HSC exam advice for Mathematics Advanced, Extension 1 and Extension 2

The new Mathematics Advanced Stage 6 syllabus contains content that is common with the Mathematics Standard Stage 6 syllabus. Support materials that identify the common content are available on the related NESA syllabus pages (Mathematics Standard and Mathematics Advanced).

The Mathematics Advanced examination will include items that are common with the Mathematics Standard 2 HSC examination.

As part of the Stronger HSC Standards Reforms (Reform 7), NESA will use these common items to place students undertaking mathematics courses on a common scale. A common scale means that student achievement in mathematics can be compared across courses.

From 2020, NESA will provide information on the common scale to the Universities Admissions Centre (UAC) and the Technical Committee on Scaling (TCOS). TCOS is responsible for the calculation of the ATAR and will review the information provided by NESA to determine how it could be used in future years for the calculation of the ATAR.

TCOS and UAC have indicated that they will communicate any changes to the calculation of the ATAR to schools and students before affected students commence Year 11.

NESA will NOT report mathematics on a common scale. NESA will continue to report HSC results on a course-by-course basis using the course performance band descriptions and NESA’s established marking, moderation and standards-setting procedures.

School assessment requirements specified in the Assessment and Reporting in Mathematics Advanced or Mathematics Extension 1 or Mathematics Extension 2 Stage 6 documents remain unchanged. Schools will not be expected to use common items in their school-based assessment tasks, nor to report using a common scale.

HSC examinations contain questions. The mark value of each question is specified on the examination. Some questions are divided into several parts, usually numbered (a), (b), etc. These parts have their mark value indicated on the examination in the right-hand margin.

An item is either a question (if it is not subdivided) or a part that carries a mark value. A shorthand way of determining how many short-answer items are in a paper is to count the number of mark values written in the right-hand margin.

For example, there are two questions shown below, Questions 12 and 16.

Question 12 has three parts: (a), (b) and (c). Altogether Question 12 contains three items, as shown by the three marks in the right-hand margin.

Question 16, shown below, has no parts, and is a 3-mark item. Again, its mark is shown in the right-hand margin.

Educational measurement advice is that common items should be presented no differently to the other items in a test.  A test containing common items should be constructed according to the same content and statistical specifications as a test that does not have such items. NESA will therefore continue to organise the mathematics examinations so that the questions increase in difficulty as the examination progresses.

Examinations should have a range of item types, consistent with the nature of what is being assessed. Well-constructed multiple-choice items can measure knowledge, understanding and problem-solving ability. They can discriminate effectively and can be written to minimise students of low ability guessing correctly.

In mathematics, while the majority of HSC questions require students to show their working, multiple-choice items enable some skills, such as conceptual understanding, to be assessed more effectively than in short-answer questions. These include:

• questions where students are asked to indicate which approach, expression, statement, shape or graph is correct in a given situation, eg students are asked to choose the correct integral for a given area, or choose the correct area diagram for a given integral
• questions that illustrate common misconceptions in mathematics and require students to identify or avoid them.

Multiple-choice items enable conceptual understanding to be assessed without being affected by the accuracy of the students’ working/calculations or their ability to perform certain processes.

Items worth larger mark values (eg 4 or 5 marks) provide opportunities for students to demonstrate depth of knowledge and application of skills. Students are presented with a substantial problem to solve with less scaffolding than a similar question broken up into smaller mark value parts. In these larger mark value items, students will be required to make more decisions about the method(s) that they use to solve the problem.

NESA mathematics HSC examinations have had this type of question in past papers; including them in the examination specifications ensures that they will be included in future HSC examinations.

There should be a range of item values in each mathematics examination, consistent with the requirements of each item, from 1 mark up to 4 or 5 marks. Specifying the number of items in each examination means that it will not be overly ‘fragmented’, ie too many 1-mark items. These item specifications are broadly consistent with current practice in examinations, and allow for the required number of 4 or 5-mark items.

These larger-value items enable students’ working and problem-solving skills to be rewarded.

The new Mathematics Advanced, Extension 1 and Extension 2 syllabuses contain outcomes (eg MA12-1, ME11-7 and MEX12-1) that require students to be able to recognise and draw the graphs of functions, so mathematical curve-drawing templates will no longer be permitted equipment for the suite of new mathematics HSC examinations.

Compasses and protractors will no longer be permitted equipment for HSC examinations for these courses as they are no longer required to answer questions.

As with the current Mathematics and Mathematics Extension 1 HSC examinations, there are no pre-determined percentages of Preliminary content. The examinations will be based on the respective Year 12 courses and will focus on the course objectives and Year 12 outcomes. The Year 11 courses will be assumed knowledge for these examinations and may be examined.