Year 11‎ > ‎Numbers‎ > ‎Graphs‎ > ‎

Algebra








 DAY

TOPIC ASSESSED 


REVISION 



18 SEPT 2014

AS91027 1.2 MCAT
Final exam
(4 CREDITS EXTERNAL) 


http://www.mathscentre.co.nz/html/blobLog.php?id=292903&name=&email=&attach=true


Lesson sequence

AS91027
 (4 CREDITS) 
  • No calculators are allowed.
 LEARNING OUTCOMES  WORK  RESOURCES

MCAT

INTRODUCING ALGEBRA

MULTIPLY AND DIVIDE INDICES

 
 
 
EX.6.01
EX.6.02



 INTRODUCE VOCABULARY VIDEO!


ADD ND SUBTRACT LIKE TERMS
PRIORITY OF OPERATIONS


EX.6.03
EX.6.04


SOLVING EQ'S FROM THE BASIC

SOLVE X+3=14,-X=18,ETC
SOLVE 2X+4=18,(X+1)/2=10,ETC
SOLVE EQUATIONS X BOTH SIDES
SOLVE EQ'S INVOLVING BRACKETS

 EX.7.01
EX.7.02
EX.7.03
EX.7.04


LINEAR GRAPHS RAP 
 
HOW MANY SOLUTIONS?

 EX.7.05

 
 
CHANGE THE SUBJECT OF AN EQUATION


 EX.7.06

 BRILLIANT ACTIVITY
 

SOLVE EQUATIONS INVOLVING FRACTIONS

 EX.7.07
EX.7.08
EX.7.09

 
 
SOLVE INEQUATIONS

EX.7.10
EX.7.11 

 INEQUATION 2X-6<10

GRAPH INEQUALITY (5MIN)

GRAPHING INEQUALITIES

 
EXPAND BRACKETS


EX.8.01
EX.8.02
EX.8.03
EX.8.04
EX.8.05
 
 
 
FACTORISE AN EXPRESSION
 EX.8.06
EX.8.07
EX.8.08
EX.8.09
 

FACTORISE A QUADRATIC WITH a NOT 1

FACTORISING (MIXED TYPE)

 EX.8.10

EX.8.11

 GENERAL TERM OF A QUADRATIC SEQ

 
SOLVE QUADRATICS FROM FACTORISED FORM

SOLVE QUADRATICS BY FACTORISING FIRST

SOLVE QUADRATICS BY REARRANGING FIRST AND THEN FACTORISING
 
EX.9.01

EX.9.02


EX.9.03


 WHY QUADRATICS?

  MOVED CONSTANT AND SOLVE

SOLVE QUADRATICS APP!

 
SOLVING QUADRATIC EQUATIONS IN CONTEXT
 
EX.9.04

 VOLUME OF A BOX

WORDS INTO EQUATIONS

 
SOLVING SIMPLE EXPONENTIAL EQUATIONS: UNKNOWN BASE

 SOLVING SIMPLE EXPONENTIAL EQUATIONS: UNKNOWN POWER
 
EX.9.0.5


EX.9.06
 

 

SIMULTANEOUS EQUATIONS: WHY? WHAT IS ALL THIS ABOUT?

 

  SIMULTANEOUS EQUATIONS BY ELIMINATION: ADDING

 

 


 SIMULTANEOUS EQUATIONS BY ELIMINATION: SUBTRACTING


 


 SIMULTANEOUS EQUATIONS BY ELIMINATION ADJUSTING COEFFICIENTS FIRST


 

EX.10.01

 

 

 EX.10.02




EX.10.03




EX.10.04


 WHAT DOES SOLVING A PAIR OF SIMULTANEOUS EQ'S MEAN?

 

 

SIMULTANEOUS BY ELIMINATION ADDING

SIMULTANEOUS BY ELIMINATION ADDING 2

 

 

SIMULTANEOUS BY ELIMINATION MINUS 3

 

 

 

SIMULTANEOUS BY ELIMINATION ADJUSTING4

 

 

SIMULTANEOUS EQS BY SUBSTITUTION

REVISION: SOLVING  SIMULTANEOUS EQS

 

EX.10.5

EX.10.6

 

 SIMULTANEOUS BY SUBSTITUTION

 
CANCEL, MULTIPLY AND DIVIDE ALGEBRAIC FRACTIONS

EX.11.01
EX.11.02
EX.11.03
 
 
CANCEL FRACTIONS BY FACTORISING EXPRESSIONS FIRST


 
EX.11.04
EX.11.05
 
 
ADDING ALGEBRAIC FRACTIONS WITH SAME DENOMINATOR

ADDING ALGEBRAIC FRACTIONS WITH DIFFERENT DENOMINATOR
 
EX.11.06


EX.11.07
 
 
REVISION
 

ALGEBRA PRACTICE 1
ALGEBRA PRACTICE 2
ALGEBRA REVISION 1
ALGEBRA REVISION 2


  • 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. 

Subpages (1): Bivariate
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