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Assessment Report
Level 1 Mathematics and Statistics 2020
Standards 91028 91031 91037
Part A: Commentary
Both teachers and candidates should be fully aware of the concepts referred to within the relevant Mathematics Assessment Specifications: https://www.nzqa.govt.nz/ncea/subjects/assessmentspecifications/mathematicsl1/
Candidates need to be aware that question parts may follow on from each other and be linked. Therefore, a candidate should be actively looking for this connection and, if necessary, turning to earlier pages in the booklet.
Candidates who have a suitable graphical calculator, and know how to use it effectively, could be advantaged. However, it must be noted that students will always be expected to demonstrate a thorough understanding of the mathematical concepts, rather than directly transferring results from a graphing calculator. As good mathematical practice, candidates should show intermediate steps in a logical manner and clearly communicate what is being calculated. By giving only the answer, candidates are likely to lose the opportunity to provide sufficient evidence for the higher grades and to have the possibility of minor errors ignored. Generally, the lack of intermediate steps is not likely to provide sufficient evidence towards a grade higher than Achievement. Additionally, questions are always designed in a manner that ensures that the use of a graphical calculator is not essential.
Part B: Report on standards
91028: Investigate relationships between tables, equations and graphs
Candidates who were awarded Achievement commonly:
 understood and formed a straightline equation from a graph or word problem
 understood and formed an equation of a parabola from its graph
 could draw part of an exponential graph
 could draw a parabola graph
 could use algebraic substitution to present information
 were able to interpret and construct either tables or graphs to present information.
Candidates whose work was assessed as Not Achieved commonly:
 were unable to demonstrate sufficient knowledge relevant to tables, equations, graphs and their relationships
 could not choose the correct graph to represent the context provided in the question
 were not able to recognise and draw an exponential graph
 were not able to recognise and draw a parabola graph.
Candidates who were awarded Achievement with Merit commonly:
 were able to represent varying contexts with graphs and equations for two or more of quadratics, exponential, and linear functions
 could recognise and then draw an exponential equation, with sufficient accuracy, from a given equation
 could recognise and then produce the correct equation from a parabola graph in context
 could recognise the relationships between equations and graphs and then comment on some of their features
 could draw a straightline graph from a given situation
 understood more than one transformation of graphs and how this affects their equation
 were able to utilise equations in order to solve problems
 were able to interpret both linear and quadratic word problems, with respect to the relationships between tables, equations and graphs
 were confident with linking equations and tables to graphs.
Candidates who were awarded Achievement with Excellence commonly:
 were able to interpret the context of problems and relate this to tables, equations, and graphs
 could find the roots of a quadratic equation and interpret these in context
 understood the context of a problem that led to a parabola graph and interpret this
 were confident with recognising the relationships between all of equations, tables, and graphs in a variety of different contexts and make appropriate interpretations
 were able to find generalised equations necessary to solve word problems, using quadratic graphs and functions and make appropriate interpretations
 were able to find generalised equations necessary to solve word problems, using exponential graphs and functions and make appropriate interpretations
 were able to apply strong algebraic skills in the solving the graphical problems.
Standardspecific comments
Candidates should be familiar with all types of graph included in this Achievement Standard i.e. linear, quadratic, exponential, step, discrete and piecewise graphs. Knowledge of only linear graphs and / or only simple parabolas will generally not be sufficient for a candidate to gain success.
This standard looks at specifically the relationship between tables, equations, and graphs, so candidates need to be able to demonstrate knowledge of and interpret such relationships.
Candidates need to explain and justify their reasoning and show sufficient evidence to support their solutions, without relying on the graphical calculator.
Candidates need to be familiar with the relationship between the rate of change of a function and the gradient of its graph.
91031: Apply geometric reasoning in solving problems
Candidates who were assessed as Achievement commonly:
 were able to apply Pythagoras’ theorem
 were able to apply the trigonometric ratios in solving simple problems
 knew the basic geometrical angle rules to identify unknown angles but included the correct geometrical reasons at only one step
 were able to use the theory of similar triangles
 provided correct answer only to their solutions.
Candidates who were awarded Not Achieved commonly:
 could not use trigonometric ratios correctly
 could not use Pythagoras’ theorem correctly
 were not familiar with the various theorems of circle geometry
 were not familiar with the concept of similar triangles
 provided the correct answer without any supporting working or reasoning
 did not provide the appropriate and relevant geometric reasons
 made incorrect assumptions from the provided information and instructions, e.g. used Pythagoras’ Theorem or the trigonometric ratios in nonrightangled triangles
 lacked basic geometric angle property knowledge.
