加拿大安大略省十年级数学试卷英文

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/C[K] Part A – Multiple Choice 25 Marks (25 questions * 1 mark each)For each of the following questions in this section, circle the letterrepresenting the correct answer.1. A linear system of two equations that has one solution representstwo lines that are:a) parallel b) coincident c) intersecting d) none of these2. The midpoint of RS is M(8, -1). If point S has coordinates (11, 4) whatare the coordinates of point Ra) (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) 2=xb) 4=yc) 2=yd) 4=x5. The equation of a line with a slope of 5=m and a y intercept of 8 is:a) 85+=x y b) 85+-=x y c) 85--=x y d) 58+=x y6. The slopes of 2 lines are -7 and 71. These lines are said to be:a) parallelb) perpendicular c) coincident d) 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 28922=+y x is:a) 15 b) 16c)17d) none of these10.The equation of a circle with a centre of (0, 0) that also passesthrough the point (-8, -6) is:a) 1022=+y x b) 10022=+y xc) 1422=+y xd) 4822=-y x11.The y-intercept of the line 01052=+-y x is:a) 2 b) -2c) 10d) 512.The slope of the line 0124=-+y x is:a) 2 b) -2c) 1d) 013.If (-3, y) is a solution to the equation 132=+y x , what is the valueof ya) 3 b) 6c) 5d) 814.The product ()()z y x z y x 323243-- is equal to:a) 2612z xy b) 26412z y xc)2612z xy - d) 00412z y x15.A simplified expression for ()()n m n m ----52 is:a) m 7 b) n m 27+c) m 3-d) n m 27-16. A simplified expression for 242927abcbc a -- is:a) ac 3 b) abc 3c) 23ac d) 223c a17.The slope of the line, which is perpendicula r to the line, 084=+-y xis:a) -4 b) 4c) 1d) -118.The shortest distance from the point (2, -3) to the line 4-=x is:a) 5 b) 3c) 2d) 619.The value of the polynomial 8542+-a a when 3-=a is:a) 59 b) 44c) 13d) 2920.Which of the following is not a function :a) ()()(){}7,6,5,4,3,2 b) 22x y = c) 22y x =d) ()()(){}3,8,3,7,2,621.The range of the relation whose equation is 52--=x y is:a) 5-≤y b) 5≤yc) 5-≥yd) 5≥y22.The vertex of the parabola ()642--=x y is:a) ()6,4-b) ()6,4-c) ()4,6- d) ()4,6-23. The equation of the axis of symmetry of the parabola ()5242+--=x y is:a) 5=xb) 5-=xc) 2=xd) 2-=x24.A parabola with a vertex of ()3,2 and a stretch factor of 41-(relative to 2x y =) would have an equation of:a) ()32412+--=x y b) ()32412++-=x y c)()23412-+-=x y d) ()23412++-=x y25 The parabola k x y +-=24 passes through the point ()3,2-. T he value ofk is:a) -19 b) 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) [K]a)domain: __________ (1Mark)[K]b) range: __________ (1Mark)[C] c) Is the relation a function Justify your answer. (2 marks)[A]2. The x-intercepts of the parabola 2892-=x y are: __________ and __________.(Show your work) (2 Marks)[A]3. The roots of the quadratic equation 0101732=+-x x are: __________ and __________.(Show your work) (3 Marks)[A]4. 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)____________________[T] 5. 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 0=++C By Ax . (Show your work) (4 Marks)____________________ ____________________SlopeEquation[K] 6. The Tangent of 45 is: __________ (1 Mark)[A]7. a) In the accompanying diagram, the two triangles are similar . What is the value of x(Show your work) (2 Marks)=x __________[T]b) If the area of the smaller triangle is 8 cm 2, what is the area of the larger triangle(Show your work) ( 2 Marks)Area = __________[K]8 Given that sin A = 21, find A ∠ (to the nearest degree) __________(1 Mark)[A] 9. In the accompanying right triangle , find the value of x to one decimal place.(Show your work) (2 Marks)=x ________[A] 10. Use the SINE LAW to find the value of side x to one decimal place. (Show your work) (2 Marks)x = ________3028x5642x30[A] 11. Use the COSINE LAW to find the value of side x to one decimalplace.(Show your work) (2 Marks)x = ________[T]12.Factor each of the following to the fullest extent possible: (4Questions * 2 marks each)a) y x my mx 22--+________________________b) 31142--x x________________________c) 2416916y x -________________________d) 2225309s rs r +-________________________A/CPart C – Full Solutions Required562030 xFor 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.[A]1. Solve the linear system using the elimination method . Remember to find values for both x and y. (5 Marks)225=+y x2132-=-y x[C]Explain what the solution above represents geometrically. How do you know that the solution you arrived at is the correct answer (2 Marks)[A] 2. Expand and simplify the polynomial ()()()21432+-+-x x x . (4 Marks)[T]3. Find the equation of the line perpendicular to the line 088=-+y x and passing through the point (-4, 1). (4 Marks)[T] 4. 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 ofdepression to the bottom of the same building is 58. The buildingsare 60 m apart. Find the height of the 2nd building to the nearestmetre. A diagram is required. (6 Marks)[T] 5. ABC 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 othertwo 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 other two angles. Round to the nearest degree. (3 Marks)[C] c) Describe a situation where you would be able to use knowledge ofthe Pythagorean theorem in a practical, real life situation. (3Marks)[T] 7. A rectangular skating rink measures 20m by 20m. It has been decidedto increase the area of the rink by a factor of 4. Determine howmuch each side should be extended. Assume that each side isextended by the same amount. (6 Marks)[C] What is the significance of keeping the skating rink in the shape ofa square Justify your answer. (3 Marks)[A] 8. a) Solve 35122+=d d using the quadratic formula. (2 Marks)[A] b) Solve 0x by factoring. Check your solutions. (2 Marks)-122=3。