Grade 11 · Math · Algebra 2

11th grade Direct, inverse, joint and combined variation worksheet

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Direct, inverse, joint and combined variation

Grade 11 Math Worksheet - Challenge Me

NameDate

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

Luz's worksheet says y varies directly as x and inversely as z. y = 10 when x = 4 and z = 2. What is y when x = 9 and z = 3?
Milo's notebook says y varies directly as x and inversely as z. y = 8 when x = 2 and z = 3. What is y when x = 5 and z = 4?
Noah's pencil notes say y varies directly as x and inversely as z. y = 15 when x = 6 and z = 8. What is y when x = 4 and z = 3?
Pia's math book says y varies directly as x and inversely as z. y = 9 when x = 2 and z = 6. What is y when x = 8 and z = 3?
5.
x = 1, 2, 3; z = 2, 3, 1; y = 4, 12, 6. Ren records x, z and y for an experiment on a worksheet. Which equation fits every row?
- y = 8x/z
- y = 4x
- y = x + z
- y = 2xz
6.
x = 2, 4, 6; z = 1, 3, 2; y = 6, 4, 9. Tala records x, z and y for an experiment in a notebook. Which equation fits every row?
- y = 3xz
- y = 3x/z
- y = 3x
- y = x + z
7.
x = 1, 3, 2; z = 2, 4, 6; y = 6, 9, 4. Bo records x, z and y for an experiment in a math book. Which equation fits every row?
- y = 12x/z
- y = 3xz
- y = x + z
- y = 6x
Esme's club folds flyers. Folding time varies directly as the flyers and inversely as the helpers. 3 helpers fold 300 flyers in 20 minutes. How many minutes do 5 helpers take for 600?
The paint Jun's class needs varies jointly as a mural's width and height. A 5 m by 2 m mural takes 2 liters. How many liters does a 6 m by 4 m mural take?
Milo's light meter reads 160 lux at 1 meter from a lamp. The reading varies inversely as the square of the distance. What does it read at 4 meters?

Direct, inverse, joint and combined variation. Every version has 10 questions, and the answer key prints on the second page.

Standard: A-CED.A.2

direct variation: y = kx: y grows as x grows, by the same factor.

inverse variation: y = k/x: y shrinks as x grows; x × y stays k.

joint variation: y = kxz: y varies directly with both x and z.

combined variation: y = kx/z: direct with x, inverse with z.

constant of variation: The number k that stays the same in every row.

Mixed up direct and inverse variation (multiplying where the rule divides, or the reverse).

Used x instead of x² in a rule with a square. Ask your child to write the rule out and square first.

Turned the constant upside down, dividing x by y instead of y by x.

Ask: when x gets bigger, should y get bigger or smaller?

Ask: in y = kx, how do we get k by itself?

What is the most common mistake with direct, inverse, joint and combined variation?

Mixed up direct and inverse variation (multiplying where the rule divides, or the reverse).

How can I help my child with direct, inverse, joint and combined variation?

Ask: when x gets bigger, should y get bigger or smaller?

Are these 11th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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