Intermediate Algebra

Test File - Spring 2001

 

Test #1

 

1.)        If A = {1, 3, 4, 5}, B = {3, 6, 7, 8} and C = {1, 3, 5, 7}, list the elements in the following sets.

            a.)        A È C                         b.)        A Ç B                          c.)        A È B È C

            d.)        A Ç B Ç C                  e.)        A È Æ

For #2 and #3, refer to the set .

2.)        Identify all elements in set A that are integers.

3.)        Identify all elements in set A that are rational numbers.

For #4 - #5, simplify each expression.

4.)                                     5.)        |4 - 16| + |-3| - |-7 - 1| - (-8)

6.)        Solve the following formula for P.     A = P + Prt

In #7 - #11, solve the equation.

7.)        3x - 8 = -2                                           8.)        9 + 2 - 3x = x + 11 - 3x

9.)        | 2 - 5x | = 8.                                        10.)     | 4 - x | - 3 = 0

11.)     |5x - 9| = |6 - 5x|

12.)     Graph the inequality -2 £ x < 4 on the number line.

13.)     Solve the inequality.  Graph the solution set.         -3x - 8 < 13

14.)     Solve the compound inequality and graph the solution set.         3 - x > 5 or 2x ³ 8

15.)     Solve the double inequality.  Graph the solution set.         -5 £ 4x - 5 £ 3

16.)     Solve the compound inequality and graph the solution set.

r + 1 £ 14 and  r - 4 > 0

17.)     Solve the inequality.   13 £ |5 - 4x|

18.)     An oil drum has the shape of a right circular cylinder.  Find the volume of the drum if its height is 150 cm and the radius is 20 cm.  You may use the fact that for a right circular cylinder, V = pr2h.

19.)     Find three consecutive integers such that 5 times the first minus three times the third is 20 more than the second.

20.)     How many liters of a 75% formaldehyde solution should be added to 15 liters of a 40% formaldehyde solution to obtain a 65% formaldehyde solution?

 

Test #2

In #1 - 5, simplify each expression completely.  Write your answer with positive exponents. Assume no variable is 0.

1.)        (-4x-3y4)3(x9y-2)-3                                 2.)       

3.)                                                            4.)       

5.)        Find the x- and y-intercepts for the line 2x - 7y = 4.  Label your answers.

In #6 - 7, write the following exercises in scientific notation and then perform the indicated operations.  Write your answer in scientific notation.

6.)        (0.000000032)(41,000,000,000)    7.)       

In #8 - 10, perform the indicated operation.

8.)        (3x2 - 2x + 7) +(-5x2 + 9x + 4)

9.)        (9r3 - r2s + 6s3) - (3r3 - rs2 - 5s3)

10.)     Divide 3x3 - 2x2 - 2x + 7 by x + 2 using long division.  Write your answer in the form quotient + remainder/divisor.

11.)     Divide 3x3 - 2x2 - 2x + 7 by x + 2 using synthetic division.  Write your answer in the form quotient + remainder/divisor.

In #12 - 14, find each product.

12.)     (3x + 8)(x - 2)

13.)     (r - 9)2

14.)     (x2 - 2x + 5)(3x + 7)

15.)     Suppose f(x) = 3x2 - x + 1.  Find the following:

            a.)        f(2)                  b.)        f(-1)                 c.)        f(a)                  d.)        f(x + 1)

16.)     Factor out the greatest common factor in 45r8t4 - 30r2t8 - 60r6t3

17.)     Does the following set of ordered pairs describe a function?  Why or why not?

            {(3, 3), (4, 5), (1, 6), (3, 11), (-2, 7), (8, 2), (5, 14)}

In #18 - 21,  factor each polynomial completely.  If it can not be factored, write "can't be factored."

18.)     x2 - 11x - 12                19.)     4y2 - 20y + 25                        20.)     x4 - 9x2 + 8

21.)     x2 + 25

22.)     Find an equation for the line on the points (-2, 1) and (3, 2).  Solve for y.

23.)     Find an equation for the line on the point (3, 4) that is parallel to the line          

            y = -3x + 5.

24.)     Solve the following system of equations using the substitution method.

            2x  - 3y = 6

              x + 4y = 3

25.)     Solve the following system of equations using the addition method.

            2x  - 3y = 6

              x + 4y = 3

 

Test #3

1.)        When is the final exam for this course?  (Hint:  See the instructions page.)

2.)        How far can a plane fly with the wind at 280 Mi/hr and still return against the wind at 220 mi/hr if it has enough fuel to last 10 hr?

In #3 - 5, solve each equation.

3.)        x2 + 3x - 4 = 6 4.)        -x2 - 24x - 23 = 0       

5.)        (5x - 3)(4x + 1) = x(4x - 7) + 46

In #6 - 7, simplify each rational expression.

6.)                                          7.)       

In #8 - 10, multiply or divide as indicated.  Write your answer in simplest form.

8.)                            9.)       

10.)    

In #11 simplify each expression.

11.)    

12.)     Solve the following equation.

                       

13.)     Simplify the following if possible.

            a.)       

            b.)        (assume all variables are positive)

            c.)       

14.)     Rationalize the denominator.                      

 

Final Examination

 

1.                  A  student earns grades of 77, 85, 83,  and 87 on four major exams. What is his average on the exams ?

2.                  Solve:

3.                  Determine whether perimeter, area or volume would be used to determine the measure of the indicated quantity.

a.                  water for a swimming pool

b.                  wallpaper to cover two walls of a bedroom.

c.                  wallpaper border for a kitchen

4.                  Simplify the expression: 

5.                  Let x represent a certain number. Denote a number that is:

a.                  twice as large as x,   b.  5 more than 3 times x,     c.  4 less than

6.  Graph y =   . Label axes completely.

7.         The campus bookstore purchases books at the wholesale price from a textbook dealer  and marks the cost up by 40% before selling to the student.

 

a.         Write an equation to represent the cost y (to the student) of a textbook purchased for x. dollars.

b.         Determine the wholesale price of a textbook that sells for $46.20. 

8.                  Write an equation of the line with slope  and passing through .

            9.         Find and label the x- and y-intercepts  of  2x + 5y = 10.

10.       Are the lines represented by 3x + 2y = 6 and 2x - 3y = 6 perpendicular ? Explain.

11.       Solve for x: 

12.       Solve the System:         3x - 4y = 9                  x + 2y =  8

13.       A standard rectangular highway billboard sign has a perimeter of 124 ft. The length is 6 ft more than three times the width. Find the dimensions.

14.       Find the domain      

            15.  Find g(2) and h(3) given  and 

            16.  Solve   and graph the solution set.

            17.   For each point, name the quadrant in which it lies or the axis on which it lies.

a)                 ( -3 , -2 )                                  b)         ( 0 , 3.14 )                   c)         ( 6 , -3 )

            18.       Solve |4 - 3x| £13

19.  Simplify the following expression. Write the following answer without using     negative exponents.                                      

            20.  Change    a.  8.706 x 105   and     b.  1.1 x 10-3    to standard notation.

            21.       Multiply  (3x + 2)(4x +9)

            22.  Factor by grouping:   

            23.  Factor: 

            24.       Multiply:  .

            25.       Divide:    .

26. Solve:                        27.  Solve:  .

            28.  Solve:     

            29.  Evaluate each expression:       a)          b)                                

            Simplify the radical expression:      30.       31.   

32.       Add or subtract. Simplify by collecting like radical terms, if possible.

33.       Multiply and simplify: