MAT 141 Exams

141-Placement test: tex file, ps file, dvi file, pdf file. 1.: they are both even. 2.: x=3.

• Old homework questions
• Unassigned homework questions
• Questions to guide your review (p76, p141-142, p232-233 up to question 16)
• Practice exercises (p77-80, p142-143; do not do the ones labeled ``T"; the practice exercises for Chapter 2, p233-238, blend the material of Chapter 2 including the sections we have not covered yet: just do the exercises from sections 2.1, 2.2, 2.3.

  MIDTERM 1 (with solutions) (Fall 2002)

  Averages: REC 01: 101.6/200; REC 02: 115.52/200.

• Old homework questions
• Unassigned homework questions
• Questions to guide your review (p232-233 questions 17-31) (p325 except questions 9,15,16,20).
• Practice exercises (p233-240, p326-332; do not do the ones labeled ``T"; do not do the ones for sections 3.4 (autonomous differential equations and 3.7 (Newton's method).
• The following is a un-official list of concepts and problems that you should be sure you understand (the textbook is the precise guideline): chain rule (several links), parametrized curves, implicit differentiation (tangents and normals), power rule, related rates problems, derivatives of inverse functions (especially how to find their derivatives at given points knowing something about the function), derivatives of exponential and logarithms, problems relating to how to find tangent lines, the extreme value theorem, extreme values, critical points, finding extreme values on intervals, Rolle's theorem, the mean value theorem, zero derivative implies constant, functions with same derivatives, motion problems, how to graph (increasing, decreasing, relevant limits, asymptotes, concavity, local extrema, global extrema...), relation between the graph of f and the properties of f' and f'', optimization, linearization, using linearizations to approximate values of functions near ``convenient points,"differentials, errors in approximating. When you learn a theorem be sure to understand the hypotheses and how they are used; find counterexamples to the statement of the theorem when one or more of the hypotheses are not true (see the textbook, for example, Rolle's theorem).

MIDTERM 2 (with solutions) (Fall 2002)

Averages: REC 01: 143/200; REC 02: 135.5/200.

• Old homework questions
• Unassigned homework questions
• Questions to guide your review (p407, p483, 1, 2, 3 ,4 , 5).
• Practice exercises (p408 up to n. 82, p484 up to n. 24).
• The following is a un-official list of concepts and problems that you should be sure you understand (the textbook is the precise guideline): antiderivatives, indefinite integrals, formulas (including special trig functions), intial value problems (that is solve a differential equation like dy/dx=f(x) with y(a)=b), motion problems, the substitution rule for indefinite integrals, sigma notation, Riemann sums, the definite integral, integrals of positive functions as areas, average values, properties of definite and indefinite integrals, the mean value theorem, the fundamental theorem of calculus I and II, variable extremes of integration, substitution for definite integrals, area between curves, trapezoidal and Simpson's rules with error estimates, volumes of solids: slicing, revolution about an axis, circular and washer cross sections, cylindrical shells, length of curves, arc length and short differential formula, parametric formula.
• When you learn a theorem be sure to understand the hypotheses and how they are used; find counterexamples to the statement of the theorem when one or more of the hypotheses are not true (see Rolle's theorem, for example).
• You may be asked to state and give examples or counterexamples to the theorems we have learned in class. A partial list is as follows (the book is your precise guideline) the sandwich theorem, the intermediate value theorem, differentiable implies continuous (*), derivative of inverse functions, extreme value theorem for continuous functions, local extrem values, Rolle's theorem (*) , the mean value theorem (*), the mean value theorem for definite integrals (*), the fundamental theorem of calculus I (*) and II (*). You may be asked to give proofs of the ones labelled by (*).

  FINAL (with solutions) (Fall 2002)

  The final median was around 200. Here is the exam curve: A 310+ (7 students) B 230+ (11) C 120+ (16) D 80+ (2) F 0+ (5)

  The curve for the whole course: A 850 (5) A- 810 (5) B+ 780 (3) B 680 (7) B- 640 (3) C+ 600 (3) C 510 (4) C- 490 (2) D+ 460 (2) D 400 (3) F 0 (7)

  
  
  

These samples are to help you prepare your tests. Consider them as extra homework. The actual test may be very different.