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Mathematics Special Messages & Answers:

Simplify:

1.                  |-2| ─ |5|

2.                  12 ÷ 3 + 2 ─ 8 • 2

3.                  (-1)⁷ (-2 + 7)(-6)

4.                  7k – 4(3k+2)

5.                  (-12)(-¾ ─ ½)
   ¼ ÷ -10

Evaluate if x = 3, y = 5, z = 8

6.                  2x² ─ 5x – 8

7.                  x² + 2x – xyz

Solve:

8.                  3x – 4=11

9.                  5x = 18 + 2x

10.             3(x─1) = -(x─5)

11.             3x – 2(x─1) = -1
       6

12.             The length, width and height of a rectangular box are consecutive integers and the largest dimension is x cm.  Find the volume of the box knowing that V=lwh.  You will not be able to solve the problem, but simply leave it terms of V= .

13.             Jim’s weekly pay is two-thirds of Mike’s.  Together they earn $600 per week.   What is each person’s weekly pay?

14.             At the homecoming football game, the Senior Class officers sold slices of pizza for $.75 each and hamburgers for $1.35 each.  They sold 40 more slices of pizza than hamburgers and sales totaled $292.50.  How many slices of pizza did they sell?

15.             At noon a cargo plane leaves Hopkins Airport and heads east at 180mph.  Its destination is Pittsburgh Airport which is 500 miles away.  At 1:00pm a jet takes off from Hopkins Airport and flies east after the cargo plane at 450mph.  At what time will the jet overtake the cargo plane?

Solve and Graph on a Number Line:

     2.   5( 3 – x ) > 7 – x

     4.   2x < ─ .5( ─6 – 4x )

     6.   x < ─5 or x £ ─8

     8.   ─2 < 2x + 8 £ 12

    10.  2 – | 3x + 4 | ³ ─7

Find the slope given the following:

1.   3x + 4y = 8

2.   Two points ( 2,─ 4) and ( ─5, 1)

3.    Vertical line x = 3

4.    Horizontal line y = ─ 5

            5.    Graph x = 3 by any method:

            6.    Graph y = ─ 5 by any method:
 

Graph 2x – 3y = ─ 9:

7.   By plotting points:

8.   By slope-intercept:

                  9.   On the calculator:

      Find the equation of the line given the following:

10. Line contains the two points ( 2,─ 4)  and ( ─5, 1)

11. Slope of 5 and y-intercept of ─ 8

12. Slope of ─ 2 and x-intercept of 5

13. Slope of 2 and containing the point     ( 2,3 )

14. Line through the point ( 0,3 ) and parallel to the line x + y = 5

15.  Line through the point ( 0,3 ) and perpendicular to the line x + y = 5

                  16.    Solve 2x - 7y = 10 and

                          5x - 6y - 2 = 0 by four methods:

                 17.  Graph x<2, x + y >7 and y>0

Given f(x) = 4x-x²  and g(x) = 3x-2:

18.  Find f(3)

19.  Find g(-5)

20.  Find f(g(-4)

21.  Find g(f(7)

22.  Find f(g(x))

23.  Find g(f(x))

Give the domain of each of the following:

            24.  f(x) = 1/(x² +9)

25.  g(x) = √(x+3)

26.   h(x) = 1/(x² - 5x)

    Find the equation of the linear function:

27.   f(1) = 2 and f(2) = 5

28.   m= -1 and f(2) = 3

29.  m= -3/2 and f(4) = -1

30.  f(1) = 2 and f(7) = -6

31.  find f(10) in the answer to  # 11

32.  find f(20) in the answer to # 11

     For the following problems, state the following:  domain, range, graph if not given, Is the graph a function, Is it one-to-one, Is it a relation.

33.  f(x) = -x² + 9

                  34.  g(x) =│x+4│                          

                 35.   h(x) = the greatest integer function

Simplify:

1.   (x² + 2xy + 3y²) + (5x² - xy - y²)

2.   2xy(x² + 2xy – 5y²) – 5xy(x² - 4xy + 2y²)

3.   4xy³(-3x²y)

4.   2x(5-4x)

5.   4x³(½ x)²

6.   (2x + 3)(2x – 3)

7.   (x + 3)(4x² - 6x +1)

8.   (2x³)²

Factor:

9.    5x² + 10x

10.   8a²bc² - 12 ab²c²

11.   y² + 6y + 9

12.   4x² - 121y²

13.   x² - x – 20

14.  14x² - 17x + 5

15.  3a + ab + 3c + bc

16.  x² + 4x + 4 – 16y²

Solve:               

