top of page

CSET 3 REVIEW 

​

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

 

​

Trigonometry 

​

a. Prove that the Pythagorean Theorem is equivalent to the trigonometric identity                                                   and that \

 

 

this identity leads to                                                                          and                                                                .

      

          Lesson 1.  Proof of Pythagorean Theorems: https://www.youtube.com/watch?v=iEKT-yAuRgQ;  https://www.youtube.com/watch?v=MyO2MFJbfi4

​

b. Prove and apply the sine, cosine, and tangent sum formulas for all real values.

 

         Lesson 2. Proof of Sin Sum Formula: https://www.youtube.com/watch?v=R0EQg9vgbQw

         Lesson 3. Visual Proof of Sine and Cos Sum Formulas: https://www.youtube.com/watch?v=ea6-ctMYn_Q

         Lesson 4. Proof of Cos Sum Formula: https://www.youtube.com/watch?v=gDOGT6NcD60

         Lesson 5. Proof of Tan Sum Formula: https://www.youtube.com/watch?v=1qCXck4ZIrk

​

c. Analyze properties of trigonometric functions in a variety of ways (e.g., graphing and solving problems, using the unit circle)

​

        Lesson 6. Properties of Trig Functions: https://www.youtube.com/watch?v=ypenWNeRdd4;  https://www.youtube.com/watch?v=r26NNufSFYg;   https://www.youtube.com/watch?v=soIt2TwV6Xk;   https://www.youtube.com/watch?v=8Z60_yXX4xA;  https://www.youtube.com/watch?v=ztlVm6COcK4https://www.youtube.com/watch?v=Dis8_Ih7slo;   https://www.youtube.com/watch?v=ZffZvSH285c

       

        Lesson 7. Evaluating Trig Functions: https://www.youtube.com/watch?v=8DdyCeTEGOo;  https://www.youtube.com/watch?v=QukM0eBDwNE;  https://www.youtube.com/watch?v=9OdJ54fGgVs

       

        Lesson 8. Symmetry of Trig Values: https://www.youtube.com/watch?v=tzQ7arA917E

       

       Lesson 9. Use Trig Identities to Evaluate Expressions: https://www.youtube.com/watch?v=sGDbKmWmTDw

     

d. Apply the definitions and properties of inverse trigonometric functions (i.e., arcsin, arccos, and arctan)

 

       Lesson 10. Introduction: https://www.youtube.com/watch?v=bBBUMHe900U;  https://www.youtube.com/watch?v=JGU74wbZMLg;   https://www.youtube.com/watch?v=hxjmtDXXCzU;  https://www.youtube.com/watch?v=Idxeo49szW0

​

       Lesson 11. Evaluating Inverse Trig Functions: https://www.youtube.com/watch?v=aRVWs1tDarI;  https://www.youtube.com/watch?v=m5DZQDzsJsE;  https://www.youtube.com/watch?v=g9S4u8eQiww

​

       Lesson 12. Simplifying Expressions with Inverse Trig Functions: https://www.youtube.com/watch?v=Zud3aCeSLRs

​

       Lesson 13. Solving Trigonometric Equations: https://www.youtube.com/watch?v=IE0FxGegdMghttps://www.youtube.com/watch?v=ZkK4ifsQoGkhttps://www.youtube.com/watch?v=iZihVtFaAkohttps://www.youtube.com/watch?v=kEcbxiLeGTchttps://www.youtube.com/watch?v=YESk2q8QEOYhttps://www.youtube.com/watch?v=CrayigBVBZohttps://www.youtube.com/watch?v=IE0FxGegdMg&list=RDQMDgpikCqDgLYhttps://www.youtube.com/watch?v=fWI0frnVHy0https://www.youtube.com/watch?v=7Eo-fuy0f7ghttps://www.youtube.com/watch?v=_PPj7eeT_7E 

​

e. Apply polar representations of complex numbers (e.g., DeMoivre's Theorem)

