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PRE-CALCULUS Semester One Study Guide Algebra/Geometry Skills: Factoring – GCF, reverse FOIL, difference of two squares, sum/difference of two cubes Quadratic Formula Graphing – lines, parabolas Add/Subtract Fractions – common denominator Multiply/Divide Fractions – factor and cancel Similar Triangles – corresponding angles congruent, corresponding sides proportional Chapter One: Functions – domain/range, parent graphs (tool kit) Graphing Transformations – vertical stretch/compress, horizontal stretch/compress, horizontal/vertical shifts Exponents – laws of exponents, negative exponents, fractional exponents Inverse of Functions – limit range of inverse (to make it one-to-one) Equations of Lines – point-slope form, parallel or perpendicular lines Laws of Sines and Cosines – for acute and obtuse triangles Area of a Triangle – ½(base)(height) or ½(b)(c)sinA Special Right Triangles – 30/60/90 and 45/45/90 Radian Angle Measures Chapter Two: Piecewise Functions – evaluate, check for continuity, shifts Sigma Notation – finding elements, evaluate the sum, represent area under a curve Area Under a Curve – left/right endpoint rectangles, trapezoids, vertical/horizontal shifts Area as a Function – area under a curve based on the amount of time Chapter Three: Graphing Transformations – vertical stretch/compress, horizontal stretch/compress, reflect over x/y axis Exponential Functions – graphing, simplifying, solving Logarithmic Functions – graphs, laws of logs, solving, change of base Chapter Four: Unit Circle – angles and coordinates (𝑐𝑜𝑠𝜃, 𝑠𝑖𝑛𝜃) Pythagorean Identities (3) Right Triangle Trig Ratios Graphs of Sine and Cosine – parent, vertical stretch/compress, horizontal stretch/compress, shifts Reciprocal Trig Functions – sine cosecant, cosine secant, tangent cotangent Simplify Complex Fractions Verifying Trig Identities Study the information from the Math Notes throughout the chapters above. Do ALL the Closure problems at the end of each chapter. Chapter One: p. 55 #155-164 Chapter Two: p. 120 #178-188 *answers for all problems are on the next pages Chapter Three: p. 172 #133-143 *info to get help, or try more, is also listed there Chapter Four: p. 223 #148-160 *Skill Builder are available in the back of the book (following ch 6) for practicing algebra/geometry skills.