90284 Manipulate algeraic expressions and solve equations - NZQA

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90284 Manipulate algeraic expressions and solve equations - NZQA

Number Version Page 1 of 3 AS90284 3

    Achievement Standard

Subject Reference Mathematics 2.1

    Title Manipulate algebraic expressions and solve equations Level Credits Assessment 2 4 External Subfield Mathematics

    Domain Algebra

    Status Status date Expiring 17 November 2011 This achievement standard is expiring. Assessment against the standard must take

    place before the expiry date set out below.

    Expiry date Date version published 31 December 2011 17 November 2011

This achievement standard requires the manipulation of algebraic expressions and the

    solution of equations.

Achievement Criteria

    Achievement Criteria Explanatory Notes

     Manipulate algebraic Assessment of manipulation will be based on a

    expressions. selection from:

     expanding brackets up to 3 factors

     factorising expressions including quadratics

     using fractional and negative indices

     using elementary properties of logarithms

     simplifying rational expressions.

     Solve equations. Assessment of solving equations will be based on a

    selection from:

     multi-step linear equations or inequations

    3(2x5)5x;7eg Achievement

     quadratics that can be factorised 22x11x21eg

     simple logarithmic equations

    x325eg log252,x

     forming and solving linear/linear simultaneous


     New Zealand Qualifications Authority 2013

Number Version Page 2 of 3 AS90284 3

    Achievement Criteria Explanatory Notes

     Solve problems Assessment will be based on a selection from:

    involving equations. quadratics requiring the use of the quadratic


     linear/non-linear simultaneous equations 4x-5 exponential eg 13 = 6.

     Non-linear equations may be given as appropriate to

    the complexity of the problem. Achievement

     Students will be expected to solve problems in with Merit


     Choose algebraic When solving a problem the student may be required

    techniques and to:

    strategies to solve interpret the solution

    problem(s). explore the nature of the roots of a quadratic

     complete a multi-step algebraic manipulation

     complete an algebraic proof. Achievement

    with Excellence

General Explanatory Notes

    1 This achievement standard is derived from Mathematics in the New Zealand

    Curriculum, Learning Media, Ministry of Education, 1992:

     achievement objectives p. 158

     suggested learning experiences p. 159

     sample assessment activities pp. 160-161

     mathematical processes p. 26.

    2 The use of the Factor/Remainder Theorem will not be assessed.

3 An algebraic proof will involve a multi-step manipulation of a given algebraic

    statement to generate another given expression.

    4 For this standard the problems may be set in a mathematical context.

Replacement Information

    This achievement standard, AS90806, AS90809, and unit standard 5246 have been

    replaced by AS91261 and AS91269.

     New Zealand Qualifications Authority 2013

Number Version Page 3 of 3 AS90284 3

Quality Assurance

    1 Providers and Industry Training Organisations must have been granted consent to

    assess by NZQA before they can register credits from assessment against

    achievement standards.

    2 Organisations with consent to assess and Industry Training Organisations assessing

    against achievement standards must engage with the moderation system that applies

    to those achievement standards.

    Consent and Moderation Requirements (CMR) reference 0226

     New Zealand Qualifications Authority 2013

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