Rearranging Formulae When the Subject Appears Twice · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Rearranging Formulae When the Subject Appears Twice

Mathematics · Algebra · ages 15-16
Name ______________________   Date ____________

  1. In the rearranged formula x = (5y + 2)/(y - 7), which value of y is not allowed?

    • -7
    • 5
    • 7
    • -5

  2. Make x the subject of P = 6x + 4xy.

    • P/(6 + 4y)
    • P/6 + 4y
    • 6P/(4y)
    • (6 + 4y)/P

  3. Make x the subject of s = 2x + 3xy.

    • s/2 + 3y
    • s(2 + 3y)
    • (2 + 3y)/s
    • s/(2 + 3y)

  4. Make x the subject of A = 4x + 5xy.

    • A/4 + 5y
    • A(4 + 5y)
    • A/(4 + 5y)
    • 4A/(5y)

  5. Make x the subject of y = (3x + 2)/(x + 5). If y = 4, what is x?

    Answer: ______________

  6. Make x the subject of P = (2x - 1)/(x + 4).

    • (4P + 1)/(2 - P)
    • (4P - 1)/(2 + P)
    • (2P + 1)/(P - 4)
    • (P + 4)/(2P - 1)

  7. Make x the subject of y = (3x + 4)/(x - 1).

    • (y + 4)/(y - 3)
    • (y - 4)/(y + 3)
    • (3y + 4)/(y - 1)
    • (y + 1)/(y - 4)

  8. Make x the subject of y = (2x + 1)/(x - 4). If y = 5, what is x?

    Answer: ______________

  9. Make x the subject of (y - 1)(x + 2) = 3x.

    • 2(y - 1)/(y - 4)
    • (y - 1)/(4 - y)
    • 2(y - 1)/(4 - y)
    • 2(y - 3)/(4 - y)

  10. The formula x = (2y + 7)/(y - 5) was made the subject of x from y = (ax + b)/(x - c). What is b - a?

    Answer: ______________

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Answer key

For grown-ups. Fold this page away before handing over the rest.

Rearranging Formulae When the Subject Appears Twice W1-mt_Velmpnxfcj-s1

  1. 7 · The new denominator is y - 7, which is zero when y = 7.
  2. P/(6 + 4y) · Every term contains x, so factorise x out to get x(6 + 4y) = P, then divide by the bracket.
  3. s/(2 + 3y) · Every term contains x, so factorise x out to get x(2 + 3y) = s, then divide by the bracket.
  4. A/(4 + 5y) · Every term contains x, so factorise x out to get x(4 + 5y) = A, then divide by the bracket.
  5. -18 · The rearranged formula is x = (2 - 5y)/(y - 3), so x = (2 - 20)/(4 - 3) = -18.
  6. (4P + 1)/(2 - P) · Clear the fraction: Px + 4P = 2x - 1, so x(P - 2) = -(4P + 1), and x = (4P + 1)/(2 - P).
  7. (y + 4)/(y - 3) · Clear the fraction, collect the x terms, factorise x out, and divide: x = (y + 4)/(y - 3).
  8. 7 · The rearranged formula is x = (4y + 1)/(y - 2), so x = 21/3 = 7.
  9. 2(y - 1)/(4 - y) · Expand first: x(y - 1) + 2(y - 1) = 3x. Collect the x terms, factorise x out, and divide: x = 2(y - 1)/(4 - y).
  10. 2 · Running the method in reverse gives y = (5x + 7)/(x - 2), so a = 5 and b = 7, and b - a = 2.
Worksheet · LightMySky