CSET MATH SUBTESTS I, II, & III RESOURCES  

CSET 1 REVIEW

 

ALGEBRA (24 Multiple Choice Items, 3 Constructed Response Items) 

 

Preliminaries: Basic Algebra (Not a part of CSET I specs)

 

         Lesson 1. Definition of a Rational Number: https://www.youtube.com/watch?v=6QKcW22IYe0, https://www.youtube.com/watch?v=X6t1e77fNU4

           Lesson 2. Definition of a Complex Number: https://www.youtube.com/watch?v=uaI_4KVtp2k, 

               https://www.youtube.com/watch?v=zE3ZV8-FJ98, https://www.youtube.com/watch?v=cTqZYEtTQhA, 

               https://www.youtube.com/watch?v=H_50Y36AK4k, https://www.youtube.com/watch?v=JoLq9NaLOvI, https://www.youtube.com/watch?v=KgYl6YIaVU4,

          

 

Functions Part I

 

a. Analyze and prove general properties of functions (i.e., domain and range, one-to-one, onto, inverses, composition, and differences between relations and functions)

 

   a.1 Functions and Relations

           Lesson 3. Functions and Relations: https://www.youtube.com/watch?v=NlhQqmLN51M

           Lesson 4. Functions and Relations: https://www.youtube.com/watch?v=Uz0MtFlLD-k

           Lesson 5. Function Notation: https://www.youtube.com/watch?v=kagLx6MW9JY

 

   a.2 Domain and Range

           Lesson 6. Interval Notation: https://www.youtube.com/watch?v=sq2SlrkZeI8

           Lesson 7. Domain and Range Graphically: https://www.youtube.com/watch?v=I0f9O7Y2xI4

           Lesson 8. Domain and Range Graphically: https://www.youtube.com/watch?v=QAxZEelInJc

           Lesson 9. Domain and Range Algebraically: https://www.youtube.com/watch?v=sbvSBH2Mo20

           Lesson 10. Finding the Domain and Range of a Function Algebraically: https://www.youtube.com/watch?v=hZEGZMb4uzQ

 

             Required Functions to Know: Linear, Quadratic, and Odd/Even Functions

                      Lesson 11. Linear Functions: Khan Academy Module on LFs

                      Lesson 12. Quadratic Functions: Khan Academy Module on QFs

                Lesson 13. Graphs of Odd and Even Functions: Definitions, Symmetry 

 

                 Assessment: Practice Problems Lines #s 1-8 excluding #7, Quadratic Equations #5, Quadratic Equations #s9 and 10

 

   a.3 One-to-One Functions

           Lesson 14. Definition: https://www.youtube.com/watch?v=1NPvkYLjjws

           Lesson 15.  Determining Whether a Function is 1-1: https://www.youtube.com/watch?v=9b8Xd77f-qk

 

   a.4 Onto Functions

          Lesson 16. Onto Functions: https://www.youtube.com/watch?v=xKNX8BUWR0g

          Lesson 17. Onto Functions: https://www.youtube.com/watch?v=KiKJt4gywYE

 

   a.4 Inverse Functions

         Lesson 18. Definition of an Inverse of a Function: https://www.youtube.com/watch?v=JPPitlVKjWQ

         Lesson 19. Finding the Inverse of a Function: https://www.youtube.com/watch?v=q739Wcf0ZUg

         Lesson 20. Checking the Inverse: https://www.youtube.com/watch?v=nSmFzOpxhbY

        Lesson 21. Finding the Inverse of a Function: https://www.youtube.com/watch?v=Bq7Jd7vXC08

 

   a.5 Operations Involving Functions

         Lesson 22. Basic Operations: https://www.youtube.com/watch?v=5934UqzXvKA

         Lesson 23. Composition of Functions: https://www.youtube.com/watch?v=PCHkzAxiJwU

         Lesson 24. All Operations of Functions: https://www.youtube.com/watch?v=X5Qyf3UxIrU

 

   F1. Assessment: Practice Problems Domain and Range, Quadratic Functions, Inverse Functions, All Functions,

           Operations Involving Functions #6, Inverse Functions #2, More Functions

 

Polynomial Equations and Inequalities 

 

a. Know why graphs of linear inequalities are half planes and be able to apply this fact (e.g., linear programming)

 

