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Transformational Geometry 

 

a. Demonstrate an understanding of the basic properties of isometries in two- and three- dimensional space (e.g., rotation, translation, reflection)

 

       Lesson 38. Transformations in Geometry: (definition) https://www.youtube.com/watch?v=F1M1MncPq2c

                                                                  (preimage/image) https://www.youtube.com/watch?v=CLBkPmsn2Mw

 

       Lesson 39. Reflection: (geometric) https://www.youtube.com/watch?v=BBOPgBVp1tU&list=PLWkr0FoP-fSl7-Zi277rqxPrOx9yEjnu&index=4

                                                         https://www.youtube.com/watch?v=j1X_UIOvEwA

                                      (algebraic) https://www.youtube.com/watch?v=j1X_UIOvEwAhttps://www.youtube.com/watch?v=s-Oq4h5AUXM

                                                      https://www.youtube.com/watch?v=XEcBaI1qL0Y

 

      Lesson 40. Translation: (geometric)  https://www.youtube.com/watch?v=oCy785o4fTQ

                                                         https://www.youtube.com/watch?v=GWHzyDyjDzQ

                                           (algebraic) https://www.youtube.com/watch?v=uDAC03677xE,

                                                           https://www.youtube.com/watch?v=j_0FLOs6PvM

 

     Lesson 41. Rotation: (geometric) https://www.youtube.com/watch?v=5trp4U4rmLM

                                                      https://www.youtube.com/watch?v=U4Hv494HwrQ

                                                      https://www.youtube.com/watch?v=C1Z87L4WV8U  

                                       (algebraic) https://www.youtube.com/watch?v=MkaF9U7LJEQ

                                                       https://www.youtube.com/watch?v=aXV3xGJ8J_o

                                                       https://www.youtube.com/watch?v=EegxlPlKuUo

                                                       https://www.youtube.com/watch?v=kmb7npLq5Pw

 

    Lesson 42. Composition of Transformations: https://www.youtube.com/watch?v=JMsenRpmhKU

                                                                   

b. Understand and prove the basic properties of dilations (e.g., similarity transformations or change of scale) 

 

      Lesson 43. Dilations: (geometric) https://www.youtube.com/watch?v=mWrvZdxQ0_Ahttps://www.youtube.com/watch?v=ydOu6ntew6w

                                       (algebraic) https://www.youtube.com/watch?v=YE5JuxtBLSkhttps://www.youtube.com/watch?v=Zc4LFSy5vRU

 

Assessment: Practice Problem   Problem 1    

 

CSET Math Problems   Problem 1

 

 Probability and Statistics (8 Multiple Choice Items, 1 Constructed Response Item)

 

Probability

 

a. Prove and apply basic principles of permutations and combinations

     

       Lesson 44. Addition and Multiplication Rules: https://www.youtube.com/watch?v=sEul6TMYDY0

                                                                                 https://www.youtube.com/watch?v=5g_h1jeBANs

      

       Lesson 45. Combinations: https://www.youtube.com/watch?v=qaFNhwNBY3khttps://www.youtube.com/watch?v=uATuM3ajhBw

 

       Lesson 46. Permutations: https://www.youtube.com/watch?v=hJRXKq2GEo8

                                                  https://www.youtube.com/watch?v=DpVnGm664E8&list=PLXcAypFGY57FOPbZdI0uZiOoKQzVTAmWv&index=24

     

        Assessment: Practice Problems   Problem 1     Problem 2       

 

b. Illustrate finite probability using a variety of examples and models (e.g., the fundamental counting principles)

 

       Lesson 47. Probability (Definition): https://www.youtube.com/watch?v=ZdDybI9Wsjw

                                                            https://www.youtube.com/watch?v=-8eSOmTPUbk

                                                            https://www.youtube.com/watch?v=AY3O_qsSnbE

 

       Lesson 48. Probability with Counting Techniques: https://www.youtube.com/watch?v=yvxxbFehj4k

                                                             https://www.youtube.com/watch?v=kLW6VLPCm-0

                                                             https://www.youtube.com/watch?v=Xb6VIHg-Acc 

 

       Assessment: Practice Problems     Problem 1     Problem 2     

 

c. Use and explain the concept of conditional probability

 

