Rearranging formulae when the subject appears twice · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.
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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 + 4x = 6x + 4xy. Assume 2 + 4y != 0.

    • P/(2 + 4y)
    • P/(10 + 4y)
    • P/(2 - 4y)
    • (2 + 4y)/P

  3. Make x the subject of A = 5x + 5xy + 6. Find x when A = 6 and y = 2.

    Answer: ______________

  4. Make x the subject of s = 2x + 3xy + 5. Assume 2 + 3y != 0.

    • (s + 5)/(2 + 3y)
    • (s - 5)/(2 - 3y)
    • (2 + 3y)/(s - 5)
    • (s - 5)/(2 + 3y)

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

    Answer: ______________

  6. Leo changes A = 4x + 5xy to x(4 + 5y) = A, then writes x = A/4 + 5y. Which instruction gives the correct final expression? Assume 4 + 5y != 0.

    • Divide A by 4, then add 5y.
    • Multiply A by all of (4 + 5y).
    • Divide A by x, then add 5y.
    • Divide A by all of (4 + 5y).

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

    Answer: ______________

  8. In A = 5x + 4xy, if A = 0 and y = -5/4, every real value of x satisfies the formula.

    Circle one:   True   False

  9. Ava starts rearranging y = (x + 6)/(x - 4). From y(x - 4) = x + 6, she writes xy - x = 6. Which term is missing from the right side?

    • The term 4x on the right.
    • The term -4y on the right.
    • The term 4y on the right.
    • The term -6x on the right.

  10. Make x the subject of (y - 1)(x + 2) = 3x. Assume y != 4.

    • 2(y - 1)/(y - 4)
    • (y - 1)/(4 - y)
    • 2(y - 1)/(4 - y)
    • 2(y - 3)/(4 - y)
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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/(2 + 4y) · Subtract 4x from both sides: P = 2x + 4xy. Factorise x out and divide by 2 + 4y.
  3. 0 · Subtract 6 and factorise: A - 6 = x(5 + 5y). At A = 6 and y = 2, x = 0/15 = 0.
  4. (s - 5)/(2 + 3y) · Subtract 5 before factorising: s - 5 = x(2 + 3y). Dividing by 2 + 3y gives x = (s - 5)/(2 + 3y).
  5. -18 · The rearranged formula is x = (2 - 5y)/(y - 3), so x = (2 - 20)/(4 - 3) = -18.
  6. Divide A by all of (4 + 5y). · The factorisation is correct. Divide both sides by the whole nonzero bracket 4 + 5y. This gives x = A/(4 + 5y).
  7. 7 · The rearranged formula is x = (4y + 1)/(y - 2), so x = 21/3 = 7.
  8. True · The factor 5 + 4y becomes zero. With A = 0, the original formula becomes 0 = 0x, which holds for every real x.
  9. The term 4y on the right. · Expansion gives xy - 4y = x + 6. Subtract x and add 4y on both sides to get xy - x = 4y + 6. Ava's line omits 4y from the right side.
  10. 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).
Worksheet · LightMySky