MCF3M1 Exam Review. 1. Which relation is not a function? a. c. b. d. 2. What is the range of the function?

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1 MCF3M1 Exam Review 1. Which relation is not a function? 2. What is the range of the function? a. R = {1, 5, 4, 7} c. R = {1, 2, 3, 4, 5, 6, 7} b. R = {1, 2, 3, 6} d. R = {2, 5, 4, 7} 3. Which function includes a translation of 3 units to the left? 4. Kevin threw a ball straight up with an initial speed of 20 metres per second. The function describes the ball s height, in metres, t seconds after Kevin threw it. What are the coordinates of the vertex? (20, 2) 5. List the sequence of steps required to graph the function a. horizontal translation 4 units to the right, vertical compression by a factor of 1, vertical translation 6 units down b. horizontal translation 4 units to the right, reflection in x-axis, vertical translation 6 units down c. horizontal translation 4 units to the left, vertical translation 6 units up, reflection in x-axis d. horizontal translation 4 units to the left, reflection in x-axis, vertical translation 6 units down 6. Which function matches the graph? 5 4 y x

2 7. A stonewashed jean company has determined the cost in dollars (c) per tonne of stones mined is given by, where x is the number of tonnes of stone. How does the vertex of the parabola of the function compare to the vertex of a. down 5 units and right 7 units c. up 7 units and right 5 units b. up 7 units and left 5 units d. up 5 units and right 7 units 8. Which graph shows the range R = {y 1 y R} y ( x 1) Expand and simplify. 10. What is the greatest common factor of the polynomial? 4 b. 2 d Name the greatest common factor of the terms of the binomial What is the missing factor? 13. Which shows the factorization of the polynomial? 14. Factor the quadratic equation fully. 15. What is the missing factor? 16. Factor the trinomial. 17. Which polynomial is not a perfect square? 18. What is the missing factor? 19. Which shows the quadratic function expressed in factored form?

3 20. What is the y-intercept of the quadratic function? a. (0, 12) c. (0, 2) b. (0, 3) d. (0, 12) 21. A rocket is shot into the air. The height of the rocket is modelled by the function is the height in metres and t is the time in seconds. When will the rocket hit the ground? a. 4.5 seconds c. 9 seconds b. 5 seconds d. 45 seconds, where h(t) 22. What are the coordinated of the vertex of? a. ( 2, 5) c. ( 2, 24) b. (1.5, 24.5) d. (5, 0) 23. A fountain shoots water from a nozzle at its top. The function describes the height of the water h(t), in metres, t seconds after it leaves the nozzle. What is the maximum height of the water spout? a. 1 metre c. 15 metres b. 3 metres d. 20 metres 24. For the function, how many solutions does the corresponding quadratic equation have? a. 0 c. 2 b. 1 d Solve. a. x = 2, 7 c. x = 2, 7 b. x = 2, 7 d. x = 2, Use factoring to solve. a. x = and x = 5 b. x = and x = 5 c. d. x = and x = 5 x = and x = Which coordinate is the vertex of the function a. (12, 9) c. (3, 9) b. (9, 3) d. (3, 9) 28. Which function represents written in standard form? 29. Which equation represents the equation of the axis of symmetry for? 30. What number must you add to to create a perfect square? a. 6 c. 36 b. 12 d What is the factored form of 32. Which equation represents in vertex form?

4 33. Which equation represents in vertex form? 34. Determine which coordinate is the vertex of a. (1, 10) c. ( 1, 7) b. (1, 12) d. (1, 7) 35. Determine which coordinate is the vertex of a. (5, 35) c. ( 5, 40) b. ( 5, 35) d. ( 5, 10) without graphing the parabola. without graphing the parabola. 36. What information can you gather immediately from a quadratic function written in standard form? a. vertex c. y-intercept b. equation of the axis of symmetry d. domain 37. A quadratic equation cannot have how many real solutions? a. 0 c. 2 b. 1 d Use the quadratic formula to solve. Round your answer to two decimal places. a c and 1.64 b d. no real solution 39. Use the quadratic formula to solve. Round your answer to two decimal places. a and 1.93 c. 4.5 and 0.98 b and 5.43 d. no real solution 40. A golf ball is chipped out of a sand trap along a path that can be modelled by the quadratic function, where time, t, is in seconds and height, h(t), is in metres. Use the quadratic formula to determine where the ball will land to the nearest hundredth. a. 0 m c m b m d m 41. Determine the discriminant of. 42. Given triangle ABC right, if A 38 and b 4.47 cm, determine a to the nearest hundredth. a cm c cm b cm d cm 43. Given the figure above, if a 3.4 m and c = 1.8 m, determine C to the nearest degree. a. 32 c. 58 b. 62 d The tallest church tower in the Netherlands is the Dom Tower in Utrecht. If the angle of elevation to the top of the tower is 77 when 25.9 m from the base, what is the height of the Dom Tower to the nearest metre. a. 25 m c. 112 m b. 115 m d. 27 m 45. What information do you need to know about a triangle in order for you use the sine law? a. two sides and an angle opposite a known side b. two angles and any side c. both a and b d. neither a and b

5 46. Using the figure right, if DCA = 110, c = 3.80 cm, and A = 84, how long is side a to the nearest hundredth of a centimetre? a cm c cm b cm d cm 47. Given three sides of an acute triangle, which of the following can you use to solve for the angles of the triangle? a. sine law c. cosine law b. primary trigonometric ratios d. Pythagorean Theorem 48. For triangle HIJ, if I = 70, j = 5.35 cm, and h = 3.80 cm, use the cosine law to solve for side i. Round your answer to the nearest hundredth of a centimetre. a cm c cm b cm d. none of the above 49. Given triangle HIJ above, if h = 35, i = 50, and j = 44, use the cosine law to solve for J. Round your answer to the nearest degree. a. 59 c. 43 b. 78 d. none of the above. 50. What is the shortest interval in which a periodic function will complete one cycle? a. a period c. an event b. a wavelength d. an action 51. What is the equation of the axis? a. the horizontal line that intersects the maximum value of a periodic function b. twice the sum of the maximum and minimum functional values c. the y-intercept of a periodic function d. the horizontal line halfway between the maximum and minimum value of a periodic function 52. What is the amplitude? a. the distance between the maximum and minimum values of the function b. the length of one cycle c. the distance between the equation of the axis and either a maximum or minimum value of the function d. the number of cycles shown 53. Consider a Ferris wheel which loads passengers at a height of 1 metre above the ground a carries them to a height of at most 15 metres. What is the amplitude of the function which models the height of a passenger above ground while in constant motion? a. 7 c. 1 b. 14 d What is the amplitude of the function 3sin(x 4)? a. 3 c. 1 b. 2 d Which of the following is equivalent to? 56. Simplify so that the expression is a single power with a positive exponent:.

6 57. Identify the growth rate in the following algebraic model:. a. 106% c. 12% b. 30% d. 6% 58. In the following exponential growth model, what does the 0.35 represent? a. the growth rate b. the initial amount c. the time since the initial period d. the percent that doubles in t time periods 59. What does the number 16 represent in the following algebraic model? a. the initial amount c. the number of decay periods b. the decay rate d. the half-life 60. What does the number 3600 represent in the following decay model? a. the number of decay periods c. the half-life b. the initial amount d. the decay rate 61. A new car costs $ It loses 16% of its value each year after it is purchased. Determine the value of the car after 40 months. a. $ c. $ b. $ d. $ A cup of coffee cools according to the equation, where T is the temperature in C after t minutes. Determine the temperature of the coffee after 30 minutes, to the nearest degree. a. 25 C c. 18 C b. 19 C d. 33 C 63. An investment of $850 earns 6.75%/a. Calculate the value of the investment when the interest is compounded quarterly for 5 years. a. $ c. $ b. $ d. $ Calculate the amount you would end up with if you invested $4000 at 11.2% compounded monthly for 5 years. a. $ c. $ b. $ d. $ How much should be invested now in order to have $ in 4 years time? The money will be invested at 6%/a compounded monthly. a. $ c. $ b. $ d. $ Shankir borrowed money at an interest rate of 5.75%/a compounded semi-annually that he will pay back in 5 years time. He will repay $ How much money did he borrow? a. $5150 c. $4450 b. $4200 d. $ Determine the present value of a loan of $ that is due in 7 years. The interest rate is 8%/a compounded quarterly. a. $ c. $ b. $ d. $

