Resources for Mathematics

Clarification of Unit Standards in Mathematics

Level 2

The following notes provide clarification of the assessment requirements for the commonly used level 2 unit standards.

US5244 Version 4 Demonstrate calculus skills

Calculators are not allowed.

Element one

• Sketching the gradient function is required. Matching graphs with their gradient function is not acceptable. Turning points of function should match x intercepts of gradient function.

Element two

• A polynomial does not include terms with fractional or negative powers.

Element three

• The constant of integration must be given at least once.

US5245 Version 4 Solve coordinate geometry problems

• Students need to select the method for solving each problem.
• Students should solve simultaneous equations to find the point of intersection of two lines but with the use of technology, the correct answer only without any working is sufficient.

US5246 Version 4 Manipulate algebraic expressions and use algebraic methods to solve problems

This standard is assessing Achievement Objectives from level 7 of MINZC so the questions need to reflect this.

Element one

• Expanding needs to be more complex than multiplying two brackets.
• Factorising needs to be more complex than . Expressions need to be fully factorised.
• If factorising and expanding is an aspect of providing evidence for this standard, the student must demonstrate both expanding and factorising (three of each is a good guideline with two required correct for each).
• Algebraic fractions could include multiplication, division, addition/subtraction of fractions, simplifying by factorising etc.
• Exponents must be of algebraic expressions, not for example .

Element two

• It is expected that equations will be given to represent the situation. Students are expected to choose the method for solving the problem.
• Solution of quadratics may require the use of the quadratic formula.
• Graphical solution to simultaneous equations is not acceptable.
• Solutions need to be interpreted in context.
• Cubics do not need to be in context.

US5248 Version 3 Use sequences and series to solve problems

• Formulae sheet should be given.
• Students need to recognise type of sequence involved in each problem.
• Students must solve problems involving both .

US5249 Version 3 Use networks to find optimal solutions to problems in geometry

• Students need to select the method for solving each problem so therefore an instruction like, "Use a minimum spanning tree to find ?" is unacceptable.
• For project management the network must be constructed from a table or list of information and have multiple pathways so students must make decisions.

US5250 Version 4 Use probability techniques to solve problems

Element one

• Students must design the simulation, describe it fully and then use the simulation to solve problems.

Element two

• Students need to solve a range of questions for normal distribution. This needs to include questions that involve the use of more than one z score.
• Inverse normal problems are not required.

US5251 Version 4 Choose and apply trigonometric methods to solve problems involving lengths and angles

• Diagrams may be included but should not show all the details and information.
• The formulae for the sine and cosine rules and area of a triangle should be given.

US5253 Version 3 Sketch and describe graphs

This standard steps up from US5238 Draw and describe graphs involving two variables (level 1). Therefore the graphs for this standard need to reflect the higher level expectation.

Element one

• Quadratics will involve multiple transformations.
• Circles should not be centred on (0,0) and must be in completed square form.
• Rectangular hyperbola may have one asymptote that is the x or y axis.
• Cubics should be in factored or transformed form.
• Trig graphs must involve at least one transformation.

Element two

• The type of feature and the detail about the feature needs to be identified by the student.
• The features must be described, not simply matched.

US5260 Version 4 Find and use derivatives to solve problems involving rate of change

• The derivative needs to be shown.

US12323 Version 3 Apply mathematics in the design of an object or process for a given purpose

• Students are to choose the mathematics needed.
• Students must use mathematics from levels 6 and 7 of MINZC in the design.
• Shapes must be more complex than a cuboid or cylinder.
• The mathematical processes involved are expected to be above NCEA level 1.

US12331 Version 3 Investigate and report on the mathematics of a given project

• The standard refers to level 7 of the curriculum; however the number and measurement strands stop at level 6. The project must draw together aspects from both the number and measurement strands and involve a connected sequence of calculations. The mathematical processes involved are expected to be above NCEA level 1.
• The investigation must consider alternatives and the conclusions in the report must give reasons for choices with reference to the appropriate mathematics.

US12332 Version 3 Demonstrate knowledge of measures and displays used to compare data sets

• The student must be able to select appropriate displays and know the appropriate measures to calculate when making comparisons.
• Comments must be backed up by reference to displays or measures.
• Comments must be in context.
• IQR and standard deviation or variance are the acceptable measures of spread.
• Students should be encouraged to make a holistic comment to compare the two data sets and use the graphs and measures to support that comment rather than making a separate comment for each graph.

US12333 Version 3 Demonstrate understanding of, and use, questionnaire design

Element one

• The student should demonstrate the ability to distinguish between inappropriate and appropriate questions, explain rationale and suggest modifications where necessary.
• This element could be assessed by asking a series of relevant questions. For example, "List the kind of things you need to consider when deciding what questions you will include in your questionnaire"; "list the kind of things you need to consider when you construct your actual questions etc."

Element two

• Students must design and trial a questionnaire.
• The report must show at least three statements about the strengths/weaknesses and/or modifications which would improve the questionnaire.

Last updated: 12 May 2009