MPM2D Learning Activity 3.5 Assessment Opportunity Learning Activity 3.5 Assessment Opportunity Task 1: Knowledge questions (25 marks) 1. Write a word equation and an algebraic equation for each situation. For the algebraic equation, choose appropriate variables to describe the independent and dependent variables. a) Jerry is selling his car and has advertised it in the local newspaper. The newspaper charges a flat fee of $50 to take a picture of the car and $5 per day for the advertisement. Word equation (1 mark): Algebraic equation (2 marks): I Lily is very happy with the fuel efficiency of her new car. She estimates that she can drive 14 km per litre of gas. Word equation (1 mark): Algebraic equation (2 marks): TVO ILC MPM2D Learning Activity 3.5 Assessment Opportunity 2. This is a two-part question: a) On one Cartesian plane, graph both of the following equations using the slope and y-intercept method. (5 marks) 3 y = -=x-3 3x + 5y - 10 = 0 b) Describe the relationship between these two lines. (1 mark)TVO ILC MPM2D Learning Activity 3.5 Assessment Opportunity 3. Solve the following system of equations using the method of substitution. (5 marks) 2x + 3y =5 4x+ y = 5 4. Solve the following system of equations using the method of elimination. (5 marks) 5x + 2y = 15 4x - y = -1 5. Complete the following table. (3 marks) Equation: Zeros Axis of Vertex Maximum or Maximum or minimum minimum value y = a(x - s)(x - t) symmetry y = 3(x - 5)(x - 17). MPM2D Learning Activity 3.5 Assessment Opportunity TVO ILC Task 2: Application (25 marks) 6. A local fitness club has two payment options: e Plan A: a monthly membership fee of $25, plus $2 per visit. e Plan B: a fee of $7 per visit. a) Create equations to represent each plan. (2 marks) b) Solve the system of equations by graphing. (3 marks) ! S 4+ ) Determine which plan is cheapest if a member attends the fitness club each day for one month (30 days). (1 mark) TVO ILC MPM2D Learning Activity 3.5 Assessment Opportunity 7. The coordinates of ALMN are L(4,7), M(6, -1), and N(-2,3). a) Sketch a graph of the triangle. (1 mark) b) Determine the equations of two of the medians. (4 marks) c) Algebraically, solve the system of equations represented by the medians to determine the location of the centroid of ALMN. (5 marks)TVO ILC 1Y s 1 . MPM2D Learning Activity 3.5 Assessment Opportunity 8. A group of students launches a model rocket from the top of a building. The students have determined the equation y = % (x 4 6)(x 18) to describe the height of the rocket above ground level, y, in metres, at any time, x, in seconds. a) Complete the following table of values to predict the flight of the rocket. (2 marks) 1 Height above ground, y | o o ~ N O 12 14 16 18 b) Use the equation to determine the zeros. (2 marks) c) Determine the equation of the axis of symmetry. (2 marks) d) Determine the maximum height of the rocket. (2 marks) TVO ILC MPM2D Learning Activity 3.5 Assessment Opportunity e) Graph your results. (1 mark) Model rocket 60 Height above ground (m) 40 20 Time after ignition (s) Task 3: Communication (25 marks) 9. The following graph represents the cost of two cell phone plans. Explain, in detail, the circumstances under which one plan is better value for the customer than the other plan. (5 marks) Cost of cellphone plans Can Talk (C-30) (100, 30) 8 8 Point of Intersection Cost ($) Digicell (C-o. 10n + 20) 10 Number of minutes.. _MPM2D Learning Activity 3.5 Assessment Opportunity 10.Use words and a diagram to describe the centroid of a triangle. (5 marks) 11.Describe the difference between a linear and quadratic relation. Consider these points to assist you in developing your response. (5 marks) e Equation e First and second differences e Graph 12. Explain how the factored form of a quadratic equation, y = a(x s)(x t), can be used to calculate the value of the vertex. Be sure to describe the mathematical steps involved in this process. (5 marks) __MPM2D Learning Activity 3.5 Assessment Opportunity 13. The following graph describes the height of a football, where the height is measured in metres (m) and time in seconds (s). Height of football Time (s) a) Determine the value of each of the following by completing the following table. (2.5 marks: 0.5 marks each) CONTENTS: What are the values of the zeros or t-intercepts? State the equation of the axis of symmetry. Is there a maximum or minimum point? What is the maximum or minimum value? State the value of the vertex. b) Write a short story that could be described by your graph as well as the information from your table. Be creative! (2.5 marks) TVO ILC MPM2D Learning Activity 3.5 Assessment Opportunity Task 4: Thinking (25 marks) 14. Adult tickets for a school fashion show cost $8 and student tickets cost $5. The total receipts for 200 tickets are $1150. Using an algebraic method (the method of substitution or elimination), determine the number of each ticket that was sold. Be sure to define the variables. (6 marks) 15.The vertices of a triangle are P(4,2), Q(0,6), and R(7,2) as shown on the following grid. The equation of the median from vertex P is y = 2. a) Find the equation of the median from vertex R. (6 marks) . MPM2D Learning Activity 3.5 Assessment Opportunity b) Use the equations of the two medians to find the centroid of triangle PQR. (3 marks) c) Calculate the length of PG where G is the centroid. (2 marks) 16.An electronics store averages 32 sales per day of blu-ray players listed at $100 each. A survey indicates that for each $5 decrease in price, two more sales would occur. The graph of the projected revenue in terms of the number of $5 decreases is shown. Identify each of the following: a) Axis of symmetry (1 mark) ___ MPM2D Learning Activity 3.5 Assessment Opportunity ) Maximum revenue (1 mark) d) The price at which the store would have maximum revenue (2 marks) e) The number of $5 decreases that would produce no revenue (2 marks)