Maths+for+Fun

__**Websites/Videos**__ Title: I am a Parallelogram! Resource Type: Video cum Song URL: [] Reasons for Recommendation: How many video cum song that allows you to learn mathematics have you ever seen? This is just one of the exceptions, with geometry coming up as the next chapter in our Term 3 syllabus; it will be good to revise your skills of the parallelogram through a fun and enriching way, but most importantly, through music. Besides, it does mention the main properties of a parallelogram, such as the parallel sides and the angles inside the figure. Thus, mathematics can be learnt through many ways, not only videos but also songs.
 * __Maths for Fun__**

Title: Polygons Resource Type: Video cum Song URL: [] Reason for Recommendation: Similar to the previous entry, it is a fun and enriching way to learn the different polygons that have different sides. Most importantly, it allows you to remember the different names of the varying polygons which have different number of sides. However, there are some limitations. What has appeared here is just the names and shows the figure of the polygon only. It does not show anything else, I would have thought that the angles inside the polygons could have been showed. Lastly, there should have been more polygons such as to make it more challenging.

Title: Trigonometric Identities Resource Type: Video Lesson URL: [] Reason for Recommendation: This will be a good video for a recap on trigonometry, especially towards the end of year examinations, where most of us will forget the trigonometric functions. Besides, it will also be a good tool for those that are unable to figure out some of the shortcut equations but this video explains how the equation is achieved through mathematical methods. However, there are some limitations, there could have been more content such as reciprocals and move on to the equations for reciprocals would make it a good video.

Title: Mathematical Figures Resource Type: Website URL: [] Reason for Recommendation: This website can be seen as an extension to the video recommended earlier because this website has highlighted much more important points, such as the properties of the figures and the angles in every figure. Besides, they provide illustrations of different figures and also provide us with formulas that we have learnt before such that we are able to recap. Besides, this website is not only about polygons but also highlights other figures such as parallelograms and the different types of triangles. However, they could have improved by using the formulas they provided to use in the different examples.

Title: Trigonometry Resource Type: Website URL: [] Reason for Recommendation: This website will serve as a good platform for thorough revision, besides, it will also be beneficial to those who are looking forward to more advanced trigonometry. This website has given us multiple links to pages where information is provided and tutorials are even given to those. Most importantly, there are questions available for students, followed by the answers, such as to test if they had fully understood that particular section of trigonometry. Besides the functions, different angles and inverse functions, it has also included unit circle which has been explored through the use of graphs.

Title: Visual Calculus Resource Type: Website URL: [] Reason for Recommendation: This is probably one of the most in-depth websites that I have ever seen. It seems like a lesson package to me on how to learn calculus, which will only be learnt in Secondary 4. Those who would like to go ahead first should visit this website. It has given us many tutorials and even revises information that is needed when doing calculus. It has the 2 most important aspects, derivatives and integration. Besides, they have also mentioned sequences and series & limit and continuity.

__**Explorative Activities**__

Q1.) If n is a natural number, show that for all values on b, (n^3 + 11n) is divisible by 6.

Substitute n with a + 1. (a + 1)^3 + 11 (a + 1) = (a+1) (a^2+2a+1) + 11a + 11 = a^3 + 2a^2 + a + a^2 + 2a + 1 + 11a + 11 =a^3 + 3a^2 + 14a + 12 (a^3 + 3a^2 + 14a + 12) – (a^3 + 11a) = 3a^2 + 3a + 12 If a is an even number, odd x even = even, so a^2 is even. 3a^2 is even, 3a is even and 12 is even. If a is an odd number, a^2 is odd. 3a^2 is odd and 3a is odd. Thus, odd + odd + even = even

Q2.) If x + y =1, find the value of x^3 + 3xy + y^3.

x^3 + 3xy + y^3 = x^3 + y^3 + 3xy = (x + y) (x^2 – xy + y^2) + 3xy =x^2 – xy + y^2 + 3xy = x^2 + 2xy + y^2 = (x + y) ^2 = 1

Q3.) Given that x + 1/y = 1, y + 1/z = 1, find the value of xyz.

xy/y + 1/y = 1 yz/z + 1/z = 1 xy + 1/y = 1 xy + 1 = y xy = y – 1 y + 1/z = 1 yz/z + 1/z = 1 yz + 1/z = 1 yz + 1 = z yz – z = -1 xyz = z( y – 1) =yz – z = -1