Elementary Algebra Final Exam I Gave Once (or use it as a review!)

 
BASIC MATH I    38103   FINAL EXAM                      12 NOV 1998
                                   

COPY DOWN EACH PROBLEM, AND THE PROBLEM NUMBER.  (YOU NEED NOT
COPY THE LONG SENTENCES, ABBREVIATE!)  SHOW ALL WORK.  WRITE
OUT ALL STEPS THAT YOU THINK OF. DON'T DO ANY IN YOUR HEAD.
WORK SLOWLY BUT SURELY AND YOU WILL FINNISH IN TIME.  CIRCLE
YOUR ANSWERS.  DON'T FORGET TO CHECK SOLUTIONS TO 'SOLVE FOR X'
PROBLEMS.  LOOK AT THE ORIGINAL QUESTION WHEN YOU FINNISH A
PROBLEM, TO MAKE SURE YOU'VE ANSWERED THE QUESTION.  QUESTIONS
ARE WORTH 4 POINTS EACH (UNLESS MARKED LIKE []) TO MAKE A TOTAL
OF 200 POINTS.  THERE ARE 4 PAGES, 57 PROBLEMS.

PART I

1) WHAT IS THE SLOPE OF THE LINE: Y= -3X+2 ?     [1]

2) WHAT IS THE Y-INTERCEPT OF THE LINE Y=4X+3 ?  [1]

3) DOES EVERY STRAIGHT LINE HAVE A Y-INTERCEPT?  [2]

4) GRAPH THE LINE Y= -3
.                          3
5) GRAPH THE LINE    Y= - ---X + 6
.                          2

6) FIND THE VALUE OF THE SLOPE OF THE LINE BETWEEN THE POINTS:
(6,3) AND (-2,3), OR TELL IF THE SLOPE IS UNDEFINED.

7) WRITE THE EQUATION OF THE LINE WITH A SLOPE OF -3/2 THAT
PASSES THROUGH THE POINT (-4,3)

8) WRITE THE EQUATION OF THE LINE THAT PASSES THROUGH THE
POINTS: (4,-5) AND (4,3)

9) WRITE THE EQUATION OF THIS LINE:



PART II

10) DOES EVERY SYSTEM OF EQUATIONS HAVE A SOLUTION?        [2]

11) CAN A SYSTEM OF LINEAR EQUATIONS HAVE EXACTLY TWO DIFFERENT
SOLUTIONS?                                                 [2]

12) MATCH THE SYSTEM OF EQUATIONS WITH THE CORRECT CONCLUSION:
                                                 [9]
A) Y=2X+1        B) X+Y=1        C) X+Y=1
.  Y=X+2            2X+2Y=2         2X+2Y=4

1) NO SOLUTION      2) EXACTLY ONE     3) INFINITE NUMBER
.                      SOLUTION           OF SOLUTIONS







.                                   2
13) IS THE GRAPH OF THE EQUATION Y=X  A STRAIGHT LINE?  [bonus]

SOLVE EACH SYSTEM OF LINEAR EQUATIONS. DON'T FORGET TO CHECK!

14) BY SUBSTITUTION:     15) BY GRAPHING:       16) BY ADDITION:
.   4X + Y = 14             Y = X - 1            X - Y = 4
.   3X - 2Y = 5             2Y + X = 4           2X - 3Y = 9
[6]                     [9]                 [6]

PART III
.                     -5       6
17) WHICH IS BIGGER  4   OR   3  ?          [1]

.                       2    2
18) TRUE OR FALSE: (X+4)  = X + 16          [2]

19) WHAT IS THE AREA OF THE FLOOR OF A ROOM 10 FT. WIDE, 8 FT.
LONG AND 12 FT. HIGH?:
A) 80 FT.  B) 960 SQUARE FT.  B) 960 CUBIC FT. C) 80 SQUARE FT.

.        3  2  2    2                        0   0
20) ( -3X  Y  ) *(4X Y) =              21)  4 * 3  =

.           -2
22) WRITE 10    AS A DECIMAL.

SIMPLIFY, WRITING THE ANSWER WITHOUT NEGATIVE EXPONENTS.

