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                                        :Q                                      1. (+5) + (-9) =                                                                (a) -4  (b) -5  (c) 0  (d) +4  (e) -1   :RCA                                    1. (a) -4 Ans.                                                                       +5                                    + -9                                    ----                                      -4 Ans.                            :RA                                     :Q                                      2. (-3) + (-6) =                                                                (a) -3  (b) -9  (c) 1  (d) -6  (e) 0    :RCB                                    2. (b) -9 Ans.                                                                  Note: When adding two numbers with like signs, add and keep the same sign.                                                   -3                                   +  -6                                   -----                                      -9 Ans.                            :RA                                     :Q                                      3. (+3) - (-7) =                                                                (a) 4  (b) -4  (c) 10  (d) 0  (e) 5     :RCC                                    3. (c) 10 Ans.                                                                       +3                                    - -7                                    ----                                     +10 Ans.                            :RA                                     :Q                                      4. (+12) - (-6) =                                                               (a) 15  (b) 18  (c) 6  (d) -18  (e) 4   :RCB                                    4. (b) 18 Ans.                                                                  Note: Change the sign of the bottom     number and follow the addition rule.                                                 +12                                   - - 6                                   -----                                     +18 Ans.                           :RA                                     :Q                                      5. (-5)(-3) =                                                                   (a) -8  (b) 5  (c) 0  (d) 15                                                    (e) -15                                 :RCD                                    5. (d) 15 Ans.                                                                  Note: Negative times negative equals a  positive.                                                                            -5                                    x -3                                    ----                                      15                                 :RA                                     :Q                                      6. (-7)(+1/3)(-9) =                                                             (a) 22  (b) 11  (c) -21  (d) 0  (e) 21  :RCE                                    6. (e) 21 Ans.                                                                  Note: Multiply one at a time.                                                        (-7) x (+1/3) = (+7/3)                                                          (-7/3) x (-9) = 21 Ans.            :RA                                     :Q                                      7. (-8)(+5)/(-2) =                                                              (a) 20  (b) 10  (c) -4  (d) -20  (e) 0  :RCA                                    7. (a) 20 Ans.                                                                  Note: Do multiplication first, then     division.                                                                            -8                                    x +5                                    ----                                     -40                                                                            -40/-2 = 20 Ans.                     :RA                                     :Q                                      8. Solve for y: 4y + 3 = 9                                                      (a) 2/3  (b) 2  (c) 3/2  (d) 1/2                                                (e) 1                                   :RCC                                    8. (c) 3/2 Ans.                                                                 Note: Subtract 3 from both sides, then  divide by 4.                                                                        4y   6                                  -- = -                                   4   4                                                                           y = 3/2 Ans.                                                               Note: Isolate the variable on one side  by adding or subtracting, then divide   the coefficient in front of the         variable to both sides.                 :RA                                     :Q                                                      K   K                   9. Solve for K: - + - = 1                               5   6                                                           (a) 30/11  (b) 3  (c)  20/11 (d) 0                                              (e)  24/11                              :RCA                                    9. (a) 30/11 Ans.                                                               Note: Find the common denominator (30), then multiply both sides by that        number. Next, solve for the variable.                                              30(K/5) + 30(K/6) = 30                                                                    6K + 5K = 30                                                                        11K = 30                                                                          K = 30/11 Ans.       :RA                                     :Q                                      10. Solve for y:  ay = by + c                                                   (a) c/(b - a)  (b) (a - b)/c                                                    (c) ab/c  (d) ab  (e) c/(a - b)         :RCE                                    10. (e) c/(a - b) Ans.                                                          Note: Move all terms with y to one      side, and solve for y.                                                                 ay = by + c                            -by = -by                           ay - by = c                                                                    y(a - b)     c                          -------- = -----                         (a - b)   a - b                                                                             c                                 y = ----- Ans.                              a - b                       :RA                                     :Q                                      11. If k + y = 8m and k - y = 6n then k is?                                                                             (a) 4m + 3n  (b) 7m + n  (c) 2m + 3n                                            (d) m + n  (e) 4m + n                   :RCA                                    11. (a) 4m + 3n Ans.                                                            