Common Core 8th Grade Math Worksheets

Are you an 8th grade math teacher in need of resources to support your students? Look no further! Common Core 8th Grade Math Worksheets provide a wide range of practice exercises to help reinforce essential math skills. Designed to align with the Common Core State Standards, these worksheets cover a variety of topics and are an excellent tool for both classroom instruction and independent practice.

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What are the properties of congruence and similarity in geometric figures?

Congruent geometric figures have the same shape and size, meaning their corresponding angles and sides are equal. Similar geometric figures have the same shape but may have different sizes, with corresponding angles being equal and corresponding sides being proportional. Both congruence and similarity involve comparing geometric figures based on their corresponding angles and sides, with congruent figures being identical in shape and size, while similar figures maintain the same shape but can differ in size.

How do you find the volume of a cylinder?

To find the volume of a cylinder, you need to multiply the area of the base (which is a circle) by the height of the cylinder. The formula is V = ?r^2h, where V is the volume, ? is pi (approximately 3.14159), r is the radius of the base of the cylinder, and h is the height of the cylinder. Calculate the area of the base by squaring the radius (r^2), then multiply that by the height of the cylinder to find its volume.

What is the quadratic formula and how is it used to solve quadratic equations?

The quadratic formula is used to solve quadratic equations of the form ax^2 + bx + c = 0. It states that the solutions for x are given by x = (-b ± ?(b^2 - 4ac)) / 2a. By substituting the values of a, b, and c into the formula, one can calculate the two potential solutions for x, which represent the x-intercepts of the parabolic graph of the quadratic equation. This formula is helpful when factoring or completing the square is not feasible, providing a straightforward method to find the roots of the quadratic equation.

Describe the process of graphing linear equations using the slope-intercept form.

To graph a linear equation using the slope-intercept form, start by identifying the y-intercept (b), which represents the point where the line crosses the y-axis. Then, use the slope (m) to determine the direction of the line: a positive slope moves upwards, while a negative slope moves downwards. Plot the y-intercept on the graph and use the slope to find another point by moving up or down and left or right accordingly. Finally, connect the two points with a straight line to represent the linear equation graphically.

How do you calculate the probability of an event using the theoretical probability?

To calculate the theoretical probability of an event, you divide the number of favorable outcomes by the total number of possible outcomes. This formula is expressed as: P(event) = Number of favorable outcomes / Total number of possible outcomes. By following this calculation method, you can determine the likelihood of a specific event occurring based on theoretical probability.

Explain the concept of scientific notation and how it is used to represent very large or very small numbers.

Scientific notation is a way to represent very large or very small numbers in a concise format by writing the number as a coefficient multiplied by 10 raised to a certain power. For large numbers, the power of 10 is positive, indicating the number of places the decimal point needs to be moved to get the original number. For small numbers, the power of 10 is negative, representing the number of decimal places the decimal point needs to be shifted to obtain the original number. This notation makes it easier to work with such numbers in calculations and comparisons.

Describe the steps involved in solving systems of equations by substitution.

To solve a system of equations by substitution, start by solving one of the equations for one variable in terms of the other. Then, substitute this expression into the other equation and solve for the remaining variable. Once you have found the value for one of the variables, plug it back into one of the original equations to find the value of the other variable. Verify the solution by checking that it satisfies both equations in the system.

What are the rules for adding, subtracting, multiplying, and dividing integers?

When adding integers with the same sign, add their absolute values and keep the same sign. When they have different signs, subtract the absolute values and keep the sign of the number with the larger absolute value. When subtracting integers, it's like adding the opposite. When multiplying integers, if the signs are the same, the product is positive; if the signs are different, the product is negative. When dividing integers, if the signs are the same, the quotient is positive; if the signs are different, the quotient is negative.

Explain the concept of functions and how to identify the domain and range of a function.

A function is a relationship between two sets where each input has exactly one output. To identify the domain of a function, look at all possible input values that the function can accept. These are the x-values that the function can operate on. The range of a function is all the possible output values that the function can produce. To determine the range, look at all possible output values that the function yields for the given domain. It is important to note that the domain and range of a function can help define its behavior and limitations.

Describe the process of finding the surface area of a rectangular prism.

To find the surface area of a rectangular prism, you would first calculate the area of each of the six sides – two for the length and width, and two for the length and height, and two for the width and height. Then, you would add up all six calculated areas to get the total surface area of the rectangular prism. The formula for finding the surface area of a rectangular prism is SA = 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height of the prism. By plugging in the values for the length, width, and height into this formula and performing the calculations, you can find the surface area of the rectangular prism.