Download EOCT Review - Brookwood High School

EOCT Review
May 7th 2010
3 Domains…
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1) ALGEBRA
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2) GEOMETRY
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3) DATA ANALYSIS
I.) ALGEBRA
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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
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Imaginary Numbers…
i  1
i  1
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2
Standard form of Complex Numbers…
a  bi
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Piecewise Functions
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Points of Discontinuity:
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Piecewise function that is continuous
Looks like stairs
Extrema:
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Point where there is a break, hole, or gap in the graph
Step Function
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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:
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Slope
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Here’s what a piecewise function looks like
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Absolute Value Functions y  a x  h  k
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The vertex is ( h , k ) – that moves the vertex
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Plot 2 other points (use symmetry)
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a – makes the graph wider / narrower (slope)
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Intervals – on either side of the vertex
3 examples of graphs of absolute value
functions. How have they been transformed?
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Exponential Functions
y  ab
x
y23
Translates the graph
left 2 units
x2
1
Translates the graph
down 1 unit
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Standard form of a Quadratic…
y  ax  bx  c
2
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Vertex form of a Quadratic…
y  a  x  h  k
2
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When graphing a Quadratic, can you find…
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Domain & Range
Vertex
Axis of Symmetry
Zeros (x-intercepts)
Y-intercepts
Max & Min Values
Intervals of Increase & Decrease
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Solving a Quadratic Equation…
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By Factoring
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By Completing the Square
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By Graphing
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2

b

b
 4ac
By Quadratic Formula x 
2a
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The Discriminant – tells you the number of solutions
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Positive – 2 real solutions
Zero – 1 real solution
Negative – 0 real solutions (2 imaginary)
b  4ac
2
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Functions vs Relations
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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
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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.
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Inverse
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Switch the x’s and the y’s
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For an inverse to be a function, it must pass the
HORIZONTAL LINE TEST
II.) GEOMETRY
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Special Right Triangles – Section 5.1
Sine, Cosine and Tangent - Sections 5.2 – 5.4
Properties of Circles – Sections 6.1 – 6.8
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Includes segments, angles, arcs, etc
Spheres – Section 6.9
45-45-90 Triangle
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If you know one of the legs…
 Multiply by 2 to find the hypotenuse
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If you know the hypotenuse…
 Divide by 2 to find the legs
30-60-90 Triangle
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If you know the shorter leg…
 Multiply by 2 to find the hypotenuse
 Multiply by
to find the longer leg
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If you know the longer leg…
 Divide by
to find the shorter leg
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If you know the hypotenuse…
 Divide by 2 to find the shorter leg
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Sine, Cosine and Tangent (Trig Ratios)
S
o
h
C
a
h
T
o
a
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Circles…
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3600 total
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Semicircle = 1800
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CIRCLES (ANGLE / ARC RULES)
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Central Angle = Intercepted Arc
A
B 100
C
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CIRCLES (ANGLE / ARC RULES)
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Inscribed Angle = ½ Intercepted Arc
A
60
D
B
C
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CIRCLES (ANGLE / ARC RULES)
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Angle Inside = ½ the sum of the Arcs
C
148
85
A
x
y
70
B
D
57
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CIRCLES (ANGLE / ARC RULES)
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Angle Outside = ½ the difference of the Arcs
120
D
E
30
B
C
x
A
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Circle / Sphere Formulas…
A r
C  2 r or  d
2
S  4 r
3
4 r
V
3
2
III.) DATA ANALYSIS
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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
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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
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NORMAL DISTRIBUTION…
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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
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Unbiased sample: represents the
population
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Biased sample: over or underestimates the
population
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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