Practice Test (8th Grade: Math) Flashcards

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?

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.

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

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.

Which of the following is a number that is an integer?

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.

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?

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.

A scatter plot is displayed. Which of the following statements about the scatter plot is 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.

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?

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.

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

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.

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

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.

Which of the statements below is 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.

In scientific notation, how would you write 564,000,000?

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.

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?

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.

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

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.

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

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.

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

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.

Which of the following statements about the square root of 10 is 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.

In scientific notation, what is.0002?

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.

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

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.

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

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.

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

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.

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

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.