加拿大安大略省十年级数学试卷-英文.doc

Feel free to use any of the material in this document. Marks are only guidelines.We have categorized each question into one of the 4 achievement chart (A/C) categories: Knowledge/Understanding (K), Thinking and Inquiry (T), Application (A) and Communication (C). You can change or modify the categories as you see fit.GRADE 10 PRINCIPLES OF MATHEMATICS (ACADEMIC)MPM 2DTotal Marks:INSTRUCTIONS:1. Calculators may be used.2. Read all instructions carefully in order to maximize your mark.A/CKPart A Multiple Choice 25 Marks (25 questions * 1 mark each)For each of the following questions in this section, circle the letter representing the correct answer.1.A linear system of two equations that has one solution represents two lines that are:a)parallelb)coincidentc)intersectingd)none of these2.The midpoint of RS is M(8, -1). If point S has coordinates (11, 4) what are the coordinates of point R?a)(3, -6)b)(15, -6)c)(5, -6)d)(3, 9)3.The midpoint of the line segment with end points A(-8, 8) and B(6, 4) is:a)(0, 10)b)(1, 2)c)(7, 2)d)(-1, 6)4.The equation of a horizontal line passing through the point (4, 2) is:a)b)c)d)5.The equation of a line with a slope of and a y intercept of 8 is:a)b)c)d)6.The slopes of 2 lines are -7 and . These lines are said to be:a)parallelb)perpendicularc)coincidentd)none of these7.The slope of a line segment passing through 2 points (10,- 4) and (-2, -16) is:a)1b)2c)-1d)-28.The length of a line segment with end points (-6, 7) and (-1, -5) is:a)12b)5c)13d)1699.The diameter of a circle whose equation is is:a)15b)16c)17d)none of these10.The equation of a circle with a centre of (0, 0) that also passes through the point (-8, -6) is:a)b)c)d)11.The y-intercept of the line is:a)2b)-2c)10d)512.The slope of the line is:a)2b)-2c)1d)013.If (-3, y) is a solution to the equation , what is the value of y?a)3b)6c)5d)814.The product is equal to: a)b)c)d)15.A simplified expression for is:a)b)c)d)16.A simplified expression for is:a)b)c)d)17.The slope of the line, which is perpendicular to the line, is:a)-4b)4c)1d)-118.The shortest distance from the point (2, -3) to the line is:a)5b)3c)2d)619.The value of the polynomial when is:a)59b)44c)13d)2920.Which of the following is not a function:a)b)c)d)21.The range of the relation whose equation is is:a)b)c)d)22.The vertex of the parabola is:a)b)c)d)23.The equation of the axis of symmetry of the parabola is:a)b)c)d)24.A parabola with a vertex of and a stretch factor of (relative to ) would have an equation of:a)b)c)d)25The parabola passes through the point . The value of is:a)-19b)11c)13d)19A/CPart B Short AnswersFor each of the questions in this section, write your answers in the spaces provided. Use the foolscap provided for any rough work. Show details of calculations wherever requested.1.In the accompanying diagram, state each of the following: (4 Marks)Ka)domain: _ (1 Mark)Kb)range: _ (1 Mark)Cc)Is the relation a function? Justify your answer. (2 marks)A2.The x-intercepts of the parabola are: _ and _.(Show your work) (2 Marks)A3.The roots of the quadratic equation are: _ and _.(Show your work) (3 Marks)A4.Write the equation of the parabola with a vertex of (4, 23) if it passes through the point (-1, -2): (Show your work) (3 Marks)_T5.A line passes through 2 points (1, 4) and (2,-4). Calculate the slope of the line. Also show the equation of the line in the form . (Show your work) (4 Marks)_SlopeEquation K6.The Tangent of is: _ (1 Mark)A7.a) In the accompanying diagram, the two triangles are similar. What is the value of ?(Show your work) (2 Marks)x181227 _Tb) If the area of the smaller triangle is 8 cm2, what is the area of the larger triangle?(Show your work) ( 2 Marks)Area = _K8Given that sin A = , find (to the nearest degree) _ (1 Mark)A9.In the accompanying right triangle, find the value of x to one decimal place. (Show your work) (2 Marks)_3028xA10.Use the SINE LAW to find the value of side x to one decimal place.(Show your work) (2 Marks)5642x30x = _A11.Use the COSINE LAW to find the value of side x to one decimal place.(Show your work) (2 Marks)562030xx = _T12.Factor each of the following to the fullest extent possible: (4 Questions * 2 marks each)a)_b)_c)_d)_A/CPart C Full Solutions RequiredFor each of the questions in this section, full solutions are required. Record your answers in the spaces provided. Use the foolscap provided for any rough work.A1.Solve the linear system using the elimination method. Remember to find values for both x and y. (5 Marks)CExplain what the solution above represents geometrically. How do you know that the solution you arrived at is the correct answer? (2 Marks)A2.Expand and simplify the polynomial . (4 Marks)T3.Find the equation of the line perpendicular to the line and passing through the point (-4, 1). (4 Marks)T4.From the window of one building, a man finds that the angle of elevation to the top of a second building is 47 and the angle of depression to the bottom of the same building is 58. The buildings are 60 m apart. Find the height of the 2nd building to the nearest metre. A diagram is required. (6 Marks)T5.DABC has vertices A(1, 7), B(-5, 3) and C(3, -1). Determine the equation for AE, the altitude from vertex A to the opposite side BC. (5 Marks)6.The hypotenuse of a right triangle is 26 cm. The sum of the other two sides is 34 cm. (9 Marks)Ta)Find the length of the other two sides of the triangle. (3 Marks)Tb)Find the measure of the other two angles. Round to the nearest deg