MATH 536 MOCK EXAM

1/ The value in dollars of a stock I bought follows the rule
V(x) = 2 | x - 5 | + 30, where x is the number of months since I bought it.
I intend to sell the stock after 12 months.

a) what was the value of the stock upon purchase?

b) what was the minimum value of the stock during the 12 months?

c) when did the stock value hit the minimum?

d) what was the value of the stock when I sold it?

e) for how many months was the value of the stock less than \$35?

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2/ a) Graph the function f(x) = and list all the properties.

b) Solve the inequality f(x) < 3.

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3) A salesperson earns \$25 commission per sale of \$500 worth of merchandise per week.
She also earns a base salary of \$600 each week.

a) Write the rule for and graph the step function which represents her weekly earnings.

b) How much will she earn in a week when her sales total is \$950?

c) How much would she have to sell for in order to earn \$625 in a week. (interval).

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4/ a) Graph and describe the properties of

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b) Solve f(x) .

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5/ Once a month, Dane cashes in his empty bottles and cans.
This month he has no more than 60 empties. 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? ( let x = bottles, y = cans).

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6/ Solve for x:

 a) log 4 (x + 2) - log 4 (x - 2) - 3 = 0 b) c) -5 | 7 - x | + 3 < -17 d) 7 x+1 = 5 3 - x .

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7/ Find the inverse function for:

 a) y = b) c) y = 2(3) x + 5 d) y = 4 log 3 (x - 5)

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8) Write the equation of the:

a) circle center (-2, 3), radius = 5.

b) diameter of (a) with slope =

c) using the slope of this diameter, find its endpoints.

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9) Find the center and radius of the circle:

a) x 2 + y 2 + 2x + 6y - 26 = 0
b) x 2 + y 2 - 75 = 0
c) find the equation of the tangent to the circle in part (b) at P (5, ).
d) find the point(s) of intersection of y = x with x 2 + y 2 = 50
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10) Find exact values (no calculator) for the following:

 a) sin (-5o /4) b) cos (5o /6) c) tan (-2o /3) d) cos (3o /2) e) csc (3o /4).
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11)

a) convert 57045' to radian measure. (hint: 60' = 1 0)
b) convert 12o /7 to degree measure.
c) Find the length of the arc created by a central angle of 450 in a circle radius 17cm.
d) Find the radian measure of a rotation if a point 24 cm from the
center makes an arc of 3 m.

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12) Graph one cycle of the function y = 4 sin (¼ x + o /8) + 3.
List the amplitude, period, phase shift, and vertical translation.

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13)Nick buys a car for \$25,000. The depreciation rate for the first year is 30%
and it is 15% for every subsequent year he owns the car.

a) How much will the car be worth at the end of the first year?

b) If Nick intends to sell the car when its value falls below \$10,000
how many years after purchase does he sell the car?

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14) Olivier gets \$3000 as a gift for his birthday.
He invests it at 7.5 % compounded yearly.
Lauren too gets a gift of \$4000 which she invests at 7% compounded yearly.
They decide they'll stay friends until they have the same amount in their accounts.

For how long will Olivier and Lauren be friends?

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15) It is the year 2015 wherein Jaclyn and Norman have opened an automotive design centre.
They are working on a futuristic car seen in the diagram.

The body of the car is an ellipse, centre (0, 0), major axis = 12 dm, minor axis = 6 dm.

The wheels are circles, centers at the endpoints of the latus rectum (ellipse),
radius = ½ the latus rectum.

The roof, a parabola, rises 2.5 dm. above the body,
touches the ellipse at the endpoints of the latus rectum.

The bumpers are a hyperbola, centre (0, 0), sharing vertices with
the ellipse which forms the body, foci 2 dm. from the vertices.

Find the equations of all the curves and the coordinates of
all the vertices, foci and centers of the conics that define the shape of the car.

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