Download Resources by Standard for Analytic Geometry

Analytic Geometry EOCT Resources
Number and Quantity
Perform arithmetic operations with complex numbers.
MCC9‐12.N.CN.1 Know there is a complex number i such that i2 = −1, and every complex number has the form a+ bi with
a and b real.
 http://www.purplemath.com/modules/complex.htm
 http://www.mathsisfun.com/numbers/complex-numbers.html
MCC9‐12.N.CN.2 Use the relation i2 = –1 and the commutative, associative, and distributive properties to add, subtract,
and multiply complex numbers.
 http://www.regentsprep.org/Regents/math/algtrig/ATO6/practicepageadd.htm
 http://www.regentsprep.org/Regents/math/algtrig/ATO6/lessonadd.htm
MCC9‐12.N.CN.3 (+) Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex
numbers.
 http://www.regentsprep.org/Regents/math/algtrig/ATO6/multprac.htm
 http://www.sparknotes.com/math/algebra2/complexnumbers/section3.rhtml
 https://www.khanacademy.org/math/algebra2/complex-numbers-a2/complex_numbers/v/dividing-complexnumbers
Use complex numbers in polynomial identities and equations.
MCC9‐12.N.CN.7 Solve quadratic equations with real coefficients that have complex solutions.
 http://www.regentsprep.org/Regents/math/algtrig/ATE3/quadcomlesson.htm
 http://www.youtube.com/watch?v=d2w6i8FpYC8
 https://www.khanacademy.org/math/algebra2/complex-numbers-a2/complex_numbers/v/complex-roots-from-thequadratic-formula
Algebra
Seeing Structure in Expressions A.SSE
Interpret the structure of expressions
 http://www.virtualnerd.com/common-core/hsa-algebra/HSA-SSE-expressions-seeing-structure/A/1/1a/variablesdefinition
 http://www.virtualnerd.com/common-core/hsa-algebra/HSA-SSE-expressions-seeing-structure/A/1/1a/coefficientdefinition
 http://www.virtualnerd.com/common-core/hsa-algebra/HSA-SSE-expressions-seeing-structure/A/1/1a/constantdefinition
 http://www.virtualnerd.com/common-core/hsa-algebra/HSA-SSE-expressions-seeing-structure/A/1/1a/constantdefinition
 http://www.virtualnerd.com/common-core/hsa-algebra/HSA-SSE-expressions-seeing-structure/A/1/1a/factordefinition
 http://www.virtualnerd.com/common-core/hsa-algebra/HSA-SSE-expressions-seeing-structure/A/1/1a/numericalalgebraic-expressions
 http://www.virtualnerd.com/common-core/grade-6/6_EE-expression-equations/A/2/2c/order-of-operationsdefinition
Write expressions in equivalent forms to solve problems
 http://www.virtualnerd.com/common-core/hsa-algebra/HSA-SSE-expressions-seeing-structure/B/3/3c/power-ofquotient-formula
 http://www.virtualnerd.com/common-core/hsa-algebra/HSA-SSE-expressions-seeing-structure/B/3/3c/functiondefinition
 http://www.virtualnerd.com/common-core/hsa-algebra/HSA-SSE-expressions-seeing-structure/B/3/3a/trinomialfactorization-example
 http://www.virtualnerd.com/common-core/hsa-algebra/HSA-SSE-expressions-seeing-structure/B/3/3a/solve-byfactoring
 http://www.virtualnerd.com/common-core/hsa-algebra/HSA-SSE-expressions-seeing-structure/B/3/3a/perfectsquare-trinomial-shortcut
Analytic Geometry EOCT Resources
Perform arithmetic operations on polynomials
 http://www.virtualnerd.com/common-core/hsa-algebra/HSA-APR-polynomial-rational-expressionsarithmetic/A/1/addition-example
 http://www.virtualnerd.com/common-core/hsa-algebra/HSA-APR-polynomial-rational-expressionsarithmetic/A/1/binomial-multiplication-distributive-property
 http://www.virtualnerd.com/common-core/hsa-algebra/HSA-APR-polynomial-rational-expressionsarithmetic/A/1/sum-and-difference-product-formula-example
