CSET MATH SUBTESTS I, II, & III RESOURCES  

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=LfPDFGvGbqk, https://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_2gc, https://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=jyLRpr2P0MQ; https://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=f6nUNTfiK5Y, https://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