17.  2x² + 5x = 12

            18.  A ball is thrown upward with an initial  
                  speed of 24.5 meters/second.  When
                  is it 19.6 meters high?
                  Note: h = rt – 4.9t² 

1.      Simplify     9xy³
               15x²y²

            2.   Simplify     (xy²z³)³
                                    (x³yz²)²

            3.   Simplify     x^-2y ^-3
                                    x ^-¹yº

4.      Change 7,920,000 to scientific notation.

            5.   Change  .00000041 to scientific notation.

6.      Express 2.7 x 10³ as a decimal.

7.      Express 6.18 x 10^-3 as a decimal.

8.      Simplify x² ─ 2x
               x² ─ 4

9.   Simplify x²   ●  x + 1  ÷        x___
                 x ─ 1     x + 2     x² + x ─ 2

10. Simplify   6 + x ─ x²    ÷   2x² ─ 5x ─ 3
                   x² ─ 13x + 42      2x² ─ 13x ─ 7

            11.  Simplify     1 ─  1/x
                                     x +  1/x²

12.   Solve   3x ─ 2 =   x ─ 1   + 1
                 8             12

            13.  Solve __x__  ─    1     =         10____
                              x ─2       x + 3        x² + x ─ 6

Simplify:            

1.                √(20)  

2.                √(2/3)       

3.                √( .0016)    

4.                ³√( - 125)      

5.                √(1200)     

6.                √(4x² + 8x + 4)      

7.                √(8) + √(98)      

8.                √(6)[√(2) + √(3)]      

9.                √(20) + √(14)
                √ 3                       

10.            [3 + √( 7)][3 - √(7)]

11.            1/[4-√(3)]

Solve:

12.           5x² = 125

13.           √(2x – 1) = 3

14.           √(2x + 5) = 2√(2x + 1)

Write as a fraction:      

15.           2.367676767…

Simplify:     

16.           √(- 50)

17.           √(- 4)  ●  √( - 25)

            18.            2/3i

            19.           √(- 5)   
                          3 + √(- 2)

Solve:

20.     x² + 144 = 0

            21.    What is the conjugate of 3 + 2i

            1.     State the quadratic formula:

            2.    State the formula for the parabola:

           3.     Given the roots are 2 and -5, find the
                   equation of the quadratic: 

           4.    Solve by factoring:   x² + 3x + 2 = 0

           5.    Solve by the quadratic formula:
                  5x² - 4x + 2 = 0

           6.    Solve by completing the square:
                  3x² - 12x + 7 = 0

Determine the nature of the roots: 

      7.   2x² + 5x – 3 = 0

      8.   9x² + 2x + 8 = 0

      9.   x² + 4x + 4 = 0

For  y = 3x² - 12x + 7 state the following:

           10.  State the equation in parabola form:

           11.  Find the vertex

           12.  Find the axis of symmetry

           13.  Is there a minimum or maximum point

           14.  Find the y-intercept

           15.  Find the x-intercept

           16.  Graph by sketching

           17.  Is it a function and why?

           18.  Is it one-to-one and why?

           19.  State the domain

           20.  State the range

Solve 2x⁴ + 3x³ – 7x² + 3x – 9 = 0

1.      How many roots does this equation have? 

By Descartes Theorem:

2.   Find the # of possible positive real roots. 

3.   Find the # of possible negative real roots.

4.   Find the # of possible imaginary roots.     

By the Rational Root Theorem:

5.   List all possible factors of h: 

6.   List all possible factors of k: 

7.   List all possible roots: 

8.   Test the roots (show all synthetic division)

9.   Sketch the graph (use calculator)

10. From all your steps above, list the roots of  the equation.

State the distance between the points                  1.    A (-3, -1) and B (-7, 5).

State the midpoint of the line segment AB:         2.  use points in problem #1.

Solve the following conic section:
x² ─ 4y + y² + 10x  + 21 = 0
(If it does not apply mark N/A)

3.     Identify the conic section by name

4.    State the equation in conic section form

5.    State the center

6.    State the radius

7.    State the whether there is a minimum or maximum point

8.     State the vertex

9.    State the axis of symmetry

10.  State the directrix

11.  State the focus(foci)

12.  State the major axis

13.  State the minor axis

14.  State the x-intercept

15.  State the y-intercept

16.  Is the conic section a function?

17.  Graph the conic section below:                   

Solve the following conic section:
x² ─ 2x ─ 2y = 0

18.  Identify the conic section by name

19.  State the equation in conic section form

20.  State the center

21.  State the radius

22.  State the whether there is a minimum or maximum point

23.  State the vertex

24.  State the axis of symmetry

25.  State the directrix

26.  State the focus(foci)

27.   State the major axis

28.  State the minor axis

29.  State the x-intercept

30.  State the y-intercept

31.  Is the conic section a function?

32.  Graph the conic section below:                  

Solve the following conic section:
4x² ─ 16x + 9y² + 18y  ─ 11 = 0

33.  Identify the conic section by name

34.  State the equation in conic section form

35.  State the center

36.  State the radius

37.   State the whether there is a minimum or maximum point

38.   State the vertex

39.  State the axis of symmetry

40.  State the directrix

41.   State the focus(foci)

42.  State the major axis

43.    State the minor axis

44.   State the x-intercept

45.   State the y-intercept

46.   Is the conic section a function?

47.   Graph the conic section below:                  

Solve the following conic section:
4x² ─ 25y² ─ 24x + 50y ─ 89 = 0

48.   Identify the conic section by name

49.   State the equation in conic section form

50.   State the center

51.   State the radius

52.   State the whether there is a minimum or maximum point

53.   State the vertex

54.   State the axis of symmetry

55.   State the directrix

56.   State the focus(foci)

57.   State the major axis

58.   State the minor axis

59.   State the x-intercept

60.   State the y-intercept

61.   Is the conic section a function?

62.   Graph the conic section below:                  

Write in Exponential Form:

             1.     ³√(3x⁵⁾   

  2.      √(5^-1) ∙ ³√(5²) 

 3.     ⁽⁴√5)³

Write in Simplest Radical Form:                    

4..     ³√(5 ^2/3)/ 8

5.        (4x ^-1)^-3/2  

                6.        Solve (y + 1)^2/3   =  9

Simplify:

7.        (2^п ∙ 2^-п )/ 2^-5

8.         8^√2 ÷ 2^√8

 Solve:

9.     27^x+1  =  81

10.   ( .1)^y   =  (100^)y+3

11.  Let h(x) = x⁴ – 1.   Show that h has no  inverse function.

12.  log₈ x = ─ 1/3       

13.  log_x 7 = 3

14.  Express log₄ 2 =1/2 in exponential form.

15.  Express 2⁹ = 512 in logarithmic form.

16.  Express log₄   A²/√B in terms of

       log₄ A and log₄ B.                 

17.  Evaluate log₂  56 ─ log₂  3.5

18.  Solve log_a x + log_a (2x + 3) = log_a  2

19.  Evaluate ln 1/( ³√e²)

20.  Evaluate – ln 1

21.  Solve ln x + ln  3 = ln (x + 4)

            22.  Solve to three significant digits

                   1.53^x = 53.1

23.  Solve to three significant digits x^5/3 = 50

24.  Solve to three significant digits               (x  + 2)⁷ = 32

For the following sequence 3,6,9,12,.....

            1.  State if the sequence is arithmetic,
                 geometric or neither.

 2.  State the common difference or common
            ratio.  

 3.  State the 10^th term

 4.  State the formula for the nth term (t_n )

For the following sequence 4,12,36,108,…….

5.  State  if the sequence is arithmetic, geometric or neither.

6.  State the common difference or common ratio

7.  State  the sum of the first 30 terms

8.  Write the formula using Σ

For the following series 5 + 2 – 1 – 4 – 7 ……….

            9.  State if the series is arithmetic,
                 geometric or neither.

          10.  State the common difference or common
                 ratio.

          11.  State the sum of the first 30 terms.

          12.  Write the formula using Σ

For the following series 1 + 1 + 1 + 1 + 1
                                          2    4     8   16

         13.   State if the series is arithmetic,
                 geometric or neither.

         14.   State the common difference or common
                 ratio.

         15.   State the sum of the first 30 terms.

         16.   Write the formula using Σ

         17.   Find (x + y)⁶ using Pascal’s Triangle
                 ( Show the ▲)          

          19.  Find the sum of the arithmetic series of
                 40 terms with t₁ = 5 & t₃₀ = 63

The matrix will not print as shown below!!!!!

Matrix A, B, C and D are used to answer to following:

              2   3  -5                -1   0   -2
Let A=  4  -8    6    Let B=   2  -3    6                     *           2    0   -6                 4   0   -1                                        

Let C=  4   2           Let D= -2    1
            -5   8                        6   -3

     2.   Find – 3B

     4.   Find 3B – 2A

     6.   Find det C

     8.   Find A • B

   10.  Solve for x, y and z  in the matrix:

                            x                   -5
                      2y - 1        =        7
                            z²                   0

Using the matrix C, find the following:

     12.   The additive inverse matrix

     13.   The multiplicative identity matrix

     14.   The multiplicative inverse matrix

      5x + 6y + 8   = 0
      3x – 2y + 16 = 0

Extra Credit:

      16.   Find the determinant of matrix B above.