 http://www.virtualnerd.com/common-core/hsa-algebra/HSA-APR-polynomial-rational-expressionsarithmetic/A/1/subtraction-example
Create equations that describe numbers or relationships
 http://www.virtualnerd.com/common-core/hsa-algebra/HSA-CED-/A/4/isolate-variable-from-formula
 http://www.virtualnerd.com/common-core/hsa-algebra/HSA-CED-/A/4/literal-equation-definition
 http://www.virtualnerd.com/common-core/hsa-algebra/HSA-CED-/A/1/compound-and-word-problem-solution
 http://www.virtualnerd.com/common-core/hsa-algebra/HSA-CED-/A/1/growth-word-problem
 http://www.virtualnerd.com/common-core/hsa-algebra/HSA-CED-/A/1/decay-word-problem
Solve equations and inequalities in one variable
 http://www.youtube.com/watch?v=srJn2ZUYB4M
 http://www.youtube.com/watch?v=1SmJq3-SWZo
 http://www.youtube.com/watch?v=Y8dq2G4XZCc
 http://www.youtube.com/watch?v=Y6tLqfkCA4A
 http://www.youtube.com/watch?v=1SmJq3-SWZo
 http://www.youtube.com/watch?v=srJn2ZUYB4M
Solve systems of equations
 http://www.virtualnerd.com/pre-algebra/inequalities-multi-step-equations/no-solution-equation-example.php
 http://www.virtualnerd.com/pre-algebra/inequalities-multi-step-equations/no-solution-definition.php
 http://www.virtualnerd.com/algebra-1/systems-equations-inequalities/solve-substitution-one-quadratic.php
 http://www.virtualnerd.com/algebra-2/linear-systems/equations-solution-by-graphing.php
 http://www.virtualnerd.com/algebra-2/linear-systems/equations-find-map-coordinates.php
 http://www.virtualnerd.com/algebra-2/linear-systems/equations-infinite-solutions-word-problem.php
Functions
Interpret functions that arise in applications in terms of the context
MCC9‐12.F.IF.4 For a function that models a relationship between two quantities, interpret key features of
graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the
relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative;
relative maximums and minimums; symmetries; end behavior; and periodicity.
 Increasing and Decreasing: http://www.youtube.com/watch?v=AGkTQW1qGMo
 Intercepts: http://www.purplemath.com/modules/intrcept.htm
 Relative Mins and Maxs: http://www.youtube.com/watch?v=Hoyv3-BMAGc
 Domain and Range: http://www.purplemath.com/modules/fcns2.htm
MCC9‐12.F.IF.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table)
over a specified interval. Estimate the rate of change from a graph. Analyze functions using different representations.

Rate of Change: http://www.youtube.com/watch?v=jkksI-mkwd0
MCC9‐12.F.IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases
and using technology for more complicated cases.
 Graphing Quadratic Functions: http://www.youtube.com/watch?v=tjroyVI8El4
 Linear and Quadratic Functions: http://www.purplemath.com/modules/index.htm
 Transformation of Functions: http://www.youtube.com/watch?v=Ccq1aQDCfVE
Analytic Geometry EOCT Resources
MCC9‐12.F.IF.7a Graph linear and quadratic functions and show intercepts, maxima, and minima.
 Graphing Quadratic Functions: http://www.youtube.com/watch?v=tjroyVI8El4
MCC9‐12.F.IF.8a Use the process of factoring and completing the square in a quadratic function to show
zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.
 http://www.youtube.com/watch?v=xGOQYTo9AKY
 http://www.purplemath.com/modules/sqrquad.htm
 http://www.mathsisfun.com/algebra/factoring-quadratics.html
Geometry
Understand congruence in terms of rigid motions
MCC9‐12.G.CO.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a
given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions
to decide if they are congruent.
