Practice Maths

Mathematical Modelling — Solutions

Click any answer to watch the solution video.

  1. Mobile phone plan

    1. Equation:
    2. Assumption:
    3. Cost at 250 min:
    4. Minutes for $39:
    5. Graph:

  2. Linear vs non-linear

    1. Constant speed:
    2. Bacteria doubling:
    3. Constant drain rate:
    4. Area of square:
    5. Flat rate per item:

  3. Ball height model

    1. Initial height:
    2. h(1) and h(3):
    3. Linear or non-linear?:
    4. Negative t² coefficient:
    5. Assumption:

  4. Tuck shop profit model

    1. Revenue:
    2. Profit:
    3. Break-even:
    4. Daily profit at 60 pies:
    5. Assumptions/limitations:

  5. Rectangular paddock

    1. Expressions:
    2. Show A = 120x − 2x²:
    3. Table:
    4. Maximum area:
    5. Assumption and limitation:

  6. Petrol cost model

    1. Formula:
    2. Cost for 350 km:
    3. Max distance on $50:
    4. Saving after service:
    5. Assumption and ignored factor:

  7. Rumour model evaluation

    1. N at Day 0:
    2. When N = 50:
    3. Shortcoming of linear model:
    4. Better model type:
    5. Assumption:

  8. Swimming pool drain and refill

    1. Volume during draining:
    2. Time to drain:
    3. Volume during refilling:
    4. Time to refill and finish time:
    5. Total cost:

  9. Hire car comparison

    1. Cost equations:
    2. Equal cost:
    3. At 150 km:
    4. At 300 km:
    5. Gradient and intercept:

  10. Maximum area garden

    1. Length in terms of w:
    2. Area function:
    3. Expanded:
    4. Table of values:
    5. Shape at maximum:
    6. Max area and perimeter check: