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Mathematical Requirements (Appendix C)

Rearranging and solving equations

  • 3 things to know
  • All units

Overview

Recall questions on Rearranging equations and solving equations.

What you need to know

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Key term

List all eight mathematical symbols commonly used in physics that you should recognise.

Key term

How do you eliminate a square root when rearranging an equation?

Key term

Describe the general method for solving a linear kinematic equation like v = u + at for an unknown quantity.

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    How do you eliminate a square root when rearranging an equation?

    Model answer

    Square both sides of the equation to eliminate the root.

  2. 2

    Describe the general method for solving a linear kinematic equation like v = u + at for an unknown quantity.

    Model answer

    Substitute the known values into the equation and rearrange to isolate and find the unknown quantity.

  3. 3

    State the quadratic formula used to solve equations of the form ax² + bx + c = 0.

    Model answer

    x = (−b ± √(b² − 4ac)) / 2a.

  4. 4

    Why might solving the kinematic equation s = ut + ½at² for time require the quadratic formula?

    Model answer

    Because when solving for time, the equation becomes quadratic in t (containing t² and t terms), requiring the quadratic formula.

  5. 5

    When a quadratic equation gives two solutions, how do you determine which is physically valid?

    Model answer

    Physical context determines validity; typically negative time values are rejected as unphysical.

  6. 6

    Define the natural logarithm ln(x).

    Model answer

    The natural logarithm ln(x) gives the power to which e must be raised to equal x, where e ≈ 2.718.

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