Math Boot Camp Fundamentals Fall 2022
Fractions, laws of exponents, common mistakes, exponent examples, interval and set-builder notation, and factoring are covered in the Math Boot Camp for Fall 2022. The content includes explanations, examples, and practice problems to enhance understanding and application of fundamental math concepts.
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Presentation Transcript
Welcome to the Math Boot Camp!! The Fundamentals Fall 2022 Please sign in using the QR code
FRACTIONS We need a common denominator to add or subtract fractions, but NOT to multiply or divide fractions. To multiply fractions, we simply multiply the numerators (tops) and the denominators (bottoms). To divide fractions, we flip the bottom fraction and multiply it to the top fraction (KEEP-CHANGE-FLIP)
FRACTION EXAMPLES 7 3 3 2 7 3+3 2 7/3 3/2 ?+2 2 1 ?
LAWSOF EXPONENTS EXPONENT RULE FORMULA EXAMPLES Product Rule Quotient Rule Power Rule Power of a Product Rule Power of a Quotient Rule
Laws of Exponents EXPONENT RULE FORMULA EXAMPLES Zero Exponent Negative Exponent Fractional Exponent
COMMON MISTAKES!!!!! COMMON MISTAKES!!!! EXAMPLES
EXPONENT EXAMPLES Rewrite the following expressions without negative or fractional exponents. 1. 1 2?2+ 1 1/2 3?2 1+ ?1/22 1 1 2? 1/2 2. ? Rewrite the following expressions as sums/differences of power functions (??) and constants. 3. 3?2 ?+ ? ? 4+?2 16 ? 4.
INTERVAL NOTATION EXAMPLES Solve and write your answer in interval AND set-builder notation. a. 5 2? 4? + 7 b. 6 < 3? + 6 9
Interval Notation Example On what interval(s) is the function below increasing? Decreasing?
Factoring While the quadratic formula can certainly find roots, it is cumbersome, time consuming, and it only works for a quadratic equation. Factoring not only provides a faster root-finding method, but it proves useful for many algebraic simplifications as well. Zero Product Property: if two numbers multiply to zero, then at least one of them must be zero. ? ? = 0 implies that ? = 0 or ? = 0
GREATEST COMMON FACTORS (GCF) When two terms are compared, they may share some factors. The greatest common factor is the factor containing all common factors. Example: Factor the following by pulling out a greatest common factor. 8? + 16?2 5? 6?4 3?3+ 18?2
Factoring Trinomials of form ?2+ ?? + ? To factor the form ?2+ ?? + ?, we look for two numbers which: multiply to ? add to ? Then these numbers go directly into the parentheses! Ex. ?2 5? + 4
FACTORING EXAMPLES(? = 1) ?2 4? 21 ?2+ 4? 21 2?3 8?2+ 6?
Factoring Trinomials of form ??2+ ?? + ? To factor the form ??2+ ?? + ?, we look for two numbers which: multiply to ?? add to ? But there is more to do! Ex. 3?2 4? 4
FACTORING EXAMPLE(? 1) 6?3 3?2 18?
SPECIAL CASES Conjugates multiply to the difference of squares: (You cannot factor the sum of squares.) The square of a binomial always has the same form:
SPECIAL CASES EXAMPLES ?2 36 ?2 6? + 9