​

       Lesson 14. Polar Representations of CI: https://www.youtube.com/watch?v=fbqakDV-IXchttps://www.youtube.com/watch?v=6HIlT6oSvXc;  https://www.youtube.com/watch?v=8RasCV_Lggg;  https://www.youtube.com/watch?v=hdlkr0t2R88https://www.youtube.com/watch?v=u3Q_0WxxdeM

​

       Lesson 15. De Moivre's Theorem: https://www.youtube.com/watch?v=kEf9gt3umnU;  https://www.youtube.com/watch?v=yf22lfJ1JCU;    https://www.youtube.com/watch?v=y2voZK3-CHA; https://www.youtube.com/watch?v=1Eu66E_MoQ8https://www.youtube.com/watch?v=irwItP7PiQg

 

f. Model periodic phenomena with periodic functions

​

       Lesson 16. Modeling: https://www.youtube.com/watch?v=kXKg56CPnpEhttps://www.youtube.com/watch?v=RX0DY9eRp8ghttps://www.youtube.com/watch?v=s4cLM0l1gd4https://www.youtube.com/watch?v=6oeBPCzaugIhttps://www.youtube.com/watch?v=DP6Drp69fGMhttps://www.youtube.com/watch?v=Ogcd_Rhk0bU

 

g. Recognize equivalent identities, including applications of the half-angle and double-angle formulas for sines and cosines 

 

       Lesson 17. Examples: https://www.youtube.com/watch?v=OJz-fOzFbEchttps://www.youtube.com/watch?v=NK4MlZXepYQhttps://www.youtube.com/watch?v=IE8q4WRubC4https://www.youtube.com/watch?v=d_NMpLSGpkUhttps://www.youtube.com/watch?v=A1iKe4HkoXchttps://www.youtube.com/watch?v=uFbbF-IYFjMhttps://www.youtube.com/watch?v=qWJ4HwJ_5LYhttps://www.youtube.com/watch?v=Wh7hM_FsN3Yhttps://www.youtube.com/watch?v=TjWa00qkYpI

​

       Assessment: Practice Problems  Problem 1   Problem 2    Problem 3   Problem 4    Problem 5   Problem 6   Problem 7  

                                                    Problem 8

 

       CSET 3 Math Questions    Do Problems 1-5 and 25

 

 

Limits and Continuity 

​

a. Derive basic properties of limits and continuity, including the Sum, Difference, Product, Constant Multiple, and Quotient Rules, using the formal definition of a limit

​

       Lesson 18. Definition of a Limit of a Function: https://www.youtube.com/watch?v=-ejyeII0i5c;    https://www.youtube.com/watch?v=G0ax2x2_Em0https://www.youtube.com/watch?v=Fdu5-aNJTzUhttps://www.youtube.com/watch?v=0sCttufU-jQhttps://www.youtube.com/watch?v=dXr6aoJ1nVI

​

       Lesson 19. Properties of Limits: https://www.youtube.com/watch?v=lSwsAFgWqR8https://www.youtube.com/watch?v=6webTCd5gEQ;  https://www.youtube.com/watch?v=yzwtrqsvCvIhttps://www.youtube.com/watch?v=GGQngIp0YGIhttps://www.youtube.com/watch?v=5T8ifCP6eIghttps://www.youtube.com/watch?v=v_Nz6UUQ4HQhttps://www.youtube.com/watch?v=v_Nz6UUQ4HQ

​

      Lesson 20. Infinite Limits: https://www.youtube.com/watch?v=-vwcLvb9A0shttps://www.youtube.com/watch?v=xvFqomOpLrshttps://www.youtube.com/watch?v=tFHALKP22ao

​

      Lesson 21. Limits at Infinity: https://www.youtube.com/watch?v=kae8X6aplf0https://www.youtube.com/watch?v=FVJNuukADeQhttps://www.youtube.com/watch?v=75xO9xy7TTQhttps://www.youtube.com/watch?v=mrKg_5CsfX0

