Practice Maths

Rearranging Formulas — Solutions

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  1. Rearrange for indicated variable

    1. A = lw, make l:
    2. P = 2(l + w), make l:
    3. v = u + at, make u:
    4. v = u + at, make a:
    5. d = st, make s:
    6. d = st, make t:
    7. I = Prt ÷ 100, make r:
    8. I = Prt ÷ 100, make t:
    9. F = ma, make m:
    10. C = 2πr, make r:
    11. y = mx + c, make x:
    12. y = mx + c, make m:

  2. Squares and square roots

    1. A = πr², make r:
    2. E = ½mv², make v:
    3. c² = a² + b², make a:
    4. V = ¾πr³, make r:

  3. Rearrange then substitute

    1. a = (v − u) ÷ t; v = 50, u = 10, t = 8:
    2. w = P ÷ 2 − l; P = 36, l = 11:
    3. P = 100I ÷ (rt); I = 180, r = 6, t = 5:
    4. r = √(A ÷ π); A = 50.27:
    5. m = 2E ÷ v²; E = 450, v = 15:

  4. Identify correct/incorrect rearrangements

    1. d = st, student claims t = d − s:
    2. A = ½bh, student claims b = 2A ÷ h:
    3. y = 3x − 7, student claims x = (y + 7) ÷ 3:
    4. c² = a² + b², student claims a = c − b:

  5. Real-world formula applications

    1. v = d ÷ t:
      1. Rearrange for d:
      2. v = 22, t = 2.25 h:
    2. I = Prt ÷ 100:
      1. Rearrange for P:
      2. I = 600, r = 5, t = 4:
    3. F = 9C⁄5 + 32:
      1. Rearrange for C:
      2. F = 98.6:
      3. C = 100:
    4. P = 220, A = 2800:

  6. Kinematic formula s = ut + ½at²

    1. Rearrange for u:
    2. u = 0, s = 80, t = 4:
    3. v = u + at = 0 + 10 × 4:

  7. Rearrange formulas with fractions

    1. T = 2πr ÷ v, make v:
    2. R = V ÷ I, make I:
    3. P = F ÷ A, make A:
    4. v² = u² + 2as, make s:

  8. Comparing rearrangements

    1. E = mc², make m:
    2. v² = u² + 2as, make a:
    3. A = ½h(a + b), make h:

  9. Rearrange and apply in context

    1. A = 113.1, use r = √(A ÷ π):
    2. V = πr²h, V = 25.13, h = 2, find r:
    3. A = P(1 + r)², make P:

  10. Extended investigation

    1. Answers will vary:
    2. d = v² ÷ (2μg):
      1. Make v the subject:
      2. d = 40, μ = 0.5, g = 10:
      3. Convert to km/h:
    3. Pool: l = 2w + 3, P = 2(l + w):
      1. Substitute:
      2. P = 54:
      3. Area: