1.1 Introductory Differential Calculus

In this activity, the average rate of change between two points is defined and then used as a concept connecting ideas of slope, difference quotients, and approximations of instantaneous rate of change.

1.1 Introductory Differential Calculus

Students learn how to find and label extrema using first and second derivatives, be able to inspect a graph and determine which extrema the function has, and be able to use trace, fMin, and fMax to verify the computed answers and find critical values for parametric functions.

In this activity, students observe the derivative as an indicator of increasing/decreasing function behavior. They also see that the derivative is an indicator of local maxima/ minima function behavior. Students learn to associate the graph of a function with its derivative.

1.4 Trigonometric Functions

Students discover the relationship between the trigonometric functions sine, cosine, and tangent and the side length ratios of a right triangle.

1.4 Trigonometric Functions

Students perform trigonometric proofs and verifying each proof through graphing.

1.4 Trigonometric Functions

Students will verify, prove, and explore trigonometric identities symbolically, numerically, and graphically.

In this activity, students calculate Riemann sums. They demonstrate when the Riemann sums will over-approximate a definite integral. They also observe the convergence of Riemann sums as the number of subintervals get larger.

In this activity, students will explore approximating the area under a curve using left endpoint, right endpoint, and midpoint Riemann sums.

In this activity, students explore the connection between an accumulation function, one defined by a definite integral, and the integrand. They also discover that the derivative of the accumulator is the integrand.

Students calculate percentiles, z-scores, and probabilities using normal distributions.

Students learn about each of the four types of random sampling methods and use the randInt command to find each kind of sample from a given population.

Students discover the Central Limit Theorem by simulating rolls of two, four, and seven number cubes via the random number generator.

Suppose two points are randomly placed inside a 1cm x 1cm square, on average, how far apart would you expect the points to be? A simulation is set up to help answer the question. Multiple samples can easily be generated using user defined sizes. The mean of each sample is automatically recorded and graphed to form a sampling distribution. Students gain an understanding of the relationship between sample size and the standard deviation of the corresponding sampling distribution.