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CAS Mathematics 2.4 Demonstrate an understanding of straightforward mathematical processes

Achievement criteria

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

Achievement

• You need to demonstrate the ability to use straightforward mathematical processes.
• Assessment will involve a selection from:
• algebraic manipulation based on:
  • using fractional and negative indices
  • using elementary properties of logarithms
  • solution of quadratics that can be factorised using integers, eg 2x² - 11x = 21
  • solution of simple logarithmic equations, eg log_x25 = 2, 3^x = 81
• calculus skills such as finding derivatives and indefinite integrals of expressions given in expanded form with terms that have natural number exponents, eg 3x⁴ + 2x² - 5x + 2
• You need to demonstrate the ability to use mathematical processes.
• Assessment will involve a selection from:
• graphing skills, which may involve sketching of graphs or demonstrating an understanding of their features and includes:
• circles with centre at the origin
• exponential functions of the form y = a^x, a ∈ N
• logarithmic functions of the form y = log_ax, a ∈ N
• transformation of quadratics which may involve functional notation.

Achievement with Merit

• You need to reach Achievement.
• You need to demonstrate the ability to use mathematical processes.
• Assessment will be based on a selection from:
• algebraic manipulation that involves simplifying rational expressions
• graphing skills involving sketching of graphs, writing equations, and demonstrating an understanding of their features and will be based on:
• finding multiple solutions of a trig equation, given one solution
• rectangular hyperbolae of the form
• circles of the form (x - a)² + (y - b)² = r²
• exponential functions of the form y = a^x-b + c and either b or c = 0
• logarithmic functions of the form y = log_a(x - b) + c, a ∈ N and either b or c = 0.
• expressions which are more complex to manipulate, eg y = (x + 2)(x - 4) in relation to calculus methods.
• You use mathematical skills to solve problems and may be required to:
• interpret the solution, which may involve a context from calculus
• formulate a proof that could include:
• demonstrating an understanding of roots of quadratic equations
• multi-step algebraic manipulation
• write the equation of a graph involving more than one equation, or piecewise function, in describing a situation.  This could include exponential and logarithmic functions where both b and c may have non-zero values.

Achievement with Excellence

• You need to reach Achievement with Merit.
• You need to demonstrate the ability to use mathematical skills to solve problems.
• When solving a problem you may be required to:
• interpret the solution, which may involve a context from calculus
• formulate a proof that could include:
• demonstrating an understanding of roots of quadratic equations
• multi-step algebraic manipulation
• write the equation of a graph involving more than one equation, or piecewise function, in describing a situation. This could include exponential and logarithmic functions where both b and c may have non-zero values.

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