More work on differentiation with trigonometric functions

Differentiation of trigonometric functions

Given the derivatives of a cubic function at a point, find the value of the function at another point.

Given a set of curves on axes, generated from a function and its first two derivatives, identify which curve corresponds to which derivative.

Given an equation or a worded formula determine if it is a function or not

A random graph is drawn and students are asked whether it represents a function or not.

Given a randomised rational function select the possible ways of writing the domain of the function.

Given a randomised log function select the possible ways of writing the domain of the function.

Given a randomised square root function select the possible ways of writing the domain of the function.

Multiple choice questions. Given randomised trig functions select the possible ways of writing the domain of the function.

Multiple choice questions. Given randomised trig functions select the possible ways of writing the domain of the function.

Find the inverse of a composite function by finding the inverses of two functions and then the composite of these; and by finding the composite of two functions then finding the inverse. The question then concludes by asking students to compare their two answers and verify they're equivalent.

Inequality involving a single absolute value, question solution uses the piecewise nature of the absolute value function.

Unit circle definition of sin, cos, tan using degrees

Identifying some of the basic properties (intercepts, asymptotes, quadrants) of a rational function (quadratic over linear)

poles of a transfer function

Students seem to struggle with Sigma notation, this is about the easiest question possible for sigma notation.

Differentiate the function $f(x)=(a + b x)^m  e ^ {n x}$ using the product and chain rule. Find $g(x)$ such that $f^{\prime}(x)= (a + b x)^{m-1}  e ^ {n x}g(x)$. Non-calculator. Advice is given.

Three graphs are given with areas underneath them shaded. The student is asked to calculate their areas, using integration.  Q1 has a polynomial. Q2 has exponentials and fractional functions. Q3 requires solving a trig equation and integration by parts.

Just showing how to use the stdev function from the stats extension to calculate the standard deviation of a list of numbers.

rebelmaths

Introduces students to the floor and ceiling functions

Dealing with functions in Numbas.

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Uses JSXGraph to generate a plot for a cubic, with given critical points, along with three other incorrect graphs with modified properties. JSXGraph code is commented.

A graph of an (invertible) cubic is given. The question is to determine values of $f$ from graph.

Finding probabilities from a survey giving a table of data on the alcohol consumption of males. This can be easily adapted to data from other types of surveys.

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A graphical approach to aiding students in writing down a formal proof of discontinuity of a function at a given point.

Uses JSXgraph to sketch the graphs and involves some interaction/experimentation by students in finding appropriate intervals.