Bart the Bear

Here are a dozen problems, in "circuit" format, involving rates of change, both average and instantaneous. Problems include those using tables of values and functions, and rates of change computed over intervals with constant and with variable endpoints. In some problems, students are asked to take a limit, and interpret the value they obtain. None of these problems require (or should allow) taking a derivative.

Here are a dozen linearization problems in circuit format. The first few are simple tangent-line finding problems. These are followed by finding and using linearizations to make various approximations. Finally, differentials are used to solve problems involving the amount by which functions change when their inputs change by a small amount.

25 quizzes (and some extras!) that run from the beginning of Calculus I to its end. Everything in Calc I is covered in this package. Tried and true!

Here are a dozen related rates problems in circuit format. The problems use pre-Calculus math concepts, including the Pythagorean theorem, similar triangles, and various area and volume formulas. An answer key is also supplied (the last 6 pages).

Here are a dozen derivative problems, laid out in "circuit" format. These problems require use of the power rule, constant multiple rule, sum rule, product rule, quotient rule, and chain rule. Derivative rules for power, trig, inverse trig, log, and exponential functions are required. A nice challenge and/or review!

Here are a dozen optimization (a.k.a. Max/Min) problems in circuit format. The first few involve finding local maxes and mins. Next come problems finding maxes and mins on closed intervals. Finally come the story problems! These involve geometry and trigonometry, as well as some basic economics (but really basic). An answer key is included.

Here are a dozen derivative problems, laid out in "circuit" format. These problems require use of the power rule, constant multiple rule, sum rule, product rule, and quotient rule. The product and quotient rules are emphasized. Derivative rules for power and trig functions are required. There are a couple of tangent line problems. No problems require the chain rule, and there are no derivatives of log or exponential functions.

Here are a dozen derivative problems, laid out in "circuit" format. These problems require use of the power rule, constant multiple rule, and sum rule. Power rule problems include fractions with integer numerators and "power" denominators, as well as powers expressed in radical form. Other problems ask the student to sketch a graph of f', given the graph of f. Finally, there are several tangent line problems and velocity problems, of various difficulty. No problems require the product rule, quot

Here are a dozen limits, laid out in "circuit" format. These limits include limits involving infinity (both as "where is x going" and as the result), one-sided limits, trig limits, and some basic algebra. There are no limits requiring L'Hopital's rule.

Here are a dozen limits, laid out in "circuit" format. These limits involve many different functions, several require L'Hopital's Rule, and a few require rationalization.

Here are a dozen limits, laid out in "circuit" format. A few of the limits are calculated graphically, while the rest require basic algebra. The algebra required includes factoring quadratics, difference of squares, and factoring by grouping. There are no trig, log, or exponential function limits. There are no limits involving infinity. There are no limits requiring L'Hopital's rule.