Characterise the cosh function as continuous, many-to-one, even, and find the limit as x approaches 1. Part of HELM book 2.4.3.

Homework Set.  Three problems to brush up on trig skills.  Right triangles and sine and cosine law.

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

rebelmaths

testing sin, cos, tan of  random(0,90,120,135,150,180,210,225,240,270,300,315,330) degrees but in radians

testing sin, cos, tan of angles that are negative or greater than 2pi radians that result in nice exact values. 

exact value of testing sin, cos, tan of angles that are negative or greater than 360 degrees that result in nice exact values. 

multiple choice testing sin, cos, tan of  random(pi/6, pi/4, pi/3) radians

exact value of sin, cos, tan of  random(0,90,120,135,150,180,210,225,240,270,300,315,330) degrees

multiple choice testing sin, cos, tan of  random(30, 45, 60) degrees

Solve a random oblique triangle for sides and angles.

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.

Used for LANTITE preparation (Australia). NA = Number & Algebra strand. Students calculate the cost of the halogen globes given electricity cost, number of globes, number of years, replacement cost and lifespan of globes. Some of these variables are randomly selected. There are more than 10 different versions of this question.

Draws a triangle based on 3 side lengths.

Calculate the change from a note given two costs.

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

Rewriting a trigonometric expression of the form $A\cos(\theta)\pm B\sin(\theta)$ to either $R\sin(\theta+\alpha)$ or $R\cos(\theta+\alpha)$ by calculating $R$ and $\alpha$. 

Rewriting a trigonometric expression of the form $A\sin(\theta)-B\cos(\theta)$ to $R\sin(\theta-\alpha)$ by calculating $R$ and $\alpha$.

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

Using the various versions of $\cos{2x}$ identity to integrate $\sin^2{x}$ and $\cos^2{x}$.

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

Match the relevant graph (sin, cos, tan) with its equation. 

Multiple choice. Students need to select the correct simplification for a given expression. 

This question has four versions. Skills required are: using Pythagorean identities, converting to sine or cosine. Some also require fraction division.

MCQ to calculate selling price when given cost price and VAT rate.

MCQ - Pick the correct cost price when given the selling price and rate of VAT.

A quick knowledge and understanding check of:

1) Work done concept.

2) Work done formulae: W = Fx and W = Fxcos(y).

3) Equivalent units of work.

Here you need to choose which trigonometric function is the red dashed side divided by the solid green side. Your goal is to get twenty correct answers quickly. Incorrect answers show a highlight of the correct answer to select to continue.  The timer starts as soon as you choose your first answer and continues until you get 20 correct.  Select save answer after your results show in the applet.

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Calculate the heat losses from a model building based on the U values, dimensions and other parameters specified. In addition calculate the annual running costs and payback period for improvements to the building Fabric.

The student has to write the general solution of a 2nd order PDE. They can choose the names of their arbitrary functions of $x$ and $y$.

The marking algorithm finds the names of the functions of $x$ and $y$ in the student's answer, and replaces them with $\sin(x)$ and $\cos(y)$ (these could be changed) so that the expression can be evaluated.