Year 12 Homework- Due wc 3/10/16

C1  Homework

Year 12- 

Your homework due next week can be downloaded using the link above. We encourage you to write your answers on a separate piece of paper as this will give you the space required to answer the question. 

Below are a selection of videos which may help! 

Year 12- Completing the Square

From the first test, completing the square was identified as an area to work on. If you are struggling, watch these videos and have a go at the questions. #

Exam questions 

Completing the square:

Using completing the square 

Proof By Induction

Proof by Induction is the domino run of the Further Maths world:

If one domino falls, and the next one definitely falls, they all will.

A nice introductory video from Khan Academy



Once you have looked through this you can attempt the questions on this sheet

Worksheet from Mr Barton's A-Level Maths site

Another worked example can be found on our Instagram feed:

Proof by Induction example for FP1

A photo posted by King Ed VII (@makerevision) on May 12, 2016 at 1:45am PDT

Trigonometry - Sine and Cosine Rule

A short video on historical use of Trigonometry in ancient Indian astronomical observatories...



When we aren't dealing with right angle triangles then the Sine Rule and Cosine Rule become very important:

For the Sine Rule we are dealing with a situation involving two sides and two angles (one of which will be unknown), for the Cosine Rule you need 3 sides and one angle (again one of which is unknown).

Using the Quadratic Formula

Whenever you're faced with a quadratic equation you have choice:

• Plot it and find the intercepts
• Factorise and solve (x+...)(x+...) etc. Each bracket =0 etc
• Complete the square and rearrange (see these older posts)
• Use the quadratic formula:

(More can be seen about the quadratic formula in this post)

You will have your own order of preference for the above methods, but one thing you can be certain of is that if there are real solutions, the formula will find them (factorising may not!).

Solving Trigonometric Equations

Let's take a look at a typical Core 2 question on solving trignomentric equations.

This is part (b), where part (a) asks you to show that the equation can be rewritten as

(1 - 5 cos 2x)( sin 2x) = 0.

A few exam tips when answering these:

1. Which trig identity should I use to simplify the equation? Is it a quadratic (using sine squared or cosine squared) or not?

2. Has the equation been factorised already? Can I see multiple solutions? Remember that if you square root, you need to use a positive and negative root.

3. Remember to find the range for 2x, or whichever function of x you find by removing the trig function.

4. Use a quick sketch of a trigonometric graph to help you remember how many solutions are in this range.

You can find worked solutions to this question, here for part a and here for part b.

There's plenty more exam questions where that came from - take a look at exam solutions, which can link you straight to this type of question for each past paper.

Completing the Square

I've been working with a few students today on Completing the Square. Here's a quick video reminder for those that need it. 

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