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 A = 5x + 5xy, then use it to find x when A = 40 and y = 1.

    Answer: ______________

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

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

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

    Answer: ______________

  6. Leo makes x the subject of A = 4x + 5xy. He factorises to x(4 + 5y) = A, then writes x = A/4 + 5y. What went wrong?

    • He should have factorised as x(4 - 5y)
    • The formula should be x = A(4 + 5y)
    • Nothing went wrong
    • He divided by only the first term of the bracket; the whole right side must be divided by (4 + 5y)

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

    Answer: ______________

  8. In x = (4y + 3)/(y - 2), the value y = 2 is not allowed.

    Circle one:   True   False

  9. Ava makes x the subject of y = (x + 6)/(x - 4). She writes y(x - 4) = x + 6, then xy - x = 6. What went wrong?

    • The factorisation should be x(y - 4)
    • The answer should be x = 6/(y - 4)
    • She dropped the 4y term; it should be xy - x = 4y + 6
    • y(x - 4) should expand to xy - 6

  10. 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)
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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. 4 · The rearranged formula is x = A/(5 + 5y), so x = 40/10 = 4.
  4. s/(2 + 3y) · Every term contains x, so factorise x out to get x(2 + 3y) = s, then divide by the bracket.
  5. -18 · The rearranged formula is x = (2 - 5y)/(y - 3), so x = (2 - 20)/(4 - 3) = -18.
  6. He divided by only the first term of the bracket; the whole right side must be divided by (4 + 5y) · His factorisation is right. Dividing by a bracket means dividing the entire right side by it, so x = A/(4 + 5y).
  7. 7 · The rearranged formula is x = (4y + 1)/(y - 2), so x = 21/3 = 7.
  8. True · The new denominator is y - 2, which is zero when y = 2, so the formula is undefined there.
  9. She dropped the 4y term; it should be xy - x = 4y + 6 · Expanding gives xy - 4y = x + 6. When the x term moves left, the 4y must move right, giving xy - x = 4y + 6.
  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).
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