T101 DEPARTMENTAL FINAL REVIEW

**This is only a sampling of some problems to review.  Previous tests and reviews should also be done.** 

 

1.         Find the 14th term of the arithmetic sequence 3, 6, 9, 12 . . .

2.         The following sequence could be either arithmetic or geometric depending on the

numbers replacing the blanks.  Find both possible sequences.

20,          , 80,          ,                

3.         List the next three terms to continue a pattern.  (Finding differences may be helpful.)

            5, 9, 16, 27, 43, 65, 94

4.         Find the first five terms of the sequence whose nth term is n3 + 5.

5.         How many dots will be in the sixth figure of this pattern?

                                    ·  ·  ·

                        ·  ·        ·  ·  ·

            ·           ·  ·        ·  ·  ·

 

6.         A store clerk sets up a display of soup cans in the form of a triangle, using 12 soup cans

at the base and 1 at the top.  (Only part of the display is shown below.)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


            How many soup cans were used by the clerk to make the arrangement?

 

7.         If U = {40, 41, 42, 43, 44, 45, 46}, A = {41, 43, 46}, and B = {41, 45}, find each of the following:

            (a)           (b)           (c)          (d) 

 

8.         Write 1492 in Roman numerals.  Use the following symbols:        I, V, X, L, C,  D, M

 

9.         Rewrite the following division sentence as a multiplication sentence; then rewrite the

             multiplication sentence as a new division sentence.        

 

10.        If it takes 30 seconds to make each cut, how long will it take to cut 16 boards that

 are 15 feet long into boards that are 5 feet long if only one board can be cut at a

 time?   (Careful – make drawing)

11.        Kathy's charge account has a starting balance of $617.  She makes purchases of $80,

 $90, $55, and $26.  She makes a payment of $23 and returns some merchandise for

 $41.  What is her balance at this time?

12.        I am thinking of a whole number.  If I divide it by 11, then multiply by 15, then subtract

 18, and then add 60, I end up with 87.  What was my original number?

 

13.        Find -x when x = -3.

 

14.        Add:     9 + (-14) + (-7) + 17 + (-12)

 

15.        Use a property of subtraction to rewrite each of the following as a sum.

             (a)  5 – 4                          (b)  -2 - (-3)         (c)  -2 – 2

16.        Simplify:           

17.        Simplify:           

18.        In a chemical experiment the temperature is -48o C at 3:00 P.M.  What is the

 temperature at 3:21 P.M. if the temperature increases 3o C per minute?

19.        Classify each of the following as true or false:

             (a)  If a number is divisible by 8 and 2, then it is divisible by 16.

             (b)  If x | (a + b) then x | a or x | b.

             (c)  0 | 4

20.        Which of the following numbers are divisible by 3?          2448,     7367,     6353,      5175

21.        Which of the following numbers are divisible by 8?          1014,     711,     4279,     135

22.        Which of the following numbers are divisible by 6?        4942,     9090,     7436,     3744

23.        Find all the factors of 33.

24.        Write the prime factorization of 300.

25.        What is the greatest prime number to consider to test whether or not 531 is prime?

26.        Farmer Welch has 725 pear trees.  He wants to plant them in rows that have the same

 number of trees in each row.  Since his property is approximately square, what are his

 best options?

27.        At 12:00 P.M. David and Tanya are sitting in a class.  Every 35 seconds David looks up

 to see if Tanya is looking at him.  Every 49 seconds Tanya looks up to see if David is

 looking at her.  If they immediately look back at their desks each time, how long will it

 be before they make eye contact?

28.        Find the least number divisible by each natural number greater than 3 and less than 15.

29.        Use < or > to write a true sentence:       

30.        Find a number between the two given numbers.             

 

31.        Subtract:          

32.        Kathy is making horse feed by mixing  pounds of rolled corn,  pounds of rolled

 barley, and  pounds of rolled oats.  How much feed did she make?

33.        Multiply:           

34.        Yoshi found a board to make a shelf.  It was  feet long.  He needed  of it for the

 shelf.  How long was the shelf?

35.        Divide:             

36.        Lee's recipe requires  cup of bran flakes.  If he has only a  cup measure, how many

            times will he need to fill it to make  cup?

 

37.        Carol has five times as much money as Nina, and Nina has $8 less than Lynn.  If n

             represents the amount Nina has, represent the total amount that Carol, Nina and Lynn

             have together.

