General info Summer midterm

• The midterm will be on thursday, July 7th, during the first hour of class. The midterm will cover the first 5 lectures. There will be 4 equally weighted questions. We will have a review session during the tutorial time on Teusday 5 July. Any "problem specific formula" will be provided on the test. (But you should still have a good working knowledge of, e.g., basic integral formulas etc. which come up again and again.)

  General info Spring midterm

  • Solutions

    General info

    • The midterm will be on thursday, may 26th, during the first hour of class.
    • There will be four short answer questions, individual questions may have several parts.
    • Expect questions to have parts involving calculation and interpretation, eg. part a) find the derivative using whatever appropriate rules, part b) use the derivative to write the equation of the tangent line, locate maxima/minima, etc.
    • standard scientific calculators are permitted... no graphing calculators!
    • closed notes, some formulas you will be expected to remember (see below), other formulas will be provided as necessary.

    Material covered

    The midterm will cover all material up to (and including) lecture 7. The important ideas which may appear on the test are as follows:
    • properties and graphs of the basic families of functions: linear, powers, roots, reciprocals, exponentials, logarithms, trig functions
    • transformations of functions, eg. vertical/horizontal shifts, etc (remember specific terminology such as amplitude and phase when discussing trig functions)
    • inverse functions (emphasis on inverse trig functions)
    • compound interest problems, using exponentials to model continously compounded interest or radioactive decay (finding half-life)
    • finding average rates of change
    • calculating limits, be able to answer questions concerning continuity, left/right hand limits
    • the limit definition of the derivative (know how to use this definition to find the derivative of a power or polynomial)
    • basic differentiation rules including the rules for powers, exponentials, logarithms, trig functions
    • product, quotient and chain rules
    • how to find the derivative of inverse trig functions
    • equation for tangent lines/linear approximations
    • interpretation/application of the derivative to specific situations, eg. distance/velocity/acceleration, marginal costs/tax rates
    • Newton's method for finding approximate solutions of equations
    • implicit differentiation
    • related rate problems
    • critical points and inflection points
    • Analyzing/graphing functions based on finding first and second derivatives (using sign charts)
    • graphing different members of a family of functions
    • Taylor polynomials of 1st and 2nd degree
    • finding limits of indeterminate form using approximations or Hopitals rule
    • finding and classifying critical points as maxima/minima
    • first and second derivative tests
    • determining global extrema (compare critical points with endpoints)
    • optimization word problems

    Things to remember

    In addition to the specific ideas described above, you will be expected to remember a few simple formulas and ideas.
    • equation for a circle or ellipse
    • Pythagorean theorem
    • areas of basic shapes: rectangles, triangles, circles
    • volumes/surface areas of rectangular boxes and cylinders (formulas for spheres and cones will be provided if necessary)
    • the basic trig identity : sin²θ + cos²θ=1 (other trig identities will be provided)
    • distance = velocity x time
    More complicated physical formulas that might appear in optimization or related rates problems will be given to you, with a description of all variables/parameters/units (eg. ideal gas law)

    How to study

    • review the notes and in-class examples
    • work through as many practice problems as you can, consult the solutions only when necessary, make note of which concepts you struggle with, and discuss these with classmates or with me
    • speak to me during office hours
    • have a look at some of the old exams (see below), the format of our exam will be similar
    • during tuesday's class (may 24th), we will take some time for a review session

    Review session and office hours

    On tuesday, for an hour or so at the end of class we will have a review session. You can ask about any topics or practice problems we have covered, and I will work through solutions on the board. In particular, I wouldlike to do a few problems from lecture 7 (optimization) since this is the material that you will have the least time to study for.

    For the week of the midterm, office hours will be tuesday and wednesday, 2-4 pm in the math help center, (instead of wednesday and friday) so we can discuss any problems you may have before the test. If you are unable to come ateither of those times, you can contact me and make a separate appointment.

    Old midterms

    Here are some examples of midterms from last year. Our midterm will be of similar style (short answer questions). Be aware that these midterms were intended to be written in 50 minutes (and many students could finish in less than 40!)Our midterm is a full hour and will have four questions, so expect it to take more time than these practice tests.

    Sample 1	solutions
    Sample 2	solutions
    Sample 3	solutions
    Sample 4	solutions
    Sample 5	solutions
    Sample 6	solutions