加拿大安大略省十年级数学试卷-英文2 of 11GRADE 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 letter representing the correct answer.1. A linear system of two equations that has one solution represents two 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) 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)2=x 4=y 2=y 4=x 5=m 85+=x y 85+-=x y 85--=x y 58+=xy3 of 116.The slopes of 2 lines are -7 and. These lines are said to be:a)parallel b)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 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)7128922=+y x 1022=+y x 10022=+y x 1422=+y x 4822=-y x 01052=+-y x 0124=-+y x 132=+y x ()()z y x z y x 323243--2612z xy 26412z y x 2612z xy -00412z y x ()()n m n m ----52m 7n m 27+m 3-nm 27-4 of 1116.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:242927abc bc a --ac 3abc 323ac 223c a 084=+-y x 4-=x 8542+-a a 3-=a ()()(){}7,6,5,4,3,222x y =22y x =()()(){}3,8,3,7,2,652--=x y 5-≤y 5≤y 5-≥y 5≥y ()642--=x y ()6,4-()6,4-()4,6-()4,6-()5242+--=x y 5=x 5-=x 2=x 2-=x ()3,241-2x y =()32412+--=x y ()32412++-=x y ()23412-+-=x y ()23412++-=x y k x y +-=24()3,2-k5 of 11a)-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 calculationswherever requested.1.In the accompanying diagram, state each of the following: (4 Marks)[K]a)domain: __________ (1 Mark)[K]b)range: __________ (1 Mark)[C]c)Is the relation a function? Justifyyour answer. (2 marks)[A] 2.The x-intercepts of the parabola are: __________ and__________.(Show your work) (2 Marks)[A] 3.The roots of the quadratic equation are: __________ and__________.(Show your work) (3 Marks)2892-=x y 0101732=+-x x 24-2-46 of 11x[A] 4.Write the equation of the parabola with a vertex of (4, 23) if it passes through thepoint (-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. Alsoshow the equation of the line in the form . (Show your work) (4 Marks)________________________________________Slope Equation[K] 6.The Tangent of is: __________ (1 Mark)[A]7.a) In the accompanying diagram, the two triangles are similar. What is the value of?(Show your work) (2 Marks)__________[T]b) If the area of the smaller triangle is 8 cm 2, what is the area of the largertriangle?(Show your work) ( 2 Marks)Area = __________[K]8Given that sin A = , find (to the nearest degree) __________ (1 Mark)0=++C By Ax 45x =x 21A ∠1127 of 11[A]9.In the accompanying right triangle, find the value of x to one decimal place.(Show your work) (2 Marks)________[A]e the SINE LAW to find the value of side x to one decimal place.(Show your work) (2 Marks)x = ________[A]e the COSINE LAW to find the value of side x to one decimal place.(Show your work) (2 Marks)x = ________[T]12.Factor each of the following to the fullest extent possible: (4 Questions * 2 marks each)a)________________________b)________________________=x y x my mx 22--+31142--x x 328︒x56︒42︒x3056︒2030x8 of 11c)________________________d)________________________A/C Part 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.[A] 1.Solve the linear system using the elimination method. Remember to find valuesfor both x and y. (5 Marks)[C]Explain what the solution above represents geometrically. How do you knowthat the solution you arrived at is the correct answer? (2 Marks)[A] 2.Expand and simplify the polynomial . (4 Marks)2416916y x -2225309s rs r +-225=+y x 2132-=-y x ()()()21432+-+-x x x9 of 11[T] 3.Find the equation of the line perpendicular to the line and passingthrough the point (-4, 1). (4 Marks)[T] 4.From the window of one building, a man finds that the angle of elevation to thetop of a second building is 47︒ and the angle of depression to the bottom of thesame building is 58︒. The buildings are 60 m apart. Find the height of the 2ndbuilding to the nearest metre. 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)088=-+y x6.The hypotenuse of a right triangle is 26 cm. The sum of the other two sides is 34cm. (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 of thePythagorean theorem in a practical, real life situation. (3 Marks)10 of 1111 of 11[T]7. A rectangular skating rink measures 20m by 20m. It has been decided toincrease the area of the rink by a factor of 4. Determine how much each side should be extended. Assume that each side is extended by the same amount. (6 Marks)[C]What is the significance of keeping the skating rink in the shape of a square?Justify your answer. (3 Marks)[A]8.a)Solve using the quadratic formula. (2 Marks)[A]b)Solve by factoring. Check your solutions. (2 Marks)35122+=d d 03122=-x。