MATH 536 XMAS EXAM |

Do as many questions as you can.

You may not have covered all the material on this exam since

different schools teach the course in a different order.

1) The algebraic solution to | *2x - 11* | = 13 is:

A) 12 | B) 12 and -1 | C) 2 | D) 1 and 12 |

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2) The vertex and range of are:

A) vertex (4, 3) range = ] - º, 3 ] | B) vertex (4, 3) range = · |

C) vertex (3, 4) range = [ 4, º [ | D) vertex (3, 4) range = ] - º, 4 ] |

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3 ) The value of 2 ß-10.1à is:

A) -20 | B) 22 | C) 20 | D) -22 |

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4) John finds his average hourly profit with the rule ,

where *P(x)* is the **average** hourly profit and *x* is the number of hours he works.

How many hours must John work to break even? (no profit, no loss)

A) 25 | B) 2 | C) 3 | D) 37.5 |

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5 ) Given *f(x) = 2x + 1* and *g(x) = x² - x - 2*, find *g [ f (x) ]*.

A) 4x² + 2x - 2 |
B) x² - x - 7 |
C) x² - 7 |
D) x³ - 6x² + 3x - 10 |

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6 ) Which of the functions below has a range of [ 3, º [ ?

A) Y_{1} = x² - 6x + 9 |
B) Y_{2} = - 2 | x | - 3 |
C) Y_{3} = |
D) |

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7) Solve (*16*)* ^{2x - 1} = *(

A) x = 3 |
B) x = 4 |
C) x = 8 |
D) x = 2 |

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8 ) Find the rule for the absolute value function with

**vertex** at **(-5, 7)** through the point (2, 0).

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9) Find the vertical separation and the horizontal length

of the steps in

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10) A submarine photographs a sunken shipwreck and then re-surfaces.

The depth in metres of the submarine follows the rule *D(t) = 15 | t - 8 | - 120*,

where ** t is the time** in minutes that the submarine is submerged.

- a) How long does the submarine stay submerged?

- b) What is the maximum depth it reaches?

- c) How long does it take to reach the maximum depth?

- d) Draw the graph of the situation.

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11) Find the zero and the y-intercept for

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12) If *g(x) = 2x - 7 *and *h(x) = 2x ^{ 2} - x - 2*1, find

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13) Find the rule for a square root function with vertex (-4, -6), through (0, -3).

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14) Find the rule for an exponential function *f (x) = ac ^{ x} + 4*

that includes the points (0, 4.5) and (1, 5.2).

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15) Thirteen months ago, Luke bought some stock whose price varied according

to the rule *P(x) = 1.25 | x - 5 | + 45* where *x* is the number of months since he

bought the stock and *P(x)* is the price of the stock in dollars.

- a) When was the stock price at its lowest?

- b) When was the stock price at its peak?

- c) For how many months did the stock increase in value?

- d) For how many months was the stock worth less than $50?

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16) . Find

a) the vertex | b) the zero | c) domain | d) positive interval |

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17) Find the equations of the asymptotes and sketch the graph of

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18) An educational consultant is making up questions for the final math exam.

He needs a total of 250 questions but can only submit 25 questions per week.

- a) Find the rule for the function to represent the number

of questions remaining to submit?

- b) Graph this step function.

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19) Paula makes a term deposit whose accumulated total is found with the rule

*T(x) = 5000 (1.1) ^{x}* where

- a) How much money does she have after 1 year?

- b) Paula receives a bank statement at the end of each year.

What is the difference between the statement balances after 3 years and 5 years?

- c) What are we finding when we calculate

- d) What is the domain and range of this situation if Paula decides

to keep her term deposit for 20 years?

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20) Solve this system of inequalities graphically: *2x - y **m** 4* and *2y + 3x **[** - 6*.

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21) In the figure, find *x* (the radius) to the nearest hundredth.

A) 19.00 | B) 13.89 | C) 6.95 | D) 9.75 |

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22) If arc AC = 50º , É P = 22º and arc AC > arc BD, find the degree measure of arc BD.

A) 6º | B) 28º | C) 72º | D) 14º |

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23) To the nearest hundredth, calculate the circumference of a circle

in which a central angle of 22º defines an arc of 10 cm.

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24) A post is supported by 2 guy wires TA and TC which are at right angles to each other. If the length of the wires are 40m and 30m respectively, how high is the post?

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25) A wooden frame which supports vines is in the shape of a parabola with equation

*f(x) = -1/2 x ^{2 }+ 2x + 160*. If the measurements are in centimetres, find the distance

between the 2 points where the frame touches the ground.

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26) Graph the polygon of constraints for

x m 0, |
y m 0, |
y [ 5, |
x - y > 0 |
x + 2y [ 0 |

Which vertex minimizes *M = 2x + y* ?

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27) Once a month, Dane cashes in his empty **bottles** and **cans**.

This month he has **no more than 60 empties**, and the number of bottles

is at least twice the number of cans. He has at least 10 empty cans and no more

than 45 empty bottles. If he gets 10¢ per bottle and 5¢ per can, what is the maximum

refund Dane can get this month? (Hint: let *x = bottles, y = cans*)

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28) The **diameter** of circle center O is **10 cm**. Find the length of arc BD.

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