.      2  -2              0  2            7    -4
23)  4X  Y       24)    4X  Y       25) (X )*(X  ) =
.   --------          ----------
.        2                -2  4
.    (XY)              12Y   X

.      3    2            2
26) (8X - 3X - 4Y) - (-4X + 8X + 2Y) =

.              2                               2
27) (X-1) * ( X + X - 1) =           28) (4X-3)  =

29) WRITE 0.00821 IN SCIENTIFIC NOTATION

.                              -5              2
30) WHICH IS GREATER?  8.98 X10    OR 1.001 X10     [2]

.             2
.           -X - X
31) IF Y = --------   AND X= -2,   CALCULATE THE VALUE OF Y.
.              3
.             X





PART IV

32)  HOW MANY DIFFERENT SOLUTIONS MIGHT A QUADRATIC EQUATION
HAVE?                               [2]

33) HOW MANY DIFFERENT SOLUTIONS MIGHT A 3RD DEGREE EQUATION
HAVE?                               [bonus]


.          2
34) SOLVE X = 4               35) FACTOR: 6X+9    [1]

36) DO THE SOLUTIONS OF QUADRATIC EQUATIONS REFER TO THE POINTS
OF INTERSECTIONS OF CURVED LINES OR STRAIGHT LINES?  [bonus]

.             2                               3    2
37) FACTOR: 2X - 5X - 3         38) FACTOR:  X - 6X  - 8X

.                 2
39) IS: 3X + 1 = 4   A QUADRATIC EQUATION?  SOLVE FOR X.

.             2
40) IS: 5X = X - 14   A QUADRATIC EQUATION?  SOLVE FOR X.

SOLVE FOR X:

.    2
41) X +100 = 0

.                                           3
42) X(X+3) = 2X + 6                    43) X -9X = 0
.                               2
44) DIVIDE BY LONG DIVISION: (2X - 5X -3) - (X-3)


PART V

45) ARRANGE THE FOLLOWING NUMBERS IN ORDER FROM THE SMALLEST TO
LARGEST: 4     4     4     4     4     4     4
.       ---,  ----, ---,  ---,  ---,  ---, -----
.        2     1     8     1     4    -1     1
.             ---                           ---
.              2                            10
.                              4
46) WHERE WOULD THE FRACTION  ---, GO IF YOU IMAGINE IT HAS A
VALUE?                         0                   [bonus]

.                      2           2
47) TRUE OR FALSE:    X + X       X
[2]                ---------- =  ---
.                     4 + X       4

48) TRUE OR FALSE:       6X + 3      9
.                       -------- = -----
[2]                      X(X+1)     X+1




.                   2
.                  X -3X - 28
49) SIMPLIFY     --------------
.                    2
.                   X  - 49

.               2              2
.              X - 64         X -8X
50) SIMPLIFY  ---------   -   -------
.                                 2
.              8X + 64          8X

.             3       4
51) ADD:     ---  + ----- =
.             X      X+1

.            X          2
52) ADD   ------  -  ------- =
.                      2
.          2X+4       X +2X

.                    3        4
53) SOLVE FOR X:   -----  =  ---
.                   X-2       X

.                         6         3X
54) SOLVE FOR X:   X +  -----  =  -----
[6]                      X-2       X-2

.                            1                1
55) SIMPLIFY:           X - ---        56)  ------  =
.                            X        [2]     1
.                      ---------             ---
.                        X + 1                2


PART VI

CHOOSE ONE QUESTION AND WRITE ABOUT A HALF A PAGE ON IT.  USE
EXAMPLES, EQUATIONS, CALCULATIONS, GRAPHS, ETC...  WRITE IN
ENGLISH SENTENCES!                   [10]

.          0
A) WHY IS 4  =1?

.                   2   3
B) WHY CAN'T I ADD X + X = X  ?

C) NOW LOOK OVER QUESTIONS #11, #13, #32 AND #36 AND DESCRIBE
THE SITUATION IN DETAIL.

.                4
D) EXPLAIN WHY  ---  IS UNDEFINED.
.                0

Thank you.  I hope you learned more than just some algebra
this semester.  I enjoyed your company.  Have a jolly winter!