Grade 12 Proportional Equations Worksheet
This worksheet covers solving and applying proportional equations for Grade 12 students, including direct, inverse, and joint variations.
Includes
Standards
Topics
Grade 12 Proportional Equations
Name:
Date:
Score:
Read each question carefully and solve for the unknown variable. Show all your work for full credit. Simplify all answers.
1. If y varies directly as x, and y = 15 when x = 5, what is the constant of proportionality?
3
5
10
75
2. The time (t) it takes to travel a certain distance is inversely proportional to the speed (s). If it takes 4 hours to travel at 60 mph, how long will it take to travel the same distance at 80 mph?
2 hours
3 hours
4.5 hours
5.33 hours
3. In a direct variation, as one quantity increases, the other quantity .
4. If y varies jointly as x and z, the equation representing this relationship is y = .
5. The volume (V) of a gas varies directly with its temperature (T) and inversely with its pressure (P). Write an equation representing this relationship and identify the constant of proportionality.
6. A map has a scale of 1 inch = 20 miles. If two cities are 3.5 inches apart on the map, what is the actual distance between them?
7. If y is inversely proportional to x, then as x increases, y also increases.
True
False
Match the type of variation with its general equation.
8. Direct Variation
a. y = kxz
9. Inverse Variation
b. y = k/x
10. Joint Variation
c. y = kx
11. The force (F) needed to stretch a spring varies directly with the distance (d) it is stretched. If 10 pounds of force stretches a spring 2 inches, how much force is needed to stretch it 5 inches?
12. The intensity (I) of light from a source is inversely proportional to the square of the distance (d) from the source. If the intensity is 100 units at a distance of 2 meters, what is the intensity at a distance of 4 meters?
Related Worksheets
Perfect Square Trinomials
This worksheet focuses on identifying, factoring, and constructing perfect square trinomials, essential skills for Grade 12 Algebra.
Solving Square Root Equations
This worksheet focuses on solving square root equations, including identifying extraneous solutions, for Grade 12 Algebra students.
Finding Polynomial Functions from Graphs
Grade 12 math worksheet on determining polynomial functions given their graphs, focusing on roots, multiplicity, and end behavior.
Combining Polynomials Worksheet
Grade 12 math worksheet on combining polynomials, including addition, subtraction, multiplication, and division.
Equations with Infinite and No Solutions
Explore linear equations that result in infinite solutions (identities) or no solutions (contradictions) at a Grade 12 level.
Grade 12: Rearranging Equations
This worksheet focuses on rearranging complex algebraic equations to solve for specific variables, suitable for Grade 12 mathematics.
Grade 12: Rearranging Equations
This worksheet focuses on rearranging complex algebraic equations to solve for specific variables, suitable for Grade 12 mathematics.
Direct Variation Worksheet
A Grade 12 mathematics worksheet focusing on direct variation, including identifying direct variation, writing equations, and solving problems.