Note: Eliminate one unknown; solve for  the other, then substitute.                                                          k + y = 8m                              k - y = 6n                            2k + 0y = 8m+6n                                                                    2k   8m   6n                            -- = -- + --                            2    2    2                                                                      k = 4m + 3n Ans.                 :RA                                     :Q                                      12. If 8y = 3y + 15 then, 4y + 5 =                                              (a) 2  (b) 17  (c) 18  (d) 5  (e) 1     :RCB                                    12. (b) 17 Ans.                                                                      8y = 3y + 15                           -3y = -3y                                                                        5y        15                            -- = 0y + --                            5y        5y                                                                     y = 3                                                                     Therefore:                                                                           4y + 5 =                              4(3) + 5 =                                12 + 5 = 17 Ans.                   :RA                                     :Q                                      13. What is the value of A in:                                                              2                                 y =  x  + Ax - 5                                                                when y = 19 and x = 3                                                     (a) -2  (b) -3  (c) 5  (d) 1  (e) 3     :RCC                                    13. (c) 5 Ans.                                                                            2                               19 = (3)  + A(3) -5                                                             19 = 9 + 3A -5                                                                  19 = 4 + 3A                             -4  -4                                                                          15   3A                                 -- = --                                  3   3                                                                           5 = A Ans.                                                                   Note: First substitute the numbers for  the variables, then solve.              :RA                                     :Q                                      14. If .69y = 2.07 then y =                                                     (a) 1  (b) 2  (c) 6  (d) 3  (e) .03     :RCD                                    14. (d) 3 Ans.                                                                  Multiply by 100 to get rid of the       decimal, then solve for the unknown.                                                        100(.69y) = 100(2.07)                                                                69y    207                              ---  = ---                              69     69                                                                         y  = 3 Ans.          :RA                                     :Q                                      15. If 5ky + 8 = 9ky                            then ky =                                                               (a) 2  (b) 3  (c) 8  (d) 4  (e) 1       :RCA                                    15. (a) 2 Ans.                                                                          5ky + 8 = 9ky                          -5ky      -5ky                                                                         8   4ky                                 - = ---                                 4    4                                                                          2 = ky Ans.                                                       Note: Treat ky as one variable then     solve for it.                           :RA                                     :Q                                      16. Solve for y:                                                                      2                                      y  + 18 = 9y                                                               (a) 2 or 6  (b) 1 or 6 (c) 6                                                    (d) 6 or 3  (e) -9                      :RCD                                    16. (d) 6 or 3 Ans.                                                                   2                                      y  + 18 = 9y                                -9y  -9y                                                                   2                                      y - 9y + 18 = 0                      (y - 6)(y - 3) = 0                                   y = 6 or 3 Ans.                                                    Note: Move everything to one side to    get the equation equal to zero, then    treat it as a Quadratic Equation and    factor. Be careful to arrange the       variables in order of descending powers before factoring.                       :RA                                     :Q                                                         2                    17. Solve for y: 5y  = 80                                                       (a) +/-2  (b) +/-4  (c) +/-8                                                    (d) +/-12  (e) +/-6                     :RCB                                    17. (b) +/-4 Ans.                                                                      2                                     5y  - 80  = 0                                                                     2                                    5(y  - 16) = 0                                                                      2                                      y  - 16 = 0                                                              (y + 4)(y - 4) = 0                                                                           y = +/-4 Ans.              :RA                                     :Q                                                          2                   18. Solve for y:  7y  = 5y                                                      (a) 0  (b) 0 or 1/2  (c) 0 or 5/7                                               (d) 1 or 2  (e) -1 or -2                :RCC                                    18. (c) 0 or 5/7 Ans.                                                                      2                                     7y  = 5y                                -5y  -5y                                                                     2                                     7y  - 5y = 0                                                                   y(7y - 5) = 0                                                                           y = 0 or 5/7 Ans.                                                    Note: Move everything to one side of    the equation and factor out what is in  common, then solve.                     :RA                                     :Q                                      19. Solve for y:                                     _____                                  / 2                                   \/ y + 8 - 2 = y                                                      (a) 2  (b) 4  (c) 0  (d) 10  (e) 1      :RCE                                    19. (e) 1 Ans.                                                                  Note: Move everything that does not     belong to the square root to the other  side; square both sides, then treat it  as a quadratic equation.                :RA                                     19.                                                 _____                                  / 2                                   \/ y + 8 = y + 2                                                                    2             2                        y + 8 = (y + 2)                                                                  2       2                              y + 8 = y + 4y + 4                                                                  8 = 4y + 4                             -4      - 4                                                                      4 = 4y                                                                          y = 1 Ans.              :RA                                     :Q                                                            __       __       20. Find the sum of \/80 and \/45.              _          _          __        (a)  7\/5  (b)  7\/2  (c)  7\/10                                                (d)  0  (e)  5                          :RCA                                                _                           20. (a)  7\/5 Ans.                            __     __  _      _                   \/80 = \/16\/5 = 4\/5                                                            +                                        __     _  _      _                    \/45 = \/9\/5 = 3\/5                                                                  _      _      _                      4\/5 + 3\/5 = 7\/5 Ans.                                                  Note: Break the square roots down until fully simplified, then add. (Only add   the coefficient and keep the square     root the same.)                         :RA                                     :Q                                      21. Find the difference between           __       __                           \/98 and \/32.                                 _         _         _            (a) 3\/4  (b) 3\/2  (c) 3\/1                          _                         (d) 1  (e) 5\/3                         :RCB                                                _                           21. (b)  3\/2 Ans.                             __     __  _      _                   \/98 = \/49\/2 = 7\/2                                                            -                                        __     __  _      _                   \/32 = \/16\/2 = 4\/2                                                                               _                                  = 3\/2 Ans.                                                 Note: Follow the same format - as in    the previous example, but subtract like roots.                                  :RA                                     :Q                                      22. Find the product of                   ___       __                          \/32y and \/2y.                                                                 (a) 64y  (b) 4y  (c) 1  (d) 8y  (e) 2y  :RCD                                    22. (d)  8y Ans.                                          ____                    ___     __     /   2                  \/32y x \/2y = \/ 64y  = 8y Ans.                                                Note: Multiply what is in the square    roots - then break it down.             :RA                                     :Q                                                          ___                 23. Solve:  1/y = \/.49                                                         (a) 5/7  (b) 2/7  (c) 10/7  (d) 0                                               (e) 1                                   :RCC                                    23. (c) 10/7 Ans.                                                               Note: Take the square root and then     solve for it.                                                                        1/y = .7                                                                        .7y =  1                                                                    10(.7y) = (1)10                                                                      7y = 10                                                                          y = 10/7 Ans.                    :RA                                     :Q                                                                 3            24. If y = 2.86 find (2.86)  to the     nearest hundredth?                                                              (a) 23.39  (b) 26.39  (c) 23  (d) 3.39                                          (e) 1                                   :RCA                                    24. (a) 23.39 Ans.                                                              Note: Raise it to the third power, then round it off to the nearest hundredth.                                          (2.86) (2.86)=  8.18                    (8.18) (2.86)= 23.39                    :RA                                     :Q                                      25. Find the square root of 23409.                                              (a) 15  (b)  5  (c) 93  (d) 90                                                  (e) 153                                 :RCE                                    25. (e)  153 Ans.                                                               A quick way to identify the correct     answer is to take the __square root of  the last digit. The \/9 = 3, leaving    choices (c) and (d) as                  possibilities. 93 squared = 8649;       whereas 153 squared = 23409.            :RA                                     :Q                                      26. Find the square root of 15775.36?                                           (a) 125.6  (b) 124.3  (c) 100                                                   (d) 26.3  (e) 24.3                      :RCA                                    26. (a) 125.6 Ans. The square root of   the last two digits is .6.  The only    possible answer among the choices is    (a) 125.6.                              :RA                                     :Q                                                    __       __               27. Divide 6\/80 by 3\/20.                                                      (a) 2  (b) 4  (c) 8  (d) 1  (e) 16      :RCB                                    27. (b) 4 Ans.                                                                  Note: Simplify each root then divide.           ______          _                    6\/16 x 5   6 x 4\/5                    --------- = --------                       _____           _                    3\/4 x 5    3 x 2\/5                           _                                   24\/5                                   -----  = 4 Ans.                            _                                    6\/5                            :RA                                     :Q                                                      _______                                / 2    2                               / y  + y                  28. Find     /  --   -                             \/   16   9                                                          (a) 1/2y  (b) 4y/12  (c) 5y/12  (d) 6y                                          (e) 8y                                  :RCC                                    28. (c) 5y/12 Ans.                                                              Note: Combine what is inside the square root, then take the square root of      that.                                          __________           ____              /  2      2          /   2             / 9y  + 16y          / 25y             /  ----------   =    /  ----          \/      144          \/   144                                                      5y/12 Ans.                         :RA                                     :Q                                      29. n/7 + 3n/2 =                                                                (a) 23n/14  (b) 24n/2  (c) 20                                                   (d) 12n/7  (e) 0                        :RCA                                    29. (a) 23n/14 Ans.                                                             Note: Find the common denominator,      convert each fraction to that           denominator, then add.                                                               2n   21n   23n                          -- + --- = --- Ans.                     14   14    14                      :RA                                     :Q                                      30. Combine into a single fraction:                                                  1 + a/b                                                                    (a) ba/b  (b) ab/b  (c) a/b                                                     (d) (b + a)/b  (e) 1                    :RCD                                    30. (d) (b + a)/b Ans.                                                          Note: b/b = 1                                                                        b/b + a/b =                                                                     (b + a)/b Ans.                     :RA                                     :Q                                                  k + y    y + k              31. Divide  ----- by -----                          k - y    y - k                                                      (a) 1  (b) 2  (c) -1  (d) 0  (e) -11    :RCC                                    31. (c) -1 Ans.                                                                 Note: When dividing by a fraction you   multiply by the reciprocal of the       divisor.                                                                         k + y   y - k   y - k                   ----- x ----- = -----                   k - y   y + k   k - y                                                                           -1(-y + k)                            =   --------                                (k - y)                                                                       -1(k - y)                             =   -------                                 (k - y)                                                                     = -1 Ans.                :RA                                     :Q                                                      1 - 1/y                 32. Simplify:   -------                                   a/y                                                           (a) (y - 1)/a  (b) -1  (c) y-1                                                  (d) (a - 1)/y  (e) (1 - a)/y            :RCA                                    32. (a) (y - 1)/a Ans.                                                          Note: To simplify a complex fraction    multiply by the common denominator.                                                    1 - 1/y   y                           = ------- x -                               a/y     y                                                                     y - 1                                 = ----- Ans.                                a                              :RA                                     :Q                                                2   3                         33.    (2k /y) =                                                                       6                  5                  8k                 2k              (a)  ---  (b) bk/y  (c) ---                    3                  3                   y                  y                                                            2           5                     (d) 6k /3y  (e) 6k /y                   :RCA                                               6                                     8k                             33. (a)  --- Ans.                                  3                                      y                                                                     Note: When a power is raised to another exponent, find the product of the       exponents.                                                                                   a b    ab                        Rule (x )  = x  .                 :RA                                     :Q                                                      1   1                                   - - -                                   k   y                   34. Simplify:   -----                                     4                                                             (a) (y - k)/2ky  (b) (y - k)/4ky                                                (c) y - k  (d) 2y - k  (e) y - k        :RCB                                    34. (b) (y - k)/4ky Ans.                                                               1   1                                 = - - -                                   k   y   (ky)                            ----- x ----                              4     (ky)                                                                    y - k                                 = ----- Ans.                               4ky                                                                     Note: To simplify a complex fraction,   multiply by the common denominator.     :RA                                     :Q                                                    2                         35. If (k - y)  = 49 and ky = 4                                                           2    2                            find k  + y                                                                 (a) 56  (b) 50  (c) 25  (d) 12  (e) 57  :RCE                                    35. (e) 57 Ans.                                                                            2     2          2               (k - y)  =  k  - 2ky + y  = 49                                                       2           2                        = k  - 2(4) + y  = 49                                                              2        2                             k  - 8 + y  = 49                                                                 2    2                                 k  + y  = 57 Ans.               :ET                                     :ET