​

b. Show that a polynomial function is continuous at a point

​

       Lesson 22. Definition of a Continuous Function: https://www.youtube.com/watch?v=InDHwh1CvOghttps://www.youtube.com/watch?v=kdEQGfeC0SEhttps://www.youtube.com/watch?v=oUgDaEwMbiU'https://www.youtube.com/watch?v=NVQBZWTKygUhttps://www.youtube.com/watch?v=SoMl89ZYJIghttps://www.youtube.com/watch?v=OEE5-M4aY4k

​

       Lesson 23. Polynomial function and continuity at a point: https://www.youtube.com/watch?v=OEE5-M4aY4k

​

c. Apply the intermediate value theorem, using the geometric implications of continuity 

​

       Lesson 24. Intermediate Value Theorem and Examples: https://www.youtube.com/watch?v=9xgO-EJ3sr0;  https://www.youtube.com/watch?v=9wEHwFrUyOUhttps://www.youtube.com/watch?v=TrQTK-B4bzMhttps://www.youtube.com/watch?v=Rpug_8nTqyw

        

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

 

       CSET 3 Math Questions    Do Problems 6-9

​

​

Derivatives and Applications

 

a. Derive the rules of differentiation for polynomial, trigonometric, and logarithmic functions using the formal definition of derivative

 

       Lesson 25. Definition of Derivative of a Function: https://www.youtube.com/watch?v=Vv1BUCkgsr8https://www.youtube.com/watch?v=vzDYOHETFlo

​

       Lesson 26. Differentiation Rules of Algebraic Functions: https://www.youtube.com/watch?v=B2qJURxVypshttps://www.youtube.com/watch?v=v8AmvKHJqTUhttps://www.youtube.com/watch?v=hCLfogkqzEk

​

       Lesson 27. Differentiation Rules for Transcendental Functions: https://www.youtube.com/watch?v=TDHI-aieyfkhttps://www.youtube.com/watch?v=OjnOgoEu6CMhttps://www.youtube.com/watch?v=0YH8BrlVTqkhttps://www.youtube.com/watch?v=dylEXVIasqs

​

      Lesson 28. Proofs: https://www.youtube.com/watch?v=JjOndio6-g4https://www.youtube.com/watch?v=c_CpxQdMejEhttps://www.youtube.com/watch?v=ho87DN9wO70https://www.youtube.com/watch?v=FztF4sJ66rY

​

      Lesson 29. Implicit Differentiation: https://www.youtube.com/watch?v=kk2HilVYAPEhttps://www.youtube.com/watch?v=5yTVUZCaU6khttps://www.youtube.com/watch?v=sL6MC-lKOrwhttps://www.youtube.com/watch?v=_kLWcuJzYh8https://www.youtube.com/watch?v=2dv_PfEFZXY

​

b. Interpret the concept of derivative geometrically, numerically, and analytically (i.e., slope of the tangent, limit of difference quotients, extrema, Newton's method, and instantaneous rate of change)

​

      Lesson 30. Graphing using derivatives: https://www.youtube.com/watch?v=hIgnece9inshttps://www.youtube.com/watch?v=4aYGmexcKnc

     

     Lesson 31. Tangents: https://www.youtube.com/watch?v=1KwW1v__T_0https://www.youtube.com/watch?v=GH8-URjRQpQ; https://www.youtube.com/watch?v=7EFYoQ6H7Tw

​

     Lesson 32. Newton's Method: https://www.youtube.com/watch?v=1uN8cBGVpfshttps://www.youtube.com/watch?v=HaUKd-UXfMQhttps://www.youtube.com/watch?v=xdLgTDlFwrc

