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CAS Mathematics 2.1 Demonstrate an understanding of mathematical relationships

Achievement criteria

The level of achievement that you reach is decided by the questions that you answer correctly.

Achievement

• You need to demonstrate an understanding of mathematical relationships which may be given in graphical, algebraic or numerical forms.
• Assessment will be based on a selection from:
  • forming and solving linear/linear simultaneous equations and interpreting results
  • solving:
  • linear/non-linear simultaneous equations and interpreting results including circles, polynomials, log and exponential graphs
  • trigonometric equations which could be in degrees or radians, and would probably include the use of trigonometric graphs such as:
    2sin (x) = 0.2, 0° ≤ x ≤ 360°
    sin (x) + 3 = 3.5, 0 ≤ x ≤ 2π
• Assessment will involve the use of:
  • quadratics and other polynomials
  • rectangular hyperbolae of the form y = where a, b ∈ I, b ≠ 0
  • exponential functions in the form y = a^x, a ∈ N
  • features of graphs.

Achievement with Merit

• You need to reach Achievement.
• You need to demonstrate an understanding of mathematical relationships in multi-step situations.
• Assessment will be based on situations selected from:
  • quadratic formula
  • features of graphs
  • polynomial, exponential, logarithmic or trigonometric relationships with multiple transformations:
    13^{(4x - 5)} = 6
    4sin (2x) = 0.8, 0° ≤ x ≤ 360°
    sin(x – 90°) = 0.3, -180° ≤ x ≤ 180°
    3 + 2sin(5x) = 2, 0 ≤ x ≤ 2π
    
• You will be expected to solve problems in contexts such as:
  • radioactive decay
  • % increase/decrease, such as compound interest
  • results of an experiment
  • using log equations to find n in geometric sequences.

Achievement with Excellence

• You need to reach Achievement with Merit.
• You need to demonstrate understanding of mathematical relationships in more complex situations.
• Situations could include:
  • long-term effects
  • sequences
  • modelling by different relationships over a domain
  • interpreting the solution
  • exploring the nature of the roots of a quadratic
  • forming/completing trigonometric relationships from a given model
  • complex manipulations of trigonometric equations.
• The use of sequences may involve relating the algebraic representation to the graphical representation for situations involving sums to infinity, and the relevance of asymptotes and discontinuities.

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