Practice Maths

Mixed Algebraic Problems — Solutions

Click any answer to watch the solution video.

  1. Collecting like terms

    1. 7x + 3x − 2x:
    2. 5a − 2b + 3a + 6b:
    3. 4m² + 3m − m² + 2m:
    4. 9p − 4q + 2p − q:
    5. 6x² + 2x − 3x² − 5x + 1:
    6. 3xy + 2x − xy + 5x:
    7. 8n + 4 − 3n − 9 + n:
    8. 2a² − 5a + a² + 7a − 3:

  2. Expanding

    1. 4(3x + 2):
    2. 5(2y − 7):
    3. −3(a + 6):
    4. x(x − 4):
    5. 2m(3m + 5):
    6. −4t(2t − 1):
    7. 6(p + q − 3):
    8. 3k(k − 2) + 5k:

  3. Factorising

    1. 8x + 12:
    2. 15y − 10:
    3. 6a² + 9a:
    4. 14m² − 21m:
    5. 4p² + 8p + 12:
    6. −5t² + 10t:

  4. Expand and simplify

    1. 3(x + 4) + 2(x + 1):
    2. 5(2a − 3) − 4(a − 2):
    3. 4(m + 3) − 2(3m − 5):
    4. 2x(x + 3) − x(x − 1):
    5. 3(y² − 2y + 4) + y(y + 5):
    6. 6(k + 1) − 3(2k − 4) + k:

  5. Substitution and evaluation

    1. 4x + 7 when x = 3:
    2. 2a² − 5a + 1 when a = 4:
    3. 3(m − 2) + m when m = −1:
    4. 2p + 3q when p = 5, q = −2:
    5. 5(2n + 3) when n = −2:
    6. 2x(x + 4) when x = 3:

  6. Problem solving

    1. Rectangle perimeter:
    2. Square area:
    3. Who is correct:
    4. P = 2(l + w):

  7. Mixed skills rapid practice

    1. 5x + 3y − 2x + y [simplify]:
    2. 3(2a − 5) [expand]:
    3. 4b2 + 6b [factorise]:
    4. 2m(m + 4) − 3m [expand and simplify]:
    5. 10n2 − 15n [factorise]:
    6. −4(x + 3) + 2x [expand and simplify]:
    7. 9p − 3q + 2p + 5q [simplify]:
    8. 6(k2 − 2k + 1) [expand]:

  8. Choose the correct skill

    1. 4(x + 3) when x = 2:
    2. 6x2 + 9x:
    3. 5a + 3b − 2a + b:
    4. 3(2n − 1) − 2(n + 4):
    5. 12y − 8:
    6. 2x(x − 5) when x = −3:

  9. Match and verify (x = 3)

    1. 3(x + 4) + x:
    2. 2x + 8 − x + 1:
    3. 4(x − 1) − (x − 7):
    4. 2(3x − 2) − 4x:

  10. Extended real-world task

    1. Landscaper:
      1. Labour cost:
      2. Paving cost:
      3. Total cost:
      4. When n = 5:
    2. Fundraiser revenue:
    3. Rectangular prism:
      1. V = 2x(x + 3)(4):
      2. Expanded:
      3. When x = 2: