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### Algebra

 DAY TOPIC ASSESSED REVISION 18 SEPT 2014 AS91027 1.2 MCATFinal exam(4 CREDITS EXTERNAL)

Lesson sequence

AS91027
(4 CREDITS)
• No calculators are allowed.

• This achievement standard involves applying algebraic procedures in solving problems.
• This achievement standard is derived from Level 6 of The New Zealand Curriculum,Learning Media, Ministry of Education, 2007, and is related to the material in the Teaching and Learning Guide for Mathematics and Statistics, Ministry of Education, 2010 at http://seniorsecondary.tki.org.nz.
• The following achievement objectives taken from the Equations and Expressions, and Patterns and Relationships threads of the Mathematics and Statistics learning area are related to this standard:
• generalise the properties of operations with fractional numbers and integers
• generalise the properties of operations with rational numbers including the
properties of exponents
• form and solve linear equations and inequations, quadratic and simple
exponential equations, and simultaneous equations with two unknowns.

•  Apply algebraic procedures involves:
• selecting and using a range of 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.

• 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.
• The phrase ‘a range of procedures’ indicates that evidence of the application of at least three different procedures is required.

• Students need to be familiar with procedures related to:
• factorising
• expanding
• simplifying algebraic expressions involving exponents
• substituting values into formulae
• manipulating and simplifying expressions such as
• rearranging formulae such as  E =m c2
• 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, x
• solving simple equations involving exponents such as x
• solving pairs of simultaneous linear equations with two unknowns.

• Electronic technology is not permitted in the assessment of this achievement standard.
• Assessment Specifications for this achievement standard can be accessed through the Mathematics and Statistics Resources page found at http://www.nzqa.govt.nz/qualifications-standards/qualifications/ncea/ncea-subjectresources/.Number  AS91027
______________________________________________________________________

AS91029 (3 CREDITS) INTERNAL

LEARNING OUTCOMES WORK RESOURCES

USING LINEAR EQ'S TO SOLVE PROBLEMS
APPLICATIONS OF SIMPLE EQ'S
APPLICATIONS OF FRACTIONAL EQ'S

EX.16.01
EX.16.02
EX.16.03

APPLICATIONS OF REARRANGING FORMULAE

EX.16.04

APPLICATIONS OF SIMULTANEOUS EQ'S

EX.16.07
EX.16.08

APPLICATIONS OF STRAIGHT LINE GRAPHS

EX.17.01

Video: application of linear functions in real life (10 min)

REVISION

• TAXI PROBLEM

EXAMPLES OF ACHIEVE,MERIT AND EXCELLENCE

• Apply linear algebra in solving problems
• Level  1  Credits  3  Assessment  Internal

•  The following achievement objectives taken from the Equations and Expressions, and Patterns and Relationships threads of the Mathematics and Statistics learning area are related to this standard:
• form and solve linear equations
• solve linear equations and inequations and simultaneous equations with two
unknowns
• relate graphs, tables, and equations to linear relationships
• relate rate of change to the gradient of a graph.
• Apply linear algebra involves:
• selecting and using a range of methods in solving problems
• demonstrating knowledge of algebraic concepts and terms
• communicating solutions which would usually require only one or two steps.
• 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:
• demonstrating understanding of abstract concepts
• developing a chain of logical reasoning, or proof
• forming a generalisation;
and also using correct mathematical statements, or communicating mathematical
insight.

• Problems are situations that provide opportunities to apply knowledge or understanding of mathematical concepts and methods.  The situation will be set in a real-life context.
• The phrase ‘a range of methods’ indicates that evidence of the application of at least three different methods is required.
• Students need to be familiar with methods related to:
• using formulae
• forming, graphing or manipulating linear models such as
when solving problems
• comparing the rate of change to the gradient of a graph
• using simultaneous equations, inequations, or graphs when solving problems
such as those involving simple linear programming.

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