Mathematics B 2018 Senior External Examination

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Statistics

Year Number of

candidates Level of achievement

VHA HA SA LA VLA

2018 45 9 14 14 4 4

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

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, demonstrated a generally consistent standard, and indicated that many candidates were well prepared for this examination. Candidates who performed at a low level in Knowledge and procedures (KP) tended to perform at a low level in Modelling and problem solving (MP) as the knowledge to solve problems is implicit in MP. Candidates needed to cover the full range of syllabus subject matter when preparing for the examination and attempt every question in both papers.

Knowledge and procedures

High-level candidate responses to questions assessing the KP criterion demonstrated:

• clear justification and working

• effective use of diagrams

• significant intermediate calculation steps

• algebraic facility

• effective use of technology.

Examples included correctly identifying or recalling a rule, formula or procedure; providing an effective diagram; creating a list/table of information to solve problems; and making efficient use of technology to solve problems and justify conclusions.

Mathematics B

2018 Senior External Examination: Assessment report

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Mathematics B

2018 Senior External Examination: Assessment report Queensland Curriculum & Assessment Authority March 2019 Page 2 of 29

High-level candidate responses also synthesised procedures and strategies to solve problems;

demonstrated mathematical initiative and insight in exploring problems; and identified, in context, mathematical strengths and limitations of models.

In the KP criterion, candidates were required to demonstrate ‘accurate recall, selection and use of basic procedures’. Low-level candidate responses did not show algebraic facility in developing solutions to problems and a number of candidates attempted to solve problems using technology even when algebraic methods were required.

Candidate responses needed to demonstrate:

• knowledge of basic formulas, including those involving volume and surface area of prisms and pyramids, so problems could be solved across the full range of subject matter. (This requirement implies that all aspects of the syllabus are covered)

• the use of clearly labelled, neatly drawn diagrams to support arguments and conclusions reached

• the ability to use technology where required

• the ability to manipulate index and logarithmic laws

• familiarity with function notation and rules of calculus involving differentiation and integration

• the ability to solve equations in a variety of simple contexts including trigonometric contexts where simple substitution and equation-solving methods are necessary.

Modelling and problem solving

In the MP criterion, all contexts required careful reading, interpretation and planning to clarify a range of mathematical situations. This was not evident in the low-level candidate responses.

As in the KP criterion, low-level candidate responses were not able to show algebraic facility in developing solutions to problems and needed to demonstrate:

• the use of clearly labelled, neatly drawn diagrams to support arguments and conclusions reached

• the ability to use technology where required

• the ability to manipulate index and logarithmic laws

• familiarity with function notation and rules of calculus involving differentiation and integration

• the ability to solve equations in a variety of simple contexts including trigonometric contexts where simple substitution and equation-solving methods are necessary.

Communication and justification

In the Communication and justification (CJ) criterion, many candidates recognised the need to justify and validate their solutions. This was clearly evident in responses that exhibited a

developed argument, examined the effects of assumptions and correctly evaluated the validity of arguments.

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Mathematics B

In the CJ criterion, low-level candidate responses did not generally demonstrate:

• 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 in support of simple logical arguments.

These issues were evident across topics and contexts in both papers.

Marker responses

The sample solutions on the following pages show possible ways of successfully responding to the questions. Other approaches and problem-solving strategies may be equally valid.

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Mathematics B

Paper One

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Paper Two

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