T-101 Final Review B

1.    If U = {q,u,e,s,t,i,o,n}, A = {q,u,e,s,t}, B = {s,i,t}, and C = {n,e,s,t}, find each of the following:

a.   =                 b. A – B =                        c.  =

2.    Classify as True or False:  

       a.                       b.  Every set is a subset of itself      

       c.  If  A = {2,3,4,5,6,7}, then  n(A) = 5

3.    Find the 26^th term of this sequence:  1,4,7,10,13,……

4.    Find the 8^th term of this sequence:  32,16,8,4, ………

5.    List the next three terms to continue a pattern.  23, 18, 13, 8, …….

6.    A pencil and a pen cost $2.50.  The pencil cost 80 cents less than the pen. 

       What is the cost of each?

7.    Tom’s income has been increasing each year by the same amount.  The first year his income

       was $25,900, and the fifteenth year his income was $60,900.  In what year will his income

       be $85,900?

8.    Find the first four terms of the sequence with nth term:  6n – 7.

9.    Suppose a number is entered on the calculator.  Then 29 is added to it; it is multiplied by 24;

      124 is subtracted from it and finally it is divided by 20.  If the answer is 61, what was the

       original number?

10.   Convert 2844 to Roman numerals.

11.   Convert 29 to base three.

12.   Convert  to base ten

13.   Tell the place value for the underlined numbers.            a.                b. 

14.   For each of the following identify the rational number property which is illustrated.

            a.  9 + (6 + 4) = 9 + (4 + 6)              b.  -3 (x + 8) = -3x + -24              c. 

15.   Draw a diagram of the collection of base pieces representing the following number.

16.   Add or multiply in the bases indicated.

            a.                                      b. 

17.   Susan is making a mixture of nuts by mixing  pounds of cashews,  pounds of peanuts,

        and  pounds of walnuts.  How many pounds of nuts are in her mixture?

18.   Use the number line model to perform the following:  (Show your work )

            a.  7 + 3                                                 b. 

19.   Write the first 15 counting numbers in base five.

20.   Find the missing numbers in each of the following.

            a. 

21.   Use both traditional and the lattice multiplication algorithm to perform the following

         multiplication: 

22.   A siren blows every 45 seconds.  Find the number of times it blows in 15 minutes.

23.   Tom had $156 in his checking account.  He wrote checks for $26, and $29 and deposited $88. 

        If he writes three more checks for $50 each, what is his current balance?

24.   Find the:  a.  additive inverse of 2x - 5y.                     b.  multiplicative inverse of 

25.   Decide whether the following are true or false using only divisibility tests.  Give a reason

        for your answer.

        a.                    b. 

26.   Find:         a.  GCD (12, 80)                      b.  LCM (20, 36)

27.   Use the Euclidean Algorithm to find the GCD and LCM  of 200 and 2924.

28.   List all primes that must be checked in order to determine if 519 is prime.

29.   What is the smallest counting number divisible by 2, 4, 6, 12 and 15?

30.   Multiply or divide as indicated       a.                       b. 

31.   Simplify:               a.                           b. 

32.   Use a rectangular region to illustrate

33.   One-fifth of the expected potato crop was destroyed by insects and one-ninth was destroyed

        by blight.

            a.  What fraction of the expected crop survived?

            b.  If 9300 lbs of potatoes were harvested, how many were expected?

34.   Sue bought  yards of ribbon.  How many bows can Sue make if each bow uses  yards

        of ribbon?  How much ribbon is left over?

35.   Solve the equation:              -2x - 15 = 27.

36.  Set up an equation and use it to solve the following problem.  If every employee's salary at the

       University increases each year by  of that person's salary of the previous year, find the following:

            a.  Seth's present salary is $50,401.  What was his salary last year?

            b.  Christy's present salary is $36,000.  What will her salary be in 2 years?

37.   If the ratio of boys to girls is 3 : 4, what is

            a.  The ratio of boys to all students in the class?

            b.  If there are 28 students in the class, how many girls are in the class?

38.   The annual sales for certain computers were $7,800 one year and $14,950 the next.  Assuming

        that the price of the computers was the same each of the two years, how many computers were

        sold each of the two years?  ( There is more than one possibility --list all the possible answers )

ANSWERS

1.  a. {s,t}     b.  {q,u,e}     c.  {s,t}	20.  a.  1,3,5,1             b.  7,2,8,7
2.  a.  True       b.  True         c.  False	21.  8642
3.  76	22.  20 times
4.  1/4	23.  $39.00
5.  3, -2, -7	24.  a.  -2x + 5y           b.
6.  pencil 85 cents, pen 165 cents	25.  a.  no 9 does not divide 30 (sum)            b.  yes divisible by 3 and 5
7.  25 year	26.  a.  4                      b.  180
8.  -1,5,11,17	27.  4,  146,200
9.  27	28.  2,3,5,7,11,13,17,19
10.  MMDCCCXLIV	29.  60
11.	30.  a.  714                  b.  25
12.  113	31.  a.  26                    b.  5
13.  a.  thousand     b.  6 or 36	32.
14.  a.  comm.        b.  dist        c.  identity	33.  a.                      b.  13,500 lbs.
15.  one 5x5, four 5x1's, and three 1x1's	34.  54 bows yds. left
16.  a.        b.	35.  -21
17.	36.  a.  $46,524           b.  $42,250
18.  a.  10                b.  -15	37.  a.  3/7                   b.  16 girls
19.  1,2,3,4,10,11,12,13,14,20,21,22,23,24,30	38.  if $650  12 and 23, if $325         24 and 46, if $130  60 and 115 etc

            .