Practice Maths

Mixed Problem Solving — Solutions

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  1. Compound interest and simple interest

    1. Simple interest:
    2. Compound interest:
    3. Difference:
    4. Years for $6 000 simple interest:

  2. Rectangular pool dimensions

    1. Length expression:
    2. Equation and solution:
    3. Area:
    4. Tiling cost:
    5. Volume in kL:

  3. Ladder and wall

    1. Height:
    2. Angle with ground:
    3. Safety check:
    4. Base at 75°:
    5. Height at 75°:

  4. School fete tickets

    1. Equations:
    2. Solution:
    3. Target check:
    4. Child ticket at $4:

  5. Maths test statistics

    1. Class means:
    2. Medians:
    3. Ranges:
    4. More consistent:
    5. New mean for Class A:

  6. Shed surface area

    1. Triangular cross-section area:
    2. Slant height:
    3. Two triangular end walls:
    4. Two roof panels:
    5. Wall area (4 rectangular walls, height 0 at triangle — use only the vertical walls):
    6. Roofing cost:

  7. Surds and index laws

    1. √(3x²):
    2. Solve 2x² = 72:
    3. Square side and perimeter:
    4. Index law:
    5. Simplify (2a³b)²÷(4a²b):

  8. Football probability and statistics

    1. P(win):
    2. P(not losing):
    3. Predicted wins in 30:
    4. Mean 2.3, range 6:
    5. This season mean:

  9. Income and budgeting

    1. Tax per fortnight:
    2. After-tax income:
    3. Rent:
    4. Savings per fortnight:
    5. Remaining:

  10. Angles of elevation and depression

    1. Diagram:
    2. Distance to Boat A:
    3. Distance to Boat B:
    4. Distance between boats:
    5. Angle to third boat at 200 m: