Achievement objective NA65
In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:
 form and solve linear equations and inequations, quadratic and simple exponential equations, and simultaneous equations with two unknowns.
Indicators
 Solves problems that can be modelled by:
 linear equations and inequations and interprets solutions in context
 quadratic equations (where neither a nor c are equal to 1) and interprets solutions in context
 simple exponential equations (of the form a^f(x)=b where f(x) is a linear function and is a positive integer) and interprets solutions in context.
 Uses algebraic manipulation skills to simplify expressions, including rational expressions involving terms with positive integer exponents, for example: 25.5^(x+3).
 Uses algebra and graphing for solving linear equations and inequations.
 Uses factorising, graphical relationships and knowledge of parabolas for solving quadratic equations and inequations.
 Uses number knowledge (not logarithms) for solving exponential equations.
 Solves problems algebraically that can be modelled by: simultaneous equations where the equations are linear–linear, and interprets solutions in context.
 Uses graphing and algebra for solving simultaneous equations.
 Makes links with manipulation
NA66 and graphs and tables
NA67.
 See
key mathematical ideas on NZmaths.
Progression
NA 65 links to
M77,
M78,
M84.
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Possible context elaborations
 Express a taxi charge as a linear equation (flag fall and per kilometre rate) and find the distance for a given cost.
 Express the exponential relationship between the number of repeated folds (in thirds) of a paper strip and the number of sections formed. Find the number of folds needed for 81 sections.
 Students should be able to form equations from tables of values, using differences between terms, constant first order differences for linear relations, constant second order differences for quadratic relations, and constant ratio for
simple exponentials.
 Simplify rational expressions, for example, 9n4/6n3.
 Students should apply their manipulation skills to solve equations by applying inverse operations with an appreciation of equality and connect their solutions to corresponding situations of inequality (care needs to be taken when manipulating inequalities especially with negative numbers).
 Solve 3x = 81 by recognising 34 = 81 so x = 4.
 Pairs of simultaneous equations may be solved by substitution, elimination, and by intercept of graphs.

Activity: Forensic formulas
Assessment for qualifications
NCEA achievement standards at level 1, 2 and 3 have been aligned to the New Zealand Curriculum. Please ensure that you are using the correct version of the standards by going to the
NZQA website.
The following achievement standard(s) could assess learning outcomes from this AO:
Last updated April 9, 2021
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