# Integrated Algebra Regents Review #1

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Integrated Algebra Regents Review #1
Rational Expressions Scientific Notation Trigonometry

Rational Expressions Rational Expressions are fractions (ratios) that contain polynomial expressions in the numerator and denominator. Examples:

Rational Expressions Simplifying Rational Expressions
with Monomial Numerators and Denominators Method 1: Use laws of exponents Method 2: Expand and divide out common factors

Rational Expressions A) B) Simplifying Rational Expressions
with Polynomial Numerators and Denominators Factor the numerator and denominator Divide out common factors Remember: Monomials can only be simplified with monomials and binomials can only be simplified with binomials that are exactly the same. A) B)

Rational Expressions When multiplying rational expressions, factor all the numerators and denominators. Divide out common factors. Factor all the numerators and denominators!

Rational Expressions When dividing rational expressions…
Keep, Change, Flip Factor all the numerators and denominators Divide out common factors Keep the first fraction Change division to multiplication Flip the second fraction (reciprocal)

Rational Expressions When adding and subtracting rational expressions, find a common denominator if necessary. Create equivalent fractions using the common denominator(Multiply by FOOs). Add or subtract numerators and keep the denominator the same. Simplify your final answer if possible. FORM OF ONE Ex:

Rational Expressions What is the sum of and expressed in simplest form? Add numerators and keep the denominator. Simplify by factoring the numerator and denominator.

Rational Expressions LCD (Least Common Denominator): 9x2 FOO FOO
Find equivalent fractions with a common denominator by multiply by a FOO (form of one).

Rational Expressions 8x(x + 12) = 2x(2x + 4) 8x2 + 96x = 4x2 + 8x
When solving rational equations (equations with algebraic fractions), combine fractions and set up a proportion. Remember: A common denominator is needed to add or subtract fractions. 8x(x + 12) = 2x(2x + 4) 8x2 + 96x = 4x2 + 8x 4x2 + 88x = 0 4x(x + 11) = 0 4x = x + 11 = 0 x = x = -11 FOO FOO Reject 0 because it makes the equation undefined. Solution: x = -11

Scientific Notation Representing Numbers in Scientific Notation
If this a skill you have not mastered and need additional instruction, re-watch FLIP #3.

Scientific Notation Multiplying Numbers in Scientific Notation
Use the commutative property and laws of exponents Calculator Corner: Press MODE Select SCI (see top row) , ENTER Press 2nd MODE to return to home screen Enter expression into the calculator (use the expression on this slide to practice) (4x10^5)(3.2x10^-9) 5) Press ENTER 6) The expression 1.28E-3 means 1.28 x 10-3 Go to MODE and select NORMAL to exit scientific notation

Scientific Notation Dividing Numbers in Scientific Notation
Calculator Corner: Press MODE Select SCI (see top row) , ENTER Press 2nd MODE to return to home screen Enter expression into the calculator (use the expression on this slide to practice) Put the numerator and denominator in ( ) (5.6x10^-12)/(4x10^6) 6) Press ENTER 7) The expression 1.4E-18 means 1.4 x 10-18 Go to MODE and select NORMAL to exit scientific notation

Trigonometry Trigonometric Ratios
What ratio represents the sine of the indicated angle pictured to the right? Answer: (1)

Trigonometry Finding Sides of a Right Triangle
Use the Pythagorean Theorem when given two sides Use Trigonometry when given a side and an angle Pythagorean Theorem SOH CAH TOA Substitute known values into the trig ratio. Solve for the variable by cross multiplying. a2 + b2 = c2 = c2 = c2 25 = c2 5 = c Calculator must be in degrees (See MODE)

Trigonometry Finding Angles of a Right Triangle
> Use inverse trig ratios Find the measure of the indicated angle to the nearest degree. Calculator: 2nd TAN

Trigonometry A 50 ft. ladder leans against a building. The foot of the ladder is 35 feet from the building. To the nearest degree, find the measure of the angle that the ladder makes with the ground. Are you looking for an angle or side? Trig Ratio or Inverse Trig Ratio? Draw a picture of the situation Looking for this angle Remember: Calculator must be in degrees in order to do a trigonometry problem. Go to Mode and highlight degree (ENTER)