Candidates who were awarded Achievement with Merit commonly:
 were confident in using a variety of geometrical angle rules, with sufficiently clear and detailed justification, to calculate an unknown angle
 could apply Pythagoras’ Theorem to solve more complex problems
 could apply the trigonometric ratios to solve more complex problems
 solved problems that incorporated the knowledge and use of the properties of similar triangles
 were confident in using the circle geometry rules to solve a problem
 were able to make progress in solving problems necessitating knowledge and understanding of bearings
 made only partial progress in producing sufficient clarity and detail in the multiply steps necessary in completing a geometrical proof
 were able to link concepts to make significant progress in complex situations
 produced an incomplete chain of geometrical reasoning whilst solving the extended problems.
Candidates who were awarded Achievement with Excellence commonly:
 could solve complex problems necessitating the use of bearings and support this with clear use of geometric reasoning
 used clear mathematical language
 correctly used and linked both geometrical and trigonometrical reasoning to solve complex problems in context
 showed confidence, knowledge and understanding when working with circle geometry
 communicated their thinking and solutions clearly and logically, using clear mathematical language
 correctly used and justified geometrical reasoning in completing geometrical proofs.
Standardspecific comments
Very few students were proficient at attempting proof questions successfully.
Students who are able to use algebraic skills are advantaged in some questions.
Candidates need to be aware that every line of a geometric proof must be accompanied by an appropriate geometric reason in order to target the higher grades. Candidates need to ensure that their calculators are in the essential “degree mode” when answering any trigonometry questions.
91037: Demonstrate understanding of chance and data
Candidates who were assessed as Achievement commonly:
 were able to calculate probabilities
 were able to draw an appropriate line of best fit in a scatter graph
 were able to compare means within a set of data
 were able to recognise similarities and differences in data
 were able to provide one reason / justification / feature / claim from a scatter graph
 were able to provide one reason / justification / feature / trend from a time series graph
 were able to provide one reason / justification / feature / claim from a boxandwhisker graph.
Candidates who were awarded Not Achieved commonly:
 were not able to solve a probability problem providing incorrect denominators
 were unable to make appropriate statistical statements
 did not provide evidence or justification for their responses
 could not read and interpret features of different types of statistical graphs.
Candidates who were awarded Achievement with Merit commonly:
 were able to provide at least two valid reasons / justifications / features / claims from a scatter graph
 were able to provide at least two valid reasons / justifications / features / trends from a time series graph
 were able to provide at least two valid reasons / justifications / features / claims from a boxandwhisker graph
 were able to provide appropriate comments in relation to a trend live in a bivariate data problem
 were able to utilise appropriate rules to deduce a correct inference from a boxandwhisker graph
 supported their claims with appropriate statistical reasoning and relating these to the data provided in the question
 understood the differences, validity and appropriateness of the different types of statistical graphs and were able to provide appropriate statements
 were able to solve problems involving simple conditional probability
 were able to evaluate claims providing appropriate and valid evidence
 used correct and appropriate statistical language.
Candidates who were awarded Achievement with Excellence commonly:
 could provide at least three distinct, valid statistical reasons / justifications with evidence and with reference to the data and by referring to the appropriate graph
 demonstrated statistical understanding and insight
 were able to interpret confidently the context used in the question
 were able to communicate their thinking, ideas, interpretations and statistical knowledge clearly and succinctly, using correct statistical language and vocabulary, displaying abstract thinking in their understanding
 were able to critique the validity of claims made about a set of sample data with reference to data collection, sample size and sample frame
 were able to provide detailed and insightful comments in relation to a time series graph
 were able to construct relevant statistical comments in context
 were able to understand the sample and population relationship.
Standardspecific comments
Candidates generally had a good understanding of time series graphs and the interpretation of its features.
Candidates need to ensure that their comments are statistically based and justifications are made with reference to the graphs provided and data contained within them.
Candidates need to be much more specific about making the call in a boxandwhisker graph, with clear and detailed reference to the relative positions of the medians and the middle50% boxes. If a candidate is selecting a comparison using the DBM/OVS then sufficient detail of the figures and their interpretation needs to be provided.
Some candidates do not read and interpret the given information in the question carefully and consequently do not provide answers with the relevant detail or responses. These responses need to demonstrate statistical understanding and evidence.
Mathematics and Statistics subject page
Previous years' reports