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• NCEA on TKI
• NZQA website

Mathematics 2.1 Manipulate algebraic expressions and solve equations

Achievement criteria

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

Achievement

• Assessment of manipulation will be based on a selection from:
  
  • expanding brackets up to three factors
  • factorising algebraic expressions including quadratics
  • using fractional and negative indices
  • changing the subject of the formula (as part of solving a problem)
  • using elementary properties of logarithms
  • simplifying rational expressions.
• Assessment of solving equations will be based on a selection from:
  
  • multi-step linear equations or inequations
    e.g. 3(2x - 5) = 5x + 7
  • quadratics that can be factorised
    e.g. 2x² - 11x = 21
  • polynomials in factorised form (assumed from level 1)
    e.g. 3x²(x - 7)(2x + 5) = 0
  • simple logarithmic and exponential equations
    e.g. log_x25 = 2, 3^x = 25
  • forming and solving linear/linear simultaneous equations.

Achievement with Merit

• You need to:
  
  • gain Achievement
  • solve problems involving equations.
• Assessment will be based on a selection from:
  
  • quadratics requiring the use of the quadratic formula
  • linear/non-linear simultaneous equations
  • exponential
    e.g. 13^4x-5 = 6.
• Non-linear equations may be given as appropriate to the difficulty of the problem.
• You will be expected to solve problems in context. See Solving Word Problems on this page.

Achievement with Excellence

• You need to gain Achievement with Merit.
• Choose algebraic techniques and strategies to solve problems. See Solving Word Problems on this page.
• When solving problems, you may be required to:
  • interpret the solution (see Solving Word Problems on this page)
  • explore the nature of the roots of a quadratic
  • complete a multi-step algebraic manipulation
  • complete an algebraic proof which involves a multi-step manipulation of a given algebraic statement to generate another given expression
  • solve problems set in a mathematical context.

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