       Lesson 49. Definition: https://www.youtube.com/watch?v=H02B3aMNKzEhttps://www.youtube.com/watch?v=t6G8mL0w4xM

 

       Lesson 50. Applications: https://www.youtube.com/watch?v=6xPkG2pA-TUhttps://www.youtube.com/watch?v=xw6utjoyMi4,

                       (Bayes Theorem) https://www.youtube.com/watch?v=yBn-eGrRHJU

 

       Assessment: Practice Problem    Problem 1

 

d. Interpret the probability of an outcome 

 

       Lesson 51. Problems: https://www.youtube.com/watch?v=zlqvSLvhIXEhttps://www.youtube.com/watch?v=5nXI1K0Pr3M

     

       Assessment: Practice Problems      Problem 1     Problem 2     

 

e. Use normal, binomial, and exponential distributions to solve and interpret probability problems (requires Statistics (a) and (b) concepts below) 

 

       Lesson 52. Normal Distribution: https://www.youtube.com/watch?v=L2VyGIFZY3whttps://www.youtube.com/watch?v=iT7-D51CZLQ    

                                                     https://www.youtube.com/watch?v=-hyuDHGb9Ec

 

       Lesson 53. Binomial Distribution: https://www.youtube.com/watch?v=jkVlNZ21Imshttps://www.youtube.com/watch?v=NaDZ0zVTyXQ

                                                      https://www.youtube.com/watch?v=xNLQuuvE9ug

 

       Lesson 54. Exponential Distribution: https://www.youtube.com/watch?v=RQ9VOaWxDFo

                       https://www.youtube.com/watch?v=IT-0oCOQrBY&list=PLOmEznjdLsNjgYS6I8f3toTEhLumCh66L

 

       Assessment: Practice Problems      Problem 1       Problem 2

 

Statistics 

 

a. Compute and interpret the mean, median, and mode of both discrete and continuous distributions

 

      Lesson 55. Mean, Median, and Mode: http://www.abs.gov.au/websitedbs/a3121120.nsf/home/statistical+language+-+measures+of+central+tendency, 

                        https://www.youtube.com/watch?v=81zcjULlh58https://www.youtube.com/watch?v=k3aKKasOmIw

                        https://www.youtube.com/watch?v=zG2UGGZXoKQ

 

      Assessment: Practice Problems     Problem 1     Problem 2     Problem 3      

 

b. Compute and interpret quartiles, range, variance, and standard deviation of both discrete and continuous distributions

 

      Lesson 56. Quartiles, Range, and Variance and Standard Deviation: https://www.youtube.com/watch?v=E4HAYd0QnRc

                        https://www.youtube.com/watch?v=Cx2tGUze60shttps://www.youtube.com/watch?v=QsQIpF_t1LI

                        https://www.youtube.com/watch?v=5kz16kbOTG0

 

      Lesson 57. Z scores: https://www.youtube.com/watch?v=1xhCL5m4nI0https://www.youtube.com/watch?v=NY2zWGBXBhU

                                    https://www.youtube.com/watch?v=1o-t_mVDDYQ

 

      Assessment: Practice Problems      Problem 1     Problem 2     Problem 3      Problem 4      

 

c. Select and evaluate sampling methods appropriate to a task (e.g., random, systematic, cluster, convenience sampling) and display the results

 

      Lesson 58. Sampling Methods: https://www.youtube.com/watch?v=be9e-Q-jC-0https://www.youtube.com/watch?v=FtZavrh0eaw

 

       Assessment: Practice Problems     Problem 1        Problem 2     

 

d. Know the method of least squares and apply it to linear regression and correlation

 

        Lesson 59.  Regression and Correlation: https://www.youtube.com/watch?v=DsI85vrKiU4

                                     https://www.youtube.com/watch?v=t5CK844MYzY, https://www.youtube.com/watch?v=MIqyiGvrUXE 

 

      Lesson 60. Method of Least Squares: https://www.youtube.com/watch?v=0T0z8d0_aY4https://www.youtube.com/watch?v=aq8VU5KLmkY,  

            https://www.youtube.com/watch?v=WPGf-LulqNk&list=PLFE18650E3626FB73,  https://www.youtube.com/watch?v=ocGEhiLwDVc

 

