MPM2D – Exam Review

MPM 2D1: PRATICE EXAM 3766185122555001. Solve each of the following by the method specified: a) Solve by Graphing. Check your answer. b) Solve by Substitution: c) Solve by Elimination: 2. State the equation of a circle with centre (0,0) that passes through the point (5,2). Include a sketch. 48799752667000 3. Given the points A(2,-4) and B(-3,8) find: a) The length of the line segment AB. b) The midpoint of the line segment AB. c) The equation of the line through A and B d) The slope of a line perpendicular to AB. 4. Complete the following table and then sketch y=x2 in pencil and each of the following parabolas in colour: 385191016573500 Equation Vertex Axis of Symmetry Domain Range 5. Expand and simplify each of the following. a) b) c) 6. Factor fully: a) b) c) d) 7. Solve each of the following quadratic equations using the method specified. a) Solve by Factoring: b) Solve by the Quadratic Formula: 8. Using trigonometry, find the missing value in each of the following diagrams. Round to 1 decimal place. 23114015875015 x 35o 0015 x 35o a) b) c) 46983651536707 9 007 9 26504904889520 x 80o 0020 x 80o 34886904000513 62o 16 m x 00 13 62o 16 m x 33591567945x 55o 75o 10 cm 00x 55o 75o 10 cm d) e) 9. The sum of two numbers is 31. The sum of the second number less 10 and twice the first number is 33. What are the two numbers? 10. Flora invests a total of $10 000 in two different bonds. One bond earns 1.5% interest per annum and the other earns 2.0% per annum. At the end of the year she received 198.40 in interest from the two bonds together. How much did she invest in each bond? 11. Expand and simplify the following: a) b) 12. Factor fully: a) b) 13. The vertices of a triangle ABC are A(1,1), B(6,5) and C(12,-7). Find the equation of the perpendicular bisector of BC. -457204445000 14. What type of triangle is formed by the vertices A(0,10), B(9,-9), and C(14,5) -228605270500 15. Match each of the equations below to the corresponding graphs. ____ ____ ____ ____ 16. Complete the square and state the vertex of the parabola . 17. Solomon kicks a soccer ball in the arc , where h is the height of the ball in metres and t is the time in seconds. a) What is the maximum height that the ball reaches? b) How long does it take for the ball to hit the ground. c) How high is the ball 2 seconds after Solomon kicked it? 18. The neighbours decided to re-carpet their rectangular living room, which is 6 m longer than it is wide. The wall to wall carpeting that they purchases covers 55 m2. What are the dimensions of the room? 19. Solve the following quadratic equation. State both the exact roots and the approximate roots rounded to 2 decimal places. 20. Hal looks out of his apartment window at the building across the street. He looks up at a 35o angle and sees a bird on a ledge 5m above his apartment. How far apart are the building? Round your answer to 2 decimal places. 21. A golf ball is hit from a raised platform in the arc , where h is the height in metres and d is the horizontal distance. a) How high is the platform? b) How far away does the ball land on the ground.