Algebra 2 Worksheet



Name______________________ Block _____ Date ______________

Intro to Variations

Writing Direct Variation Equations

Model #1 Example #1

C varies directly as D P varies directly as Q

Equation: C = kD Equation:

Model #2 Example #2

a varies inversely as b h varies inversely as i

Equation: [pic] Equation:

Model #3 Example #3

f varies jointly as r and t s varies jointly as w and x

Equation: f = krt Equation:

Model #4 Example #4

a varies directly as b and inversely as c r varies directly as s and inversely as t

Equation: [pic] Equation:

Model #5 Example #5

q varies inversely as m and jointly as l and r h varies inversely as j and jointly as m and n

Equation: [pic] Equation:

Model #6 Example #6

w varies directly with y and inversely as c varies directly with e and inversely as

the square of z the square of d

Equation: [pic] Equation:

Translate each statement into a formula. Use k as the constant of variation.

7. V varies jointly as B and H

8. P varies directly as the square of V and inversely as R

9. The mass, M, of a cement block varies jointly as the length, L, width, W, and thickness, T, of the block

10. The volume, V, of a gas varies directly as the temperature, T, and inversely as the pressure, P.

11. E varies jointly as M and the square of V.

12. The distance, D, that a free-falling object falls varies directly as the square of the time, T, that it falls.

13. The price, P, of a diamond is directly proportional to the square of the weight, W.

14. The price, P, of a pizza varies directly as the square root of its radius, R.

15. A company has found that the monthly demand, D, for one of its products varies inversely with the price, P, of the product.

16. Intensity, I, varies inversely with the square of its distance, D.

17. The simple interest, I (in dollars), for a savings account is jointly proportional to the product of the time, T (in years), and the principal, P (in dollars).

Name____ANSWER KEY_____________ Block _____ Date ______________

Intro to Variations

Writing Direct Variation Equations

Model #1 Example #1

C varies directly as D P varies directly as Q

Equation: C = kD Equation: P=kQ

Model #2 Example #2

a varies inversely as b h varies inversely as i

Equation: [pic] Equation: [pic]

Model #3 Example #3

f varies jointly as r and t s varies jointly as w and x

Equation: f = krt Equation: s=kwx

Model #4 Example #4

a varies directly as b and inversely as c r varies directly as s and inversely as t

Equation: [pic] Equation: [pic]

Model #5 Example #5

q varies inversely as m and jointly as l and r h varies inversely as j and jointly as m and n

Equation: [pic] Equation: [pic]

Model #6 Example #6

w varies directly with y and inversely as c varies directly with e and inversely as

the square of z the square of d

Equation: [pic] Equation: [pic]

Translate each statement into a formula. Use k as the constant of variation.

7. V varies jointly as B and H V=kBH

8. P varies directly as the square of V and inversely as R [pic]

9. The mass, M, of a cement block varies jointly as the length, L, width, W, and thickness, T, of the block

M=kLWT

10. The volume, V, of a gas varies directly as the temperature, T, and inversely as the pressure, P. [pic]

11. E varies jointly as M and the square of V. E=kMV2

12. The distance, D, that a free-falling object falls varies directly as the square of the time, T, that it falls.

D=kT2

13. The price, P, of a diamond is directly proportional to the square of the weight, W. P=kW2

14. The price, P, of a pizza varies directly as the square root of its radius, R. [pic] [pic]

15. A company has found that the monthly demand, D, for one of its products varies inversely with the price, P, of the product. [pic]

16. Intensity, I, varies inversely with the square of its distance, D. [pic]

17. The simple interest, I (in dollars), for a savings account is jointly proportional to the product of the time, T (in years), and the principal, P (in dollars). I=kTP

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Three types of variation:

1. Direct Variation 2. Inverse Variation 3. Joint Variation

y = kx y = k y = kxz

x

In each variation equation, k is a number that refers to the constant of variation or constant of proportionality.

Three types of variation:

1. Direct Variation 2. Inverse Variation 3. Joint Variation

y = kx y = k y = kxz

x

In each variation equation, k is a number that refers to the constant of variation or the constant of proportionality.

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