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Worksheet: Inverse Variation

Q1:

𝑦 varies inversely with π‘₯ 3 . The constant of proportionality is 13. Which of the following equations represents this relation?

  • A 𝑦 = 1 3 π‘₯ 3
  • B 𝑦 = 1 3 π‘₯
  • C 𝑦 = 1 3 βˆ’ π‘₯ 3
  • D 𝑦 = 1 3 π‘₯ 3

Q2:

𝑦 varies inversely with π‘₯ 3 . The constant of proportionality is 6. Which of the following equations represents this relation?

  • A 𝑦 = 6 π‘₯ 3
  • B 𝑦 = 6 π‘₯
  • C 𝑦 = 6 βˆ’ π‘₯ 3
  • D 𝑦 = 6 π‘₯ 3

Q3:

varies inversely with . Given that when , what is the constant of proportionality?

Q4:

varies inversely with . Given that when , what is the constant of proportionality?

Q5:

Decide if π‘₯ varies directly or inversely with 𝑦 and use this to find the value of 𝑦 when π‘₯ = 3 .

π‘₯ 2 4 70
𝑦 70 35 2
  • A 3 1 4 0
  • B420
  • C 1 5 5 9
  • D 4 6 2 3

Q6:

If 𝑦 ∝ 1 √ π‘₯ then which of the following is true?

  • A π‘₯ is inversely proportional to 𝑦
  • B π‘₯ is directly proportional to 𝑦 2
  • C π‘₯ is directly proportional to 𝑦
  • D π‘₯ is inversely proportional to 𝑦 2
  • E π‘₯ is inversely proportional to 𝑦 3

Q7:

The table below shows how 𝑦 varies with π‘₯ . Use this information to find the value of π‘₯ when 𝑦 = 1 4 .

π‘₯ 2 7 28
𝑦 28 8 2

Q8:

For a rectangle of fixed area, the length 𝑙 varies inversely with its width 𝑀 . Given that 𝑙 = 2 2 c m when 𝑀 = 1 6 c m , determine the value of 𝑙 when 𝑀 = 4 4 c m .

Q9:

For a rectangle of fixed area, the length 𝑙 varies inversely with its width 𝑀 . Given that 𝑙 = 1 3 c m when 𝑀 = 1 1 c m , determine the value of 𝑙 when 𝑀 = 1 3 c m .

Q10:

Given that 𝑦 varies inversely as π‘₯ , write an equation for 𝑦 in terms of π‘₯ using π‘˜ as a non-zero constant.

  • A 𝑦 = π‘˜ π‘₯
  • B 𝑦 = π‘˜ π‘₯ 2
  • C 𝑦 = π‘˜ π‘₯ 2
  • D 𝑦 = π‘˜ π‘₯

Q11:

If 𝑧 = π‘š π‘₯ , where π‘š is a constant, then 𝑧 ∝ .

  • A π‘₯ 2
  • B 1 π‘₯ 2
  • C π‘₯
  • D 1 π‘₯

Q12:

At the beginning of the month, Jacob bought 70 eggs. Every morning he eats 2 eggs for breakfast. Is the number of remaining eggs proportional to the number of the days that have passed?

  • Ano
  • Byes

Q13:

Given that 𝑦 varies inversely as π‘₯ 2 , write an equation for 𝑦 in terms of π‘₯ using π‘˜ as a nonzero constant.

  • A 𝑦 = π‘˜ π‘₯
  • B 𝑦 = π‘˜ π‘₯
  • C 𝑦 = π‘˜ π‘₯ 2
  • D 𝑦 = π‘˜ π‘₯ 2

Q14:

The weight of an object above Earth’s surface varies inversely with the square of the distance from Earth’s center. If a body weighs 50 pounds when it is 3 9 6 0 miles from the earth’s center, what would it weigh if it was 3 9 7 0 miles miles from Earth’s center?