8th Grade Math Worksheets Homework

Are you searching for a reliable resource to reinforce your 8th-grade math skills? Look no further! We understand the importance of mastering concepts like algebra, geometry, and statistics at this stage. That's why our collection of 8th grade math worksheets is designed to provide comprehensive practice on various topics, allowing you to strengthen your understanding and confidence in solving math problems.

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What is the Pythagorean Theorem?

The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Mathematically, it can be expressed as a² + b² = c², where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

How do you simplify expressions with exponents?

To simplify expressions with exponents, you can apply various exponent rules. Combine like terms with the same bases by adding or subtracting the exponents. When multiplying two terms with the same base, add the exponents. When dividing two terms with the same base, subtract the exponents. To simplify exponents raised to another exponent, multiply the exponents. Additionally, remember that any term raised to the power of 0 is equal to 1. Apply these rules systematically to simplify expressions with exponents efficiently.

How can you solve equations with variables on both sides?

To solve equations with variables on both sides, you first want to simplify the equation by combining like terms on each side. Next, you aim to get all the variables to one side of the equation by performing inverse operations. Start by isolating the variable with the highest coefficient or one that makes the equation simpler to solve. Once you have the variable on one side, simplify the equation again and solve for the variable by performing the necessary operations. Finally, check your solution by substituting it back into the original equation to ensure it satisfies the equation.

What are the properties of congruent triangles?

Congruent triangles have the same size and shape, meaning that all corresponding sides are equal in length and all corresponding angles are equal in measure. This implies that if two triangles are congruent, then their corresponding sides and angles are also congruent and can be proven using various methods such as side-angle-side (SAS), side-side-side (SSS), angle-side-angle (ASA), angle-angle-side (AAS), and hypotenuse-leg (HL) congruence criteria.

How can you find the area and perimeter of a rectangle?

To find the area of a rectangle, multiply its length by its width. The formula for the area of a rectangle is A = length x width. To find the perimeter of a rectangle, add up all four sides. The formula for the perimeter of a rectangle is P = 2(length + width).

What is the probability of rolling a 6 on a standard die?

The probability of rolling a 6 on a standard die is 1 out of 6, or approximately 16.67%. Each of the six sides of a standard die has an equal chance of landing face-up when rolled, so the probability of rolling any specific number, such as a 6, is 1 out of the total 6 possible outcomes.

How do you graph linear equations using slope-intercept form?

To graph a linear equation using slope-intercept form, start by identifying the y-intercept, which is represented by the constant term in the equation. Plot this point on the y-axis. Then use the slope, which is represented by the coefficient of x in the equation, to find additional points on the line. The slope indicates the rise over run, so move up or down from the y-intercept based on the slope to find another point on the line. Connect these points to draw a straight line extending infinitely in both directions, representing the graph of the linear equation.

What is the equation of a line given two points on the line?

To find the equation of a line passing through two points, (x1, y1) and (x2, y2), you can use the point-slope form of a line equation: y - y1 = m(x - x1), where m is the slope of the line given by (y2 - y1) / (x2 - x1). By substituting the values of the slope and one of the points into the point-slope form, you can determine the equation of the line that passes through these two points.

How do you determine the volume of a rectangular prism?

To determine the volume of a rectangular prism, you multiply the length, width, and height of the prism together. The formula for the volume of a rectangular prism is V = l x w x h, where V represents the volume, l is the length, w is the width, and h is the height of the prism. Simply plug in the values for length, width, and height into the formula and multiply them to find the total volume of the rectangular prism.

What is the difference between mean, median, and mode in statistics?

In statistics, the mean is the average of a set of numbers calculated by adding all numbers together and then dividing by the total count. The median is the middle value of a set of numbers when they are arranged in ascending order. The mode is the number that appears most frequently in a set of numbers. Essentially, mean represents the central tendency, median represents the middle value, and mode represents the most frequent value in a data set.