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Pre‐calculus 12

Final Assignment (22 marks)

Each question is worth 1 mark. You must show all your work to obtain full marks.

Marks will be deducted for no work shown.

1. What happens to the graph ofݕൌ ݔଶ െ ݔ1 if the equation is changed to ݕൌ െݔଶ ݔെ 1?

2. The graph of y =√ ݔundergoes the transformation (x, y) ( 3,2 5) x y . What is the resulting

equation?

3. Determine the equation of the polynomial in factored form of the least degree that is symmetric

to the y‐axis, touches but does not go through the x‐axis at (3, 0), and has P(0) = 27

4. Determine the measure of all angles that satisfy the following conditions. Give exact answers.

csc =2 in the domain 2 2

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5. Solve: 3 cos ² ݔെ 8 cos ݔ4 ൌ 0, over all real numbers

6. Use factoring to help to prove each identity for all permissible values of x. Must state

restrictions over all real numbers.

sin sin 2

tan

cos sin cos

x x

x

x x x

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7. In a population of moths, 78 moths increase to 1000 moths in 40 weeks. What is the

doubling time for this population of moths?

8. Solve the following equation: logଷሺ ݔ3ሻ logଷሺ ݔെ 5ሻ ൌ 2

9. Solve for x algebraically: 5௫ାଵ ൌ 2ሺ3ଶ௫ሻ. State your answer to the nearest hundredth.

10. A radioactive substance has a half‐life of 92 hours. If 48g were present initially, how long will it

take for the substance to decay to 3g? Show algebraically.

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11. Given the following two functions ݂ሺݔሻ ൌ √ ݔെ 1 and ݃ሺݔሻ ൌ ݔଶ 1, evaluate

݃൫݂ሺ3ሻ൯.

12. A sample of 5 people is selected from 3 smokers and 12non‐smokers. In how many ways can

the 5 people be selected?

13. Given the functions݂ሺݔሻ ൌ 7 െ ݔଶ and ݃ሺݔሻ ൌ ଵ

√௫, determine an explicit equation for

ሺݔሻ ൌ ݃൫݂ሺݔሻ൯ െ ݂ሺ݃ሺݔሻሻ, then state its domain.

14. Determine the 4th term of ሺ3 ݔെ 2ሻ.

15. Solve by algebra√13 െ ݔെ ݔ1 ൌ 0

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16. Determine the domain, range, and intercepts of ݕൌ െ2√4 െ 2 ݔ3. Graph the function.

17. For the graph ofݕൌ ௫ାସ

௫మା௫ି, determine an non‐permissible values of ,ݔwrite the coordinates of

any hole and write the equation of any vertical asymptote.

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18. Sketch the graph of ݕൌ െ3ሺ4ሻି

భ మ

௫ିଷ

5. State the domain, range, and equation of the

horizontal asymptote.

19. Suppose you play a game of cards in which only 5 cards are dealt from a standard 52 deck. How

many ways are there to obtain at least 3 cards of the same suit? An example of a hand that

contains at least 3 cards of the same suit is 4 hearts and 1 club.

20. Given݂ሺݔሻ ൌ ଶ௫

ଵି௫

, determine ݂ିଵሺݔሻ, the inverse of ݂ሺݔሻ.

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21. Consider the digits 0, 2, 4, 5, 6, 8. How many 3‐digit even numbers less than 700 can be

formed if repetition of digits is not allowed? Note: the first digit cannot be zero.

22. If݂ሺݔሻ ൌ ݔଷ and ݃ሺݔሻ ൌ 2 ݔെ 3, determine the value of ቀቁ ሺെ1ሻ.

# Pre‐calculus 12 Final Assignment

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