      Assessment: Practice Problems     Problem 1     Problem 2     Problem 3      Problem 4

 

e. Know and apply the chi-square test 

 

      Lesson 61. Chi-Square Test: https://www.youtube.com/watch?v=2QeDRsxSF9Mhttp://www.slideshare.net/mhsgeography/chi-square-worked-example

                        https://www.youtube.com/watch?v=gKY8TqndNo4https://www.youtube.com/watch?v=VskmMgXmkMQ

                        https://www.youtube.com/watch?v=s1xEB9XknBI

 

      Assessment: Practice Problems     Problem 1     Problem 2      

 

 

ADDITIONAL CSET MATH SUBTEST II REVIEW PROBLEMS - MUST DO!

 

Released CSET Math Subtest II Items

 

Free CSET Math Subtest II Practice Tests:   Version 1    Version 2

CSET 2 REVIEW

 

Geometry (22 Multiple Choice Items, 3 Constructed Response Items)

 

Preliminaries (Not a part of CSET II specs)

 

Lesson 1. Deductive Reasoning: https://www.youtube.com/watch?v=yMzNaqdxiZY

Lesson 2. Conditional Statement: https://www.youtube.com/watch?v=oEr27P1bX9o

Lesson 3. Contrapositive, Converse, and Inverse of a Conditional Statement: https://www.youtube.com/watch?v=IHd8jiUF3Lk

Lesson 4. Counterexamples: https://www.youtube.com/watch?v=oEr27P1bX9o

Lesson 5. Points, Lines, and Planes: https://www.youtube.com/watch?v=GK3h7LzqsUg

                                                       https://www.youtube.com/watch?v=4jIb2ZWFHm0

Lesson 6. Collinearity, Betweeness, and Midpoint: https://www.youtube.com/watch?v=wThxtFhsX0I

                                                                           https://www.youtube.com/watch?v=5Au4bynMgFY

Lesson 7. Angles and Angle Relationships (Linear Pair, Adjacent Angles, Vertical Angles, Complementary and Supplementary

              Angles): https://www.youtube.com/watch?v=DGKwdHMiqCg

                           https://www.youtube.com/watch?v=H-de6Tkxej8

                           https://www.youtube.com/watch?v=ARk7ttW4FAs

Lesson 8. Triangles and Classifications: https://www.youtube.com/watch?v=Bb8e3ZkU3Sw,

                                                            https://www.youtube.com/watch?v=hY5KDuDap00

Lesson 9. Quadrilaterals and Classifications: http://www.cut-the-knot.org/Curriculum/Geometry/Quadrilaterals.shtml

Lesson 10. Polygons: https://www.youtube.com/watch?v=LfPDFGvGbqkhttps://www.youtube.com/watch?v=W8Zq_A1MPqs

Lesson 11. Circles: Definition, Related Terms, Tangents

Lesson 12. Algebra of Curves: Midpoint, Distance, Parabola 1, Parabola 2, Parabola 3, Parabola 4, Parabola 5, Circle 1, Circle 2,                   Ellipse 1, Ellipse 2, Hyperbola 1, Hyperbola 2, Deriving the Conics By Applying the Distance Formula (this is a must)

 

Assessment: Practice Problems: Opposite Rays    Conics 1   Conics 2  

 

Parallelism

 

a. Know the Parallel Postulate and its implications, and justify its equivalents (e.g., the Alternate Interior Angle Theorem, the angle sum of every triangle is 180 degrees)

 

       Lesson 13. Parallel Postulate and the Interior Angle Sum of a Triangle: https://www.youtube.com/watch?v=W-_JMf6Sc9A

                       https://www.youtube.com/watch?v=3xGbdYNkoL0

                       https://www.youtube.com/watch?v=0hLyG3sNZuI

                       https://www.youtube.com/watch?v=TFkeWn25E9c

       Lesson 14. Theorems Involving Angles and Parallel Lines: https://www.youtube.com/watch?v=5nltsBUDdkQ

                        https://www.youtube.com/watch?v=0ALpdgXowFg

 

b. Know that variants of the Parallel Postulate produce non-Euclidean geometries (e.g., spherical, hyperbolic) 

 

       Lesson 15. Non-Euclidean Geometries: https://www.youtube.com/watch?v=LPET_HhN0VM

                                                                              https://www.youtube.com/watch?v=an0dXEImGHM

 