7 MCF3M1 Exam Review Answer Section MULTIPLE CHOICE 1. ANS: C PTS: 1 REF: Knowledge and Understanding OBJ: The Characteristics of a Function 2. ANS: A PTS: 1 REF: Knowledge and Understanding OBJ: The Characteristics of a Function 3. ANS: A PTS: 1 REF: Knowledge and Understanding OBJ: Graphing Quadratic Functions by Using Transformations 4. ANS: B PTS: 1 REF: Application OBJ: Graphing Quadratic Functions by Using Transformations 5. ANS: D PTS: 1 REF: Communication OBJ: Using Multiple Transformations to Graph Quadratic Functions 6. ANS: B PTS: 1 REF: Knowledge and Understanding OBJ: Using Multiple Transformations to Graph Quadratic Functions 7. ANS: D PTS: 1 REF: Application OBJ: Using Multiple Transformations to Graph Quadratic Functions 8. ANS: B PTS: 1 REF: Thinking OBJ: The Domain and Range of a Quadratic Function 9. ANS: A PTS: 1 REF: Knowledge and Understanding OBJ: Working with Quadratic Expressions 10. ANS: B PTS: 1 REF: Knowledge and Understanding OBJ: Factoring Polynomials: Common Factoring 11. ANS: A PTS: 1 REF: Knowledge and Understanding OBJ: Factoring Polynomials: Common Factoring 12. ANS: D PTS: 1 REF: Knowledge and Understanding OBJ: Factoring Quadratic Expressions: x^2 + bx +c 13. ANS: C PTS: 1 REF: Knowledge and Understanding OBJ: Factoring Quadratic Expressions: x^2 + bx +c 14. ANS: B PTS: 1 REF: Knowledge and Understanding OBJ: Factoring Quadratic Expressions: x^2 + bx +c 15. ANS: D PTS: 1 REF: Knowledge and Understanding OBJ: Factoring Quadratic Expressions: ax^2 + bx + c 16. ANS: B PTS: 1 REF: Knowledge and Understanding OBJ: Factoring Quadratic Expressions: ax^2 + bx + c 17. ANS: C PTS: 1 REF: Knowledge and Understanding OBJ: Factoring Quadratic Expressions: Special Cases 18. ANS: D PTS: 1 REF: Knowledge and Understanding OBJ: Factoring Quadratic Expressions: Special Cases 19. ANS: B PTS: 1 REF: Knowledge and Understanding OBJ: Relating the Standard and Factored Forms 20. ANS: A PTS: 1 REF: Knowledge and Understanding OBJ: Relating the Standard and Factored Forms 21. ANS: C PTS: 1 REF: Application OBJ: Relating the Standard and Factored Forms 22. ANS: B PTS: 1 REF: Knowledge and Understanding

