Math 125 Exam 1 Study Guide

Earl M. Rodd - Fall 2008

The exam will have these kinds of problems similar to homework problems. For some kinds, samples are shown to remind you what kinds of problems these are:

• A warmup of simple simplifications like: (8 points) | -5x | = 5x 15/20 = 3/4 3 + 2 + x = 5 + x 3x - (10 - 5) = 3x - 5 15 15 ------- = -- = 1 (10 - 9) 1

• Given inequalities, graph them on the number line. (6 points)

• Factor numbers into their prime factors. (4 points)

• Simplify 4 expressions. 4(x2 -3) = 4x2 - 12 (8 points)

• Reduce several fractions to lowest terms. (3 points)

• Identify numbers as Counting, Integers (but not counting), Rational (but not Integersi), or Irrational. (5 points)

• Multiply, divide, add, and subtract fractions (for adding and subtracting, you must find a common denominator). (10 points)

• Compute the value of several algebraic expressions given certain values for the unknowns. The expressions can include absolute values. (4 points) For example: If a=3 and b=5 4(a + b -2) = 4(3 + 5 -2) = 4(6) = 24
• You will be given a set of simplifications and asked to indicate the principle demonstrated (4 points) For example: a + 10b - 20 = -20 + a + 10b Commutative principle of addition 5(x + y -2z) = 5x + 5y - 10z Distributive principle 10(xy) = 10x(y) Associative principle of addition
• Know what the additive inverse(opposite), multiplicative inverse (reciprocal), additive identity and muliplicative identity are. (4 points)
• Simplify simple expressions in which additive and multiplicative identies and inverses and divide by 0 may come into play. (6 points) For example: (a + b)/(a - a) UNDEFINED (divide by 0) (a + b) (a - a) zero (a-a) is zero and anything times zero is zero 6(x + 2) -------- = x + 2 since 6/6 = 1 and anything times 1 is itself. 6
• Convert words to algebra. (5 points)
  1. Five times the sum of x and y: 5(x + y)
  2. x is at most 15: x < 15