 http://www.youtube.com/watch?v=YHwSe-0c7Xo
 http://ceemrr.com/Geometry1/HingeTheorem/HingeTheorem_print.html
MCC9‐12.G.CO.7 Use the definition of congruence in terms of rigid motions to show that two triangles are
congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
 http://www.mathwarehouse.com/geometry/triangles/triangle-inequality-theorem-rule-explained.php
MCC9‐12.G.CO.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition
of congruence in terms of rigid motions.
 http://www.mathwarehouse.com/geometry/congruent_triangles/
 http://www.basic-mathematics.com/congruent-triangles.html
 http://www.youtube.com/watch?v=-k1ECA6jWsY
 http://www.virtualnerd.com/geometry/congruent-triangles/proof-asa-aas-hl/definition-asa-triangle-congruencepostulate
 http://www.virtualnerd.com/geometry/congruent-triangles/proof-sss-sas/coordinate-plane-congruence
 http://www.analyzemath.com/Geometry/congruent_triangles.html
 http://www.regentsprep.org/Regents/math/geometry/GP4/Ltriangles.htm
 http://www.nexuslearning.net/books/ml-geometry/Chapter4/ML%20Geometry%2044%20ASA%20and%20AAS.pdf
Prove geometric theorems
MCC9‐12.G.CO.9 Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when
a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are
congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the
segment’s endpoints.
 http://feromax.com/cgi-bin/ProveIt.pl
 http://www.youtube.com/watch?v=sBUsOXUyqSQ
MCC9‐12.G.CO.10 Prove theorems about triangles. Theorems include: measures of interior angles of a triangle
sum to 180 degrees; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides
of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.
 http://www.regentsprep.org/Regents/math/geometry/GPB/theorems.htm
MCC9‐12.G.CO.11 Prove theorems about parallelograms. Theorems include: opposite sides are congruent,
opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles
are parallelograms with congruent diagonals.
 http://www.mathsisfun.com/quadrilaterals.html
 http://www.khanacademy.org/math/geometry/quadrilaterals-and-polygons/v/quadrilateral-properties
Make geometric constructions
MCC9‐12.G.CO.12 Make formal geometric constructions with a variety of tools and methods (compass and
straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment;
copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the
perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on
the line.
 https://www.youtube.com/watch?v=kbr3S_JOntk
Analytic Geometry EOCT Resources
Similarity, Right Triangles, and Trigonometry
MCC9‐12.G.SRT.1 Verify experimentally the properties of dilations given by a center and a scale factor:
a. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a
line passing through the center unchanged.
 http://www.youtube.com/watch?v=lNxZjs-62K0
b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
Prove theorems involving similarity
MCC9‐12.G.SRT.4 Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle
divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.
 http://hotmath.com/hotmath_help/topics/triangle-proportionality-theorem.html
 http://www.youtube.com/watch?v=F_0rA_9WkVE
 http://www.ixl.com/math/geometry/triangle-proportionality-theorem
MCC9‐12.G.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove
relationships in geometric figures.
 https://www.khanacademy.org/math/geometry/similarity/triangle_similarlity/v/similarity-postulates
 http://www.mathwarehouse.com/geometry/similar/triangles/similar-triangle-theorems.php
 http://www.mathvillage.info/node/94
 http://www.purplemath.com/modules/ratio6.htm
 http://www.youtube.com/watch?v=LdjqS2bISSw
 http://www.youtube.com/watch?v=4wCSW69N0BA
 http://www.onlinemathlearning.com/similar-triangles-2.html
Define trigonometric ratios and solve problems involving right triangles
MCC9‐12.G.SRT.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the
triangle, leading to definitions of trigonometric ratios for acute angles.
 http://www.regentsprep.org/regents/math/algtrig/ATT2/Ltri30.htm
 http://www.mathwarehouse.com/geometry/triangles/right-triangles/special-right-triangles.php
 http://www.youtube.com/watch?v=VVKUOdyzQ98
 http://www.regentsprep.org/regents/math/algtrig/ATT2/Ltri45.htm
 http://www.youtube.com/watch?v=7B1yrRLSRT8
MCC9‐12.G.SRT.7 Explain and use the relationship between the sine and cosine of complementary angles.
