MPM2D Final Exam Review Questions PDF

# MPM2D Final Exam Review Questions ## Linear Systems 1. Does the ordered pair (2, 3) satisfy the equation 2x + 4y = 16? Show your work. * Yes the ordered pair (2, 3) satisfies the equation 2. Solve the following linear system by graphing. Check your solution. * y = 2x-1 * y=-x+5 3. Without gra...

# MPM2D Final Exam Review Questions ## Linear Systems 1. Does the ordered pair (2, 3) satisfy the equation 2x + 4y = 16? Show your work. * Yes the ordered pair (2, 3) satisfies the equation 2. Solve the following linear system by graphing. Check your solution. * y = 2x-1 * y=-x+5 3. Without graphing, determine whether each system has one solution, no solution, or infinitely many solutions. * y = 2x - 5 * 4x-2y = 10 * 3x - y = 17 * 6x + 2y= -8 * 12x + 8y + 4 = 0 * 15x + 10y = 5 4. Solve the following system of equations by substitution. Check your solution. * 4x + 3y = 7 * 3x + y = -1 5. Solve the following system of equations by elimination. Check your solution: * 3x + y = 17 * 2x - y = -2 6. Design (do not solve) a system of equations for the following scenarios: * A supermarket sells 2-kg and 4-kg bags of sugar. A shipment of 1100 bags of sugar has a total mass of 2900 kg. How many 2-kg bags and 4-kg bags are in the shipment? * The school car wash charged $5 for a car and $6 for a van. A total of 86 cars and vans were washed on Saturday, and the amount earned was $475. How many vans were washed on Saturday? ## Coordinate Geometry 7. Determine the length of the line segment joining the points (3, 7) and (-1, -5). Round to the nearest tenth. 8. Find the slope of the line with points (0, 5) and (6, 10). 9. Write the equation for a circle with centre (0, 0) and through the point (3, 4). 10. The equation for a circle with centre (0, 0) is x² + y² = 361. What is the radius? 11. Determine the midpoint of the line segment with the endpoints (-6, 2) and (4, 8). 12. Explain how you can determine whether two lines are perpendicular or parallel based on their slopes. 13. The vertices of a quadrilateral are S(1,2), T(3, 5), U(6, 7), and V(4, 4). Verify that STUV is a parallelogram. 14. Find the equation of the median from vertex A in AABC, if the coordinates of the vertices are A(-3, -1), B(3, 5), and C(7, -3). ## Quadratics 15. What is the degree of the following polynomials? * 3x²-2x * 4a-b³ * 4x²-2x² + x² + 4 16. Expand and Simplify * 2(m-3)(m+8) * (x+4)² * 6(m-2)(m+3)-3(3m-4) 17. Factor the following completely. * 2ax+10ay-8az * x²-5x+6 * 3x²y-6x² - 2y + y² * x²-25 * 3y² + y-4 * 4x²-16x-48 18. Sketch the parabola and state the direction of the opening, the coordinates of the vertex, the equation of the axis of symmetry and the maximum or minimum value. * y = 2(x-1)²+1 19. Describe the transformations you need to apply to the graph of y = x² to create each of the following parabolas: * y = -(x-4)²-3 * y=-1/2(x+2)² +7 20. A quadratic relation has a vertex of (3, -1) and passes through the point (2, -3). Determine its equation in vertex form. 21. Given the quadratic function y = 4x²-20x+7, determine the vertex by completing the square. 22. A ball is thrown upward with an initial velocity of 18 m/s. Its height, h metres after t seconds, is given by the equation h = -5t²+18t+1.8 where 1.8 represents the height at which the ball is released by the thrower. At what time the ball will reach 15 m? 23. Phil wants to make the largest possible rectangular vegetable garden using 18 m of fencing. The garden is right behind the back of his house, so he has to fence it on only three sides. Determine the dimensions that maximize the area of the garden. 24. A pizza company's research shows that a $0.25 decrease in the price of a pizza results in 50 more pizzas being sold. The usual price of $15 for a three-item pizza results in sales of 1000 pizzas. Write the algebraic expression that models the maximum revenue for this situation, and find the price of a pizza that will produce a maximum revenue. 25. State the roots of each equation. * (x-2)(x + 7) = 0 * (3x+1)(2x-3) = 0 26. Solve 3x²-6x-8 = 0 using the quadratic formula. Round to the nearest hundredth. ## Trigonometry 27. Use a calculator to find each of the following, to four decimal places. * tan 84° = * sin 21° = * cos 43° = 28. Find ∠K, to the nearest degree. * tan ∠K = 2.750 * sin ∠K = 0.208 * cos ∠K = 6/13 29. Solve each triangle. Round each side length to the nearest tenth of a unit, and each angle, to the nearest degree. * △ STU * ST= 15 m * ∠S = 40º * △ WX * WX = 14 cm * WY = 24 cm 30. From the window of one building, Sam finds the angle of depression of the top of a second building is 41° and the angle of depression of the bottom is 54°. The buildings are 56 m apart. Find, to the nearest metre, the height of the second building. 31. In ∆ABC, ∠A = 50°, a = 9 m, and b = 8 m. What is the measure of ∠B? 32. Solve for the length of side t. * △ STU * ST = 8.6 m * TU = 11.2 m * ∠S = 57º 33. Solve for the measure of ∠T. * △ STU * ST = 14.1 cm * SU = 23.9 cm * TU = 19.7 cm