Elementary Algebra     TEST 2   SOLUTION   25 February 2004

 

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A.  (10 points) Circle T or F, whichever is correct.

1.                        F          Two equations are equal if they have the same solution sets.

2.               T                   5, rt, 3b, and d2y are all terms.

3.                        F          Like terms are terms with exactly the same variables and exactly the same coefficients.

4.               T                   The formula which relates radius and circumference of a circle is C = 2pr.

5.                        F          The formula for the volume of a cylinder is V = 2prh.

6.                        F          The symbol > means “is less than”.

7.               T                   A solution of an inequality is any number which makes the inequality true.

8.                        F          The inequality –3x < -6 is equivalent to x < 2.

9.               T                   The equation –3x = -6 is equivalent to x = 2.

10.           T                   The statement 3(h + 9) = 3h + 27 is an illustration of the distributive property.

 

B.  (10 points) Fill in the blanks to correctly complete each statement.

1.      The formula for the area of a circle with radius r is  A = pr2.

2.      The formula that relates distance, rate, and time is d = rt.

3.      The formula which relates percent, percentage, and base is percentage = (percent)(base)

4.      If both sides of an inequality are multiplied by a positive real number, the resulting inequality will be equivalent to the original inequality.

5.      If both sides of an inequality are multiplied by a negative real number and the sense of the inequality is reversed, the resulting inequality will be equivalent to the original inequality.

6.      If an expression is added to both sides of an inequality, the resulting inequality will be equivalent to the original inequality.

7.      To add like terms, add their coefficients and keep the same variables with the same exponents.

8.      A term is a number or a product of a number and one or more variables.

9.      Percent means parts per one hundred.

10.  The product of a number and its reciprocal is 1.

 

 

C.  (10 points)

1.      Is 3 a solution of the equation x3  - 3x2 + x – 3 = 1

33 –3(32) + 3 – 3 = 33 – 33 + 3 – 3 = 0 Ή 1.  Therefore, 3 is not a solution.

2.      When solving the equation 4x = 16 do we divide both sides of the equation by 4 or do we subtract 4 from both sides of the equation.  Divide both sides of the equation by 4.

 

3.      Change 3.5% to a decimal 3.5% = 0.035

 

4.      Translate the following sentence into an equation.  DO NOT SOLVE. 

57 is  36.2% of what number?

Use percentage = (percent)(base) to obtain 57 = (.362)(base)

5.      Use the distributive property to remove parenthesis from 3(k –2k3) = 3k –6k3


D.  (30 points)  Perform the indicated operations.  

1.      Simplify by combining like terms    3x + 5x – 7x = 8x – 7x = x

2.      Simplify by combining like terms    12(m + 11) – 11

                                                                = 12m +(12)(11) – 11 = 12m + 132 – 11 = 12m +121

3.      Evaluate | y3 – x | for y = -5 and x = -3

|(-5)3 – (-3)| = |-125 + 3| = |-122| = 122

4.      Simplify    –(-8) = 8

5.      Solve   -5x –2 = 1

                  -5x = 3

                  

6.      Solve 9(x + 11) + 5(13 – x) = 0

9x + 99 + 65 _ 5x = 0

4x = -99 – 65 = -164

x = (-164)/4 = -41

7.      Solve A = P + Prt for P

A = P(1 + rt)

8.      Solve   V = pr2h  for h

9.        Solve –3x – 7 > -1

         -3x > -1 + 7 = 6

            

10.  Solve 5x + 7 < 2x + 1

5x  < 2x + 1 – 7

5x – 2x < -6

3x < -6

x < -2

E. (5 points) Write an equation for the area of the figure shown here.  I just want the equation.

   A = (x - 4)(3x – 5)

                                                                                               

F. (5 points) 

Formula for Converting Fahrenheit to Celsius: 

Convert 72°F to degrees Centigrade.    


G. (10 points) 

A slice of pie with a scoop of ice cream has 850 calories.  The calories in the pie alone are 100 more than twice the calories in the ice cream alone.  How many calories are in each food?

Let x be the calories in the ice cream

Then the calories in the pie are 2x + 100 and the total calories are    x + (2x + 100) as well as 850.

This yields the equation x + 2x + 100 = 850

So 3x = 750 and x = 250.  Then 2x + 100 = 600

There are 250 calories in the ice cream and 600 calories in the pie.

H.  (10 points)

The total area of the 50 states and the District of Columbia is 3,618,770 square miles.  If Alaska covers 591,004 square miles, what percent is this of the U. S. total?

I want to see the equation and then I want to see the steps used to solve the equation.

 

Use percentage = (percent)(base) to obtain 591004 = (percent)(3618770)

I.  (5 points)

Suppose a florist buys a dozen roses wholesale for $12.95 and sells them for $37.50. 

Write an equation which relates the wholesale price, retail price, and markup in this situation.

IMPORTANT:  I want the equation NOT the solution.

 

 Use Retail price = Wholesale price + markup  to obtain

37.50 = 12.95 + markup

 

J.  (5 points)

The length of a rectangular picture is 11.75 inches less than twice the width.  The perimeter is 102.5 inches.  What are the dimensions of the picture?  I want to see the equation and then I want to see the steps used to solve the equation.

 

Let x be the width then the length is 2x – 11.75 and the perimeter is 2x + 2(2x – 11.75) as well as 102.5.

This yields the equation  2x + 2(2x – 11.75) = 102.5

2x + 4x – 23.5 = 102.5

6x = 126

x = 21 is the width and the length is 2(21) – 11.75 = 42 – 11.75 = 30.25