Worksheet Chapter 1: Variation

1. True or False: For joint variation y ∝ x z, the constant k can be written as k = yx z.

2. Which equation represents joint variation where z varies directly as x² and inversely as y?

3. It is given that y varies directly as x. If y = 15 when x = 3, calculate the value of y when x = 7.

4. Given p varies inversely as √q. If p = 4 when q = 9, find the value of p when q = 36.

5. Fill in the blank: If y varies directly as x, the graph of y against x is a straight line passing through the ________.

6. Given that y varies directly as x³ and inversely as z. If y = 24 when x = 2 and z = 3, find the value of z when y = 81 and x = 3.

7. The gravitational force F between two objects varies directly as the product of their masses m₁ and m₂, and inversely as the square of the distance r between them. Write the relation using the symbol ∝ and in equation form.

8. Given that P varies directly as the square of Q and inversely as R. If Q decreases by 20% and R increases by 60%, determine the percentage change in P.

9. True or False: In an inverse variation y = kx, as x increases, y also increases at the same rate.

10. The extension of a spring, s cm, varies directly as the attached mass, m kg. If a mass of 4 kg extends the spring by 10 cm, calculate (a) the constant of variation k, and (b) the extension when the mass is 10 kg.