This year you can even use the Desmos API …
A new slideshow has been added to the page demonstrating WolframAlpha syntax. WolframAlpha can be very useful for checking for example normal probabilities. Each query as you will see in the slides is illustrated with a diagram. It is always useful to sketch a diagram when solving any normal distribution problems.
Explore transformations of graphs with the Desmos Graphing Calculator.
(See also Learning to use the Desmos Graphing Calculator)
Try the examples here and experiment with the outstanding (free) Desmos graphing calculator.
The way to improve your mathematical skills is to do lots of questions (then do some more!) You need to apply what you know and just reading your notes will not help you do that. Worked examples can be very helpful – particularly if you cover up the solution and try answering the question yourself first.
If you are looking for questions the following sites provide many for you.
Maths Centre (age 16+)
An extensive collection of very clear notes and other resources are available from the mathcentre. There are many very clearly worked examples, also exercises (with answers). Check the resource types, choosing Practice & Revision for example would lead you to this Calculus Refresher (under the Chain rule) which is a whole workbook of mixed calculus examples. mathtutor provides mathcentre resources conveniently structured as a course.
Just the Maths (age 18+)
Just the Maths by Tony Hobson is another extensive collection of notes which include numerous worked examples and also exercises to try (with answers). These notes are very useful for students in their last years at school and at university.
The Maths Teacher (age 11-17)
David Smith’s site, The Maths Teacher has an extensive collection of videos to help you study Mathematics. GCSE (age 14-16, though many of these resources would be helpful for younger students also) and A-Level (age 16-18) lessons are available. For each topic not only is a video available but also a transcript and exercises with solutions. This makes the site ideal for revision – you have the choice of perhaps just trying the exercises or if you feel you need more help you can watch the video – whatever is right for you.
Diagnostic Questions (Craig Barton & Simon Woodhead) (age 11 – 16+)
A totally brilliant site – thousands of multiple choice questions with your misconceptions anticipated. Try some diagnostic questions (all multiple choice) to check your understanding.
BBC Sites (ages 5 to 18)
All the BBC sites have quizzes and/or tests for you to try as well as notes and examples.
BBC Skillswise although aimed at adults, this site has information on basic Mathematics (and English) skills useful for any age.
BBC Higher Maths (age 17+)
Scroll down this page to see all the material available for students of all ages. The student texts include worked examples in every section. The texts also have exercises which are usually password protected. (Schools can obtain the password from CIMT). Note in particular the Interactive Material (examples with online checking of answers for Year 7 | Year 8 | Year 9 (have a look at the topics here which may be useful for slightly older students also).
If you choose the GCSE course material for example and scroll down the page you will see all the pupil textbook chapters.
Trinity School have very helpful Mathematics resources – many examples for you to try (answers included)
If you are trying any exercises you can obviously check the answers given in the notes; remember that you can also check your answers with WolframAlpha. You could make up questions of your own and check the answers on WolframAlpha, for example suppose you want to make sure you can multiply out brackets – make up your own question (writing questions is actually a good way to check your understanding), for example multiply out (x+3)(x+2), write your answer, then check it on WolframAlpha. Perhaps some calculus? Differentiate sinxcosx wrt x.
On the subject of WolframAlpha, there are several slideshows on the WolframAlpha page on this blog to help you get used to the syntax.
An updated version of the 11 commandments, which seems appropriate at this time of year!
If you are feeling a little unsure on identifying the equation of a straight line then use this Desmos graph and experiment by changing the gradient, intercept or points marked on the line. The image above shows the line y=2x+1. We can see that the intercept is 1 (where the line crosses the y axis) and the gradient is 2. Looking at the graph we can see that the gradient is positive and you can verify that the gradient is 2 by dividing the difference between the y coordinates (6 in this image) by the difference in the x coordinates (3 in this image). Try moving the points, you will see that this ratio remains constant.
Compare the second image. We can see that the intercept is 1. Looking at the slope, the gradient is positive. The gradient is given by 2÷4 = 0.5. So the equation of the line is y = 0.5x + 1.
In the third example; looking at the slope of the line we can see it is negative. The gradient is given by 6÷2 which is 3 and the line crosses the y axis at 2 giving the equation of the line as y = ─3x + 2
Since writing this post Desmos have taken the page and created a superior version!
Direct link to TED video
To quote Angela Lee Duckworth:
“Grit is passion and perseverance for very long-term goals. Grit is having stamina. Grit is sticking with your future, day in, day out, not just for the week, not just for the month, but for years, and working really hard to make that future a reality. Grit is living life like it’s a marathon, not a sprint.”
The following resources will help you practise solving equations.
subtangent.com – Linear Equation Calculator
Choose the type of equation you require then the sequence of operations required to solve the equation.
Select Do it after each operation, for example -32 Do it were the keys selected to start the above problem.
The slideshow below shows how to use the calculator to solve equations where the unknown is on both sides.
The next sites work in a similar way to the subtangent resource.
There are 4 levels to choose from: the level 1 equations are of the type ax = b,
level 2, x±c = d, level 3, ex±f = g and level 4, hx±i = hx±j = k.
Choose the series of operations you require to solve the equation selecting apply at each stage to see the result of your chosen operation.
Choose numbers to add and subtract integers and letters to add and subtract variables.
Remember you can use WolframAlpha to check your solution to any equation, see for example this link which checks the equation 2x+7=11.
To learn more about using WolframAlpha to check your work see the slideshows here.