加拿大安大略省十级数学试卷 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 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) 2=x b) 4=y c) 2=y d) 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 and71. 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) 1 b) 2 c) -1 d) -28. The length of a line segment with end points (-6, 7) and (-1, -5) is:a) 12 b) 5 c) 13 d) 1699. The diameter of a circle whose equation is 28922=+y x is:a) 15 b) 16 c)17 d) none of these10. The equation of a circle with a centre of (0, 0) that also passes through the point (-8, -6) is:a) 1022=+y x b) 10022=+y x c) 1422=+y x d) 4822=-y x11. The y-intercept of the line 01052=+-y x is:a) 2 b) -2 c) 10 d) 512. The slope of the line 0124=-+y x is:a) 2 b) -2 c) 1 d) 013. If (-3, y) is a solution to the equation 132=+y x , what is the value of y ?a) 3 b) 6 c) 5 d) 814. The product ()()z y x z y x 323243-- is equal to:a) 2612z xy b) 26412z y x c) 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 3 c) 23ac d) 223c a17. The slope of the line, which is perpendicula r to the line, 084=+-y x is:a) -4 b) 4 c) 1 d) -118. The shortest distance from the point (2, -3) to the line 4-=x is:a) 5 b) 3 c) 2 d) 619. The value of the polynomial 8542+-a a when 3-=a is:a) 59 b) 44 c) 13 d) 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≤y c) 5-≥y d) 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=x b) 5-=x c) 2=x d) 2-=x24. A parabola with a vertex of ()3,2 and a stretch factor of 41- (relative to 2x y =) wouldhave 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 of k is:a) -19 b) 11 c) 13 d) 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: __________ (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 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=++CByAx. (Show your work) (4 Marks)____________________ ____________________Slope Equation[K] 6. The Tangent of45 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 cm2, 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 = ________[A] 11. Use 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) y x my mx 22--+________________________b) 31142--x x________________________c) 2416916y x -________________________3028︒x56︒42︒x3056︒2030xd) 2225309s rs r +-________________________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.[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 ofa second building is 47︒ and the angle of depression to the bottom of the samebuilding is 58︒. The buildings are 60 m apart. Find the height of the 2nd building tothe 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)6. The hypotenuse of a right 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 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)[T] 7. A rectangular skating rink measures 20m by 20m. It has been decided to increase the area of the rink by a factor of 4. Determine how much each side should beextended. 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 35122+=d d using the quadratic formula. (2 Marks)[A]b) Solve 03122=-x by factoring. Check your solutions. (2 Marks)。