           Lesson 25. Graphing Lines: https://www.youtube.com/watch?v=2UrcUfBizyw

           Lesson 26. Graphing Linear Inequalities: https://www.youtube.com/watch?v=lxTQrsUip9g

           Lesson 27. Solving Linear Programming Problems Introduction: https://www.youtube.com/watch?v=6M6jKr4rMoI

           Lesson 28. Solving Linear Programming Problems: https://www.youtube.com/watch?v=2ACJ9ewUC6U

           Lesson 29. Solving Linear Programming Problems: https://www.youtube.com/watch?v=hccsOVEqizU

           

    PEI1. Assessment: Practice Problems Review 1 #7, Review 2 #5, Review 3 #7

 

b. Prove and use the following:
         b.1 The Rational Root Theorem for polynomials with integer coefficients

 

                       Lesson 30. Rational Roots Theorem: https://www.youtube.com/watch?v=YMyv9-9VXw4

                       Lesson 31. Rational Roots Theorem: https://www.youtube.com/watch?v=jERVeo3Dtkw

         b.2 The Factor Theorem

 

                  Lesson 32. Factor and Remainder Theorems: https://www.youtube.com/watch?v=_IPqCaspZOs

                  Lesson 33. Factor Theorem Problems: https://www.youtube.com/watch?v=6G3iAgpK4kA

                      CSET Math Questions: https://www.youtube.com/watch?v=6G3iAgpK4kA&list=PL6AC21728CD1693DC

                                                  https://www.youtube.com/watch?v=yseY3IIGVus

    

         b.3 The Conjugate Roots Theorem for polynomial equations with real coefficients

 

                  Lesson 34. Conjugate Pairs: https://www.youtube.com/watch?v=ZQjq-o9ZBek

                  Lesson 35. Polynomials that Have Conjugate Pairs: https://www.youtube.com/watch?v=PQr0yVq5ysc

 

         b.4 The Quadratic Formula for real and complex quadratic polynomials

 

                 Lesson 36. Quadratic Formula with Real Roots: https://www.youtube.com/watch?v=i7idZfS8t8w

                 Lesson 37. Quadratic Formula with Complex Roots: https://www.youtube.com/watch?v=dnjK4DPqh0k

                     CSET Math Questions: https://www.youtube.com/watch?v=ciFe5sRdRzI, https://www.youtube.com/watch?v=0vkqaOOfn1A, 

https://www.youtube.com/watch?v=LWOK7IoHgd4&list=PL06D3A067F97DA04F

 

         b.5 The Binomial Theorem

 

                 Lesson 38. Binomial Theorem Using Pascal's Triangle: https://www.youtube.com/watch?v=NLQmQGA4a3M

                 Lesson 39. Binomial Theorem: https://www.youtube.com/watch?v=iPwrDWQ7hPc

 

         PEI2. Assessment: Practice Problems (p. 8)

 

c. Analyze and solve polynomial equations with real coefficients using the Fundamental Theorem of Algebra

 

                Lesson 40. Fundamental Theorem of Algebra: https://www.youtube.com/watch?v=d8-LO6FCna0

                Lesson 41. Fundamental Theorem of Algebra: https://www.youtube.com/watch?v=b4VHq7NDsVo

              

Functions Part II

 

b. Analyze properties of polynomial, rational, radical, and absolute value functions in a variety of ways (e.g., graphing, solving problems)

 

    b.1 Properties of Graphs of Polynomial Functions

               Lesson 42. End Behavior of Graphs of Polynomial Functions: https://www.youtube.com/watch?v=PSGL95nQBy8

               Lesson 43. Graphs of Polynomial Functions with Repeated Zeros: https://www.youtube.com/watch?v=honyxJPl0-0

               CSET Math Question: https://www.youtube.com/watch?v=4vh8sTztdz0&index=12&list=PLS0TM4AjRKMbYou37x7I4eMTTmI_eSagw

 

   b.2 Properties of Graphs of Rational Functions

               Lesson 44. Graphs of Rational Functions Introduction: https://www.youtube.com/watch?v=-DUMVzvu7-g

               Lesson 45. Graphs of Rational Functions: https://www.youtube.com/watch?v=hWjMovgqvi4

               Lesson 46. Graphs of Rational Functions (Harder): https://www.youtube.com/watch?v=IbsLYHzKoH0

 

   b.3 Properties of Graphs of Radical Functions

               Lesson 47. Graphs of Radical Functions and Transformations: https://www.youtube.com/watch?v=CnH5cs_SPpM

