MATH 151 - CALCULUS II - SPRING 2021

COMMON MINI-TESTS/FINAL INSTRUCTIONS

It is crucial that your read in detail these instructions.
It is your responsibility to understand them and to abide by them.
If you have any questions or concerns please talk to your instructor.

Dates:
Fri, Feb. 26: Mini-test#1, 5:00-6:10pm
Fri, Mar. 19: Mini-test#2, 5:00-6:10pm
Fri, Apr. 09: Mini-test#3, 5:00-6:10pm
Fri, Apr. 30: Mini-test#4, 5:00-6:10pm
Sun, May. 09: FINAL 14:30-16:30pm

Format:
The test will take place in GradeScope (GS). You will access the mini-test in GS from your BlackBoard account. A few notes:

  • You do not need to print the test nor copy the questions. Just make sure that you start each question on a SEPARATE page by writing the question number.
  • BOX your answers
  • For all question you must provide FULL derivation on how you obtained it. Answers without full work will earn NO points and will be deemed suspicious.
  • If the question has a graph (and you are not printing the test) that needs to be filled just reproduce/sketch the graph on your paper and fill it there.
  • Start each question in a clean/blank piece of a paper. Collect ALL your answers in a single PDF to upload into GS.
  • Use a soft pencil or a pen so that your writing has good contrast.
  • You will be responsible for submitting on time. The mini-test is designed to be one hour long and we are giving you an extra 10 minutes for uploading/submitting. Late submissions are NOT accepted.
  • Please read carefully question#1 and sign with you name and date that you have read carefully and understood the rules thereby explained. Failing to complete question#1 will result in a zero for the test.

Cheating:
There will be absolute zero tolerance towards cheating (please see more details in the official syllabus). All work that you complete in this class must be your own and only your own. Any (yes any) form of cheating will automatically result in an F for the whole semester and direct disciplinary action with the Center for Students Rights and Responsibilities (which may include punitive sanctions such as probation, suspension, or even, expulsion).

  • Using any external help during the test is cheating. You cannot consult the internet, nor send/post/upload, nor download any portion of the test (for instance Chegg or Slader or WolframAlpha or IntegralCalculator.com or WhatsApp or Instagram or any social media or etc...)

  • Uploading/dowloading/sharing (Chegg, Slader, Discord, WhatsApp, Reddit, Instagram, etc.) any portions of the test during or after the test will be considered cheating.

  • If others cheat you are at a disadvantage; thus, if you are aware of any form of cheating that is taking place please contact your instructor (full anonymity will be guaranteed).

Topics to be included in MINI-TEST#1:

  • Sec. 3.11 Hyperbolic Functions
  • Sec. 6.1: Areas Between Curves
  • Sec. 6.2: Volumes (by slices, disks and washers)
  • Sec. 6.3: Volumes by Cylindrical Shells
  • Sec. 6.4: Work
  • Sec. 6.5: Average Value of a Function
  • Sec. 7.1: Integration by Parts
  • Sec. 7.2: Trigonometric Integrals
  • Sec. 7.3: Trigonometric Substitution
  • Sec. 7.4: Integration of Rational Functions by Partial Fractions

Topics to be included in MINI-TEST#2:

  • Sec. 7.8: Improper Integrals
  • Sec. 8.1: Arc Length
  • Sec. 8.2: Area of a Surface of Revolution
  • Sec. 9.1: Modeling with Differential Equations
  • Sec. 9.2: Direction Fields and Euler's Method
  • Sec. 9.3: Separable Equations (including orthogonal curves AND mixing problems)
  • Sec. 9.4: Models of Population Growth. [Please refer to Activity#8: link]

Topics to be included in MINI-TEST#3:

  • Sec. 9.5: Linear Equations
  • Sec. 11.1: Sequences
  • Sec. 11.2: Series
  • Sec. 11.3: Integral Test and Estimates of Sums
  • Sec. 11.4: The Comparison Tests
  • Sec. 11.5: Alternating Series
  • Sec. 11.6: Absolute Convergence and the Ratio Test and Root Test
  • Sec. 11.7: Strategy for Testing Series
  • Sec. 11.8: Power Series (including inetrval and radius of convergence)

Topics to be included in MINI-TEST#4:

  • Sec. 11.8: Power Series (including inetrval and radius of convergence)
  • Sec. 11.9: Representations of Functions as Power Series
  • Sec. 11.10: Taylor and Maclaurin Series
  • Sec. 11.11: Applications of Taylor Polynomials (no Taylor inequality and no remainder)
  • Sec. 10.1: Curves Defined by Parametric Equations
  • Sec. 10.2: Calculus with parametric Equations
  • Sec. 10.3: Polar Coordinates

