Statistics
Year Number of candidates
Level of achievement
VHA HA SA LA VLA
2017 39 8 10 15 3 3
2016 22 4 5 6 5 2
2015 32 4 6 11 8 3
2014 30 4 7 9 6 4
2013 50 9 12 14 10 5
General comments
The Mathematics B Senior External Examination consisted of two papers. Both papers sampled subject matter and learning experiences across the full range of syllabus contexts.
Candidate responses across both papers generally addressed all three objectives of the assessment criteria and demonstrated a generally consistent standard.
Candidates who performed poorly in Knowledge and procedures (KP) tended to perform poorly in Modelling and problem solving (MP) as the knowledge to solve problems is implicit in MP. In preparing for the examinations, candidates must cover the full range of syllabus subject matter and they should attempt every question in both papers.
Characteristics of good responses
In high-scoring responses to questions assessing the KP criterion, candidates characteristically demonstrated:
• clear justification and working
• an effective use of diagrams
• the significant intermediate calculation steps
• algebraic facility
• effective use of technology.
Examples of these include correctly identifying or recalling a rule, formula or procedure; providing an effective diagram, or creating a list/table of information that may be used to solve problems;
and using technology to solve problems efficiently and/or to justify conclusions reached. High- performing candidates demonstrated a synthesis of procedures and strategies to solve problems;
Mathematics B
2017 Senior External Examination: Assessment report
demonstrated mathematical initiative and insight in exploring problems; and were able to identify, in context, mathematical strengths and limitations of models. The quality of candidate responses in both papers indicated that many candidates were well prepared for this examination.
In the Communication and justification (CJ) criterion, many candidates recognised the need to justify and validate their solutions. This was clearly evident in the responses that exhibited a developed argument, examined the effects of assumptions and correctly evaluated the validity of arguments.
Common weaknesses
In the KP criterion, candidates were required to demonstrate ‘accurate recall, selection and use of basic procedures’. Candidates who performed poorly did not demonstrate this requirement and, as a consequence, they were not able to show algebraic facility in developing solutions to problems in both KP and MP. A few candidates attempted to solve problems using technology even when algebraic methods were required. Candidates must know basic formulas and how they are used across the full range of subject matter.
Candidates are expected to cover all aspects of the syllabus subject matter in their preparation for these examinations. In both KP and MP, candidates should demonstrate an ability to use technology; manipulate index and logarithmic laws; be familiar with function notation; understand rules of calculus involving differentiation and integration; and be able to solve equations in a variety of simple contexts, including trigonometric contexts where simple substitution and equation-solving methods are required.
In the MP criterion, all contexts require careful reading, interpretation and planning to clarify a range of mathematical situations. This was not evident in responses provided by candidates who performed poorly. Candidates should use clearly labelled, neatly drawn diagrams to support arguments and conclusions reached.
In the CJ criterion, candidates who performed poorly did not generally exhibit:
• the accurate use of basic mathematical terms, symbols and language
• the identification and clarification of information to solve problems across a range of contexts
• the correct organisation of information into a variety of forms such as lists, diagrams and graphs
• mathematical reasoning to support simple logical arguments.
These issues were evident across topics and contexts in both papers.
Marker responses
The following solutions are not prescriptive model responses and are not necessarily the only way of solving a problem. Other approaches and problem-solving strategies may be just as acceptable.
