List of public pages created with Protopage

# Main Page

## Plain sticky notes

I started this website at the beginning of Year Seven because I had to for homework. The maths work from Year Seven can be accessed at the top via the LIGHT BLUE tabs. 2014 UPDATE: This website may be added to frequently now, due to the new Take-Away Homework scheme. Take-Away Homework tabs will be made accessible from the RED tabs at the top of the page.

### About the creator the this website - Kate Whetton

14 years old. Year 9 schoolkid at HTC. Dreamer. Unsure whether to like maths or hate it. In the top set but I don't think I will be for much longer. Dislike the theory 'set one students are better at maths'. Love writing - dream of being an author... I don't take responsibility for anyone who has come to this page looking for maths helpers who then gets answers wrong. You shouldn't have followed my advice... -_-

## Calendars

### Calendar

• Wed October 3 - Join eco club
• Sun October 7 - Due date for this website Science P2i due
• Sat October 27 - Family birthday
• Thu October 25 - Start of half-term! :)
• Sat October 20 - Due date for this
• Mon November 5 - bonfire night

# Algebra

## Plain sticky notes

### Einsteins famous equation

E=MC2 Einstein's famous equation meaning energy equals mass times the speed of light squared and that the mass and the energy are interchangable.

### How to simplify equations

Algebra is where lazy mathemeticians use letters instead of numbers. Also, this is where mathemeticians can simplify maths. For example: 2a+5a+1b+4b can be simplified as 7a+5b and 7B is basically 7 x B

### How to solve very long algebra sequences

When solving an algebraic problem, remember BIDMAS BRACKETS INDICES DIVISION MULTIPLICATION ADDITION SUBTRACTION If all else fails, look at a website.

### Applying the box method

Arrange your box as neccessary. Then, put each of your parts into a box. Then, add it all together.

# Indices and roots

## Plain sticky notes

### What are indices?

Indices are a posh word for powers. For example 54 (not fifty-four) is five to the power of 4. Indices are also simplified sums, for example: Sum: 3x3x3x3=81 Indice: 34 (not thirty-four) three to the power of four = 81

### What are roots?

Roots are short for square-roots. For example, the square root of 16 is 4, because 4 squared is 16.

# Fun maths

## Plain sticky notes

### I think...

Maths shouldn't be all doom and gloom.

### FAIR SUDOKU WARNING

Warning. Even the easy ones are very very hard!!!

# Changing the Subject of a Formula

## Plain sticky notes

### Rearranging Equations and Changing the Subject

This may sound VERY COMPLICATED and trust me, it is. But not if you ACTUALLY know what you're doing! Browse around this page for some words of wisdom (helpful hints) and some practice questions that tell you how to go about solving such questions. And, before you ask, no, I do not really understand this.

### Helpful Hint #1 - Letters to Numbers

If all the letters in an algebraic equation are messing with your mind, pretend they are numbers. Then, at the end, change them back to letters. This may also help you decide whether to add or subtract, divide or multiply. Changing the letters to small numbers will help you as it will make the equation look a lot more simple than it really is.

### Introduction to Practice Questions

Here are some practice questions. I have gone through how to do them for two of the questions, with explanations, and the rest are just to do.

### Question 2:

The question is: Z = Y - XW. You need to make W the subject of the formula this time. Similar to Question 1, you should +XW to both sides of the equation. It would look like this: Z + XW = Y But Y is the current subject. You want W, and you want W on it's own. But before that, you should subtract Y from both sides of the equation so that Y stops being on it's own. Now the formula should look like this: XW = Y - Z Now X multiplied by W is the subject of the formula. Now it's time to get W on it's own. Similar to Question 1, the last step is to divide both sides of the equation by X. Your answer should be this W = Y - Z --------- X

### Others

K = A - TE Make E the subject. M = A - TH Make H the subject. H = O - ME Make E the subject. W = O - RK Make K the subject.

### Question 1:

The question is: A = B - CD. You need to make D the subject of the formula. As you want to make D the subject and it is multiplied to C, you should +CD to BOTH SIDES of the equation. It would look like this: A + CD = B Now B is the subject of the formula. But you want D. So the next step is to subract B from BOTH SIDES of the equation. The formula now looks like this: CD = B - A. Now CD is the subject. But you want just D on it's own. Furthermore, the last step is to DIVIDE both sides of the equation by C. Your answer should be this: D = B - A ------- C

### Helpful Hint #2 - The Sum Looks Hard :-(

Don't be put of by a sum question that looks like this 44563ghie + (6k/11a) = f(d-m). NOW MAKE 'M' THE SUBJECT! Yes - it looks impossible, and I wouldn't know where to start, but if you know the correct method or formula, there's no reason why you shouldn't be able to do it.

