加拿大安大略省十年級數學試卷英文

1、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 a

2、s you see fit.i IIGRADE 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/CK Part A - Multiple Choice 25 Marks (25 questions * 1 mark each)For each of the following questions in this se

3、ction,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 theoordinates of point

4、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)x 2b)y 4c) y 2d)x 45. The equation of a line with a slope of m 5 and ay inte

5、rcept of 8 is:6. The slopes of 2 lines are -7 and . These lines are said to be:a) parallelb) perpendicular c) coincidentd) none of these7. The slope of a line segment passing through2 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)

6、 is:a)12b)5c) 13d)169229. The diameter of a circle whoseequation is x y 289 is:a) 15b) 16c)17d) none of thesea) 7mb) 7m 2nc) 3md) 7m 2n10. The equation of a circle with a centre of (0, 0) that also passes through thepoint (-8, -6) is:、22_. .22_ _a)xy 10b)xy 100c)22x y 14d)22x y 4811. The y-intercept

7、 of the line 2x 5y 10is:a) 2b) -2c)10d)12. The slope of the line 4x 2y 1 0 is:a) 2b) -2c)d)2y 13, what is the value of y?13. If (-3, y) is a solution to the equation xa) 3b)c) 5d)14. The productc 233x y z,2 34x y z is equal to:一、“6 2a) 12xy zb)“46212x y zc)/八 6212xy zd)/c 40012x y z15. A simplified

8、expressionfor 2m n5m nis:27a2bc4-is:9abc16. A simplified expression for22 2a) 3acb) 3abcc) 3acd) 3a c17. The slope of the line, which is perpendicular to the line, x 4y 8 0 is:a) -4b) 4c) 1d) -118. The shortest distance from the point (2, -3) to the line x 4 is:a) 5b) 3c) 2219. The value of the poly

9、nomial 4a 5a 8 when a 3 is:a) 59b) 44c) 1320. Which of the following is not a function :2、一 2a) 2,3 , 4,5, 6,7 b) y 2xc) x 2y221. The range of the relation whose equation is y x 5 is:a) y 5b) y 5c) y 5222. The vertex of the parabola y x 46 is:a) 4,6b) 4, 6c) 6,4d) 6d) 29d) 6,2 , 7,3 , 8,3d) y 5d) 6,

10、 42.23. The equation of the axis of symmetry of the parabola y 4x25 is:d) x 212、-(relative to y x ) woulda) x 5b) x 5c) x 2、1- 2 八.、a) y x 23 b) y424. A parabola with a vertex of 2,3 and astretch factor of have an equation of:1 八2 八 、1 八2八 .、-x 23 c) y - x 32 d) y442,25 The parabola y 4x kpasses thr

11、ough the point2,3The value of kis:a) -19b) 11c) 13d) 19A/C Part 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 eac

12、h of the following:(4 Marks)KKa) domain: ( Mark)b) range: Mark)c) Is the relation afunction? Justifyyour answer. (2 marks)2A2. The x-intercepts of the parabola y x 289 are:(Show your work) (2 Marks)and2A3. The roots of the quadratic equation 3x 17x 10 0 are: and(Show your work) (3 Marks)A4. Write th

13、e equation of the parabola with a vertex of (4, 23) if it passes through thepoint (-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 showthe equation of the line in the form Ax By C 0 . (Show your work) (4 Marks)SlopeEquation

14、K6. The Tangent of 45 is: (1 Mark)A7. a) In the accompanying diagram,the two triangles are similar . What is the value of x(Show your work) (2 Marks)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 =K8 Given that sin A = f= , f

15、ind A (to the nearest degree) (1 Mark)2A9. In the accompanying right triangle , find the value of x to one decimal place. (Show your work) (2 Marks)xA10. Use the SINE LAWAo find the value of side x to one decimal place. (Show your work) (2 Marks)A11. Use the COSINE LAWo find the value of side x to o

16、ne decimal place. (Show your work) (2 Marks)T12. Factor each of the following to the fullest extent possible: (4 Questions * 2 marks each)a) mx my 2x 2y 、2_b) 4x 11x 3c) 16x4 169y2d) 9r2 30rs 25s2A/C Part C -Full Solutions RequiredFor each of the questions in this section, full solutions are require

17、d. Record your answers in the spaces provided. Use the foolscap provided for any rough work.A1.Solve the linear system using theelimination method . Remember to find values forboth x and y. (5 Marks)x 5y 22C2x 3y 21Explain what the solution above represents geometrically. How do you know that the so

18、lution you arrived at is the correct answer? (2 Marks)2A2. Expand and simplify the polynomial 2 x 3 x 4 x 1 . (4 Marks)T3. Find the equation of the line perpendicular to the line 8x y 8 0 and passing through the point (-4, 1). (4 Marks)T4. From the window of one building, a man finds that the angle

19、of elevation to the topof 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. ?ABC has vertices A(1, 7), B(-5, 3) and C(3, -1D).etermine the equation for AE, thealtitude from vertex A to the opposite side BC. (5 Marks)6. The hypotenuse of aright triangle is 26 cm. The sum of the other two sides is 34 cm. (9 Marks)T a) Find the length of the other two sides of the triangle. (3 Marks)T b) Find the measure of the