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EOCT Review May 7th 2010 3 Domains… 1) ALGEBRA 2) GEOMETRY 3) DATA ANALYSIS I.) ALGEBRA Complex Numbers – Sections 1.1 – 1.3 Piecewise Functions – Section 2.5 Absolute Value Functions – Section 2.2 Exponential Functions – Sections 4.4 – 4.6 Quadratic Functions – Sections 3.1 – 3.3 Solve Quadratics – Sections 3.4 – 3.9 Inverse of Functions – Section 4.3 Imaginary Numbers… i 1 i 1 2 Standard form of Complex Numbers… a bi Piecewise Functions Points of Discontinuity: Piecewise function that is continuous Looks like stairs Extrema: Point where there is a break, hole, or gap in the graph Step Function Have at least 2 equations Each has a different part of the domain (X) Max/Min of function Local (within given domain) or Global (within entire domain) Average rate of change: Slope Here’s what a piecewise function looks like Absolute Value Functions y a x h k The vertex is ( h , k ) – that moves the vertex Plot 2 other points (use symmetry) a – makes the graph wider / narrower (slope) Intervals – on either side of the vertex 3 examples of graphs of absolute value functions. How have they been transformed? Exponential Functions y ab x y23 Translates the graph left 2 units x2 1 Translates the graph down 1 unit Standard form of a Quadratic… y ax bx c 2 Vertex form of a Quadratic… y a x h k 2 When graphing a Quadratic, can you find… Domain & Range Vertex Axis of Symmetry Zeros (x-intercepts) Y-intercepts Max & Min Values Intervals of Increase & Decrease Solving a Quadratic Equation… By Factoring By Completing the Square By Graphing 2 b b 4ac By Quadratic Formula x 2a The Discriminant – tells you the number of solutions Positive – 2 real solutions Zero – 1 real solution Negative – 0 real solutions (2 imaginary) b 4ac 2 Functions vs Relations In a function, X cannot repeat! If x does repeat, it’s a relation. If neither x or y repeat, it’s a 1-TO-1 Function By the vertical line test, a relation is a function if and only if no vertical line intersects the graph of the relation at more than one point. Inverse Switch the x’s and the y’s For an inverse to be a function, it must pass the HORIZONTAL LINE TEST II.) GEOMETRY Special Right Triangles – Section 5.1 Sine, Cosine and Tangent - Sections 5.2 – 5.4 Properties of Circles – Sections 6.1 – 6.8 Includes segments, angles, arcs, etc Spheres – Section 6.9 45-45-90 Triangle If you know one of the legs… Multiply by 2 to find the hypotenuse If you know the hypotenuse… Divide by 2 to find the legs 30-60-90 Triangle If you know the shorter leg… Multiply by 2 to find the hypotenuse Multiply by to find the longer leg If you know the longer leg… Divide by to find the shorter leg If you know the hypotenuse… Divide by 2 to find the shorter leg Sine, Cosine and Tangent (Trig Ratios) S o h C a h T o a Circles… 3600 total Semicircle = 1800 CIRCLES (ANGLE / ARC RULES) Central Angle = Intercepted Arc A B 100 C CIRCLES (ANGLE / ARC RULES) Inscribed Angle = ½ Intercepted Arc A 60 D B C CIRCLES (ANGLE / ARC RULES) Angle Inside = ½ the sum of the Arcs C 148 85 A x y 70 B D 57 CIRCLES (ANGLE / ARC RULES) Angle Outside = ½ the difference of the Arcs 120 D E 30 B C x A Circle / Sphere Formulas… A r C 2 r or d 2 S 4 r 3 4 r V 3 2 III.) DATA ANALYSIS Use sample data to make inferences using population means & standard deviation Sections 7.3 – 7.6 Determine algebraic models to quantify the association between 2 quantitative variables Sections 7.1, 7.2, 7.7 Measure of central tendency: number used to represent the center or middle set of data Mean - the average Median – the middle number Mode – number that occurs most Measure of Dispersion: statistic that tells you how spread out the values are Range – biggest - smallest Standard Deviation: “sigma” x X x 2 1 2 X ... xn X 2 n 2 NORMAL DISTRIBUTION… Sample: part / subset of population Self-selected sample: people volunteer responses Systematic sample: rule selects members Ex: every other person Convenience sample: easy-to-reach members Random sample: every member has an equal chance of being selected Unbiased sample: represents the population Biased sample: over or underestimates the population Margin of Error How much it differs from population smaller margin of error = more like population = 1 (where n is sample size) n To find range of possibility, take percent and then add/subtract your margin of error. 1 p n