Elementary Algebra     TEST 1    SOLUTION     4 February 2004

 

NAME:   _____________________________________________  Score___________ /100

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

1.               T                   5 is a natural number.

2.               T                   is a real number.

3.                        F          Every rational number is an integer.

4.               T                   Every integer is a rational number.

5.                        F          {0, 1, 2, 3, 4, …} is the set of natural numbers.

6.               T                   7 is a prime number.

7.                        F          12 is a prime number.

8.               T                   The absolute value of a number is its distance from 0.

9.                        F          {1, 2, 3, 4, 5, …} is the set of rational numbers.

10.                    F          If x represents a number, then x + (-x) = 2x.

 

B.  (20 points) Fill in the blanks to correctly complete each statement.

1.      In the expression an, n is called the __exponent________________________________.

2.      In the expression an, a is called the __base________________________________.

3.      In the expression (5x –3)n, the base is  __ (5x – 3) ____________________________ .

4.      (Commutative Laws) For real numbers a and b, a + b  = _b + a _________ and ab = _ ba _______

5.      The reciprocal (multiplicative inverse) of  is ____________________

6.      The reciprocal (multiplicative inverse) of 5 is _____________________

7.      An equation is a mathematical sentence that contains _ an = sign _________________________.

8.      Two fractions that represent the same number are called ___ equivalent __________ fractions.

9.      The ____denominator____________________ of the fraction  is 3.

10.  The _____numerator_____________________ of the fraction  is 5.

 

C.  (10 points) Write each phrase as an algebraic expression.

1.      One more than six times a number.  ______ 6x + 1 ______________________________________

2.      Twelve added to three times a number.  ______ 3x + 12 ___________________________________

3.      Eight times the difference of a number minus nine.  __ 8(x - 9) _____________________________

4.      5 times the sum of 6 and y is –35.  __ 5(y + 6) =  - 35 ___________________________________

5.      Negative two is equal to x divided by the sum of x and 5.  ________________________


D.  (30 points)  Perform the indicated operations.   Show your work

1.      32  =  (3)(3) = 9

2.      –32 =  -(3)(3) = -9

3.      (-3)2 = (-3)(-3) = 9

4.      (-3)3 = (-3)(-3)(-3) = -27

5.      [3(6+2) – (-4)] Έ [2 – (-3)] = [3(8) + 4] Έ [2 + 3] = [24 + 4] Έ 5 = 28 Έ 5 =  

6.      12 + (-7) = 5

7.      3(4 – 6)3 = 3(-2)3 = 3(-2)(-2)(-2) = 3(-8) = -24

8.      (23 – 32) – (5 – 7) = (8 – 9) – (5 – 7) = (-1) – (-2) = -1 + 2 = 1

9.       

 

10.            

E. (10 points) Find the value of each expression when x = 2, y = -1 and z = 0.  Show your work

1.      x2 + y2 = 22 +(-1)2 = 4 + 1 = 5

2.      3x – 5z = 3(2) – 5(0) = 6 – 0 = 6

3.       (5x – z) Έ (2y + xy) = [5(2) – 0]  Έ [2(-1) - 2(-1)] = 10 Έ (-2 –2) = 10 Έ (-4) =

4.       =

5.     


F. (10 points)  Write each number in prime factored form.  Show your work

1.      24 = (2)(2)(2)(3)                                                               2.  117 = (3)(3)(13)

                            

3.       270 =  (2)(3)(3)(3)(5)

G.  (10 points) Solve each of the following “word problems”.  Show your work 

1.      The formula for the volume of a cone is .  What is the volume of an ice cream cone which is 7.5 inches tall and has a radius of 1.5 inches at the large end.  Express your answer correct to the nearest tenth of a cubic inch.

 

 

      

 

2.      The distance a tire rolls in one revolution can be found by computing the circumference of the circular tire using the formula C = pD where d is the diameter of the tire.  If the diameter of a tire is 26 inches, how far will the tire roll in one revolution?  Express your answer to the nearest tenth of an inch.

 

 

   C = (3.14)(26) = 81.64 = 81.6 in.