## Friday, January 7, 2011

### 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 NOTCOPY THE LONG SENTENCES, ABBREVIATE!)  SHOW ALL WORK.  WRITEOUT ALL STEPS THAT YOU THINK OF. DON'T DO ANY IN YOUR HEAD.WORK SLOWLY BUT SURELY AND YOU WILL FINNISH IN TIME.  CIRCLEYOUR ANSWERS.  DON'T FORGET TO CHECK SOLUTIONS TO 'SOLVE FOR X'PROBLEMS.  LOOK AT THE ORIGINAL QUESTION WHEN YOU FINNISH APROBLEM, TO MAKE SURE YOU'VE ANSWERED THE QUESTION.  QUESTIONSARE WORTH 4 POINTS EACH (UNLESS MARKED LIKE []) TO MAKE A TOTALOF 200 POINTS.  THERE ARE 4 PAGES, 57 PROBLEMS.PART I1) 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.                          35) GRAPH THE LINE    Y= - ---X + 6.                          26) 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 THATPASSES THROUGH THE POINT (-4,3)8) WRITE THE EQUATION OF THE LINE THAT PASSES THROUGH THEPOINTS: (4,-5) AND (4,3)9) WRITE THE EQUATION OF THIS LINE:PART II10) DOES EVERY SYSTEM OF EQUATIONS HAVE A SOLUTION?        [2]11) CAN A SYSTEM OF LINEAR EQUATIONS HAVE EXACTLY TWO DIFFERENTSOLUTIONS?                                                 [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=41) NO SOLUTION      2) EXACTLY ONE     3) INFINITE NUMBER.                      SOLUTION           OF SOLUTIONS.                                   213) 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       617) WHICH IS BIGGER  4   OR   3  ?          [1].                       2    218) 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   020) ( -3X  Y  ) *(4X Y) =              21)  4 * 3  =.           -222) WRITE 10    AS A DECIMAL.SIMPLIFY, WRITING THE ANSWER WITHOUT NEGATIVE EXPONENTS..      2  -2              0  2            7    -423)  4X  Y       24)    4X  Y       25) (X )*(X  ) =.   --------          ----------.        2                -2  4.    (XY)              12Y   X.      3    2            226) (8X - 3X - 4Y) - (-4X + 8X + 2Y) =.              2                               227) (X-1) * ( X + X - 1) =           28) (4X-3)  =29) WRITE 0.00821 IN SCIENTIFIC NOTATION.                              -5              230) WHICH IS GREATER?  8.98 X10    OR 1.001 X10     [2].             2.           -X - X31) IF Y = --------   AND X= -2,   CALCULATE THE VALUE OF Y..              3.             XPART IV32)  HOW MANY DIFFERENT SOLUTIONS MIGHT A QUADRATIC EQUATIONHAVE?                               [2]33) HOW MANY DIFFERENT SOLUTIONS MIGHT A 3RD DEGREE EQUATIONHAVE?                               [bonus].          234) SOLVE X = 4               35) FACTOR: 6X+9    [1]36) DO THE SOLUTIONS OF QUADRATIC EQUATIONS REFER TO THE POINTSOF INTERSECTIONS OF CURVED LINES OR STRAIGHT LINES?  [bonus].             2                               3    237) FACTOR: 2X - 5X - 3         38) FACTOR:  X - 6X  - 8X.                 239) IS: 3X + 1 = 4   A QUADRATIC EQUATION?  SOLVE FOR X..             240) IS: 5X = X - 14   A QUADRATIC EQUATION?  SOLVE FOR X.SOLVE FOR X:.    241) X +100 = 0.                                           342) X(X+3) = 2X + 6                    43) X -9X = 0.                               244) DIVIDE BY LONG DIVISION: (2X - 5X -3) - (X-3)PART V45) ARRANGE THE FOLLOWING NUMBERS IN ORDER FROM THE SMALLEST TOLARGEST: 4     4     4     4     4     4     4.       ---,  ----, ---,  ---,  ---,  ---, -----.        2     1     8     1     4    -1     1.             ---                           ---.              2                            10.                              446) WHERE WOULD THE FRACTION  ---, GO IF YOU IMAGINE IT HAS AVALUE?                         0                   [bonus].                      2           247) TRUE OR FALSE:    X + X       X[2]                ---------- =  ---.                     4 + X       448) TRUE OR FALSE:       6X + 3      9.                       -------- = -----[2]                      X(X+1)     X+1.                   2.                  X -3X - 2849) SIMPLIFY     --------------.                    2.                   X  - 49.               2              2.              X - 64         X -8X50) SIMPLIFY  ---------   -   -------.                                 2.              8X + 64          8X.             3       451) ADD:     ---  + ----- =.             X      X+1.            X          252) ADD   ------  -  ------- =.                      2.          2X+4       X +2X.                    3        453) SOLVE FOR X:   -----  =  ---.                   X-2       X.                         6         3X54) SOLVE FOR X:   X +  -----  =  -----[6]                      X-2       X-2.                            1                155) SIMPLIFY:           X - ---        56)  ------  =.                            X        [2]     1.                      ---------             ---.                        X + 1                2PART VICHOOSE ONE QUESTION AND WRITE ABOUT A HALF A PAGE ON IT.  USEEXAMPLES, EQUATIONS, CALCULATIONS, GRAPHS, ETC...  WRITE INENGLISH SENTENCES!                   [10].          0A) WHY IS 4  =1?.                   2   3B) WHY CAN'T I ADD X + X = X  ?C) NOW LOOK OVER QUESTIONS #11, #13, #32 AND #36 AND DESCRIBETHE SITUATION IN DETAIL..                4D) EXPLAIN WHY  ---  IS UNDEFINED..                0Thank you.  I hope you learned more than just some algebrathis semester.  I enjoyed your company.  Have a jolly winter!`