       Assessment: Practice Problems  Problem 1   Problem 2    Problem 3   Problem 4    Problem 5   Problem 6  

 

       CSET Math Questions    Problem 1   

 

Plane Euclidean Geometry 

 

a. Prove theorems and solve problems involving similarity and congruence

 

       Lesson 16. Definition of Similarity and Congruence: https://www.youtube.com/watch?v=nTXJKNMTOYo

                         https://www.youtube.com/watch?v=Ly86lwq_2gchttps://www.youtube.com/watch?v=OEp7YK6WEXE

         Lesson 17. Theorems and Postulates Involving Congruence: https://www.youtube.com/watch?v=-k1ECA6jWsY

                       https://www.youtube.com/watch?v=NAhcmPS5k9g

       Lesson 18. Theorems and Postulates Involving Similarity: https://www.youtube.com/watch?v=7bO0TmJ6Ba4

                       https://www.youtube.com/watch?v=wlMuiKCYoWs

 

       Assessment: Practice Problems     Problem 1        Problem 2       Problem 3     

 

b. Understand, apply, and justify properties of triangles (e.g., the Exterior Angle Theorem, concurrence theorems, trigonometric ratios, Triangle Inequality, Law of Sines, Law of Cosines, the Pythagorean Theorem and its converse)

 

         Lesson 19. Exterior Angle Theorem:  https://www.youtube.com/watch?v=LORpNcWMDNg, Proof of the Exterior Angle Theorem 

 

        Assessment: Practice Problems    Problem 1   Problem 2

         

        Lesson 20. Concurrence Theorems: http://www.ck12.org/book/CK-12-Geometry-Honors-Concepts/section/4.5

                                                          http://www.youtube.com/watch?v=E6W8bo0Pevk

 

        Assessment: Practice Problem   Problem 1

         

        Lesson 21. Right Triangle Trigonometric Ratio: https://www.youtube.com/watch?v=Jsiy4TxgIME

                                                                          https://www.youtube.com/watch?v=G-T_6hCdMQc

                                                                          https://www.youtube.com/watch?v=3umBUlrUCPQ

 

        Assessment: Practice Problem   Problem 1   

         

        Lesson 22. Triangle Inequality Theorem: http://www.khanacademy.org/math/geometry/basic-geometry/triangle_inequality_theorem/v/triangle-inqequality-theorem

                               http://www.wyzant.com/resources/lessons/math/geometry/triangles/inequalities_and_relationships

         

        Lesson 23. Pythagorean Theorem and its Converse: http://www.khanacademy.org/math/geometry/right_triangles_topic/pyth_theor/v/the-pythagorean-theorem

 

        Assessment: Practice Problem  Problem 1

         

        Lesson 24. Law of Sines: http://www.khanacademy.org/math/trigonometry/less-basic-trigonometry/law-sines-cosines/v/proof--law-of-sines

 

        Assessment: Practice Problems   Problem 1    Problem 2

         

        Lesson 25. Law of Cosines: http://www.khanacademy.org/math/trigonometry/less-basic-trigonometry/law-sines-cosines/v/proof--law-of-sines

 

        Assessment: Practice Problems   Problem 1    Problem 2

 

c. Understand, apply, and justify properties of polygons and circles from an advanced standpoint (e.g., derive the area formulas for regular polygons and circles from the area of a triangle)

 

       Lesson 26. Polygons: Exterior Angle Sum, Interior Angle Sum

        Lesson 27. Perimeters and Areas of Regular Polygons: https://www.youtube.com/watch?v=7S1MLJOG-5A

                           https://www.youtube.com/watch?v=XgDC1qb48ps,  

                           https://www.youtube.com/watch?v=hqqtumES-rQ,

                           https://www.youtube.com/watch?v=MGy7QG1uxZs

                           https://www.youtube.com/watch?v=rEnsk34S2L0

                           https://www.youtube.com/watch?v=0-uu6EF3d1I

                           https://www.youtube.com/watch?v=sjruQYW4qY0,

                                http://www.analyzemath.com/Geometry/regular_polygons.html

 

         Assessment: Practice Problem     Problem 1   

 