 https://www.illustrativemathematics.org/illustrations/1443
MCC9‐12.G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied
problems.
 http://www.mathsisfun.com/pythagoras.html
 http://www.purplemath.com/modules/pythagthm.htm
 https://www.khanacademy.org/math/geometry/right_triangles_topic/pyth_theor/v/pythagorean-theorem
 http://www.purplemath.com/modules/basirati.htm
 https://www.khanacademy.org/math/trigonometry/basic-trigonometry/basic_trig_ratios/v/basic-trigonometry
 http://www.virtualnerd.com/algebra-2/trigonometric-functions/right-triangle/right-triangle-examples
Understand and apply theorems about circles
MCC9‐12.G.C.1 Prove that all circles are similar.
 http://learnzillion.com/lessons/2688-establish-circle-similarity-using-similar-triangles
MCC9‐12.G.C.2 Identify and describe relationships among inscribed angles, radii, and chords. Include the
relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right
angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.
 http://www.geogebra.org/en/upload/files/UC_MAT/chords_in_a_circle.html
 http://www.geogebra.org/en/upload/files/UC_MAT/chords_outside_a_circle.html
 http://www.ricksmath.com/circles.html
 http://www.algebra.com/algebra/homework/Circles/Circles.faq.hide_answers.1.html
MCC9‐12.G.C.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for
a quadrilateral inscribed in a circle.
 https://www.brightstorm.com/math/geometry/constructions/circumscribed-and-inscribed-circles-and-polygons/
Analytic Geometry EOCT Resources
Find arc lengths and areas of sectors of circles
MCC9‐12.G.C.5 Derive using similarity the fact that the length of the arc intercepted by an angle is proportional
to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula
for the area of a sector.
 http://www.mathsisfun.com/geometry/circle-area-by-sectors.html
 http://www.mathsisfun.com/geometry/circle-sector-segment.html
Statistics and Probability
Understand independence and conditional probability and use them to interpret data
MCC9-12.S.CP.1 Describe events as subsets of a sample space (the set of outcomes) using characteristics (or
categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”).
 http://www.regentsprep.org/regents/math/algebra/APR6/indexAPR6.htm
 http://www.shmoop.com/common-core-standards/ccss-hs-s-cp-1.html
MCC9-12.S.CP.2 Understand that two events A and B are independent if the probability of A and B occurring together is
the product of their probabilities, and use this characterization to determine if they are independent.
 http://www.regentsprep.org/regents/math/algebra/APR6/Lindep.htm
 http://www.shmoop.com/video/independent-and-dependent-events
MCC9-12.S.CP.3 Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A
and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional
probability of B given A is the same as the probability of B.
 http://www.regentsprep.org/regents/math/algebra/APR3/indexAPR3.htm
 http://www.khanacademy.org/math/probability/independent-dependentprobability/dependent_probability/v/independent-dependent-probability
 http://www.shmoop.com/common-core-standards/ccss-hs-s-cp-3.html
MCC9-12.S.CP.4 Construct and interpret two-way frequency tables of data when two categories are associated with each
object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate
conditional probabilities.
 http://www.shmoop.com/common-core-standards/ccss-hs-s-cp-4.html
MCC9-12.S.CP.5 Recognize and explain the concepts of conditional probability and independence in everyday language
and everyday situations.
 http://www.shmoop.com/common-core-standards/ccss-hs-s-cp-5.html
Use the rules of probability to compute probabilities of compound events in a uniform probability model
MCC9-12.S.CP.6 Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and
interpret the answer in terms of the model.
 http://www.khanacademy.org/math/probability/independent-dependentprobability/dependent_probability/v/calculating-conditional-probability
 http://www.shmoop.com/common-core-standards/ccss-hs-s-cp-6.html
MCC9-12.S.CP.7 Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in terms of the
model



http://www.regentsprep.org/regents/math/algebra/APR8/indexAPR8.htm
http://www.khanacademy.org/math/probability/independent-dependentprobability/addition_rule_probability/v/addition-rule-for-probability
http://www.shmoop.com/common-core-standards/ccss-hs-s-cp-7.html