Grade 12 Proportional Equations Worksheet
This worksheet covers solving and applying proportional equations for Grade 12 students, including direct, inverse, and joint variations.
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Grade 12 Proportional Equations
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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?