​

    Lesson 33. Instantaneous rate of change: https://www.youtube.com/watch?v=hSK7f4durxIhttps://www.youtube.com/watch?v=MRDPyXgxN78https://www.youtube.com/watch?v=jlihNi_Mkoshttps://www.youtube.com/watch?v=4Up5gsDeluwhttps://www.youtube.com/watch?v=dPZcJSctp38

​

c. Interpret both continuous and differentiable functions geometrically and analytically and apply Rolle's theorem, the mean value theorem, and L'Hôpital's rule

​

    Lesson 34. Rolle's Theorem and MVT: https://www.youtube.com/watch?v=0jiVRRKmGoEhttps://www.youtube.com/watch?v=jgDykHxQxqMhttps://www.youtube.com/watch?v=Du3PuJjME8khttps://www.youtube.com/watch?v=xYOrYLq3fE0https://www.youtube.com/watch?v=M2b2ok-jto4

​

    Lesson 35. L'Hopital's Rule: https://www.youtube.com/watch?v=PdSzruR5OeEhttps://www.youtube.com/watch?v=RQSnbJd04GYhttps://www.youtube.com/watch?v=thEnl_gCjXAhttps://www.youtube.com/watch?v=Haapl1SrB5Ihttps://www.youtube.com/watch?v=Zd7wd24jeokhttps://www.youtube.com/watch?v=6g_g9-AU188https://www.youtube.com/watch?v=BU2QhCk3ExY

​

d. Use the derivative to solve rectilinear motion, related rate, and optimization problems

​

      Lesson 36. Optimization: https://www.youtube.com/watch?v=lzLgtk-lrW0https://www.youtube.com/watch?v=Zq7g1nc2MJ8https://www.youtube.com/watch?v=mamH094uw_Uhttps://www.youtube.com/watch?v=EOJbmMB8uCQ

​

     Lesson 37. Related Rates: https://www.youtube.com/watch?v=BmWmue6sDFghttps://www.youtube.com/watch?v=_kbd6troMgA;  https://www.youtube.com/watch?v=kQF9pOqmS0Uhttps://www.youtube.com/watch?v=kBVDSu7v8os

​

    Lesson 38. Rectilinear Motion: https://www.youtube.com/watch?v=9ot21Up_mj4https://www.youtube.com/watch?v=HDntI7zfBNshttps://www.youtube.com/watch?v=HzN99FYCg5Ihttps://www.youtube.com/watch?v=pFeuGMMiZWw

​

e. Use the derivative to analyze functions and planar curves (e.g., maxima, minima, inflection points, concavity)

​

    Lesson 39. Graphing Functions Using Derivative Concepts: https://www.youtube.com/watch?v=15awMHeP1Ychttps://www.youtube.com/watch?v=pQT2fZRMcf4https://www.youtube.com/watch?v=3TJLOCYrTeshttps://www.youtube.com/watch?v=lDY9JcFaRd4https://www.youtube.com/watch?v=RoxefQ_Qgm8https://www.youtube.com/watch?v=kTWXVJHdrwMhttps://www.youtube.com/watch?v=Gy9jKk28XHY

​

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

​

       CSET 3 Math Questions    Do Problems 10-15

​

​

Integrals and Applications 

 

a. Derive definite integrals of standard algebraic functions using the formal definition of integral and interpret the concept of a definite integral geometrically, numerically, and analytically (e.g., limit of Riemann sums)

 

      Lesson 40. Finding Area using Reimann Sums: https://www.youtube.com/watch?v=AkUa9Fkz2rwhttps://www.youtube.com/watch?v=gFpHHTxsDkIhttps://www.youtube.com/watch?v=ODwkTt0RMDghttps://www.youtube.com/watch?v=Himr2l8Rd18

​

      Lesson 41. Definite Integral: https://www.youtube.com/watch?v=xR4AnXDBnswhttps://www.youtube.com/watch?v=rCWOdfQ3cwQhttps://www.youtube.com/watch?v=0dDIPzqKgYkhttps://www.youtube.com/watch?v=hTTDI49LhjEhttps://www.youtube.com/watch?v=8BzIOowS77Ahttps://www.youtube.com/watch?v=nopnFjMy3rQ