### Helpful Hint #3 - Persevere

There's no point just 'giving up' on algebra without at least trying. If you fail - so what - you'll learn from it. Every mistake is a lesson, and every lesson makes you better. Understanding algebra and algebraic equations is like understanding a foreign language. At a glance, you wouldn't know what anything means - it's only when you really look into it that you begin to understand. Similar to a foreign language, you have to learn new symbols (like brackets), new terminology (like 'equation') and new grammar (like writing equations out properly).

Ensure that the method you intend to use is the right one. Don't forget that with changing the subject, the inverse operation is usually the best way to go. Also, make sure you do the same operation to BOTH SIDES of the equation to keep it balanced.

# Sequences

## Plain sticky notes

### Sequences As A Topic

On this page I am going to cover everything I have learnt about sequences in this topic. This includes working out the terms of a sequence from easy rules and nth terms, as well as figuring out the nth term of a sequence. I will also cover quadratic sequences.

### Using The Nth Term

A formula with 'n' in it which gives you every term in a sequence when you put different values for 'n' in.

### Basic Example Of The Nth Term

The example of an nth term could be something like this: 2n+1 To start with, you want to find the first term (or number) in the sequence. So you want to substitute 1 into the formula for the value of 'n'. So if 'n' is 1, you need to times 1 by 2 for 2n. 1x2=2. You then add on the 1. 2+1=3 - so the first term of the sequence is 3. You then substitute 2 as the value for 'n'. 2x2=4 4+1=5 so the next term of the sequence is 5. And so on and so forth. The first six terms of the 2n+1 sequence are: 3,5,7,9,11,13.

### Number Sequences

A number sequence is a set of numbers in a given order. They follow a pattern. Each number in the sequence is called a term.

### Famous Number Sequences

1. The square numbers: 1,4,9,16,25,36... etc 2. The cube numbers: 1,8,27,64,125,216... etc 3. The triangle numbers: 1,3,6,10,15,21... etc 4. The Fibonacci sequence: 1,1,2,3,5,8...etc

### Other Examples Of The Nth Term

Here are some nth term formulas and the first six terms of their sequences. 3n-1 ~ 2,5,8,11,14,17 2n-2 ~ 0,2,4,6,8,10 4n-1 ~3,7,11,15,19,23 1n+5 ~ 6,7,8,9,10,11 2n+3 ~ 5,7,9,11,13,15 3n-2 ~ 1,4,7,10,13,16 5n-4 ~ 1,6,11,16,21,26

Possibly the hardest type of sequence on this page, quadratic sequences are complicated although they are a method of calculating the nth term for a sequence. (An alternative would be to times the difference between the terms by 'n' and then adding or subtracting whatever comes before the first term).

The first step is to figure out what the actual sequence is. This example sequence will be: 3,6,11,18,27... The next step is to establish the differences between these numbers: 3 6 11 18 27 3 5 7 9 2 2 2 I have also done the next step, which is to find the differences between the differences. Next, you need to half the difference. Half of 2 is 1, which means the first part of the formula is 1n2 (squared). Now you need to find the second part of the formula for this sequence. I suggest you do this by making a table. Sequence 3 6 11 18 27 n2 1 4 9 16 25 Difference 2 2 2 2 2 In this table, I have put the original sequence, the values for n2, and the differences between these values. They are all 2. As the terms in the sequence increase each time, the second part of the formula is +2. So the whole formula, and the answer, is n2+2 (n squared + 2).

### An Alternative Method/Formula

Another way to calculate the nth term of a sequence is to follow this long, complicated formula: a+d(n-1)+0.5(n-1)(n-2)c. A= the value of the first term. D= the first difference. c= the change between one difference and the next. This formula is complicated and difficult to memorise, so I would advise against using it.

### The 7 Steps For (Quadratic) Sequence Success

1. Find the differences between the terms in the sequence. 2. Find the second differences (the differences between the differences). 3. Half of the second difference put in front on n2 (n squared). 4. Work out the second part of the formula using a table. 5. Subtract the values to find the difference. 6. If these differences are consistent, it's easy. If not, find the nth term of that sequence of differences. 7. Join up to find a final answer. Check the formula on a couple of terms to ensure your answer is correct.

## Photos 