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Mathematics Special Messages & Answers:

Simplify:

    1.     7 + (35 ÷ 7)

    2.     4(36 ÷ 9)

    3.     (12 - 7) • 6

    4.    19 - 7 + 12 • 2 ÷ 8

    5.    | -5|

    6.    |7 – 2|

Evaluate: if x = 2, y = 3, z = 4, t = 5

Solve:

   10.    2x = 12

   11.     x – x = 0

   12.    2x + 5x + 8 = 22

   13.   10x + 3 = 5x + 8

   14.    | x | = 2

   15.    | x | = -2

Set up the equation and Solve:

Graph on a number line:

Translate each statement into symbols:

    23.   One fourth of a number.

    24.   A number decreased by four.

    25.   x is less than or equal to 5.

Simplify:

         2.     – 21 +(x – 2)

         4.     – 4 + (─5) – (─6) + (+8)

         6.     5x – 3x +(4 – 2)

         8.    ─4(2x – 8)

        10.  ─2(4x + 5) – 3(2x + 4)

        12.   2 + 4(3x – 8)

        14.   3x – 7 + 5x + 2

        16.   (245)(─678)(0)(549)

        18.   ─(2x – 3) + 3x

        20.   ⅓(42m – 3v)

        22.   What is the reciprocal of 2/3?

        24.   The sum of two consecutive integers is 43.  Find
                the integers and show all work!

Extra Credit:  3(4x + 2) – (2x – 3)+ 8(x – 3)

Solve:  Check all of your answers to avoid careless mistakes. 

1. x + 5 = 9
    
2. ─3 = x + 2
    
3. 3x = ─21
    
4. 2x + 3 = x + 7
    
5. ⅔x = 12
    
6. 2|x| = 6
    
7. 3|x|/2 = ─ 15
    
8. Five times a number is ─375.  Find the number. (Show the equation and solve)
    
9. The sum of 38 and twice a number is 124.  Find the number. (Show the equation and solve)
    
10. An apple sells for 25 cents and a peach sells for 15 cents.  A total of 10 pieces of fruit were sold for a total cost of $2.10.  How many apples and peaches were sold?

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:

1.    5x² + 10x

2.    8a²bc² - 12 ab²c²

3.    y² + 6y + 9

4.    4x² - 121y²

5.    x² - x – 20

6.    14x² - 17x + 5

7.    3a + ab + 3c + bc

8.    x² + 4x + 4 – 16y²

Solve:

9.    2x² + 5x = 12

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

11.  Solve the formula (PV)/T = K  for V              

12.  Solve the formula A = (V – U)/T for T

13.  A helicopter leaves the Hopkins Airport and flies north at 180 mi/h.  Twenty minutes later a plane leaves the same airport and follows the helicopter at 330 mi/h.  How long does it take the plane to overtake the helicopter?  (Show your chart and solve to get the full points)                                             

Simplify:

1.         30x /48x

            2.         6xy³/20x³y²

            3.         (x²/y)³

            4.         (2x²y/z)³   ●   (z²/6x)²

            5.                  (x² ─ 2x )/(x² ─ 4)

             6.         (5x² ─ 15x )/(10x²)

             7.         (x² ─ 5x + 6)/(x² ─ 7x + 12)

             8.                   (x² ─ 1)/(1 ─ x)

             9.         (5x³/3)   ●  (6/10x²)

             10.       (x ─ 2)   ●   x² + 2x ─ 3
                           x + 3           x² ─ x ─ 2

             11.       28x/25    ÷   21x³/15

             12.        x² ─ 4         ÷    2x² ─ 3x ─ 2
                       2x² ─ 5x + 2            4x² ─ 1

             13.        2/x      ─    1/2x

             14.       (x + 2)/3   + (x ─ 4)/6

             15.       1/6x²    ─    1/2xy  +    3/8y² 

Simplify:

            1.          3 hours : 15 minutes

            2.         (27x³)/(3²)³

Solve:

            3.          (2x – 3)/5 = (x + 2)/6

            4.         (cy)/(d-c) = (dx)/(d² - c²)

            5.         Maria drove 111 miles in 3 hours, if she continues
                        to drive at the same rate, how many miles will she
                        drive in 5 hours?

