SAMPLE ASSESSMENT TASKS MATHEMATICS SPECIALIST ATAR YEAR 11

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1 SAMPLE ASSESSMENT TASKS MATHEMATICS SPECIALIST ATAR YEAR

2 Cpyright Schl Curriculum and Standards Authrity, 08 This dcument apart frm any third party cpyright material cntained in it may be freely cpied, r cmmunicated n an intranet, fr nn cmmercial purpses in educatinal institutins, prvided that the Schl Curriculum and Standards Authrity is acknwledged as the cpyright wner, and that the Authrity s mral rights are nt infringed. Cpying r cmmunicatin fr any ther purpse can be dne nly within the terms f the Cpyright Act 968 r with prir written permissin f the Schl Curriculum and Standards Authrity. Cpying r cmmunicatin f any third party cpyright material can be dne nly within the terms f the Cpyright Act 968 r with permissin f the cpyright wners. Any cntent in this dcument that has been derived frm the Australian Curriculum may be used under the terms f the Creative Cmmns Attributin 4.0 Internatinal (CC BY) licence. Disclaimer Any resurces such as texts, websites and s n that may be referred t in this dcument are prvided as examples f resurces that teachers can use t supprt their learning prgrams. Their inclusin des nt imply that they are mandatry r that they are the nly resurces relevant t the curse. 04/7367v8

3 Sample assessment task Mathematics Specialist ATAR Year Unit Schl Name Sample test 3 Student name: Teacher name: Class: Task type: Respnse Time allwed fr this task: 55 minutes, in class, under test cnditins Sectin One: Calculatr free 35 minutes Sectin Tw: Calculatr assumed 0 minutes (8 marks) ( marks) Materials required: Standard items: Special items: Calculatr with CAS capability (t be prvided by the student) Pens (blue/black preferred), pencils (including clured), sharpener, crrectin fluid/tape, eraser, ruler, highlighters Drawing instruments, templates, ntes n tw unflded sheets f A4 paper, and up t three calculatrs apprved fr use in the WACE examinatins Marks available: 49 marks Task weighting: 6% Sample assessment tasks Mathematics Specialist ATAR Year

4 Sectin One: Calculatr-free (8 marks) Time allwed: 35 minutes Questin (Sectin )..5 A grup f 67 Year 9 students respnded t a survey stating they wned ne r mre f the fllwing items. A: An internet cnnected mbile phne B: A tablet r ipad C: A laptp cmputer The fllwing infrmatin was recrded using set ntatin n(a) = 37, n(b) = 8 and n(c) = 3 and the fllwing ntes were made. (7 marks) There were as many students wh wned all three as thse wh wned a phne and ipad but nt a laptp. There were as many students wh wned all three as thse wh wned a laptp and ipad but nt a phne. There were twice as many students wh wned a phne and laptp but nt an ipad as thse wh wned all three. Calculate hw many students wned all three devices. Calculate hw many students wned nly ne f these devices. Questin (Sectin )..9 (6 marks) Given.00= calculate the expansin (.00) 4 using the cefficients f Pascal s triangle. Sample assessment tasks Mathematics Specialist ATAR Year

5 3 Questin 3 (Sectin ).3.7,.3.9 (7 marks) Tw tangents are drawn frm pint T t pints A and B n a circle as shwn in the diagram. Given the angle between the tangents is 44 0 calculate the size f ADB and ACB shwing prf f each result. A y D 44 T C x B Questin 4 (Sectin ).3.3 (8 marks) Cnsider pint M external t the circumference f the circle centre C. A secant is drawn frm M passing thrugh the centre C als intersecting the circumference f the circle at pints A and B. A line is als drawn frm M t the circle at a pint f tangency T. Prve that TM AM MB. B T C A M Sample assessment tasks Mathematics Specialist ATAR Year

6 4 Sectin Tw: Calculatr-assumed ( marks) Time allwed: 0 minutes Questin 5 (Sectin )..4,..7,..8 ( marks) Tw frces act n an bject in a flat plane. F has a magnitude f 4 newtns and acts n a bearing f and F with a magnitude f 5 newtns acts n a bearing 3 0. (a) Use the triangle rule t calculate the magnitude and directin f the resultant frce t an accuracy f tw () decimal places. (7 marks) (b) Calculate the i and j cmpnents f F and F given the unit vectr i is n a bearing 0 0 T and the unit vectr j is n a bearing 90 0 T (3 marks) (c) Evaluate F + F in i and j cmpnent frm. ( marks) Questin 6 (Sectin )..3 The vectrs a = 3i + 5j and b = 5i + j calculate the prjectin f (i) a nt the axis and (ii) b nt the axis (iii) a nt b. (9 marks) Sample assessment tasks Mathematics Specialist ATAR Year

7 5 Slutins fr sample test 3 Questin (Sectin )..5 A grup f 67 Year 9 students respnded t a survey stating they wned ne r mre f the fllwing items. A: An internet cnnected mbile phne B: A tablet r ipad C: A laptp cmputer The fllwing infrmatin was recrded using set ntatin n(a) = 37, n(b) = 8 and n(c) = 3 and the fllwing ntes were made. (7 marks) There were as many students wh wned all three as thse wh wned a phne and ipad but nt a laptp. There were as many students wh wned all three as thse wh wned a laptp and ipad but nt a phne. There were twice as many students wh wned a phne and laptp but nt an ipad as thse wh wned all three. (a) Calculate hw many students wned all three devices. (b) Calculate hw many students wned nly ne f these devices. Slutin B A 37 8 x 67 x x x C 3 n ABC 0 Let n ABC x then n ABC n BCA x and n A C B x n A n B n c n ABC x x 5 One nly n ABC 5 n 4 Sample assessment tasks Mathematics Specialist ATAR Year

8 6 Defines n ABC x Specific behaviurs Sets up an equatin in x fr the intersectin areas Sets up an equatin t slve fr x Crrectly evaluates the number f students wned all three devices Crrectly evaluates the number f students wned ne device Mark allcatin 3 Item classificatin Questin (Sectin )..9 (6 marks) Given.00= calculate the expansin (.00) 4 using the cefficients f Pascal s triangle. Slutin Given.00= calculate the expansin (.00) 4 using the cefficients f Pascal s triangle Specific behaviurs Expands the term with the crrect cefficients Calculates each decimal term crrectly Adds the terms accurately Mark allcatin 4 Item classificatin Sample assessment tasks Mathematics Specialist ATAR Year

9 7 Questin 3 (Sectin )..4,..7,..8 (7 marks) Tw tangents are drawn frm pint T t pints A and B n a circle as shwn in the diagram. Given the angle between the tangents is 44 0 calculate the size f ADB and ACB shwing prf f each result. Slutin A y D O 44 T C x B Cnstruct a radius frm the centre f the circle O t each f the pints A and B ATO BTO cngruent s AOT BOT 68 Right s AOB adjacent s ATO BTO RHS 68 at circumference n arc ADB ppsite f cyclic quadrilateral ACB x ADB y s Specific behaviurs Draws the tw radii OA OB and line segment OT Draws quadrilateral ADBC Determines AOB 36 Determines ACB 68 Crrectly determines the angles BDA Mark allcatin 3 Item classificatin Sample assessment tasks Mathematics Specialist ATAR Year

10 8 Questin 4 (Sectin ).3.3 (8 marks) Cnsider the pint M external t the circumference f the circle whse centre is at C. A secant is drawn frm M passing thrugh the centre C als intersecting the circumference f the circle at tw pints A and B. A tangent is drawn frm M t the circle at T. TM AM MB Slutin B T C A M Prve that TM AM MB Specific behaviurs Uses Pythagras in MTC as in equatin MC MA+AC Expresses Expands MC MA+AC In VMTC: MC TM +CT Pythagras MC AC AC Determines equatin crrectly Equates RHS f equatin t RHS f equatin TM AM MB Simplifies t get the required expressin Equating RHS f equatin RHS f equatin MA+AC AM ACAM+AC AM ABAM+AC AB = AC radius AM MA+AB AM MB TM +CT AM MB AC AC=CT=radius TM AM MB () Mark allcatin Item classificatin Sample assessment tasks Mathematics Specialist ATAR Year

11 9 Questin 5 (Sectin )..4,..7,..8 ( marks) Tw frces act n an bject in a flat plane. F has a magnitude f 4 newtns and acts n a bearing f and F with a magnitude f 5 newtns acts n a bearing 3 0. (a) Use the triangle rule t calculate the magnitude and directin f the resultant frce t an accuracy f tw () decimal places. (7 marks) Slutin B N 4 N 35 C A 3 5 N In ABC AC cs0 AC sin0 sin 44.4 Bearing Specific behaviurs Cnstructs a triangle f frces Crrectly evaluates the included angle = 0 0 Uses the csine rule t evaluate the magnitude States the crrect magnitude in newtns Uses the sine rule t calculate angle Evaluates the angle between F and the resultant Calculates the crrect bearing f the resultant Mark allcatin Item classificatin Sample assessment tasks Mathematics Specialist ATAR Year

12 0 (b) Calculate the i and j cmpnents f F and F t decimal places, given the unit vectr i is n a bearing 0 0 T and the unit vectr j is n a bearing 90 0 T (4 marks) (c) Evaluate F + F in i and j cmpnent frm. ( mark) Slutin 35 4 N N F 4cs55 i + 4sin55 j F 5cs 3 i + 5sin 3 j.9i j 4.60i j Evaluate F + F in i and j cmpnent frm. Slutin F + F 6.90 i +.3 j Specific behaviurs Calculates the i and j cmpnents f F Calculates the i and j cmpnents f F Adds F and F accurately Mark allcatin Item classificatin Sample assessment tasks Mathematics Specialist ATAR Year

13 Questin 6 (Sectin )..3 The vectrs a = 3i + 5j and b = 5i + j calculate the prjectin f (i) a nt the x axis and (ii) b nt the y axis (iii) a nt b. (9 marks) 3 a3i5j a and cs where is the angle between vectr a and 34 uuur the x axis where OX ki b5ij a 5 6 and cs where is the angle between vectr b and 6 uuur the y axis where OY kj ( i) The prjectin f a nt the x axis = a csi i3i (ii) The prjectin f b nt the y axis = bcsi 6 6 jj 3 5 $ 5 (iii) The prjectin f a nt b a csb 34 5ij where is the angle between a and b 0 5 ij 6 Specific behaviurs Mark Item allcatin classificatin Crrectly determines a 34 3 Crrectly determines cs 34 Crrectly calculates the prjectin f a nt the axis Crrectly determines b 6 Crrectly determines cs 6 Crrectly calculates the prjectin f b nt the axis 0 Crrectly determines cs 34 6 Crrectly calculates b ) Crrectly simplifies the expressin fr prjectin f a nt b Questin Ttal Simple Cmplex Cmb Cmb Gem Gem Vectr Vectr Sample assessment tasks Mathematics Specialist ATAR Year

Year 12 Units 3 & 4 Chemistry COURSE OUTLINE 2017

1 Science Learning Area Year 12 Units 3 & 4 Chemistry COURSE OUTLINE 2017 IMPORTANT INFORMATION: This syllabus is effective frm 1 January 2016. Users f this syllabus are respnsible fr checking its currency.