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      = ;            &n= bsp;            = ;            &n= bsp;            = ;            &n= bsp;            = ;     Merced College<= /a>; Don Power

MATH-C Final Exam -- Study Guide&= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;  

 

 

1.     &nb= sp; Subtract 4z from the product of 5 and (3−z)

 

 

2.     &nb= sp; Simplify  =

 

 

3.     &nb= sp; Multiply using FOIL:  =

 

 

4.     &nb= sp; Factor:         = a.  =

 

 

      = ;            &n= bsp;          b.  =

 

 

5.     &nb= sp; Solve:  90x3 + 60x2 − 80x =3D 0

 

 

6.     &nb= sp; Solve   A =3D a + (n − 1)d  for n

 

 

7.     &nb= sp; Fred returns from a trip to Las Veg= as with $427, which is 30% less money than he had at the beginning of the trip.  How much money did he s= tart with?

 

 

8.     &nb= sp; The longest side of a right triangle is 3 inches less than twice the shortest side.  The third side measures= 12 inches.  Find the length of th= e shortest side.

 

 

9.     &nb= sp; Solve  =

 

 

10.     = Solve  | 2(2x + 3) | − 5 =3D −= ;1

 

 

11.     = Solve  =

 

 

12.     = Solve  (2x  − 1) (x + 3) =3D −6

 

 

13.     = Write the equation of the graph:

 

=

 

 

14.     = Find the slope and the y-intercept; write the equation: 

 

=

 

 

 

 

 

 

15.     = Graph        &= nbsp;          a.  y =3D 3/5 x + 1<= /font>

 

 

      = ;            &= nbsp;         &= nbsp; b.  3x − 2y =3D 12

 

 

      = ;            &= nbsp;         &= nbsp; c.  2x − 3y > −6

 

 

=

 

 

16.     = Determine the domain and range from the graph;

      = ;    Does this represent a function? (Why?)

      = ;    Is it one-to-one? (How do you know?)

 

=

 

 

17.     = Let f(x) =3D 4x −1 and g(x) =3D x2 − 3x + 2

      = ;    a.       Find<= span style=3D'mso-spacerun:yes'>  g(−4)

      = ;    b.       Write= a formula for (f−g)(x)

 

 

18.     = The volume of a gas varies directly with the temperature (in degrees Kelvin).  If a volume of 32 cubic meters corresponds to a temperature of 300o K, what temperature is requ= ired to reduce the volume to 24 cubic meters? [Physics note:  this problem assumes that the pres= sure is held constant]

 

 

19.     = The volume of a gas is inversely proportional to the pressure.  If 18 cubic inches of gas is trapp= ed inside a cylinder at a pressure of 15 pounds per square inch, what pressure must be applied to reduce the volume to 4 cubic inches?  [Physics note:  this problem assumes that the temperature is held constant]

 

 

20.     = Solve the systems of equations:

 

 

      = ;    a.       = =

 

 

      = ;    b.       = =

 

 

      = ;    c.       = =

      = ;   

 

      = ;    d.       = =

 

 

21.     = Solve the determinant equation  =

 

 

22.     = Write the determinant equation in slope-intercept form:  =

 

 

23.     = Calculate the determinant:  =

 

 

24.     = Solve for y using Cramer's rule:  =

 

 

25.     = How many liters of a 25% alcohol solution and how many liters of a 50% alcohol solution must be mixed to get 40 liters of a 30% alcohol solution?

 

 

26.     A collection of nickels, dimes and quarters has a value of $9.60.  If there are two more nickels than quarters, and one more dime than nickels, how many of each type of coin are= in the collection?

 

 

27.     =

 
Graph the = solution set:

 

  =   =

 

 

 

 

 

 

 

 

 

28.     =

 
Wri= te a system of inequalities

to describe the shaded region

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

29.     = State the domains: 

 

      = ;    a.       = =

 

      = ;    b.       = =

 

 

30.     = Divide  =

 

 

31.     = Solve  =

 

 

32.     = A boat moves at 18 mph in still water.  It travels 28 miles downstream in the same time it takes to travel 20 miles upstream.  Find the speed of t= he current

 

 

 

33.     = A ski lift is 1320 feet long.  If a = ride on this lift takes 6 minutes, find the speed in miles per hour.<= /span>

 

 

34.     = The  current of a river is 3 mph.  It takes a motorboat a total of 10= hours to travel 72 miles upstream and return [72 miles] downstream.  What is the speed of the boat in s= till water?

 

 

35.     = Write with an appropriate radical symbol; then simplify:  =

 

 

36.     = Use properties of exponents to simplify:  =

 

 

37.     = Solve:  =

 

 

38.     = Combine the complex numbers:  (3 + 2i) − (5 − 7i)

 

 

39.     = Simplify [divide]  =

 

 

40.     = Solve by the square root principle:

 

      = ;    a.  =

 

      = ;    b.  2x2 − 98 =3D 0

 

 

41.     = Solve by completing the square:  x2 − 8x + 13 =3D 0

 

 

42.     = Solve  2x − 3 =3D 3x2     Suggestion:  use the quadratic formula.

 

 

43.     = Solve  =

 

 

44.     = Give the x- and y-intercepts and the coordinates of the vertex; then graph:=

y =3D −x2 + 4x + 5

 

 

45.     = Solve, and graph the solution set:  x= 2 − 4x − 12 ≥ 0

 

 

46.     Suppose you depos= it $1500 in a savings account with an annual interest rate of 4.8.% compounded quarterly:

 =

      = ;    a.  Write an equation that gives the a= mount of money in the account after t years.

 

 

      = ;    b.  Find the amount of money in the ac= count after 7 years.

 

 

47.     = You are conducting an experiment with a radioactive substance.  You start with 18.2 grams of the substance.  The amount of the substance remaining after t minutes is described by the function A(t) =3D A= oe−0.03t, where Ao is the initial amount and A(t) is the amount when time = =3D t.  How much of the substance remains after 20 minutes?

 

 

48.     = Find the equation of the inverse function f−1(x) if =

 

 

49.     = Convert to exponential form:  log= 327 =3D 3

 

 

50.     = Solve for x:

 

      = ;    a.  log4x =3D 3<= /span>

 

      = ;    b.  logx32=3D5

 

      = ;    c.  Solve log6x + log6= (x − 1) =3D 1

 

 

 

51.     = Use the change of base theorem and a calculator to find a decimal approximation= to log317, correct to the nearest hundredth

 

 

52.     = Find the center and radius, and sketch the circle:  (x − 3)2 + (y + 1= )2 =3D 4

 
 
 = ;

 

 

 

 

 

 

 

 

 

 

 

 

 

 


53.     = Sketch the graphs:

 

      = ;    a.       x2 + 16y2 =3D 16

 

      = ;    b.       9x2 − 4y2 =3D 36

 

      = ;    c.       25y2 − 4x2 =3D 100

 

 

54.     = Use synthetic division to divide:  =

 

 

55.     = Complete the synthetic division;  give = the original problem and the answer:

&= nbsp;        

      = ;    =

Return to:  Merced College; Don Power   =             Updated 01/08/03 by Don Power

 

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