       Lesson 28. Circle Properties: https://www.youtube.com/watch?v=so7Uh1oQXdg

                                                   https://www.youtube.com/watch?v=V1pM9cYFXMU

                                                   https://www.youtube.com/watch?v=dNtl5f20vQg

                                                   https://www.youtube.com/watch?v=g2ld_Nx5LKo

                                                   https://www.youtube.com/watch?v=zdxe30vo-OY

                       Circumference and Area of a Circle: https://www.youtube.com/watch?v=jyLRpr2P0MQhttps://www.youtube.com/watch?v=YokKp3pwVFc

       

       Assessment: Practice Problems   Problem 1    Problem 2    

 

       CSET Math Question   Problem 1     

 

d. Justify and perform the classical constructions (e.g., angle bisector, perpendicular bisector, replicating shapes, regular n-gons for n equal to 3, 4, 5, 6, and 8) 

 

      Lesson 29. Popular Geometric Constructions: https://www.youtube.com/watch?v=MWjxyo9BPxA&list=PL8BDF1FF750C2B4A8

 

      Lesson 30. Replicating Figures by Construction: https://www.youtube.com/watch?v=m9d1SBudYno

 

       Lesson 31. Classical Constructions 3: Regular n-gons https://www.youtube.com/watch?v=TAHczLeIUTc 

 

        Assessment: Practice Problem   Problem 1

 

e. Use techniques in coordinate geometry to prove geometric theorems 

 

       Lesson 32. Proving by Using Coordinate Geometry   Introduction 1   Introduction 2   Variable-Based CG 

                            More Variable-Based CG   Lots More Variable-Based CG

 

 

       Assessment: Practice Problems    Problem 1    Problem 2    Problem 3      Problem 4

 

Three-Dimensional Geometry 

 

a. Demonstrate an understanding of parallelism and perpendicularity of lines and planes in three dimensions

 

       Lesson 33. Parallelism in Three Dimensions: https://www.youtube.com/watch?v=J2Qz-7ZWDAE

                                                                       https://www.youtube.com/watch?v=FTceGiZi85Y

                                                                       https://www.youtube.com/watch?v=NaaroGmZC3g

                                                                       https://www.youtube.com/watch?v=i9JYy4QWgO8,

       Lesson 34. Perpendicularity in Three Dimensions: https://www.youtube.com/watch?v=NaaroGmZC3g

                                                                              https://www.youtube.com/watch?v=AVKw8KhXdrw

 

       Assessment: Practice Problem    Problem 1

 

b. Understand, apply, and justify properties of three-dimensional objects from an advanced standpoint (e.g., derive the volume and surface area formulas for prisms, pyramids, cones, cylinders, and spheres) 

 

      Lesson 35. Surface Area: (prism) https://www.youtube.com/watch?v=Pcjnz26pnwY,

                                           (prism) https://www.youtube.com/watch?v=Aigefhb-1NM,

                                           (prism) https://www.youtube.com/watch?v=mL7E_NBhyIw

                                           (cylinder) https://www.youtube.com/watch?v=7zy6IajGe2w,

                                           (cone) https://www.youtube.com/watch?v=NGunDMoHdks,

                                           (sphere) https://www.youtube.com/watch?v=6EzQEdBX_30

                                           (cube) https://www.youtube.com/watch?v=sskf3tF2heU,

                                           (pyramid) https://www.youtube.com/watch?v=i31InzuKabY

 

      Lesson 36. Volume: (pyramid) https://www.youtube.com/watch?v=f6nUNTfiK5Yhttps://www.youtube.com/watch?v=e7-am8JtREI

                                     (prism) https://www.youtube.com/watch?v=O5rlivS7ZhE

                                     (cylinder) https://www.youtube.com/watch?v=302TotMfNFk

                                     (cone) https://www.youtube.com/watch?v=G3wEgkUqc-k

                                     (sphere) https://www.youtube.com/watch?v=xuPl_8o_j7k, https://www.youtube.com/watch?v=9RsBnMwV7mw

 

      Lesson 37. Volume of shapes https://www.youtube.com/watch?v=I3vYW5SUp3Y

 

      Assessment: Practice Problems     Problem 1    Problem 2     

 

     CSET Problems    Problem 1   Problem 2

 

 

 

      

        

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