​

      Lesson 42. Properties of Definite Integrals: https://www.youtube.com/watch?v=MM0FTzvedH4https://www.youtube.com/watch?v=wycadSRDID4

​

c. Prove the fundamental theorem of calculus, and use it to interpret definite integrals as antiderivatives

 

     Lesson 43. FTC: https://www.youtube.com/watch?v=C7ducZoLKgwhttps://www.youtube.com/watch?v=PGmVvIglZx8

​

     Lesson 44: Proof of FTC: https://www.youtube.com/watch?v=pWtt0AvU0KAhttps://www.youtube.com/watch?v=mhb0epc6aFk

​

     Lesson 45: Applications of FTC: https://www.youtube.com/watch?v=FcLeaD3UII4https://www.youtube.com/watch?v=TQTDkpZP02Ahttps://www.youtube.com/watch?v=lvdnTXZGEF0&list=PL823769CE78CC2EE4

​

d. Apply the concept of integrals to compute the length of curves and the areas and volumes of geometric figures 

​

    Lesson 46: Find length of a curve: https://www.youtube.com/watch?v=neOQXrZv1rYhttps://www.youtube.com/watch?v=PwmCZAWeRNEhttps://www.youtube.com/watch?v=OhISsmqv4_8https://www.youtube.com/watch?v=qFowh4Ir7GUhttps://www.youtube.com/watch?v=DNDAwWIL5FY

​

    Lesson 47: Area Problems: https://www.youtube.com/watch?v=4bZyfvKazzQhttps://www.youtube.com/watch?v=RebqJ1wqP2Ihttps://www.youtube.com/watch?v=70NQ3ISYihwhttps://www.youtube.com/watch?v=I3bxriE3XbMhttps://www.youtube.com/watch?v=B5441_DREY0https://www.youtube.com/watch?v=LbTH7MGMNjk

​

    Lesson 48: Volume Problems: https://www.youtube.com/watch?v=E5OOMbz5jZkhttps://www.youtube.com/watch?v=GJOJl47l2_4https://www.youtube.com/watch?v=lBSLPUbYFsUhttps://www.youtube.com/watch?v=nZqOKc067Z8https://www.youtube.com/watch?v=R_aqSL-q6_8https://www.youtube.com/watch?v=43AS7bPUORchttps://www.youtube.com/watch?v=V6nTsxumjgUhttps://www.youtube.com/watch?v=cYJRMejnBqIhttps://www.youtube.com/watch?v=puSlVA6mwNQ

​

e. f. Solve separable first-order differential equations and apply them to growth and decay problems 

​

    Lesson 49: Examples: https://www.youtube.com/watch?v=nNHlSB6b1HUhttps://www.youtube.com/watch?v=6vUjGgI8Dsohttps://www.youtube.com/watch?v=DL-ozRGDlkYhttps://www.youtube.com/watch?v=XExEixAPK6shttps://www.youtube.com/watch?v=Et4Y41ZNyaohttps://www.youtube.com/watch?v=C5-lz0hcqsEhttps://www.youtube.com/watch?v=xVWCfMe97wshttps://www.youtube.com/watch?v=9wwaC_jnQQ0https://www.youtube.com/watch?v=3jpiW_oueaA

​

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

 

       CSET 3 Math Questions    Do Problems 16-20 and 26

​

​

Sequences and Series

​

a. Derive and apply the formulas for the sums of finite arithmetic series and finite and infinite geometric series (e.g., express repeating decimals as a rational number)

​

     Lesson 50: Arithmetic Sum: https://www.youtube.com/watch?v=RM644gFKo_ghttps://www.youtube.com/watch?v=Uy_L8tnihDM

