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.
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
1. • • 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

/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

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

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.
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
1. • • 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

/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

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

Sequences and Series    (where -1< r <1)

Financial Applications

Trigonometric Functions

a2 = b2 + c2 – 2bc cosA

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