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Assessment Report
Level 1 Mathematics and Statistics 2017
Standards 91028 91031 91037
Part A: Commentary
It is important that teachers and students are fully aware of the content of the examination specifications e.g. the expectation that they will know the formula for the area of basic geometric shapes which was required for the triangle in Achievement Standard 91028.
Students without a graphics calculator were disadvantaged, especially in Achievement Standard 91028
Part B: Report on standards
91028: Investigate relationships between tables, equations and graphs
Candidates who were awarded Achievement commonly:
 performed simple calculations from values that had been read off a graph
 understood and could find the features of graphs such as intercepts, gradients, rate of change and vertex
 used information given:
  in the context of the question
  on tables/ graphs to find solutions and interpreted these points
 found the equation of a given graph
 investigated the relationship between the side length of a triangle and area of a triangle
 understood and correctly interpreted problems given in context
 substituted into an equation
 could draw a graph by plotting points
 recognised and explained basic features of a graph.
Candidates who were assessed as Not Achieved commonly:
 did not attempt sufficient questions
 could not interpret the question
 did not have the confidence to choose whether to begin with a graph, table or equation in order to start the question
 could not relate features of graphs to the given equation
 could not generate aspects of a linear equation from a given contextual (graph) model
 could not calculate the area of a triangle
 did not know how to conduct an investigation, via a table of results
 could not correctly or consistently substitute into an exponential equation
 could not perform basic algebra
 made calculation errors when substituting into equations
 could not plot points accurately
 could not set up appropriate axes and draw basic graphs.
Candidates who were awarded Achievement with Merit commonly:
 formed equations
 sketched graphs
 transformed graphs and gave the resulting equation
 compared models.
Candidates who were awarded Achievement with Excellence commonly:
 reflected and translated graphs including reflecting in the yaxis
 gave the equation of a transformed graph
 used inequality statements
 applied a range of algebra and graphical skills to the context
 linked tables and graphs to their equations to solve problems
 found equations in the investigations by using a table and/or graph
 accurately and clearly explained their mathematical thinking
 gave the equation for a parabola when the equation required the use of negative, noninteger coefficients
 had rigorous algebraic understanding.
Standard specific comments
Q2(iv) there were at least three Level 1 ways to solve the swing question modelled by a parabola  substitution, create a table and improve results, graphics calculator in equations mode or graphical intersections mode, transformational operations tended to miss these when the candidates had some knowledge of the Level 2 Quadratic Formula.
Candidates should use a ruler for the drawing of axes and straightline graphs.
Axes and points must be clearly labelled.
Key points on the graph should be clearly marked and labelled.
91031: Apply geometric reasoning in solving problems
Candidates who were awarded Achievement commonly:
 attempted most parts of all three questions
 annotated the diagrams – this often helped clarify the intention behind their response written in the answer space provided
 correctly solved at least two twostep angle problems, often supporting their steps with at least one appropriately stated geometric reason in each case OR correctly used trigonometry to solve at least two problems, attempting to show their step(s) in each case
 found angles and lengths associated with rightangled triangles, parallel lines, simple polygons, and simple circle geometry situations.
Candidates who were assessed as Not Achieved commonly:
 did not use a calculator in trigonometry and Pythagoras questions
 had little, if any, knowledge of relevant geometric reasons and how to communicate them
 were unable to use trigonometry and Pythagoras methods appropriately.
 made little progress with the any questions that involved variables.
Candidates who were awarded Achievement with Merit commonly:
 attempted all parts of all three questions
 correctly solved at least two 2step angle problems, supporting their steps with at least one appropriately stated geometric reason in each case AND correctly used trigonometry to solve at least two problems, showing their step(s) appropriately in each case
 made significant progress with the questions that involved variables
 frequently provided a chain of geometric reasoning, often with sufficient evidence for “t” (excellence) in at least one part of one question.
Candidates who were awarded Achievement with Excellence commonly:
 attempted all parts of all three questions
 correctly solved multistep angle problems, supporting almost all their steps with appropriately stated geometric reasons
 correctly used trigonometry to solve problems, showing their step(s) appropriately often with extra comments about the processes being used
 solved problems that involved variables
 showed confidence and understanding when working with circle geometry.
Standard specific comments
Most successful candidates, increasingly so the higher the level of achievement, stated their geometric reason/justification AT THE SAME TIME as they presented a mathematical statement (equation).
Some candidates stated the words: “Alternate Segment Theorem” as a proof. They did not show or explain any geometric steps in their proof of the problem. They bypassed the opportunity to show evidence for abstract thinking for excellence (a “logical chain of reasoning”). Such responses only gained “u” (achieved). Some candidates had clearly been exposed to this theorem, even though it (and the rote learning and quoting of any such theorem) has not been a part of the NZ Curriculum for a great many years.
To provide evidence of a proof sufficient a candidate was required to demonstrate a sequence of steps with justification.
The use of variables was signalled in Level 1 Specifications and was wellhandled by most candidates. Some candidates substituted a value for the variable in order to proceed with a problem – they still achieved, but at a lower level than those who could operate “in general” – an important component at excellence.
91037: Demonstate understanding of chance and data
Candidates who were awarded Achievement commonly:
 were able to read a graph and answer a straightforward question.
 understood features of a graph
 calculated simple probabilities.
Candidates who were assessed as Not Achieved commonly:
 were unable to read graphs correctly
 struggled with the context of the question and misinterpreted it
 did not understand simple probability
 gave nonstatistical answers but in a realworld situation were relevant. Eg. “Better to buy a more expensive car because it will be a better car”. “Males are more reckless drivers than females”, “The vehicle with zero carbon dioxide emissions must have been electric”.
Candidates who were awarded Achievement with Merit commonly:
 answered questions in context
 justifed their answers numerically
 compared graphs
 understood the concept of a question.
Candidates who were awarded Achievement with Excellence commonly:
 made precise statements with justification.
 were able to explain more than one feature of a graph
 showed insight into the reallife contexts and were able to bring understanding to their answers.
Standard specific comments
Unfamiliar realworld contexts proved challenging for some students at all levels of achievement.
Many candidates were able to make quite insightful answers about the context but were unable to make valid statistical statements.
Mathematics and Statistics subject page
Previous years' reports
2016 (PDF, 244KB)