​

     Lesson 51: Finite Geometric Series: https://www.youtube.com/watch?v=AXP5PGSaaYkhttps://www.youtube.com/watch?v=i8THsl3AYFI

​

     Lesson 52: Infinite Geometric Series: https://www.youtube.com/watch?v=b-7kCymoUpghttps://www.youtube.com/watch?v=yYxzq_O18Mghttps://www.youtube.com/watch?v=x2Xmldq0ll8https://www.youtube.com/watch?v=ocVBZjuJUdc

​

     Lesson 53: Expressing Repeating Decimals as Rational Numbers: https://www.youtube.com/watch?v=2BgWWsypzLAhttps://www.youtube.com/watch?v=7tDK_UjdWOs

​

b. Determine convergence of a given sequence or series using standard techniques (e.g., ratio, comparison, integral tests)

 

     Lesson 54: Definitions and Examples: https://www.youtube.com/watch?v=FoNLQvf4NUshttps://www.youtube.com/watch?v=lfZGtjSWcQshttps://www.youtube.com/watch?v=muqyereWEh4https://www.youtube.com/watch?v=NjDk8HiPOhkhttps://www.youtube.com/watch?v=7_52IGDHrqY

​

     Lesson 55: Ratio Test - https://www.youtube.com/watch?v=iy8mhbZTY7ghttps://www.youtube.com/watch?v=av947KCWf2Uhttps://www.youtube.com/watch?v=AwJ0P8B25tYhttps://www.youtube.com/watch?v=rUis1mSzwyA

​

     Lesson 56: Root Test - https://www.youtube.com/watch?v=vDdDLfIya0I

​

     Lesson 57: Comparison Test - https://www.youtube.com/watch?v=b7OetOcd188https://www.youtube.com/watch?v=0tXxFPHzFFIhttps://www.youtube.com/watch?v=AtbZZiSLemQhttps://www.youtube.com/watch?v=xesQnFWw8f8

​

     Lesson 58: Integral Test - https://www.youtube.com/watch?v=xRyXz_UZ14Qhttps://www.youtube.com/watch?v=8jPpNK4GIVshttps://www.youtube.com/watch?v=ojztrQMqLgEhttps://www.youtube.com/watch?v=XHUxLLu_c_0https://www.youtube.com/watch?v=wXDXe9YI4mchttps://www.youtube.com/watch?v=gvZ7UIaC50M

​

    Lesson 59: Divergence Test - https://www.youtube.com/watch?v=1yInzfzDDKY

​

    Lesson 60: Alternating Series Test - https://www.youtube.com/watch?v=91qVGeyTl44

​

    Lesson 61: P Series Test for C or D - https://www.youtube.com/watch?v=w9fC8RaklhAhttps://www.youtube.com/watch?v=gvZ7UIaC50M

​

    Lesson 62: Strategies for Testing Series - https://www.youtube.com/watch?v=DvadVYHf3pMhttps://www.youtube.com/watch?v=ac00oud9z4A

​

c. Calculate Taylor series and Taylor polynomials of basic functions 

​

    Lesson 63: Taylor and MacLaurin Series - https://www.youtube.com/watch?v=epgwuzzDHsQ&list=PLA5FB0434B1C097D0https://www.youtube.com/watch?v=cjPoEZ0I5wQhttps://www.youtube.com/watch?v=3d6DsjIBzJ4https://www.youtube.com/watch?v=Os8OtXFBLkY

​

    Lesson 64: Finding Taylor polynomials of basic functions - https://www.youtube.com/watch?v=epgwuzzDHsQhttps://www.youtube.com/watch?v=19x213y_uk4https://www.youtube.com/watch?v=8SsC5st4LnIhttps://www.youtube.com/watch?v=UINFWG0ErSA

​

        Assessment: Practice Problems  Problem 1   Problem 2    Problem 3   Problem 4    Problem 5   Problem 6   Problem 7

                                               

       CSET 3 Math Questions    Do Problems 21-24

bottom of page