8 OBJ: Relating the Standard and Factored Forms 23. ANS: D PTS: 1 REF: Application OBJ: Relating the Standard and Factored Forms 24. ANS: B PTS: 1 REF: Knowledge and Understanding OBJ: Solving Quadratic Equations by Graphing 25. ANS: C PTS: 1 REF: Knowledge and Understanding OBJ: Solving Quadratic Equations by Factoring 26. ANS: D PTS: 1 REF: Knowledge and Understanding OBJ: Solving Problems Involving Quadratic Functions 27. ANS: C PTS: 1 REF: Knowledge and Understanding OBJ: The Vertex Form of a Quadratic Function 28. ANS: C PTS: 1 REF: Knowledge and Understanding OBJ: The Vertex Form of a Quadratic Function 29. ANS: B PTS: 1 REF: Knowledge and Understanding OBJ: The Vertex Form of a Quadratic Function 30. ANS: C PTS: 1 REF: Knowledge and Understanding 31. ANS: B PTS: 1 REF: Knowledge and Understanding 32. ANS: A PTS: 1 REF: Knowledge and Understanding 33. ANS: D PTS: 1 REF: Knowledge and Understanding 34. ANS: D PTS: 1 REF: Knowledge and Understanding 35. ANS: B PTS: 1 REF: Knowledge and Understanding 36. ANS: C PTS: 1 REF: Knowledge and Understanding 37. ANS: D PTS: 1 REF: Knowledge and Understanding OBJ: Solving Quadratic Equations Using the Quadratic Formula 38. ANS: C PTS: 1 REF: Knowledge and Understanding OBJ: Solving Quadratic Equations Using the Quadratic Formula 39. ANS: D PTS: 1 REF: Knowledge and Understanding OBJ: Solving Quadratic Equations Using the Quadratic Formula 40. ANS: B PTS: 1 REF: Application OBJ: Solving Quadratic Equations Using the Quadratic Formula 41. ANS: A PTS: 1 REF: Knowledge and Understanding OBJ: Investigating the Nature of the Roots 42. ANS: B PTS: 1 REF: Knowledge and Understanding OBJ: Applying the Primary Trigonometric Ratios 43. ANS: D PTS: 1 REF: Knowledge and Understanding OBJ: Applying the Primary Trigonometric Ratios 44. ANS: C PTS: 1 REF: Knowledge and Understanding OBJ: Applying the Primary Trigonometric Ratios 45. ANS: C PTS: 1 REF: Knowledge and Understanding OBJ: Investigating and Applying the Sine Law in Acute Triangles 46. ANS: A PTS: 1 REF: Application OBJ: Investigating and Applying the Sine Law in Acute Triangles

9 47. ANS: C PTS: 1 REF: Knowledge and Understanding OBJ: Investigating and Applying the Cosine Law in Acute Triangles 48. ANS: B PTS: 1 REF: Application OBJ: Investigating and Applying the Cosine Law in Acute Triangles 49. ANS: A PTS: 1 REF: Application OBJ: Investigating and Applying the Cosine Law in Acute Triangles 50. ANS: A PTS: 1 REF: Knowledge and Understanding OBJ: Periodic Behaviour 51. ANS: D PTS: 1 REF: Knowledge and Understanding OBJ: Investigating the Sine Function 52. ANS: C PTS: 1 REF: Knowledge and Understanding OBJ: Investigating the Sine Function 53. ANS: A PTS: 1 REF: Thinking OBJ: Investigating the Sine Function 54. ANS: A PTS: 1 REF: Knowledge and Understanding OBJ: More Transformations of sin x: f(x) = a sin x 55. ANS: A PTS: 1 REF: Knowledge and Understanding OBJ: The Laws of Exponents 56. ANS: A PTS: 1 REF: Knowledge and Understanding OBJ: Working with Integer Exponents 57. ANS: D PTS: 1 REF: Knowledge and Understanding OBJ: Solving Problems Involving Exponential Growth 58. ANS: B PTS: 1 REF: Communication OBJ: Solving Problems Involving Exponential Growth 59. ANS: C PTS: 1 REF: Communication OBJ: Problems Involving Exponential Decay 60. ANS: B PTS: 1 REF: Communication OBJ: Problems Involving Exponential Decay 61. ANS: D PTS: 1 REF: Application OBJ: Problems Involving Exponential Decay 62. ANS: A PTS: 1 REF: Knowledge and Understanding OBJ: Problems Involving Exponential Decay 63. ANS: A PTS: 1 REF: Knowledge and Understanding OBJ: Compound Interest: Determining Future Value 64. ANS: B PTS: 1 REF: Knowledge and Understanding OBJ: Compound Interest: Determining Future Value 65. ANS: A PTS: 1 REF: Knowledge and Understanding OBJ: Compound Interest: Determining Present Value 66. ANS: B PTS: 1 REF: Application OBJ: Compound Interest: Determining Present Value 67. ANS: D PTS: 1 REF: Knowledge and Understanding OBJ: Compound Interest: Determining Present Value