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• NCEA on TKI
• NZQA website

Mathematics 2.2 Draw straightforward non-linear graphs

Achievement criteria

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

Achievement

• Assessment of drawing graphs will be based on a selection from:
  
  • quadratics that can be factorised or put in the form y = ±(x – a)² + b (coefficient of x² = ±1)
  • factorised polynomials (coefficient of xⁿ = ±1)
  • rectangular hyperbolae of the form y = where a and b are integers, b 0
  • circles with centre at the origin
  • exponential functions of the form y
  • logarithmic functions of the form y = log_ax, aN
• Equations will be given for the graphs to be drawn.
• You need to show correct use of relevant features which could include intercepts, symmetry, maxima and minima (for quadratics), or asymptotes.

Achievement with Merit

• You need to gain Achievement.
• Assessment of drawing graphs and identifying features will be based on a selection from:
  
  • rectangular hyperbolae of the form y = + b
  • circles of the form (x – a)² + (y – b)² = r²
  • any factorised or exponential functions of the form y = a^x-b + c and either b or c equal to zero
  • logarithmic functions in the form y = log_a(x – b) +c, aN and either b or c = 0
• You use non-linear graphs to solve problems which will include:
  - writing equations selected from the following types of graphs:
  • any graphs listed for achievement
  • hyperbola as listed above for merit, where b or c = 0
  • circle as listed above for merit
  - interpreting features.

Achievement with Excellence

• You need to gain Achievement with Merit.
• You determine and apply an appropriate model for a situation involving graphs.
• You write an equation (or equations for a piecewise function) to describe a situation.
• The application of a model could include:
  • a situation requiring finding points of intersection
  • using equations of graphs to solve problems.
• Polynomials may have coefficients of xⁿ other than ±1, and for exponential and logarithmic functions both b and c may have non-zero values.

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