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_UIOvEwA, https://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_A, https://www.youtube.com/watch?v=ydOu6ntew6w
(algebraic) https://www.youtube.com/watch?v=YE5JuxtBLSk, https://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=qaFNhwNBY3k, https://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=H02B3aMNKzE, https://www.youtube.com/watch?v=t6G8mL0w4xM
Lesson 50. Applications: https://www.youtube.com/watch?v=6xPkG2pA-TU, https://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=zlqvSLvhIXE, https://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=L2VyGIFZY3w, https://www.youtube.com/watch?v=iT7-D51CZLQ,
https://www.youtube.com/watch?v=-hyuDHGb9Ec
Lesson 53. Binomial Distribution: https://www.youtube.com/watch?v=jkVlNZ21Ims, https://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=81zcjULlh58, https://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=Cx2tGUze60s, https://www.youtube.com/watch?v=QsQIpF_t1LI,
https://www.youtube.com/watch?v=5kz16kbOTG0
Lesson 57. Z scores: https://www.youtube.com/watch?v=1xhCL5m4nI0, https://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-0, https://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_aY4, https://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=2QeDRsxSF9M, http://www.slideshare.net/mhsgeography/chi-square-worked-example,
https://www.youtube.com/watch?v=gKY8TqndNo4, https://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=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