Differentiation of  polynomials, cos, sin, exp, log functions. Product, quotient and chain rules.

rebelmaths

A random dataset given by a linear function with noise (gradient and y-intercept of the linear function are randomised as is distribution of x values).

Using the unit circle definition of sin, cos and tan, to calculate the exact value of trig functions evaluated at angles that depend on 0, 30, 45, 60 or 90 degrees.

Homework set.  Use integration to find the centroid of shapes bounded by functions.

Homework set.  Use integration to find the centroid of shapes bounded by functions.

Harder inequalities that involve terms like $\frac{1}{x}$ where multiplication by the denominator requires you to split into cases for positive or negative, or you multiply by the square of the denominator.

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

Use two points on a line graph to calculate the gradient and $y$-intercept and hence the equation of the straight line running through both points.

The answer box for the third part plots the function which allows the student to check their answer against the graph before submitting.

This particular example has a positive gradient.

 Students must derive the shear and bending moment functions for beam loaded with a parabolic distributed load described with a loading function.  Diagrams are given, but the students must derive the equations by integration.

This question uses a Geogebra applet to solve a linear program with two variables using the graphical method. It contains three steps:

1. Construct the feasible area (polygon) by adding the constraints one by one. The students can see what happens when the constraints are added.
2. Add the objective function, and the level set of the objective value is shown, as well as its (normalised) gradient.
3. Compute the optimal solution by moving the level set of the objective around.

Shear and bending moment diagram for a beam loaded with an arbitrary parabolic distributed load described with a loading function.  Integrate to find reactions and equations for shear and bending moment.

Match the graphs to the functions. No randomisation. Multiple choice.

Calculating the integral of a function of the form $ax^2 \cos(bx)$ using integration by parts.

Calculating the integral of a function of the form $\frac{nx^{n-1}}{x^n+a}$ using integration by substitution.

Calculating the integral of a function of the form $\frac{c}{(x+a)(x+b)}$ using partial fractions.

Calculating the integral of a function of the form $a_1x^{b_1}+a_2x^{b_2}+a_3x^{b_3}$ using a table of integrals. 

Calculating the derivative of a function of the form $\frac{ax^n}{bx+c}$ using the quotient rule.

Calculating the derivative a function of the form $ax^n \sin(bx)$ using the product rule.

Calculating the derivative of a function of the form $\sin(ax^m+bx^n)$ using the chain rule.

Find the derivative of a function of the form $y=a \tan(bx+c)$ using a table of derivatives.

Find the derivative of a function of the form $y=a \sin(bx+c)$ using a table of derivatives.

Find the derivative of a function of the form $y=a \cos(bx+c)$ using a table of derivatives.

Calculating the derivative of an exponential function of the form $ae^{bx}$, using a table of derivatives.

Calculating the derivative of a function of the form $a \ln(bx)$ using a table of derivatives.

Find the derivative of a function of the form $y=ax^b$ using a table of derivatives.

Finding composite functions of 2 linear functions.

Finding the inverse of a function of the form $f(x)=\frac{mx+c}{x+a},\,x\neq-a$.

Determining the range of a function of the form $f = m|x| + a$.

Evaluating a linear function for a given value of $x$.