
2 and 3 (Correct answer)

Correct answer: 2 and 3

To locate √5 on a number line, consider the perfect squares closest to 5. We know that 2² = 4 and 3² = 9. Since 5 is between 4 and 9, its square root (√5) must be between the square roots of 4 and 9. Therefore, √5 lies between 2 and 3.

Question 21: Solve the equation: 3 - 5x = -9 + x

2 (Correct answer)
3
1
4

Correct answer: 2

To solve the equation 3 - 5x = -9 + x, first gather all x terms on one side by adding 5x to both sides: 3 = -9 + 6x. Next, gather constants on the other side by adding 9 to both sides: 3 + 9 = 6x, which simplifies to 12 = 6x. Finally, divide by 6 to find x: x = 12 / 6 = 2.

Question 22: Which equation is the most accurate representation of the graph's line?

y = –5 (Correct answer)
y = 5
x = –5
x = 5

Correct answer: y = –5

A horizontal line on a coordinate grid has a constant y-value for all x-values. If the line passes through the y-axis at -5 and remains flat, its equation is simply y = -5. This means every point on the line has a y-coordinate of -5, regardless of its x-coordinate.

Question 23: If x is proportional to the square of y, and y=2 when x=12, what is the value of y when x=75?

1
1/5
12
5 (Correct answer)

Correct answer: 5

The statement 'x is proportional to the square of y' can be written as x = ky², where k is the constant of proportionality. Using the given values y=2 when x=12, we find k: 12 = k * (2²), so 12 = 4k, which means k=3. Now, use k=3 and the new x-value (x=75) to find y: 75 = 3 * y². Dividing by 3 gives 25 = y², so y = 5 (assuming y is positive).

Question 24: What are the answers to the following system of equations? 3y = x – 2 y = -2x + 4

x = 1, y = -2
x = -2, y = 4
x = 0, y = 2
x = 2, y = 0 (Correct answer)

Correct answer: x = 2, y = 0

To solve this system of equations, use the substitution method. Substitute the expression for y from the second equation (y = -2x + 4) into the first equation: 3(-2x + 4) = x - 2. Distribute the 3: -6x + 12 = x - 2. Combine like terms by adding 6x to both sides and adding 2 to both sides: 14 = 7x. Divide by 7 to find x = 2. Substitute x=2 back into y = -2x + 4 to find y: y = -2(2) + 4 = -4 + 4 = 0. Thus, the solution is x=2, y=0.

Question 25: On a number line, arrange the numbers in the following order (least to greatest).

1.35, 1.8, 2.5, √5
1.8, 1.35, 2.5, √5
1.35,√5, 1.8, 2.5
1.35, 1.8, √5, 2.5 (Correct answer)

Correct answer: 1.35, 1.8, √5, 2.5

To arrange these numbers from least to greatest, first approximate the value of √5. Since 2²=4 and 3²=9, √5 is between 2 and 3, approximately 2.236. Now, compare all the decimal values: 1.35, 1.8, 2.236 (for √5), and 2.5. Arranging them in ascending order gives 1.35, 1.8, √5, 2.5.

Question 26: Which of the following numbers is an irrational number?

Square root of 49
Square root of 25
Square root of 81
Square root of 50 (Correct answer)

Correct answer: Square root of 50

An irrational number cannot be expressed as a simple fraction and has a non-repeating, non-terminating decimal expansion. The square roots of 49 (which is 7), 25 (which is 5), and 81 (which is 9) are all whole numbers, making them rational. However, the square root of 50 is not a whole number and cannot be simplified to a rational number, making it irrational.

Question 27: To the following inequality, what are the solutions? 2x + 6 < 4

x > 1
x > –1
x < 1
x < –1 (Correct answer)

Correct answer: x < –1

To solve the inequality 2x + 6 < 4, first subtract 6 from both sides: 2x < 4 - 6, which simplifies to 2x < -2. Next, divide both sides by 2: x < -2 / 2. This results in x < -1.

Question 28: In the cities A, C and E, what percent of the respective cities are in the type of pollution?

40%,60%,90%
30%,40%,60%
60%,40%,90% (Correct answer)
30%,40%,90%

Correct answer: 60%,40%,90%

To determine the percentage of pollution for cities A, C, and E, you would consult the provided graph (e.g., a bar chart or pie chart). For each city, identify the segment or bar representing 'type of pollution' and read the corresponding percentage value directly from the graph. Based on the correct answer, City A shows 60%, City C shows 40%, and City E shows 90% for that pollution type.

Question 29: On the coordinate grid below, lines p and q are shown. Which of the following statements is the most accurate description of the lines?

Line p has a greater slope than line q. (Correct answer)
The y-intercept of line p is greater than the y-intercept of line q.
The x-intercept of line q is greater than the x-intercept of line p.
Line p has the same slope as line q.

Correct answer: Line p has a greater slope than line q.

The slope of a line indicates its steepness. A line with a greater absolute slope is steeper. By visually comparing lines p and q on the coordinate grid, if line p appears to rise or fall more sharply than line q for the same horizontal distance, then line p has a greater slope. This means it has a larger numerical value for its slope compared to line q.

Question 30: Is the equation below correct? -5² = (-5)²

Yes, because they both equal -10.
Yes, because they both equal -25.
No, because -5² equals -25 and (-5)² equals 25. (Correct answer)
Yes, because they both equal 25.

Correct answer: No, because -5² equals -25 and (-5)² equals 25.

The expression -5² means -(5²), where the exponent applies only to the 5, resulting in -(25) = -25. In contrast, the expression (-5)² means (-5) multiplied by (-5), where the exponent applies to the entire -5, resulting in 25. Since -25 is not equal to 25, the given equation is incorrect.

FSA Practice Test (8th Grade: Math) 1

For the first 44 hours of labor in a week, King is paid $616, and for any further hours, he is paid 1.5 times his regular hourly rate.
King requires $826 this week to cover his rent, bills, and other expenses.
How many hours must he work this week to make enough money?