INSTRUCTIONS:

  1. Read over the entire culminating assignment before you begin.
  2. Note the mark value for each section.
  3. Show ALL your work.  No marks will be given unless work is shown.
  4. Attempt ALL questions but do not spend too much time on any one question. Use your time wisely.
  5. Answer ALL questions to the best of your ability.
  6. All formulas are given on the last page.

Part A. Communication (14 marks)

Communication marks will be given for proper forms in answers throughout the assignment:

  • All operations signs (+ – x  ) and appropriate symbols such as {  } are present                                                        

                                                                                                                                /2

  • All steps are clear and organized neatly;  parts of the expressions being simplified     are not  separated but kept within each step                                                               /2                                    

 –  Answers for word problems are in correct digits with correct units in concluding 

    statements                                                                                                                   /2              

  1. Determine whether each function represents exponential growth or decay. 

Explain.                                                                                                                      /4

  1.                                    b.  
  • Describe the transformations on the following sinusoidal function, using correct terminology.                                                                                                             /4
                                               y = -3sin – 5 

Part B. Knowledge and Understanding (25 Marks)

  1. Consider the following relations.
    1. State whether each of the following relations represents a function. 

Explain your reasoning in each case.                                                                 /4

  1.  
    1. {(4, –1), (3,  –5), (2, 6), (4, 3,), (1, –5)}
  • Determine the domain and range for each of the above.                                       /2
  1.  
  • Factor each of the following:
  1. 3n2 – 10n + 8          /2             b.   121p2 – 81q2      /1         c.    x3 – 4x2 – 9(x – 4)     /2
  • For the quadratic function: f(x) = 9x2 + 6x + 1, determine the number of zeros.            /2
  • a. Find the inverse of  algebraically.                                              /2

b. Is the inverse a function? Why or why not?                                                              /2

  • Simplify the following using the exponent laws then evaluate where possible.                /4
  • Solve the following.                                                   /2
  • Solve for the unknown.  Round your answer to two decimal places.

     x = ________________                                                                                   /2


Part C. Application (22 marks)

  1. The equation    models the height of a rocket shot into the air from a 40-metre platform, where  is the height of the rocket from the ground, in metres, and t is the time in seconds.
  1. Use the completing the square method to find the maximum height of the ball.    /4
  • When does the rocket reach its maximum height?                                                 /1
  • A lab has 300 g of an unknown radioactive substance. The curve below shows the mass of the substance recorded each minute.
    • Estimate the half-life of the substance.                                         

                                                                 /1

  • Write a function that can be used to

determine the mass of the substance, M,

remaining after t minutes.                        /2

  • How much of the substance will remain

after 10 minutes? Use the above equation

and round your answer to two decimal places.

                                                                 /1

  • Your credit card charges 21%/a compounded monthly.  After 3 months of not paying a loan, you owe $208.50 on your card. How much did you originally owe? Round your answer to two decimal places.                                                                               /3
  • For the given sinusoidal function, f() = –2sin ( + 30°) + 1          
  1. What is the amplitude?                                     _____________                       /1
  • What is the equation of the axis?                      ____________                        /1
  • Sketch 1 period of the function (transformed from f() = sin ,  0°≤  ≤360°).  /4                       
Trigonometric Graph Paper | Download Trig Graph Paper 1 For Free Page 7 Tidyform

5.  Write the mapping notation for the transformations of and to                 .  Then graph and label both functions on the same grid.                  /4

     (x, y) 🡪 _____________________


Part D. Thinking Inquiry  (7 marks)

  1. Prove the following identity.                                                                                    /4                                        
  1. The following graph shows a person’s height on a Ferris Wheel over time.                 

                                                                                                                         /3

  1. What is the radius of the Ferris Wheel?
  • What is the height at which you get on 

          the Ferris Wheel?

  • How long does it take to travel around

           the Ferris wheel once?

 Congratulations! You’re done!

 Formulas

Quadratic Functions

Sequences and Series


                (where -1< r <1)    

Financial Applications            

Trigonometric Functions

              a2 = b2 + c2 – 2bc cosA

   INSTRUCTIONS:

  1. Read over the entire culminating assignment before you begin.
  2. Note the mark value for each section.
  3. Show ALL your work.  No marks will be given unless work is shown.
  4. Attempt ALL questions but do not spend too much time on any one question. Use your time wisely.
  5. Answer ALL questions to the best of your ability.
  6. All formulas are given on the last page.

Part A. Communication (14 marks)

Communication marks will be given for proper forms in answers throughout the assignment:

  • All operations signs (+ – x  ) and appropriate symbols such as {  } are present                                                        

                                                                                                                                /2

  • All steps are clear and organized neatly;  parts of the expressions being simplified     are not  separated but kept within each step                                                               /2                                    

 –  Answers for word problems are in correct digits with correct units in concluding 

    statements                                                                                                                   /2              

  1. Determine whether each function represents exponential growth or decay. 

Explain.                                                                                                                      /4

  1.                                    b.  
  • Describe the transformations on the following sinusoidal function, using correct terminology.                                                                                                             /4
                                               y = -3sin – 5 

Part B. Knowledge and Understanding (25 Marks)

  1. Consider the following relations.
    1. State whether each of the following relations represents a function. 

Explain your reasoning in each case.                                                                 /4

  1.  
    1. {(4, –1), (3,  –5), (2, 6), (4, 3,), (1, –5)}
  • Determine the domain and range for each of the above.                                       /2
  1.  
  • Factor each of the following:
  1. 3n2 – 10n + 8          /2             b.   121p2 – 81q2      /1         c.    x3 – 4x2 – 9(x – 4)     /2
  • For the quadratic function: f(x) = 9x2 + 6x + 1, determine the number of zeros.            /2
  • a. Find the inverse of  algebraically.                                              /2

b. Is the inverse a function? Why or why not?                                                              /2

  • Simplify the following using the exponent laws then evaluate where possible.                /4
  • Solve the following.                                                   /2
  • Solve for the unknown.  Round your answer to two decimal places.

     x = ________________                                                                                   /2


Part C. Application (22 marks)

  1. The equation    models the height of a rocket shot into the air from a 40-metre platform, where  is the height of the rocket from the ground, in metres, and t is the time in seconds.
  1. Use the completing the square method to find the maximum height of the ball.    /4
  • When does the rocket reach its maximum height?                                                 /1
  • A lab has 300 g of an unknown radioactive substance. The curve below shows the mass of the substance recorded each minute.
    • Estimate the half-life of the substance.                                         

                                                                 /1

  • Write a function that can be used to

determine the mass of the substance, M,

remaining after t minutes.                        /2

  • How much of the substance will remain

after 10 minutes? Use the above equation

and round your answer to two decimal places.

                                                                 /1

  • Your credit card charges 21%/a compounded monthly.  After 3 months of not paying a loan, you owe $208.50 on your card. How much did you originally owe? Round your answer to two decimal places.                                                                               /3
  • For the given sinusoidal function, f() = –2sin ( + 30°) + 1          
  1. What is the amplitude?                                     _____________                       /1
  • What is the equation of the axis?                      ____________                        /1
  • Sketch 1 period of the function (transformed from f() = sin ,  0°≤  ≤360°).  /4                       
Trigonometric Graph Paper | Download Trig Graph Paper 1 For Free Page 7 Tidyform

5.  Write the mapping notation for the transformations of and to                 .  Then graph and label both functions on the same grid.                  /4

     (x, y) 🡪 _____________________


Part D. Thinking Inquiry  (7 marks)

  1. Prove the following identity.                                                                                    /4                                        
  1. The following graph shows a person’s height on a Ferris Wheel over time.                 

                                                                                                                         /3

  1. What is the radius of the Ferris Wheel?
  • What is the height at which you get on 

          the Ferris Wheel?

  • How long does it take to travel around

           the Ferris wheel once?

 Congratulations! You’re done!

 Formulas

Quadratic Functions

Sequences and Series


                (where -1< r <1)    

Financial Applications            

Trigonometric Functions

              a2 = b2 + c2 – 2bc cosA

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