Practice Maths

Topic Review — Further Algebra — Solutions

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  1. Substitution fluency

    1. 5x − 2y, x = 4, y = −3:
    2. A = ½bh, b = 14, h = 9:
    3. v = u + at, u = 6, a = 4, t = 5:
    4. I = Prt ÷ 100, P = 3000, r = 4, t = 2:
    5. 3a² − 2a + 5, a = −3:
    6. V = πr²h, r = 3, h = 10:

  2. Rearranging formulas

    1. P = 2(l + w), make w:
    2. v = u + at, make a:
    3. C = 2πr, make r:
    4. A = πr², make r:
    5. y = 4x − 3, make x:
    6. A = ½bh, make h:

  3. Mixed algebra

    1. (x + 5)(x − 3) − 2(x + 4):
    2. Factorise 3x² − 27:
    3. Solve 2x² − 8x = 0:
    4. F = 9C⁄5 + 32, make C:
    5. Consecutive integers, product 182:
    6. (2x − 1)² = 4x² − 4x + 1:

  4. Applying formulas in context

    1. A = 42, b = 12, find h:
    2. u = 0, v = 30, t = 10, find a:
    3. V = 905, find r:
    4. I = 400, P = 2500, t = 4, find r:

  5. Problem solving

    1. Swimming pool:
      1. Length:
      2. Equation:
      3. Perimeter:
    2. Ball h = −4t² + 16t:
      1. Factorise:
      2. Lands when h = 0:
      3. Maximum height:
    3. Trapezium A = 55, a = 8, h = 5: