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S / N  \n\n| Multiple Choice Questions (8 marks) |  |\n| --- | --- |\n| 1 Using the diagram below, choose the correct alternative.\u003Cbr>\u003Cbr>A.  + y = 􀀄\u003Cbr>B.  − y = −􀀄\u003Cbr>C. −  + y = 􀀄\u003Cbr>D.  + y = −􀀄\u003Cbr>E.  − y = 􀀄\u003Cbr>2 Expressed in simplest form,\u003Cbr>􀁊􀁊􀁇 􀁊􀁊􀁇 􀁊􀁊􀁇 􀁊􀁊􀁇\u003Cbr>DE + FH − FG + EG equals\u003Cbr>A. 0\u003Cbr>􀀄\u003Cbr>􀁊􀁊􀁇\u003Cbr>B. DF\u003Cbr>􀁊􀁊􀁇\u003Cbr>C. FE\u003Cbr>􀁊􀁊􀁇\u003Cbr>D. DH\u003Cbr>􀁊􀁊􀁇\u003Cbr>E. DG\u003Cbr>3 The angle that the vector 4 + 2 j makes 􀀄\u003Cbr>with the positive direction of the x-axis is found by solving:\u003Cbr>A. tan(θ) = ~~ ~~12\u003Cbr>B. tan(θ) = 2\u003Cbr>C. sin(θ) = ~~ ~~12\u003Cbr>D. cos(θ) = 2\u003Cbr>E. tan(θ) = − ~~ ~~12 | 4 If  = −2 + nj ,  =􀀄\u003Cbr>A. n2 – 4\u003Cbr>B. n2 + 5\u003Cbr>C. n2 + 4\u003Cbr>D. n2 + 5\u003Cbr>E. n2 − 4\u003Cbr>5 A unit vector in the direction of  − 2j is:􀀄\u003Cbr>A.  − 2j 􀀄\u003Cbr>B.  1 (i − 2 j)\u003Cbr>3 􀀄 􀀄\u003Cbr>C. 2j − 􀀄\u003Cbr>D.  1 ( − 2 j)\u003Cbr> 5 􀀄\u003Cbr>E.  1 (i − 2 j)\u003Cbr>5 􀀄 􀀄 |\n\n\n| 6 In the diagram shown, LOM is a diameter of the circle with centre O. N is a point on the circumference of the circle.\u003Cbr>􀁊􀁊􀁊􀁇 􀁊􀁊􀁇\u003Cbr>Let OM =  = q . Which one of the\u003Cbr>􀀄\u003Cbr>following must be true? |  |  | 8 Given the vectors  =  − 2 j and  = 2 + 3 j\u003Cbr>􀀄 􀀄\u003Cbr>the scalar resolute of a in the direction of\u003Cbr>􀀄\u003Cbr>b is:\u003Cbr>􀀄\u003Cbr>4\u003Cbr>A. − ~~ ~~\u003Cbr>13\u003Cbr>4\u003Cbr>B. − ~~   ~~\u003Cbr>13\u003Cbr>4\u003Cbr>C. − ~~ ~~\u003Cbr>5\u003Cbr>4\u003Cbr>D. − ~~   ~~\u003Cbr> 5\u003Cbr>E. −4\u003Cbr>END OF MULTIPLE CHOICE QUESTIONS\u003Cbr>|\n| --- | --- | --- | --- |\n| L | | M |  |\n| A. 2 + q = 0 􀀄\u003Cbr>B. 2 − q = 0 􀀄\u003Cbr>C. .q = q.q\u003Cbr>􀀄 􀀄􀀄\u003Cbr>D. 2.q = q.q\u003Cbr>􀀄 􀀄􀀄\u003Cbr>E. .q = −q.q\u003Cbr>􀀄 􀀄􀀄\u003Cbr>7 P, Q and R are three collinear points with\u003Cbr>position vectors p, q and  respectively,􀀄 􀀄\u003Cbr>where Q lies between P and R.\u003Cbr>􀁊􀁊􀁇 1 􀁊􀁊􀁇\u003Cbr>If QR = ~~ ~~ PQ  then  is equal to\u003Cbr>2\u003Cbr>3 1\u003Cbr>A. ~~ ~~ q − ~~ ~~ p\u003Cbr>2 􀀄 2 􀀄 3 1\u003Cbr>B. ~~ ~~ p − ~~ ~~ q\u003Cbr>2 􀀄 2 􀀄 3 3\u003Cbr>C. ~~ ~~ q − ~~ ~~ p\u003Cbr>2 􀀄 2 􀀄 1 3\u003Cbr>D. ~~ ~~ p − ~~ ~~ q\u003Cbr>2 􀀄 2 􀀄 3 3\u003Cbr>E. ~~ ~~ p − ~~ ~~ q\u003Cbr>2 􀀄 2 􀀄 |  |  |  |\n\n\n| Short-answer questions (25 marks)\u003Cbr>Answer in the space provided. In all questions where a numerical answer is required, an exact value must be given unless otherwise specified. In questions where more than one mark is available, appropriate working must be shown.\u003Cbr>1. Let  = 3 − 5 j and  = − + 2 j . Find the angle between these two vectors in degrees to the\u003Cbr>􀀄 􀀄\u003Cbr>nearest degree.\u003Cbr>[3 marks] |  |  |\n| --- | --- | --- |\n| 2. Find the value(s) of p such that p + 2(1− 3p)j 􀀄 | is perpendicular to | 2p + 3 j 􀀄 |\n| [5 marks] |  |  |\n| 3. Let  = 2 + 3 j −  and  =  + j − 2 .\u003Cbr>􀀄 􀀄\u003Cbr>(a) Find a unit vector parallel to u\u003Cbr>􀀄 |  |  |\n\n(b) Resolve v into components parallel and perpendicular to u  \n􀀄 􀀄  \n [2+4=6 marks]  ","cbCaibj2TV6sbyOl","https://ap.wps.com/l/cbCaibj2TV6sbyOl","pdf",216603,"English","# Assessment Overview\n## Outcomes\n## Conditions\n## Results Structure\n# Multiple Choice Questions\n# Short-answer Questions\n# Applications and Modelling","[{\"question\":\"What assessment outcomes does the Vectors test evaluate?\",\"answer\":\"It evaluates students’ ability to define and apply key vector concepts, apply mathematics in non-routine contexts and analyze those applications, and use technology for results and analysis in problem-solving, modelling, or investigative situations.\"},{\"question\":\"What tools are allowed during the test?\",\"answer\":\"An approved CAS calculator and reference material (either a notebook or text) are allowed.\"},{\"question\":\"How are marks distributed and what is the passing condition?\",\"answer\":\"Marks total 47, split into multiple choice (/8), short answer (/25), and applications/modelling (/14). Satisfactory completion requires an overall result of 40% or above, and results may be subject to moderation.\"}]","Unit 2 VCE Specialist Maths - Vectors Test - AT 2.1 - Assessment Task | PDF",1789909551]