EOCT Review May 7 th 2010

3 Domains… 1) ALGEBRA 1) ALGEBRA 2) GEOMETRY 2) GEOMETRY 3) DATA ANALYSIS 3) DATA ANALYSIS

I.) ALGEBRA Complex Numbers – Sections 1.1 – 1.3 Complex Numbers – Sections 1.1 – 1.3 Piecewise Functions – Section 2.5 Piecewise Functions – Section 2.5 Absolute Value Functions – Section 2.2 Absolute Value Functions – Section 2.2 Exponential Functions – Sections 4.4 – 4.6 Exponential Functions – Sections 4.4 – 4.6 Quadratic Functions – Sections 3.1 – 3.3 Quadratic Functions – Sections 3.1 – 3.3 Solve Quadratics – Sections 3.4 – 3.9 Solve Quadratics – Sections 3.4 – 3.9 Inverse of Functions – Section 4.3 Inverse of Functions – Section 4.3

Imaginary Numbers… Imaginary Numbers… Standard form of Complex Numbers… Standard form of Complex Numbers…

Piecewise Functions Piecewise Functions Have at least 2 equations Have at least 2 equations Each has a different part of the domain (X) Each has a different part of the domain (X) Points of Discontinuity: Points of Discontinuity: Point where there is a break, hole, or gap in the graph Point where there is a break, hole, or gap in the graph Step Function Step Function Piecewise function that is continuous Piecewise function that is continuous Looks like stairs Looks like stairs Extrema: Extrema: Max/Min of function Max/Min of function Local (within given domain) or Global (within entire domain) Local (within given domain) or Global (within entire domain) Average rate of change: Average rate of change: Slope Slope

Here’s what a piecewise function looks like Here’s what a piecewise function looks like

Absolute Value Functions Absolute Value Functions The vertex is ( h, k ) – that moves the vertex The vertex is ( h, k ) – that moves the vertex Plot 2 other points (use symmetry) Plot 2 other points (use symmetry) a – makes the graph wider / narrower (slope) a – makes the graph wider / narrower (slope) Intervals – on either side of the vertex Intervals – on either side of the vertex

3 examples of graphs of absolute value functions. How have they been transformed?

Exponential Functions Exponential Functions Translates the graph left 2 units Translates the graph down 1 unit

Standard form of a Quadratic… Standard form of a Quadratic… Vertex form of a Quadratic… Vertex form of a Quadratic…

When graphing a Quadratic, can you find… When graphing a Quadratic, can you find… Domain & Range Domain & Range Vertex Vertex Axis of Symmetry Axis of Symmetry Zeros (x-intercepts) Zeros (x-intercepts) Y-intercepts Y-intercepts Max & Min Values Max & Min Values Intervals of Increase & Decrease Intervals of Increase & Decrease

Solving a Quadratic Equation… Solving a Quadratic Equation… By Factoring By Factoring By Completing the Square By Completing the Square By Graphing By Graphing By Quadratic Formula By Quadratic Formula

The Discriminant – tells you the number of solutions The Discriminant – tells you the number of solutions Positive – 2 real solutions Positive – 2 real solutions Zero – 1 real solution Zero – 1 real solution Negative – 0 real solutions (2 imaginary) Negative – 0 real solutions (2 imaginary)

Functions vs Relations Functions vs Relations In a function, X cannot repeat! If x does repeat, it’s a relation. 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 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. 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 Inverse Switch the x’s and the y’s Switch the x’s and the y’s For an inverse to be a function, it must pass the HORIZONTAL LINE TEST For an inverse to be a function, it must pass the HORIZONTAL LINE TEST

II.) GEOMETRY Special Right Triangles – Section 5.1 Special Right Triangles – Section 5.1 Sine, Cosine and Tangent - Sections 5.2 – 5.4 Sine, Cosine and Tangent - Sections 5.2 – 5.4 Properties of Circles – Sections 6.1 – 6.8 Properties of Circles – Sections 6.1 – 6.8 Includes segments, angles, arcs, etc Includes segments, angles, arcs, etc Spheres – Section 6.9 Spheres – Section 6.9

Triangle If you know one of the legs… If you know one of the legs… Multiply by to find the hypotenuse Multiply by to find the hypotenuse If you know the hypotenuse… If you know the hypotenuse… Divide by to find the legs Divide by to find the legs

Triangle If you know the shorter leg… If you know the shorter leg… Multiply by 2 to find the hypotenuse Multiply by 2 to find the hypotenuse Multiply by to find the longer leg Multiply by to find the longer leg If you know the longer leg… If you know the longer leg… Divide by to find the shorter leg Divide by to find the shorter leg If you know the hypotenuse… If you know the hypotenuse… Divide by 2 to find the shorter leg Divide by 2 to find the shorter leg

Sine, Cosine and Tangent (Trig Ratios) Sine, Cosine and Tangent (Trig Ratios) S C T S C T

Circles… Circles… total total Semicircle = Semicircle = 180 0

CIRCLES (ANGLE / ARC RULES) CIRCLES (ANGLE / ARC RULES) Central Angle = Intercepted Arc Central Angle = Intercepted Arc

CIRCLES (ANGLE / ARC RULES) CIRCLES (ANGLE / ARC RULES) Inscribed Angle = ½ Intercepted Arc Inscribed Angle = ½ Intercepted Arc

CIRCLES (ANGLE / ARC RULES) CIRCLES (ANGLE / ARC RULES) Angle Inside = ½ the sum of the Arcs Angle Inside = ½ the sum of the Arcs

CIRCLES (ANGLE / ARC RULES) CIRCLES (ANGLE / ARC RULES) Angle Outside = ½ the difference of the Arcs Angle Outside = ½ the difference of the Arcs

Circle / Sphere Formulas… Circle / Sphere Formulas…

III.) DATA ANALYSIS Use sample data to make inferences using population means & standard deviation Sections 7.3 – 7.6 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 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 Measure of central tendency: number used to represent the center or middle set of data Mean - the average Mean - the average Median – the middle number Median – the middle number Mode – number that occurs most Mode – number that occurs most

Measure of Dispersion: statistic that tells you how spread out the values are Range – biggest - smallest Standard Deviation: “sigma”

NORMAL DISTRIBUTION… NORMAL DISTRIBUTION…

Sample: part / subset of population Sample: part / subset of population Self-selected sample: people volunteer responses Self-selected sample: people volunteer responses Systematic sample: rule selects members Systematic sample: rule selects members Ex: every other person Ex: every other person Convenience sample: easy-to-reach members Convenience sample: easy-to-reach members Random sample: every member has an equal chance of being selected Random sample: every member has an equal chance of being selected

Unbiased sample: represents the population Unbiased sample: represents the population Biased sample: over or underestimates the population Biased sample: over or underestimates the population

Margin of Error Margin of Error How much it differs from population How much it differs from population smaller margin of error = more like population smaller margin of error = more like population =(where n is sample size) =(where n is sample size) To find range of possibility, take percent and then add/subtract your margin of error. To find range of possibility, take percent and then add/subtract your margin of error.