INSTRUCTIONS:
- Read over the entire culminating assignment before you begin.
- Note the mark value for each section.
- Show ALL your work. No marks will be given unless work is shown.
- Attempt ALL questions but do not spend too much time on any one question. Use your time wisely.
- Answer ALL questions to the best of your ability.
- 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
- Determine whether each function represents exponential growth or decay.
Explain. /4
b.
- Describe the transformations on the following sinusoidal function, using correct terminology. /4
y = -3sin– 5
Part B. Knowledge and Understanding (25 Marks)
- Consider the following relations.
- State whether each of the following relations represents a function.
Explain your reasoning in each case. /4
-
- {(4, –1), (3, –5), (2, 6), (4, 3,), (1, –5)}
- Determine the domain and range for each of the above. /2
- Factor each of the following:
- 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)
- 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.
- 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.
- 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
- 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)
- Prove the following identity. /4
- The following graph shows a person’s height on a Ferris Wheel over time.
/3
- 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:
- Read over the entire culminating assignment before you begin.
- Note the mark value for each section.
- Show ALL your work. No marks will be given unless work is shown.
- Attempt ALL questions but do not spend too much time on any one question. Use your time wisely.
- Answer ALL questions to the best of your ability.
- 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
- Determine whether each function represents exponential growth or decay.
Explain. /4
b.
- Describe the transformations on the following sinusoidal function, using correct terminology. /4
y = -3sin– 5
Part B. Knowledge and Understanding (25 Marks)
- Consider the following relations.
- State whether each of the following relations represents a function.
Explain your reasoning in each case. /4
-
- {(4, –1), (3, –5), (2, 6), (4, 3,), (1, –5)}
- Determine the domain and range for each of the above. /2
- Factor each of the following:
- 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)
- 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.
- 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.
- 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
- 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)
- Prove the following identity. /4
- The following graph shows a person’s height on a Ferris Wheel over time.
/3
- 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
