Direct And Inverse Variation Worksheet With Answers Pdf
Introduction
Direct and inverse variations are concepts that you will encounter in many math problems. These concepts are important because they help you understand how variables relate to each other. You might have already had an introduction to these concepts, but it never hurts to practice and refresh your memory.
What is Direct Variation?
Direct variation is a relationship between two variables where one variable increases as the other increases, or decreases as the other decreases. In other words, the two variables change in the same direction. The general formula for direct variation is y = kx, where k is the constant of variation. Another way to write this formula is y/x = k, which shows that the ratio of y to x is constant.
What is Inverse Variation?
Inverse variation is a relationship between two variables where one variable increases as the other decreases, or vice versa. In other words, the two variables change in opposite directions. The general formula for inverse variation is y = k/x, where k is the constant of variation. Another way to write this formula is xy = k, which shows that the product of x and y is constant.
Direct and Inverse Variation Worksheet with Answers PDF
If you want to practice your skills in direct and inverse variation, you can download a worksheet with answers in PDF format. These worksheets are available online for free and will help you test your understanding of the concepts. Some worksheets will ask you to identify whether a relationship is direct or inverse, while others will ask you to find the constant of variation or solve for one of the variables.
How to Solve Direct and Inverse Variation Problems?
Solving direct and inverse variation problems involves using the formulas mentioned earlier. Here are the steps you can follow:
1. Identify the two variables in the problem and determine if the relationship is direct or inverse.
2. Write the formula for the type of variation you are dealing with.
3. Use the given information to find the constant of variation, k.
4. Use the formula to solve for the missing variable.
5. Check your answer and make sure it makes sense in the context of the problem.
Examples of Direct and Inverse Variation Problems
Here are some examples of direct and inverse variation problems:
1. A car travels at a constant speed of 60 mph. How far will it travel in 4 hours?
Solution: This is an example of direct variation. We can use the formula y = kx, where y represents the distance travelled, x represents the time, and k is the constant of variation. We know that when x = 4, y = 240 miles. So, we can solve for k by dividing y by x. k = y/x = 240/4 = 60. The formula is now y = 60x, and we can solve for y when x = 6. The car will travel 360 miles in 6 hours.
2. The force of gravity acting on an object is inversely proportional to the square of the distance between the object and the center of the earth. If the force of gravity on an object is 50 N when it is 10 m from the center of the earth, what is the force of gravity when it is 20 m from the center of the earth?
Solution: This is an example of inverse variation. We can use the formula y = k/x^2, where y represents the force of gravity, x represents the distance from the center of the earth, and k is the constant of variation. We know that when x = 10, y = 50 N. So, we can solve for k by multiplying y by x^2. k = xy^2 = 10(50) = 500. The formula is now y = 500/x^2, and we can solve for y when x = 20. The force of gravity is 12.5 N when the object is 20 m from the center of the earth.
Conclusion
Direct and inverse variation are important concepts in mathematics that you will encounter in many problems. Learning how to identify and solve problems involving direct and inverse variation will help you in your studies and everyday life. By practicing with worksheets and examples, you can strengthen your skills and gain confidence in these concepts.