噩梦般的数学题
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1、Sample Assessment TasksMathematics MethodsATAR Year 11Acknowledgement of CountryKaya. The School Curriculum and Standards Authority (the Authority) acknowledges that our offices are on Whadjuk Noongar boodjar and that we deliver our services on the country of many traditional custodians and language
2、 groups throughout Western Australia. The Authority acknowledges the traditional custodians throughout Western Australia and their continuing connection to land, waters and community. We offer our respect to Elders past and present.Copyright School Curriculum and Standards Authority, 2018This docume
3、nt apart from any third party copyright material contained in it may be freely copied, or communicated on an intranet, for non-commercial purposes in educational institutions, provided that the School Curriculum and Standards Authority is acknowledged as the copyright owner, and that the Authoritys
4、moral rights are not infringed.Copying or communication for any other purpose can be done only within the terms of the Copyright Act 1968 or with prior written permission of the School Curriculum and Standards Authority. Copying or communication of any third party copyright material can be done only
5、 within the terms of the Copyright Act 1968 or with permission of the copyright owners.Any content in this document that has been derived from the Australian Curriculum may be used under the terms of the Creative Commons Attribution 4.0 International licence.DisclaimerAny resources such as texts, we
6、bsites and so on that may be referred to in this document are provided as examples of resources that teachers can use to support their learning programs. Their inclusion does not imply that they are mandatory or that they are the only resources relevant to the course.2014/14296v719Sample assessment
7、taskMathematics Methods ATAR Year 11Task 1 Unit 1Assessment type: ResponseContent: Trigonometric functions (1.2.1 1.2.8), Functions and graphs (1.1.1 1.1.12)Conditions:Time for the task: Up to 60 minutes, in class, under test conditions Note: while the Authority provides sample assessment tasks for
8、guidance, it is the expectation of the Authority that teachers will develop tasks customised to reflect their schools context and the needs of the student cohort. This resource is available on a public website and use of the resource without modification may affect the integrity of the assessment.Ma
9、terials required: Section One: Calculator-free. Standard writing equipmentSection Two: Calculator-assumed. Calculator (to be provided by the student)Other materials allowed:Drawing templates, 1 A4 page of notes in Section TwoMarks available:70 marksSection One: Calculator-free41 marksSection Two: Ca
10、lculator-assumed29 marksTask weighting: 6%Section One: Calculator-free(41 marks)Suggested time: 35 minutesQuestion 1(7 marks)Choose a suitable method to solve each of the equations below:(a) 32a-14+a=0(2 marks)(b) 2t+5=3(t-7)(2 marks)(c) x2+4x+1=0(3 marks)Question 2(8 marks)The diagram below shows a
11、 unit circle, centre O. The rays OA, OB, OC and OD define the angles 20, 50, 75 and 143 as shown. (a) Use the unit circle to determine an approximate value for each of the following:(5 marks)(i) sin 50(ii) cos 105(iii) sin 340(iv) tan 143(b) Using the unit circle, explain why sin 50= sin 130(3 marks
12、)Question 3 (3 marks)The function y = 2x 2+ bx+ c has a y intercept at (0, 2) and it has no roots.Determine the value of c and the range of possible values for b.Question 4(4 marks)Use exact values to show that:(a) (sin45)2+2cos30-tan60=12(2 marks)(b) tan6sin3+sin6cos=0(2 marks)Question 5(3 marks)Us
13、e the diagram to find the exact value of:(a) y(b) sin Question 6(7 marks)(a) Determine the equation of the straight line that passes through the point (5, 3) and is perpendicular to x+2y-9=0.(3 marks)(b) Find the value(s) of k if kx-2y=3 is parallel to 3x + (k + 7)y = 1 .(4 marks)Question 7(5 marks)
14、(a) Determine the coordinates of the root(s) and y intercept of the graph y=x2+x-6.(2 marks)(b) Sketch the graph on the axes below, clearly showing the coordinates of all significant points. (3 marks)Question 8(4 marks)Determine:(a) the coordinates of the turning point of the graph of y=3(x+4)2+2.(1
15、 mark)(b) the equation of the quadratic function that passes through the point (0, 9) and has a turning point at (2, 3).(3 marks)Section Two: Calculator-assumed(29 marks)Suggested time: 25 minutesQuestion 9 (5 marks)Triangle ABC has sides AB=16.5 cm, BC=12.8 cm and CAB=36.(a)Determine the possible s
16、ize(s) of ABC(3 marks)(b)Hence determine the shortest possible length of the side AC(2 marks)Question 10(4 marks)A triangle with an area of 36 m2 has two equal sides with an included angle of 100. Find the perimeter of the triangle.Question 11 (5 marks)The length of the minor arc AB in the circle be
17、low is 163 cm and the circle has a radius of 12 cm. If the angle subtended by the arc CD is 35 , determine the area of the shaded region. Question 12(4 marks)A line is inclined at an angle of 120 to the positive x-axis and cuts the y-axis at (0, 2). Determine the exact coordinates of the midpoint of
18、 the line segment determined by the x and y intercepts. Question 13 (5 marks)Marks Kerbing Company makes concrete kerbing. One design is shown below and its cross-section is modelled on the axes. The curve is created by two quadratic functions that intersect when w=9.The upper curve is modelled by t
19、he equation h=-2w227+8w3-9, where w and h are measured in centimetres.Kerbing designThe equation of the lower curve is of the form h=aw2.(a) Determine the coordinates of the point where the upper and lower curves intersect.(1 mark)(b) Determine the equation of the lower curve.(2 marks)(c) The volume
20、 of concrete used is directly proportional to the length of kerbing made. A length of 2 m requires 0.036 m3 of concrete. Determine the volume of concrete needed to make a 1.2 km length of kerbing.(2 marks)Question 14 (6 marks)In a cricket match, a batsman at B hits a ball toward the spectators stand
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