Topics to be included in FINAL:

  • Sec. 3.11 Hyperbolic Functions
  • Sec. 6.1: Areas Between Curves
  • Sec. 6.2: Volumes (by slices, disks and washers)
  • Sec. 6.3: Volumes by Cylindrical Shells
  • Sec. 7.1: Integration by Parts
  • Sec. 7.2: Trigonometric Integrals
  • Sec. 7.3: Trigonometric Substitution
  • Sec. 7.4: Integration of Rational Functions by Partial Fractions
  • Sec. 7.8: Improper Integrals
  • Sec. 8.1: Arc Length
  • Sec. 8.2: Area of a Surface of Revolution
  • Sec. 9.3: Separable Equations (NO orthogonal curves and NO mixing problems)
  • Sec. 9.5: Linear Equations
  • Sec. 11.2: Series (only geometric series and its applications)
  • Sec. 11.6: Ratio Test: interval and radius of convergence (NO absolute convergence and NO Root test)
  • Sec. 11.9: Representations of Functions as Power Series
  • Sec. 11.10: Taylor and Maclaurin Series (NO Taylor inequality and NO remainder)
  • Sec. 11.11: Applications of Taylor Series (only Approximating Functions by Polynomials, NO Remainder)
  • Sec. 10.1: Curves Defined by Parametric Equations
  • Sec. 10.2: Calculus with parametric Equations
  • Sec. 10.3: Polar Coordinates (inc. slopes that was not included in MiniTest#4)
  • Sec. 10.4: Areas and Lengths in Polar Coordinates (this material was not included in MiniTest#4)
  • Secs. 10.5 and 10.6 will NOT be icluded in Final test

Must-Know material, Cheat Sheets and suggested problems to study:

