Practice Maths

Topic Review — Algebraic Expressions — Solutions

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  1. Like terms and simplifying

    1. 9x + 4x − 3x:
    2. 6a + 3b − 2a + 5b:
    3. 5m² − 3m + 2m² + m:
    4. Like terms in 4x, 3y, 7x, 2x², 5y, x²:
    5. 3pq + 5p − pq + 2p:
    6. 7t² − 4t + 3 − 2t² + 6t − 1:

  2. Expanding with the distributive law

    1. 3(5x + 4):
    2. −2(3y − 8):
    3. 4a(2a + 7):
    4. 5(x + 3) + 2(x − 1):
    5. 3(2m − 4) − (m + 2):
    6. 2n(n + 4) − 3n(n − 2):

  3. Factorising

    1. 6x + 10:
    2. 9y − 12:
    3. 8a² + 20a:
    4. 15m² − 10m:
    5. 6p² + 9p − 3:
    6. −4t² − 8t:

  4. Substitution and mixed operations

    1. 3x² − 4x + 2, x = 5:
    2. 2a + a², a = −3:
    3. 4(3k − 2) + 5k, k = 2:
    4. Factorise 12x + 18:
    5. 3(x + 4) = 3x + 12 (not 3x + 4):
    6. 2x(x + 3) − x(2x − 1):

  5. Problem solving

    1. Rectangle perimeter:
      1. Perimeter expression:
      2. P when x = 2:
    2. 12x² + 8x:
    3. Bike hire:
    4. 2(3a + 1) − 4a: