Common Core 8th Math Worksheets

If you're a teacher or a parent looking for engaging and effective educational resources to support 8th-grade math skills aligned with the Common Core standards, you've come to the right place. Our collection of 8th-grade math worksheets provides a wide variety of practice exercises that cover key concepts and topics, ensuring that students grasp the essential skills needed to excel in this subject.

  Order of Operations Worksheets 5th

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  7th Grade Math Problems Worksheets

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  First Grade Common Core Math Examples

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  Solving Two-Step Equations

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  Math Worksheets for 4th Grade Line Segments

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  Reading Comprehension Worksheets Grade 3

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  Weekly Homework Sheet 4th Grade Math

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  Free Printable Teacher Grade Book Template

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  Basic Math Fact Practice Sheets

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  Christmas Math Color by Number Subtraction Worksheet

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  Big Ideas Math 8th Grade Chapter 5 Test

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  Food and Exercise Log Printable

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  Set Up Function Notation

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  Subtracting Mixed Numbers with Unlike Denominators

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  Math Worksheets Fractions and Decimals

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What is the Pythagorean theorem?

The Pythagorean theorem states that in a right 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. In other words, a² + b² = c², where a and b are the lengths of the two shorter sides, and c is the length of the hypotenuse. This theorem is fundamental in geometry and is used to solve for unknown sides or angles in right triangles.

How do you simplify expressions involving exponents?

To simplify expressions involving exponents, you can apply the rules of exponents. When you have the same base raised to different exponents, you can combine them by using the properties of exponents. For example, when multiplying two terms with the same base, you can add their exponents. When raising a power to another power, you can multiply the exponents. Additionally, when dividing terms with the same base, you can subtract their exponents. By following these rules, you can simplify expressions involving exponents efficiently.

Describe the process of solving linear equations.

To solve a linear equation, start by isolating the variable term by using inverse operations (addition, subtraction, multiplication, division) on both sides of the equation. Apply the same operation to both sides to maintain the equality. Repeat these steps until the variable is isolated on one side of the equation. Lastly, simplify the equation to find the solution, which is the value of the variable that makes the equation true.

What is the difference between rational and irrational numbers?

Rational numbers can be expressed as a simple fraction where the numerator and denominator are both integers, while irrational numbers cannot be expressed as a fraction and have non-repeating, non-terminating decimal representations. In other words, rational numbers can be written as a ratio of two integers, while irrational numbers cannot be represented in this way.

What is the formula to find the area of a triangle?

The formula to find the area of a triangle is 1/2 * base * height, where the base is the length of the triangle's bottom side and the height is the perpendicular distance from the base to the top vertex opposite the base.

Describe the concept of slope and its relationship to linear equations.

The slope of a line is a measure of its steepness or incline, calculated as the ratio of the vertical change between two points to the horizontal change between those same points. In linear equations, the slope represents the rate at which the line rises or falls as we move from left to right along the x-axis. Specifically, the slope coefficient in a linear equation determines how much the dependent variable changes for a one-unit change in the independent variable. Therefore, the slope is crucial in understanding the direction and steepness of a line and plays a fundamental role in modeling relationships between variables in a linear context.

How do you graph linear inequalities on a coordinate plane?

To graph a linear inequality on a coordinate plane, first convert the inequality to slope-intercept form (y = mx + b). Then, plot the y-intercept (b) on the y-axis and use the slope (m) to identify additional points on the line. Typically, a solid line is used for "greater than" or "less than" inequalities, and a dashed line is used for "greater than or equal to" or "less than or equal to" inequalities. Finally, shade the region above or below the line based on the inequality direction, remembering to exclude or include boundary points as needed.

Explain the process of factoring quadratics.

Factoring quadratics involves finding two binomials that, when multiplied together, equals the original quadratic expression. The first step is to divide the quadratic expression by a common factor if present. Next, look for two numbers that multiply to the constant term in the quadratic expression and add up to the coefficient of the linear term. These numbers will be used to factor the quadratic expression into two binomials. Then, write out the factors in the form of (x + a)(x + b), where 'a' and 'b' are the two numbers found earlier. Finally, simplify the expression if possible and check your factorization by multiplying the binomials back out to ensure you get the original quadratic expression.

Describe the steps to solve a system of equations using substitution.

To solve a system of equations using substitution, first solve one of the equations for a variable in terms of the other variable. Then, substitute this expression into the other equation, which will now have only one variable. Solve this equation for the variable, and then substitute this value back into one of the original equations to find the value of the other variable. Finally, check your solution by verifying that it satisfies both original equations in the system.

How do you find the volume of a rectangular prism?

To find 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. By plugging in the values for length, width, and height into this formula, you can calculate the volume of the rectangular prism.