            6.         1(x + 2)/4 – 1 (x – 2)/6 = 3/2

            7.         2/(x²-x)  ─  2 /(x-1)  = 1 

 Evaluate:

            8.         11^-2

            9.         6/6^-2

            10.       7º

            11.       2^-3

            12.      (3^-2)^-1

 Write as a decimal number:

            13.      5.95 x 10³

            14.      4.67 x 10^-2

 Write in scientific notation:

            15.      57,600,000,000

16.     .0000000000065

      1.   Graph by plotting points: 2x + 7y = 14

                  2.   Graph by slope intercept form: 3x + 8y = 24

                  3.   Graph by calculator and sketch -5x –3y = 12

Find the equation of the line given the following:

                 4.   Given (2,3) & (-6, 7)

                 5.   Given slope of -4 and y-intercept of 7

                 6.   Given slope of  5 and x-intercept of -2

                 7.   Given the line is parallel to the line
                        2x + 3y =5 and contains the point ( - 5, 6)

                 8.  Given the line is perpendicular to the line
                       -5y +9x=15 and contains the point (2,1)

If f(x) = x + 2 and g(x) = x² ─ 3:

                  9.   Find f(5)

                  10. Find g(-2)

                  11. Find f(g(x))

                  12. Find g(f(x))

For the equation y = 2x² + 5x +3:

                  13. Is the graph a function and why?

                  14. Is the graph one-to-one and why?

                  15. Find the domain

                  16. Find the range

                  17. Find the vertex
 
                  18. Find the axis of symmetry

                  19. Graph the parabola by plotting points

    1.   Solve by substitution::

─2x + y  = ─ 7
              4x + 5y = 0

2. Solve by graphing using slope intercept form:

─2x + y = ─7
   4x + 5y = 0

3. Solve by calculator using intersect function:

─2x + y = ─7
   4x + 5y = 0

4. Solve by simultaneous equations:

─2x + y = ─7
   4x + 5y = 0

1.    ≤        

 2.   >        

 3.    ≥        

 4.   <

5.    2x + 2 > 5      

6.    -2 < x ≤ 3       

7.    x + 8 > 3        

8.    2 – 3x ≥ 8      

9.    2x – 4 + 5(5 + x) ≥ 0

10.   2(3 – 2x) > 10 – 4x  

11.  4x – (1 + x) < 2x + (1 + x) 

12.  -4 < 2x + 6 ≤ 8

13.   | x + 5 | = 8     

14.    | 2x – 6 | ≥ 4

15.   | 3x + 4 | < 5   

Arrange the numbers in order from least to greatest:

1.    4/21,   2/15,    5/27

Express as a decimal:

            2.    7/12

Express as a fraction in lowest terms:

                 3.     .166666….  

      Simplify:                 

               5.     4√(98)

              6.     √(121/625)  

              7.    √(4/5 ) • √(35/4)

              9.    4√(2)  +  √(72)

             11.    (√(5)  +  3)²

Rationalize the denominator:

            13.    3/√(2)   

            14.    3/(2+√5)

           15.     3x² ─ 108 = 0

           16.    √(3x + 2)  = 4

1.                  State the quadratic equation in standard form:

2.                  State the quadratic formula.

3.                  Solve 2x² + 9x – 5 = 0 using the quadratic formula:

4.                  Solve x² + 4x + 3 = 0 by completing the square:

5.                  Using your calculator and the left & right bound technique, state the x-intercepts (zeros or roots of the equation) of       x² + 2x – 35 = 0. 

6.                  Using your quad program on the calculator, solve
5x² + 9x – 3 = 0

7.                  Solve by two methods not listed above: x² ─ 16 = 0

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

9.        State the discriminant formula.
                    

Determine the nature of the roots using the discriminant: 

10.      2x² + 5x – 3 = 0

11.      9x² + 2x + 8 = 0

12.      x² + 4x + 4 = 0