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The first HSC examination for the new Mathematics Standard Stage 6 syllabus will be held. The Mathematics Standard 2 examination specifications can be found in the Assessment. and Reporting in Mathematics Standard Stage 6 document. The examination will focus on the Mathematics Standard 2 Year 12 course objectives and. outcomes Questions may require candidates to integrate knowledge understanding and. skills developed through studying the course The Mathematics Standard Year 11 course. content will be assumed knowledge for this examination and may be used to examine. Year 12 outcomes, There is no expectation that all the Year 12 content will be examined each year In any. given year the examination will test a representative sample of the Year 12 content. The following sample questions provide examples of some questions that may be found. in HSC examinations for Mathematics Standard 2 Each question has been mapped to. show how the sample question relates to syllabus outcomes and content Answers for. the objective response questions Section I and marking guidelines for the short answer. questions Section II are provided The marking guidelines indicate the criteria associated. with each mark or mark range, In the examination students will record their answers to Section I on a multiple choice. answer sheet and their answers to Section II in the spaces provided on the examination. The sample questions annotations and marking guidelines provide teachers and students. with guidance as to the types of questions to expect and how they may be marked They are. not meant to be prescriptive Each year the structure of the examination may differ in the. number and type of questions or focus on different syllabus outcomes and content. Comments in coloured boxes are annotations for the purpose of providing guidance for. future examinations, In this set of sample questions some stimuli are used in both Section I and Section II This. is to illustrate how the same content area can be examined differently. Teachers and students should still refer to past HSC examination papers for examples of. other questions that may be included,Past examination This is NOT a. papers provide complete sample,Section I guidance for other examination paper.

types of multiple Six sample questions, 15 marks choice questions that are included in this. Attempt Questions 1 15 could be included in section. Allow about 25 minutes for this section the examination. Use the multiple choice answer sheet for Questions 1 15. A variety of stimulus material such as text diagrams pictures graphs photographs and. illustrations may be included in the questions in Section I However stimulus material. will only be included when it is essential for answering the question. Multiple choice options A D may be presented in different formats for example text. graphs photographs diagrams, 1 This diagram shows the possible paths in km for laying gas pipes between various. Old Town 11,12 Newville,8 Students,Beachview 10,7 should note. Parkview that not all,diagrams are,15 Summerville drawn to scale. Gas is to be supplied from one location Any one of the locations can be the source of. the supply, What is the minimum total length of the pipes required to provide gas to all the locations.

This question is common to Mathematics Standard 1 and Mathematics Standard 2. This question is based on new content, 2 A computer application was used to draw the graphs of the equations. x y 5 and x y 5,Part of the screen is shown, Which row of the table correctly matches the equations with the lines drawn and identifies. the solution when the equations are solved simultaneously. x y 5 x y 5 Solution,A Line 1 Line 2 x 5 y 0,B Line 1 Line 2 x 5 y 5. C Line 2 Line 1 x 5 y 0,D Line 2 Line 1 x 5 y 5, This question uses content from both Year 11 and Year 12 to examine a Year 12 outcome. The Mathematics Standard Year 11 course content will be assumed knowledge for this. examination and may be used to examine Year 12 outcomes. This question uses stimulus material common to Mathematics Standard 1 Question 2. 3 A survey was conducted into the number of hours worked by casual staff in the hospitality. industry It was found that the weekly average was 18 hours with a standard deviation of. 2 5 hours and that the number of hours worked was normally distributed. Based on the survey what is the percentage of casual staff working fewer than 23 hours. 4 What amount must be invested now at 4 per annum compounded quarterly so that in. five years it will have grown to 60 000, This question is common to Mathematics Standard 1 and Mathematics Standard 2.

5 The table shows the average energy used in kilojoules per kilogram of body mass by a. person walking for 30 minutes at different speeds,Walking speed Energy used in 30 minutes. 3 km h 5 53 kJ kg,5 km h 7 37 kJ kg, Sam who weighs 65 kg drinks a regular cappuccino made with full cream milk It. contains 73 kilocalories, For approximately how long must Sam walk at 3 km h to burn off the energy contained. in the cappuccino 1 kilocalorie 4 184 kJ,A 20 minutes. If information required to answer,B 25 minutes a question is not available on the.

