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) | 2x - 11 | = 13 becomes

2x - 11 = -13 2x = -2 , so x = -1

2x - 11 = 13 2x = 24 , so x = 12 answer is B x = 12 and x = -1

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2) A) vertex (4, 3) range = ] - º, 3 ]

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3 ) The value of 2 ß-10.1à is D) -22
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4) For no profit, no loss, P(x) must = 0.
We set 25x - 75 = 0 .
answer is C) x = 3 hrs.

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5 ) g [ f (x) ] = g ( 2x + 1) = ( 2x + 1)² - ( 2x + 1) - 2
answer is A) 4x² + 2x - 2

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6 ) D) has a range of [ 3, º [ ?

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7) Using 4 as a common base:
(4 ² ) ^{2x - 1} = (4 ³ ) ^x t (4 ) ^{4x - 2} = (4) ^3x so 4x - 2 = 3x, answer is D) x = 2

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8 ) Using standard form for the rule of an absolute value function:
f (x) = a | x - h | + k t f (x) = a | x + 5 | + 7
Substitute (2, 0) for x and f (x) to get
0 = a | 2 + 5 | + 7 so a = -1
f (x) = -| x + 5 | + 7

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9) Vertical separation = a = 5 horizontal length = 1/ b = 10.

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10)

a) The submarine stays submerged for 16 minutes.

b) The maximum depth is 120 metres.

c) It takes 8 minutes to reach the maximum depth

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11) For the zero, set the numerator = 0 to get x = - 5/2
For the y-intercept, set x = 0 to get f (0) = 5.

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12) If g(x) = 2x - 7 and h(x) = 2x ² - x - 21, find

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13) We can see from the location of the vertex and point that b = +1
since the curve moves right from the vertex to reach (0, -3).
Using standard form for the rule of a square root function:

Substitute (0, -3) for x and f (x) to get

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14) We substitute (0, 4.5) to get 4.5 = ac ⁰ + 4 which means a = 0.5
Now we substitute (1, 5.2) to find c.
5.2 = 0.5c ¹ + 4 which gives us c = 2.4
the function is f(x) = 0.5(2.4) ^x + 4.

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15) P(x) = 1.25 | x - 5 | + 45
x is the number of months since he bought the stock, x ` [0, 13]
P(x) is the price of the stock in dollars.

a) the stock price was at its lowest 5 months after purchase.

b) the stock price was at its peak 13 months after purchase.

c) the stock increased in value for 8 months.

d) Set P(x) < $50 and solve to find 1 < x < 9 so for 8 months.

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16) .

a) vertex = (-2, -12)

b) zero = (-11, 0)

c) domain ] - º, -2]

d) positive when x > -11

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

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18) He starts at 250 questions and reduces that number by 25/week

a) a = - 25; b = 1 ; h = 0 and k = 250

So, f(t) = - 25 [ t ] + 250 ; t ` Z; t in weeks

b)

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19) a) set x = 1 to get T(1) = 5000 (1.1) ¹ = 5500.

b) T(5) = 5000 (1.1) ⁵ = 8052.55 and T(3) = 5000 (1.1) ³ = 6655
so the difference is $1397.55

c) We're finding the amount of money accumulated after 13 years.

d) domain: [0, 20] and range: [$5000, $33,637.50] (the maximum value is T(20).)

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20) 2x - y m 4 u y m 2x -4 and 2y + 3x [ - 6 u y [ -3/2 x - 3.
We draw the graphs of y m 2x -4 and y [ -3/2 x - 3

the solution is the set of all points in the
plane with the blue line as ceiling and the red line as floor.
The x-values that generate the solution are x [ 2/7 which is the x-value
for the point of intersection.

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21) If we join AB, it is a diameter since the angle = 90°.
This means that AB, the hypotenuse = 2x since diameter = 2 (radius).
By the Pythagorean theorem, AB = 13.89, so x = ½(13.89) = 6.95 or C

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22) using the exterior angle property that É P = ½ (arc AC - arc BD) we get
22º= ½ (50º- x) u 44° = 50º- x u x = 6º

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23) Use the proportion C : 10 = 360° : 22° to get C = 163.64 cm.
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24) First we find AC = 50 m -- it's the 3, 4, 5 triangle
now we use the product of the sides theorem which states h(AC) = AT (CT).
Using this statement we know that h(50) = 30 (40) u h = 24 m.

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25) We need to find the distance between the zeros.
Set -1/2 x² + 2x + 160 = 0 then multiply through by -2.
We get x² - 4x - 320 = 0 which factors as (x - 20)(x + 16) = 0
So the zeros are at x = - 16 and x = 20.
The distance between them is 36 cm.

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26)

Vertex (-10, 5) minimizes M = 2x + y .

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27)

5) let x = # of bottles	y = # of cans
The inequalities are: x > 0, y > 0 x + y [ 60 x m 2y y m 10, x [ 45		we want max profit: P = 0.10x + 0.05y
graph the lines and test the coordinates of the vertices.		profit max = $5.25 with 45 bottles, 15 cans

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28) Arc AC = 30° (arc double angle at circumference.)
Now we use the interior angle property to find arc BD.
We solve 80° = ½(30° + BD) which makes the degree measure of BD = 130°.
Since C = od, C = 10o.
So the length of arc BD is

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