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MCATPACK - Achievement Criteria and Guidelines

Achievement Standard 91027

Subject Reference Mathematics and Statistics 1.2
Title Apply algebraic procedures in solving problems

Level 1  |   Credits  4  |  Assessment  External

What’s it all about?

This achievement standard is derived from Level 6 of The New Zealand Curriculum,

What’s inside the Assessment?

Achievement Criteria

• Apply algebraic procedures in solving problems.

Achievement with Merit
• Apply algebraic procedures, using relational thinking, in solving problems.

Achievement with Excellence
• Apply algebraic procedures, using extended abstract thinking, in solving problems.


  1. Apply algebraic procedures involves:
  • selecting and using procedures in solving problems
  • demonstrating knowledge of algebraic concepts and terms
  • ·communicating solutions using appropriate mathematical symbols.

Relational thinking involves one or more of:

  • selecting and carrying out a logical sequence of steps
  • connecting different concepts and representations
  • demonstrating understanding of concepts
  • forming and using a model;
    and also relating findings to a context, or communicating thinking using appropriate mathematical statements.

Extended abstract thinking involves one or more of:

  • devising a strategy to investigate or solve a problem
  • identifying relevant concepts in context
  • developing a chain of logical reasoning, or proof
  • forming a generalisation;
    and also using correct mathematical statements, or communicating mathematical insight.

2 . Problems are situations that provide opportunities to apply knowledge or understanding of mathematical concepts and procedures and methods.  The situation will be set in a real-life or mathematical context.

3. Students need to be familiar with procedures related to:
  • factorising
  • expanding
  • simplifying algebraic expressions involving exponents, such as or 
  • substituting values into formulae
  • manipulating and simplifying expressions such as or 
  • rearranging formulae such as  or  
  • solving linear equations or inequations such as 5x + 12 = 3 - 2x  or 3(x - 2) < 7
  • solving quadratic equations such as (8x + 3)(x - 6) = 0, x2 + 5x – 6 = 0, 3x2 =10x -8 (completing the square and the quadratic formula are not required)
  • solving simple equations involving exponents such as x3 = 8, 5x=125
  • solving pairs of simultaneous linear equations with two unknowns.
Can Impact help?

We can help!  We have 3 Collections specifically designed to reduce any anxiety you may feel OR extend your knowledge to the level you want to achieve.

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Algebra without Anxiety – MCAT 1- Achievement level

  • Finding substitution solutions
  • What is a formula?, Changing the subject
  • Solving quadratic equations
  • Simplifying fractions formed by quadratic expressions
  • How to solve linear and quadratic inequations


Algebra without Anxiety – MCAT 1- Merit and Excellence level

  • Solving equations where the variable is an exponent
  • Finding area and perimeter when dimensions are algebraic expressions
  • Solve similtaneous equations using the substitution method
  • Intersections of non-straight lines, Complicated or unorthodox problems
  • Unearthing the equations and expressions from word problems


Algebra without Anxiety – Brackets

  • One bracket expansions
  • Factorising with a common factor
  • Expanding 2 brackets, FOIL
  • Factorising quadratics
  • Factorising advanced quadratics


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