C 90 minutes Reference Sheet it may be provided,with the question. D 120 minutes, This question uses Year 11 content to examine a Year 12 outcome. The Mathematics Standard Year 11 course content will be assumed knowledge for this. examination and may be used to examine Year 12 outcomes. This question is based on new content, 6 The network diagram represents a system of roads connecting a shopping centre to the. on ramp of a freeway Traffic moves via several routes For example there are two. routes from the shopping centre to P and one route from T to U The number on the edge. of each road indicates the number of vehicles that can travel on it per hour. 70 65 45 T,Shopping P 30 63,Centre R 50, At present the capacity of the network from the shopping centre to the on ramp is not. Which additional road s would increase the network capacity to its maximum. A A road from P to U with a capacity of 20 vehicles per hour. B A road from Q to T with a capacity of 20 vehicles per hour. C A road from R to T with a capacity of 20 vehicles per hour and a road from T to U. with a capacity of 40 vehicles per hour, D A road from Q to U with a capacity of 20 vehicles per hour and a road from S to U.

with a capacity of 20 vehicles per hour, Question 17 is a short answer question based on the same stimulus and demonstrates. another method of examining similar knowledge and skills. This question is based on new content,Sample HIGHER SCHOOL CERTIFICATE. Questions EXAMINATION Questions in Section II may,contain parts There will be. 35 to 40 items and at least,two items will be worth 4 or. Mathematics Standard 2 5 marks,Section II Answer Booklet This is NOT a complete.

sample examination paper,Four sample questions seven. items have been included in,this section,Attempt Questions 16 XX. Allow about 2 hours and 5 minutes for this section. Instructions Answer the questions in the spaces provided These spaces. provide guidance for the expected length of response. Your responses should include relevant mathematical reasoning. and or calculations, Extra writing space is provided at the back of this booklet. If you use this space clearly indicate which question you are. A variety of stimulus material such as text diagrams pictures graphs photographs and. illustrations may be included in the questions in Section II. Equipment such as a ruler a protractor and a pair of compasses may be required to answer. questions in this examination,Question 16 3 marks, The scale diagram shows the aerial view of a block of land bounded on one side by a 3. road The length of the block AB is known to be 45 metres. Calculate the approximate area of the block of land using three applications of the. Trapezoidal rule,Question 17 3 marks, The network diagram represents a system of roads connecting a shopping centre to 3.

the on ramp of a freeway Traffic moves via several routes For example there are. two routes from the shopping centre to P and one route from T to U The number on. the edge of each road indicates the number of vehicles that can travel on it per hour. 70 65 45 T,Shopping P 30 63,Centre R 50, At present the capacity of the network from the shopping centre to the on ramp is not. maximised It is not possible to construct a road directly between the shopping centre. and the on ramp, Suggest ONE way that the network capacity can be maximised with additional. road s Justify your answer, An alternative question that examines similar knowledge and skills. Draw additional road s on the diagram to maximise the network. capacity Include the number of vehicles that can travel on each road. A response in this section may need to be expressed in a particular. format such as text graphs tables diagrams calculations. A combination of these formats may also be required. Question 6 is a multiple choice question based on the same stimulus. and demonstrates another method of examining similar knowledge and. This question is based on new content,Question 18 9 marks. The diagram shows three towns X Y and Z Town Z is due east of Town X The. bearing of Town Y from Town X is N39 E and the bearing of Town Z from Town Y. is S51 E The distance between Town X and Town Y is 1330 km. A plane flies between the three towns, a Mark the given information on the diagram and explain why XYZ is 90 2.

b If the speed of the plane is 570 km h how long does the flight take from Town X 2. to Town Y in hours and minutes, c Find the distance between Town X and Town Z to the nearest kilometre 2. Students should show all relevant working in responses involving. calculations This ensures that marks can be allocated for working. even if the student s final answer is incorrect,Question 18 continues on page 12. Question 18 continued, d The plane is going to fly from Town Y to Town X stopping at Town Z on the 3. way Leaving Town Y the pilot incorrectly sets the bearing of Town Z to S50 E. The pilot flies for 1650 km before realising the mistake then changes course. and flies directly to Town X without going to Town Z. From where the pilot changes course is it a shorter or longer distance to Town X. than if the plane had flown from Town Z to Town X, Whenever possible question parts are sequenced in order of difficulty. An incorrect answer in a previous part will not necessarily preclude students from. achieving full marks in a later part, Question 18 parts a c are common to Mathematics Standard 1 Question 12 parts a c.

End of Question 18,Question 19 5 marks, A project requires activities A to G to be completed as shown in the table 5. Activity Immediate prerequisite s Duration in days. The minimum completion time for the project is 50 days and the critical path includes. activities B D E and F The float for G is three days and the float for C is 8 days. This question is based on new content,Question 19 continues on page 14. Question 19 continued, Find a possible duration for each of the activities A C F and G Include a network. diagram in your answer, Some questions in this section may specify that the response must be. supported with a diagram or other material such as a graph. In some cases students may find it useful to support their answer with. a diagram or other material although no specific requirement is made. in the question,End of sample questions,Section II extra writing space.

If you use this space clearly indicate which question you are answering. Year 12 outcomes There is no expectation that all the Year 12 content will be examined each year In any given year the examination will test a representative sample of the Year 12 content The following sample questions provide examples of some questions that may be found in HSC examinations for Mathematics Standard 2 Each question has been

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