               Lesson 48. Graphs of Radical Functions: https://www.youtube.com/watch?v=Uteoh0PtWwI

 

   b.4 Properties of Graphs of Absolute Value Functions

               Lesson 49. Graphs of Absolute Value Functions Introduction: https://www.youtube.com/watch?v=uSCfgSK7J-k

               Lesson 50. Graphs of Absolute Value Function Using a Piecewise Approach: https://www.youtube.com/watch?v=71SfBO-B4dE

               Lesson 51. Graphs of Absolute Value Functions: https://www.youtube.com/watch?v=1OtzfP8fCNU

  

   F2. Assessment: Practice Problems Functions 1, Functions 2, Functions 3, Functions 4, Functions 5 (#s 1-5), Functions 6, Functions 7,                                     Functions 8, Functions 9

 

c. Analyze properties of exponential and logarithmic functions in a variety of ways (e.g., graphing, solving problems) 

 

   c.1 Properties of Graphs of Exponential Functions

              Lesson 52. Graphs of Exponential Functions: https://www.youtube.com/watch?v=8ZNpM7aSkuA

              Lesson 53. Finding the Equation, Given the Graph of an Exponential Function: https://www.youtube.com/watch?v=vmFiraM8qTw

 

   c.2 Properties of Graphs of Logarithmic Functions

             Lesson 54. Definition of a Logarithm: https://www.youtube.com/watch?v=mQTWzLpCcW0

             Lesson 55. Graphs of Logarithmic Function: https://www.youtube.com/watch?v=jS_52xEjT_k

             Lesson 56. Graphs of Logarithmic Functions: https://www.youtube.com/watch?v=qTLezcX3jNo

             Lesson 57. Comparing Graphs of Exponential and Logarithmic Functions: https://www.youtube.com/watch?v=w1A2ZYmfGco

             Lesson 58. Domain and Range of Logarithmic Functions: https://www.youtube.com/watch?v=qTLezcX3jNo

                CSET Math Question: https://www.youtube.com/watch?v=eTRlmWj1Xkc

    

    Assesssment: Exponential and Logarithmic Problems:  Set A       Set B        Set C

                   CSET Math Questions: https://www.youtube.com/watch?v=eTRlmWj1Xkc, 

                                  https://www.youtube.com/watch?v=eu7Ufwuhvf8&list=PLS0TM4AjRKMbYou37x7I4eMTTmI_eSagw

   

Preliminaries: Writing Proofs (Not a part of CSET I specs) 

     

     Lesson 59. Proofs Involving Odd and Even Numbers: https://www.youtube.com/watch?v=Ei3lFjDvXD0

     Lesson 60. Direct Proofs: https://www.youtube.com/watch?v=W2v6FG7u4HY

     Lesson 61. More Direct Proofs: https://www.youtube.com/watch?v=qlpFIx2eVR8

     Lesson 62. Indirect Proofs: https://www.youtube.com/watch?v=IZ2MJO1HtMY

     Lesson 63. More Indirect Proofs: https://www.youtube.com/watch?v=JlvGxZndAG4

    

Algebraic Structures 

 

a. Know why the real and complex numbers are each a field, and that particular rings are not fields (e.g., integers, polynomial rings, matrix rings)

 

             Lesson 64. Axioms for the Real Numbers: http://www.math.uchicago.edu/~boller/HarrisMathCamp/axioms.pdf

             Lesson 65. Groups with Examples: https://www.youtube.com/watch?v=WwndchnEDS4

             Lesson 66. Rings and Fields with Examples: https://www.youtube.com/watch?v=syHBApgJhsA

             Lesson 67. Number Systems and Fields: http://www.math.uchicago.edu/~boller/HarrisMathCamp/systems.pdf

             Lesson 68.  More Rings and Fields: http://mathrefresher.blogspot.com/2006/05/fields-and-rings.html

             

    A1. Assessment: Practice Problems (3.1 #32)

​

b. Apply basic properties of real and complex numbers in constructing mathematical arguments (e.g., if a < b and c < 0, then ac > bc)

 

            Lesson 69. Basic Proof Techniques: http://www.math.psu.edu/wysocki/M403/Notes403_2.pdf

            Lesson 70. Properties of Real Numbers: http://www.cengage.com/resource_uploads/downloads/1133963021_375161.pdf

