Beginning Algebra Semester Review Sheet

1.  Find the balue of each expression>

    a.  [(4)(-8) + (-6)² ]/[(-2)(-2)]

    b.  5(4 + 3) + 6[14 - 6(2 - 3)]

2.  Add or subtract.

    a.  (6x³ + 3x² + 2) - (5x³ + 4x² + 3) - (5x² - 4x - 6)

    b.  4/(8xy² ) - 2/(12x² y)

    c.  5/(x² - 16) - 2/(x² - 3x - 4) + 3/(x² - 1)

    d.  (4x²  - 3) + (3x²  - 4x - 4)

    e.  (x + 5)/(x - 10) + (3x - 2)/(x - 10)

3.  Multiply or divide.

    a.  8x² y³ (2x²  + 3y² )

    b.  (2xy³ )(x² y)(7xy)

    c.  (x² y - z)(x³ y²  - x² yz)

    d.  (2x + 1)(3x - 2)

    e.  (ab - 3)(ab + 3)

    f.  (x + 5)² (x - 1)

    g.  [(x - 3)/(2x + 1)][(4x²  -1)/(x² - 5x + 6)]

    h.  (36a³ b³ c²)/(6ab³ c³ )

    i.  (x - y)/(y - x)

    j.  [(x²  - 25)/(x²  + 7x + 12)][(x - 2)/(4x²  - 9)]divided by [(x - 3)/(2x²  + 11x + 12)]

        Remark:  I do not know how to print the symbol used in arithmetic to denote division.

    k.  (64x³ y² - 32xy³ )/(8xy² )

    l.  (3x²  + 6x + 1)/(x - 2)

4.  Factor completely.

    a.  2m² n³  - 6m² n²  + 4m³ n² 

    b.  x²  - 2x - 8

    c.  2x³ y + 8x² y - 24xy

    d.  x²  + 14x + 49

    e.  4y²  - 169

    f.  21x²  + 4x - 1

    g.  9x² - 12x + 4

    h.  8x³  + 125

    i.  27a³ b³  - 64

5.  Solve each of the following equations or inequalities.

    a.  y + 9 = 18

    b.  17x + 8(1 - 2x) = 2/3

    c.  6(x + 2) = 4 + 5(x - 4)

    d.  8y - 18 = 2y + 30

    e.  3 > 4 - 2x

    f.  (x - 1)/x = (x + 1)/(x - 1)

    g.  1/4 - 2/x = 3/2

    h.  -4 <  5 - 3x

    i.  7/t = 14

6.  Solve the word problems.

    a.  If two more than a number is equal to four less than three
        times the number, find the number.

    b.  If a rug is 3 feet longer than it is wide and its perimeter
        is 38 feet, find its dimensions.

    c.  If two consecutive odd integers sum to 24, find the integers.

    d.  A triangle whose base is 16 cm has an area of 144 square
        centimeters.  Find the altitude of the triangle.

    e.  If you drive for 2 hours and go 110 miles, what is your 
        average speed?

    f.  How many quarts of a 40% salt solution must be added to 40
        quarts of a 10% salt solution to obtain a 20% salt solution?

    g.  An amount of money is invested at 9% and $1200 more than that
        amount is invested at 10%.  How much income is received from
        each investment if the total income from the two investments 
        is $1013?

    i.  A woman drives 120 miles in the same time a man drives 80 miles.
        If the speed of the woman is 20 miles per hour greater than the
        speed of the man, find the speed of each.

7.  Find the equation of the line that passes through (5,2) and (-3,-2).
    Express answer in slope-intercept form.

8.  Find the equation of the line that passes through (6,2) which is
    parallel to the line y = (1/3)x + 5.  Express answer in standard
    form, that is of the form Ax + By + c = 0 where A, B, and C are
    integers.

9.  Find the equation of the line that passes through (-1,-5) and is 
    perpendicular to the line x + 2y = 2.  Express your answer in standard
    form, that is of the form Ax + By + c = 0 where A, B, and C are
    integers.

10.  Use the intercept method to graph the line 2x + y = 2.

11.  Graph the line 6x - 3y = 12.

12.  Graph the inequality x - 3y > -6.

13.  Write in scientific notation.

     a.  0.05026

     b.  99.103

14.  Simplify the following radical expressions.
     Notation:  Sqrt (x) denotes the principal square root of x.
     In what follows all variables are positive.

     a.  Sqrt (36/9x² )

     b.  Sqrt (98xy³ z² )

     c.  Sqrt (49x³ )

     d.  2(Sqrt(6)) - 2(Sqrt(24)) + Sqrt(54)

     e.  Sqrt(18)/2 - 2(Sqrt(2))/3

     f.  Sqrt(2)(Sqrt(6) + 3)

     g.  (Sqrt(3) + 2)(2(Sqrt(3)) - 1)

     h.  Sqrt((8x)/(3y))

     i.  (5x)/Sqrt(3)