Mastering Direct and Indirect Variation: A Guide for JSS 2 Students

Evaluation

1. In direct variation, when one quantity increases, the other __________.
   • a) decreases
   • b) stays the same
   • c) increases
   • d) disappears
2. The formula for direct variation is __________.
   • a) y = kx
   • b) y = k / x
   • c) y = x + k
   • d) y = x – k
3. In indirect variation, when one quantity increases, the other __________.
   • a) increases
   • b) stays the same
   • c) decreases
   • d) disappears
4. The formula for indirect variation is __________.
   • a) y = kx
   • b) y = k / x
   • c) y = x + k
   • d) y = x – k
5. If y varies directly as x and y = 10 when x = 2, the constant k is __________.
   • a) 5
   • b) 10
   • c) 2
   • d) 20
6. If y varies inversely as x and y = 4 when x = 3, the constant k is __________.
   • a) 12
   • b) 7
   • c) 1
   • d) 4
7. In a direct variation, the graph is a __________ line.
   • a) curved
   • b) horizontal
   • c) vertical
   • d) straight
8. In an indirect variation, the graph is a __________.
   • a) straight line
   • b) parabola
   • c) hyperbola
   • d) circle
9. If y varies directly as x and y = 15 when x = 3, find y when x = 6.
   • a) 30
   • b) 45
   • c) 5
   • d) 25
10. If y varies inversely as x and y = 8 when x = 2, find y when x = 4.
    • a) 2
    • b) 4
    • c) 8
    • d) 16
11. The cost of apples varies directly with the weight. If 3 kg costs 9 dollars, 6 kg will cost __________ dollars.
    • a) 18
    • b) 12
    • c) 6
    • d) 3
12. The time to finish a job varies inversely with the number of workers. If 5 workers can finish in 8 hours, 10 workers will finish in __________ hours.
    • a) 4
    • b) 16
    • c) 2
    • d) 8
13. Direct variation can be written as y = __________ x.
    • a) k
    • b) k / x
    • c) kx
    • d) x / k
14. Indirect variation can be written as y = k / __________.
    • a) y
    • b) x
    • c) k
    • d) 1
15. Which of the following is an example of indirect variation?
    • a) The cost of fuel with the amount of fuel
    • b) The speed of a car with the time to travel a distance
    • c) The weight of fruits with the number of fruits
    • d) The height of a plant with the amount of sunlight

Class Activity Discussion

1. Q: What is direct variation?

• A: Direct variation is when two quantities increase or decrease together.

2. Q: What is the formula for direct variation?

• A: The formula is y = kx, where k is the constant of variation.

3. Q: What is indirect variation?

• A: Indirect variation is when one quantity increases as the other decreases.

4. Q: What is the formula for indirect variation?

• A: The formula is y = k / x, where k is the constant of variation.

5. Q: How do you find the constant of variation in direct variation?

• A: Divide y by x (k = y / x).

6. Q: How do you find the constant of variation in indirect variation?

• A: Multiply y and x (k = y * x).

7. Q: What does the graph of direct variation look like?

• A: It is a straight line passing through the origin (0, 0).

8. Q: What does the graph of indirect variation look like?

• A: It is a hyperbola, a curve that gets closer to the axes but never touches them.

9. Q: Can you give an example of direct variation?

• A: Yes, the cost of apples varies directly with the weight of apples bought.

10. Q: Can you give an example of indirect variation? – A: Yes, the time to complete a task varies inversely with the number of people working on it.

11. Q: If y = 15 when x = 3 in direct variation, what is the constant k? – A: k = 15 / 3 = 5.

12. Q: If y = 8 when x = 2 in indirect variation, what is the constant k? – A: k = 8 * 2 = 16.

13. Q: How do you find y in direct variation if you know x and k? – A: Multiply x by k (y = kx).

14. Q: How do you find y in indirect variation if you know x and k? – A: Divide k by x (y = k / x).

15. Q: Why is it important to understand direct and indirect variation? – A: It helps solve real-world problems and understand the relationships between variables.

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