Direct, inverse, joint and combined variation

Answer Key - Grade 11 Math Worksheet

Circle the best answer, or write your answer on the line.

1. 1.

   Esme's worksheet says y varies directly as the square of x. y = 12 when x = 2. What is y when x = 5?

   75
2. 2.

   Milo's math book says y varies inversely as the square of x. y = 3 when x = 4. What is y when x = 6?

   4/3
3. 3.

   Noah's worksheet says y varies jointly as x and z. y = 24 when x = 2 and z = 3. What is y when x = 5 and z = 2?

   40
4. 4.

   Pia's notebook says y varies jointly as x and z. y = 30 when x = 5 and z = 2. What is y when x = 6 and z = 7?

   126
5. 5.

   Ren's pencil notes say y varies jointly as x and z. y = 36 when x = 3 and z = 4. What is y when x = 2 and z = 5?

   30
6. 6.

   Tala's math book says y varies jointly as x and z. y = 28 when x = 7 and z = 2. What is y when x = 3 and z = 6?

   36
7. 7.

   Ari's worksheet says y varies jointly as x and z. y = 30 when x = 2 and z = 3. What is the equation for y?

   y = 5xz
8. 8.

   Bo's notebook says y varies directly as x and inversely as z. y = 12 when x = 4 and z = 2. What is the equation for y?

   y = 6x/z
9. 9.

   Esme's pencil notes say y varies jointly as x and z. y = 40 when x = 4 and z = 5. What is the equation for y?

   y = 2xz
10. 10.

    Jun's math book says y varies directly as x and inversely as z. y = 21 when x = 3 and z = 7. What is the equation for y?

    y = 49x/z