            Lesson 71. Properties of Real Numbers: http://www.math.psu.edu/wysocki/M403/Notes403_2.pdf

            Lesson 72. Properties of Real Numbers: http://www.cs.sunysb.edu/~pfodor/courses/CSE215/L08_1-Number.pdf

        

c. Know that the rational numbers and real numbers can be ordered and that the complex numbers cannot be ordered, but that any polynomial equation with real coefficients can be solved in the complex field

​

            Lesson 73. Axioms for Ordered Fields: http://homepages.math.uic.edu/~kauffman/axioms1.pdf

            Lesson 74. More Ordered Fields: https://faculty.etsu.edu/gardnerr/4217/notes/1-2.pdf

            Lesson 75. More Ordered Fields: http://www.uobabylon.edu.iq/eprints/paper_12_27257_140.pdf

            Lesson 76. Real Numbers and Fields: http://www.math.vanderbilt.edu/~schectex/courses/thereals/

            Lesson 77. Real Numbers and Fields: http://www.math.louisville.edu/~lee/RealAnalysis/IntroRealAnal-ch02.pdf

           

    

Preliminaries: Right Triangle Trigonometry and the Pythagorean Theorem (Not a part of CSET I specs)

 

            Lesson 78. Pythagorean Theorem: https://www.youtube.com/watch?v=AA6RfgP-AHU

           Lesson 79. Pythagorean Theorem Problems: https://www.youtube.com/watch?v=-vXr5gwBxVg

           Lesson 80. Basic Right Triangle Trigonometry: https://www.youtube.com/watch?v=Jsiy4TxgIME

           Lesson 81. More Right Triangle Trigonometry: https://www.youtube.com/watch?v=G-T_6hCdMQc

 

Linear Algebra 

 

a. Understand and apply the geometric interpretation and basic operations of vectors in two and three dimensions, including their scalar multiples and scalar (dot) and cross products

 

           Lesson 82. Vectors in Two Dimensions: https://www.youtube.com/playlist?list=PLtvClhypCw9lfliZAg-rJx_ah_qNLHl6i

           Lesson 83. Vectors in Three Dimensions: https://www.youtube.com/watch?v=cQVTMmGurCQ, 

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

           Lesson 84. Dot Product: https://www.youtube.com/watch?v=KDHuWxy53uM, https://www.youtube.com/watch?v=SpEnXMzDZAI

           Lesson 85. Dot Product vs Cross Product: https://www.youtube.com/watch?v=E34CftP455k

              CSET Math Question: https://www.youtube.com/watch?v=z6w6o55PJok,https://www.youtube.com/watch?v=2tAmJLEz9gs

​

b. Prove the basic properties of vectors (e.g., perpendicular vectors have zero dot product)

​

             Lesson 86. Proofs of Basic Properties: https://www.youtube.com/watch?v=rVQ3G9epCjw,                                                            

​

c. Understand and apply the basic properties and operations of matrices and determinants (e.g., to determine the solvability of linear systems of equations) 

 

          Lesson 87. Introduction: https://www.youtube.com/watch?v=ZR9nVXWTfcY,

                                              https://www.youtube.com/watch?v=rBkWTQ_D3wA (complex numbers in matrix form)

          Lesson 88. More on Operations: https://www.youtube.com/watch?v=5o8GRIzfYP8, 

                          https://www.youtube.com/watch?v=iWnhjBl5xOs

          Lesson 89. Determinants: https://www.youtube.com/watch?v=umXgFjqPfsk

          Lesson 90. Inverse of a Square Matrix: https://www.youtube.com/watch?v=kZwItfmFtyk, 

                          https://www.youtube.com/watch?v=iUQR0enP7RQ

          Lesson 91. Solving Linear Systems of Equations Using Matrices: https://www.youtube.com/watch?v=9LYVi-n-6Jw,            

                          https://www.youtube.com/watch?v=PTN8rganLWo, 

                          https://www.youtube.com/watch?v=eXhf18KlYdg, https://www.youtube.com/watch?v=Re1F4d24Fxc

             CSET Math Questions: https://www.youtube.com/watch?v=vZHgXtX9O9A&list=PLS0TM4AjRKMbYou37x7I4eMTTmI_eSagw&index=7, 

                                           https://www.youtube.com/watch?v=017nmnFFcVg, https://www.youtube.com/watch?v=8L-VRz9JTk0