  • Mini-Test#1:
    • MiniTest1_must_know.pdf: This document contains all the Must-Know material for Mini-Test#1.
    • List of good pratice problems (some of these are part of HWs). This ist is not meant to be comprehensive, it is meant to give you an idea of the type of exercises and concepts that you should be familiar with.
      • Good compendium of problems: week05_Sp21.pdf
      • Sec. 3.11 Hyperbolic Functions: 9 + 43 + Lab#1
      • Sec. 6.1: Areas Between Curves: 3 + 9 + 29 + Lab#2 + worksheet#2
      • Sec. 6.2: Volumes (by slices, disks and washers): 11 + 34 + 49 + 63a + worksheet#3
      • Sec. 6.3: Volumes by Cylindrical Shells: 15 + 19 + lab#3 + worksheet#3
      • Sec. 6.4: Work: 7 + 13 + 17 + worksheet#3
      • Sec. 6.5: Average Value of a Function: 9 + 15 + 17
      • Sec. 7.1: Integration by Parts: 3 + 8 + 15 + 24 + worksheet#4
      • Sec. 7.2: Trigonometric Integrals: 2 + 10 + 23 + 41
      • Sec. 7.3: Trigonometric Substitution: 4 + 13 + 12 + 23 + 26
      • Sec. 7.4: Integration of Rational Functions by Partial Fractions: Lab#5
    • Cheat sheet: Formulas that we will be given to you in case they are needed (no need to memorize these, but you need to know how to use them!!!):
      • double/half angle formulas
      • angle summation formulas for sines and cosines
      • formulas converting products of sine/cosines into sums of sines/cosines
      • formulas involving integrals/derivatives of inverse trigonometric/hyperbolic functions
      • integrals of tan and sec
    • Past midterms (no solutions/keys will ever be posted/distributed. You are encouraged to ask instructor/TAs/SI/MLC any questions about this material).
      Note These are past midterms, but this semester we are doing Mini-tests so the material and length will be adjusted to only cover Secs. 3.11 + 6.1 + 6.2 + 6.3 + 6.4 + 6.5 + 7.1 + 7.2 + 7.3 + 7.4:
      MT#1 Fa'17 | MT#1 Sp'18 | MT#1 Fa'18 | MT#1 Sp'19 | MT#1 Fa'19 | MT#2 Fa'17 | MT#2 Sp'18 | MT#2 Fa'18 | MT#2 Sp'19 | MT#2 Fa'19
  • Mini-Test#2:
    • MiniTest2_must_know.pdf: This document contains all the Must-Know material for Mini-Test#2.
    • MT2_sample_problems_S20.pdf: collection of typical problems to give you an idea of what you might encouter in the midterm. [Disregard the problems on partial fractions as the were already covered in Mini-Test#2]
    • MT2_sample_problems_sols_scanned.pdf: solutions to most sample problems [Courtesy of TA Chris Bates].
    • Good collection of mixing problems from previous tests: mixing_problems.pdf (no solutions will be posted, if you need help solving these please talk to your TAs).
    • Please refer to Activity#08: link
    • Past midterms (no solutions/keys will ever be posted/distributed. You are encouraged to ask instructor/TAs/SI/MLC any questions about this material):
      Note These are past midterms, but this semester we are doing Mini-test so the material and length will be adjusted to only cover Secs. 7.8 + 8.1+8.2 + 9.1+9.2+9.3+9.4 :
      MT#2 Fa'17 | MT#2 Sp'18 | MT#2 Fa'18 | MT#2 Sp'19 | MT#2 Fa'19
    • There will be NO cheat sheet for this Mini-Test.
  • Mini-Test#3:
    • MiniTest3_must_know.pdf: This document contains all the Must-Know material for Mini-Test#3.
    • MT3-review.pdf: Nice review for past Mideterm#3 [Courtesy of Prof. Chavez-Ross] (it is missing to include linear Diff. Eqs. and remember that only Secs. 11.1-11.8 will be included).
    • Sequence_and_Series_Review_long.pdf: Nice/compact review of sequences and series (inc. all the necessary conditions for each series test and many examples) [Courtesy of TA Dartanyon].
    • SeriesTestsFlattened.pdf. Nice/compact summary of all series tests.
    • Mini-Test#3 MT3 sample problems: [ problems , answers , solutions ] (Note: disregard the last two problems [corresponding to Secs. 11.9 and 11.10])
    • Please refer to week#11's worksheet: link
    • Please refer to Activity#10: link
    • Past midterms (no solutions/keys will ever be posted/distributed. You are encouraged to ask instructor/TAs/SI/MLC any questions about this material):
      Note These are past midterms, but this semester we are doing Mini-test so the material and length will be adjusted to only cover Secs. 9.5 + 11.1-11.8 :
      MT#3 Fa'17 | MT#3 Sp'18 | MT#3 Fa'18 | MT#3 Sp'19 | MT#3 Fa'19
    • There will be NO cheat sheet for this Mini-Test.
  • Mini-Test#4:
    • MiniTest4_must_know.pdf: This document contains all the Must-Know material for Mini-Test#4.
    • Please refer to week#12's worksheet: link
    • Please refer to week#13's worksheet: link
    • Please refer to week#14's worksheet: link
    • Please refer to Activity#13: link
    • Please refer to DJ's review: link [we will NOT include calculus for polar curves].
    • Please refer to DJ's review from last semester: link [we will NOT include calculus for polar curves].
    • Past midterms (no solutions/keys will ever be posted/distributed. You are encouraged to ask instructor/TAs/SI/MLC any questions about this material):
      Note These are past midterms, but this semester we are doing Mini-test so the material and length will be adjusted to only cover Secs. 11.8-11.1 + 10.1-10.3 :
      MT#3 Fa'17 | MT#3 Sp'18 | MT#3 Fa'18 | MT#3 Sp'19 | MT#3 Fa'19
    • There will be NO cheat sheet for this Mini-Test.

  • FINAL:
    • The final inlcudes ALL material from Mini-Tests. Notes:
      • No Work (Sec 6.4).
      • No Average of Functions (Sec 6.5).
      • No mixing nor orthogonal curve problems.
      • Sec. 10.4 that was not in MiniTest#4 will be included in the final.
      • From the Chap 11 material (sequences and series), the final will only include the following topics:
        * Geometric series (inc. applications, word problems)
        * Interval/radius of convergence using the ratio test
        * Taylor/McLaurin series
    • FINAL_must_know_S21pdf: This document contains all the Must-Know material for FINAL.
    • Please refer to DJ's review for the final: link
    • Sample_Ex_Final_scan.pdf: Sample practice problems for final [Courtesy of Prof. Chavez-Ross].
    • Sample_Ex_Final_scan_more.pdf: More sample practice problems for final [Courtesy of Prof. Chavez-Ross].
    • week_final.pdf worksheet [ answers , solution key ]. [Courtesy of TAs Katie Yoo and Jay Bonthius].
    • As a good set of sample problems for the final, use the previous Mini-Tests as a guide.
      This semester's Mini-Tests (no solutions/keys will ever be posted/distributed. You are encouraged to ask instructor/TAs/SI/MLC any questions about this material):
      MiniTest#1 Sp'21 | MiniTest#2 Sp'21 | MiniTest#3 Sp'21 | MiniTest#4 Sp'21
    • Past finals will never, ever, be posted/distributed.
    • There will be NO cheat sheet for FINAL. As in Mini-Tets, any obscure formula that you need will be explicitely given to you if needed.