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Transcript
Analytic Geometry Review Notes
Create a booklet with the students using these key concepts. The review is organized into sections,
probability, coordinate geometry, quadratics, numbers, circles, and triangles and theorems. The review
is set up to go from the newest material to the oldest, so the first semester stuff should be fresh in the
students’ minds for the EOCT. Try to spend some class time creating the review booklet and some class
time letting students work through and go over the corresponding EOCT review questions. Make sure
every student has a copy of the EOCT formula sheet (the back page of the review packet) and that they
use it during the review.
Probability
 Union 𝐴 ∪ 𝐵
 Intersection
𝐴∩𝐵


Complement
A or A’
Compound Probability
o or
addition +
o and
multiplication x
o mutually exclusive
P(A or B) = P(A) + P(B)
o not mutually exclusive or overlapping P(A or B) = P(A) + P(B) – P(𝐴 ∩ 𝐵)
o
Conditional Probability P( A B) 
o
o
Independent
Dependent
P( A  B)
P( A)
P(A and B) = P(A) x P(B)
P(A and B) = P(A) x P(B given A)
Coordinate Geometry – Conics and Parabolas
 Circles
o standard form (x-h)2 + (y-k)2 = r2
(h, k) center
o convert to standard with completing the square
o find intersection of circle with line
o show a given point is on a circle
 Parabola
o terms- focus, directrix, axis of symmetry
o
vertical equation





o
o
yk 
1
( x  h) 2
4p
(h, k) vertex
(h, k+p) focus
x=h axis of symmetry
y = k – p equation of directrix
p > 0 opens up
p < 0 opens down
horizontal equation
xh 
1
( y  k)2
4p
 (h, k) vertex
 (h+p, k) focus
 y = k axis of symmetry
 x = h – p equation of directrix
 p > 0 opens right
Prove theorems
 midpoint formula
 distance formula
 slope formula
p < 0 opens left
r = radius
Quadratics
 factoring
 solving by quadratic formula
 completing the square
 solving using square roots
 Characteristics
o zeros (solving)
o

shandard form f(x) = ax2 + bx + c
o vertex form
f(x) = a(x – h)2 + k
o min/max (vertex)
o x and y intercepts
o increase, decrease
o end behavior
o domain
o rate of change
Comparing/transformations
o shifts, stretches, shrinks, reflections
b
,
 2a
vertex 
vertex (h, k)
Number System
 Rational Exponents
 Radical Expressions
 Rational vs Irrational numbers
 Polynomials
o add, subtract
o distribute, double distribute FOIL
o perimeter, area
 Imaginary Numbers
o simplify exponents, add, subtract, multiply
Circles
 Vocab – diameter, radius, tangent, arc
 Angles
o central angle
o inscribed
o angles inside the circle
o angles outside the circle
 Segments
o intersection inside the circle
o intersection outside the circle
 Sectors
o arc length
o sector area
 Volumes – cylinder, cone, pyramid, sphere
  b 
f
 
 2a  
Right Triangles
 Sin, Cos, Tangent
 Angle of Elevation, depression
Triangles, Lines, and Proofs
 transformations – rigid transformations and dilations
 Similar Triangles
o AA~
o similar triangles proportional sides
 Congruent Triangles
o SSS, SAS, ASA, AAS, HL
 Proofs
o vertical angles
o alt interior angles
o corresponding angles
o Pythagorean theorem
o triangle sum theorem
o isosceles triangle theorem
o triangle midsegment theorem
 Constructions
o angle bisector
o perpendicular lines
o circumscribed triangle, square, hexagon