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Transcript
Math 1310 Review Section 0 1.1 Sets and the Structure of Algebra Integers (positive, negative, zero): Prime Numbers: only integer factors are itself & 1 Rational Numbers: numerator where both are integers; the denominator can not be zero. deno min ator They can also be depicted as terminating or repeating decimals. On tests they will be reduced 6 ) 8 7 , but not 3 . 8 . (otherwise they are incorrect, e.g. 1.2 1.3 1.4 2.1 Irrational Numbers: Π , e, 2 , 4 Real Numbers: Union of Rational and Irrational Absolute Value: identified by | |, never negative Compare Numbers: > , = , < Operations with Real Numbers Additive Identity is 0 Multiplicative Identity is 1 When multiplying a number of terms odd number of negatives = even number of negatives = + Divide & Multiply are interconnected. 6 divided by 3, means find which number multiplied by 3 is 6 Note: You CANNOT DIVIDE BY 0. n/0 (n≠0) is undefined; 0/0 is indefinite. Exponent, Roots, and Order of Operations ( OOO ) -2 4 = -16 ( -2 ) 4 = +16 Order of operations: parentheses (inner first) powers (exponents) ÷, × (left to right) -, + (left to right) Note: ( x + y ) 2 ≠ x 2 + y 2 Evaluating and Rewriting Translate words to expressions Read the whole problem to get general ideas Read again, converting phrases to find out what you know Read again to determine what you need Determine equation to use Solve the equation Write solution (including units) Check if the solution fits Linear Equations and Formulas Solve linear equations clear parenthesis simplify both sides (combine terms) move variable to the left side if variable still exists move constant to the right side divide both sides by coefficient of variable else if constants are equal, infinite solutions if constants are not equal, no solution endif 2.2 Solving Problems (very similar to 1.4) Word problems (rewrite of method in 1.4) read for understanding determine what you know determine what you need to find determine what formula to use solve identify solutions (don’t forget units) check to see if solution is OK 2.3 Solving Linear Inequalities Number line -4 -3 -2 -1 0 1 2 3 4 | | | | | | | | | Inequalities are solved the same way as equalities, with one difference - if the coefficient of the variable is negative, reverse the direction of the inequality. Inequalities in set notation e.g. { x | x > 2 } in interval notation e.g. ( 2, ∞ ) visually e.g. -4 -3 -2 -1 0 1 2 3 4 | | | | | | ( | | 2.4 Compound Inequalities Interval(s) Solution Bounded both above and below (AND) e.g. 3 < x < 8 ( 3, 8 ] or ( 3, +∞ ) ∩ [ 8, + ∞ ) Split intervals (OR) e.g. x < -4 or x > 1 ( -∞, -4 ) U [ -1, +∞ ) 3.1 Graphing Linear Equations Cartesian coordinate system axis origin identifying points intercepts graphing a linear equation intercepts solve for y, and use values for x