38.        A teacher instructed her class as follows:

            Take any number and subtract 12 from it.  Now multiply that difference by 5.  Next add

20, and divide the sum by 5.  If you now add 16 to the quotient and tell me the number, I

will tell you the number you started with.  Show how it is possible for the teacher to find

the starting number.

39.        Last week Mrs. Baker's cats got into Mrs. Murphy's chicken coop with her chickens. 

During the commotion, I counted 26 heads and 60 feet.  None of the animals was

harmed.  How many of Mrs. Baker's cats were in the coop with how many of Mrs.

Murphy's chickens?

40.        Twenty acres are required to produce 125 bushels of cucumbers.  At this rate, how many

             acres would be required to produce 195 bushels of cucumbers?

41.        A 20-oz bottle of gourmet popcorn oil sells for $1.68.  A 60-oz bottle of generic popcorn

oil costs $2.71.  Which is the better buy?

42.        There is a law stating that "the ratio of width to length for the American flag should be 10

to 19."  Is a flag measuring 40 by 76 feet of the correct ratio?                       

 

43.        Classify as True or False:  

            a.  Every set is a subset of itself      

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

 

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

 

45.      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?

 

46.     Convert 29 to base three.

 

47.     Convert  to base ten

 

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

 

49.     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. 

 

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

           

 51.     Add or multiply in the bases indicated.

            a.                                      b.   

 

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

            a.  7 + 3                                                 b. 

 

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

 

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

            a.                                                

 

55.     Use both traditional and the lattice multiplication algorithm to perform the

          following multiplication:   

 

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

 

57.     Find the: 

          a.  additive inverse of 2x - 5y.                     b.  multiplicative inverse of 

 

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

          reason for your answer.

          a.                    b. 

 

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

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

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

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

 

63.     Simplify:            a.                           b.   

64.     Use a rectangular region to illustrate

 

65.     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?

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

          uses  yards of ribbon?  How much ribbon is left over?

 

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

68.     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?

69.     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?

70.     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 to T101 DEPARTMENTAL FINAL REVIEW     

1.   a14 = 42            

2.  20, 50, 80, 110, 140 and

     20, 40, 80, 160, 320

3.   131, 177, 233 

4.   6, 13, 32, 69, 130 

5.   36

6.  78 

7.   (a) {41,43,45,46}      (b) {41}

      (c) {40,42,44}      (d)  {40,42,43,44,45,46}

8.   MCDXCII

9.   1431 X 224 = 320, 544 

      320, 544  1431 = 224 

10.  16 minutes

11.  $804 

12.  33 

13.  3

14.   –7

15.  (a)  5 + (-4)   (b)  -2 + 3   (c)  -2 + (-2)

16.  -26

17.  -40  

18.  15o C  

19.  (a) false  (b)  false  (c)  false

20.  2448, 5175 

21.  none of these numbers 

22.  9090, 3744

23.  1, 3, 11, 33 

24.  2  2  3  5  5   

25.   23

26. 25 rows of 29 trees; 

      29 rows of 25 trees

27.  245 seconds

28.  360,360  

29.  >    

30.   Sample answer: 

31.       

32.   pounds

33.

34.   ft

35.  

36.  2 times

37.  7n + 8 dollars

38.   To tell the student's number the teacher merely subtracts 8 from the student's answer

39.  4 cats and 22 chickens  

40.  31.2 acres 

41.  the 60-oz bottle

42.  Yes

43.  a.  True         b.  False 

44   Ό

45.  25 year

46. 

47.  113

48.   a.  thousand     b.  6 or 36

49.  a.  Commutative Prop of +

       b.  Distributive Prop of  X Over Add.                  c.  Identity Property of Addition

50. one 5x5, four 5x1's, and

three 1x1's  or 

one flat, four longs, and three units

51.  a.        b. 

52.  a.  10                b.  –15

53. 1,2,3,4,10,11,12,13,14,20,21,22,23,24,30

54.  a.  1,3,5,1             b.  7,2,8,7

55.   8642

56.  20 times

57.   a.  -2x + 5y           b. 

58.  a.  no 9 does not divide 30 (sum)    

       b.  yes divisible by 3 and 5

59.   a.  4                      b.  180

60.  GCD = 4,  LCM = 146,200

61.   2,3,5,7,11,13,17,19

62.  60

63.   a.  26                    b.  5

64. 

65.   a.                      b.  13,500 lbs.

66.  54 bows   yds. Left

67.   -21

68.  a.  $46,524           b.  $42,250

69.   a.  3/7                   b.  16 girls

70.  if $650  12 and 23, if $325 

       24 and 46, if $130  60 and 115 etc