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
Achievement
• 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.
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- 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.
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- Finding substitution solutions
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- Solving quadratic equations
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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
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- 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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