calculations guide - financial planning

8/11/2019 Calculations Guide - Financial Planning

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The Chartered Insurance Institute 2011

Calculations:a basic help guide


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Calculations: a basic help guide

The Chartered Insurance Institute 2011 2

Contents

1. Introduct ion 3

2. Glossary of common terms 3

3. Golden rules for calculation 4

4. Income Tax 6A - Grossing up different types of income received (for example: dividends /interest)Example question 4A1: DividendsExample question 4A2: Interest

B Percentages 8Example question 4B1: Basic percentage calculationExample question 4B2: Higher rate tax calculations on (i) dividends and(ii) interest

C - Chargeable gains within onshore insurance bonds 9Example question 4C1: Basic Rate Tax payerExample question 4C2: Basic Rate Tax payer close to higher rate thresholdExample question 4C3: To calculate any tax payable on top slicingExample question 4C4: Higher Rate Tax payer

D - Age allowances 12Example question 4D1: Basic OOA calculation all allowance lostExample question 4D2: Some allowance lost

5. CGT 13A - Capital gains tax calculationsExample question 5A1: CGT at basic rateExample question 5A2: CGT at higher rate

6. IHT 14A - Inheritance tax calculations

Example question 6A1: IHT after NRB deductionExample question 6A2: Inherited NRB from deceased spouse

7. Other 16A - Future & present valuesExample question 7A1: Calculating the future value of an investmentExample question 7A2: Calculating an annual rate of return

8. Links to some useful free web resources 18


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1. Introduction

The ability to perform calculations is a requisite skill of any financial planner. Questionsrequiring you to work through a calculation correctly appear regularly in examinations, andso you will find many types of calculation exercises in the CII study texts. However, theseexercises assume you already have a basic knowledge of how calculations work. If youdont, or if your memory could do with refreshing, you may struggle to cope.

This help guide is intended to cover the basics and, although not covering every calculationthat could be tested, it should give you some extra help with the particular calculations thatstudents most often find challenging.

2. Glossary of common terms

Glossary of some common terms, formulae and symbols

/ This means divided by. So 10 / 2 is 10 divided by 2, i.e. 5

= This means Equals, which means the same as. Two sides of anequation can contain different formulae which, once worked out, equalthe same number. There are several examples of equations thatfollow.

10 = 52

The line between the two figures means divided by.So 10 divided by 2 = (is the same as) 5

10 (12 4) = 80 The full calculation would be read aloud as:Twelve minus four (which is 8) times by 10 equals 80So, deal with the figures in brackets first, then multiply the outcome ofthis by the number next to the brackets.

20 (14 + 6) = 4010

Read aloud, this formula is:Fourteen plus six (which is 20), multiplied by 20 (which is 400) dividedby 10 equals 40You complete all the calculations that sit above the dividing lineBEFORE doing the dividing.

7 x (10 - 6) = 14

2

Read aloud, this time it is:

Ten minus six (which is 4) divided by two (which is 2) then multiply byseven equals 14

2011/12 tax year This is the tax year starting 6 April 2011 and running to midnight on5thApril 2012

Grossing up Youll be seeing this phrase a lot in your exams. Some forms of incomeare paid to people net of tax deducted by the provider (tax deducted atsource). HMRC work out someones full tax liability using the grossfigure, so have to gross up the net income by adding back the tax thatwas stopped at source.

% Percentage means parts per 100. So 10% written another way is10 ; This is 10 / 100 which is 0.10.

100


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Equation andformula

An equation is where there is a mathematical expression with an = inthe middle; in other words both sides are actually the same.

A formula is the content of either of the sides of the equation.

For example: Equation is 2 x 3 = Z / 6

The two formulae are: 2 x 3 and Z / 6

3. Golden rules for calculations

Before explaining the calculation steps for some of the tricky areas, there are a few goldenrules that you should remember every time you are asked to perform a mathematical

calculation.

1 Write down the formula you intend to use in full

For example, for R03/J01 there is a formula for working out someones extended basicrate tax band to cater for gift aid or Personal Pension contributions. The formula is:

(Net premium per month x 12) + 35,000 = Extended basic rate tax band (EBRTB)0.8

2 Insert the relevant figures into the formula

Assume the client is paying 50.00 per month:

(50 x 12) + 35,000 = EBRTB0.8

3 Work out the answer, dealing with each item in the formula in a logical order. Alwayscalculate the items in the brackets first.

(50 x 12 = 600) + 35,000 = EBRTB0.8

600 ; This is 600 / 0.8 which is 750; so we now have 750 + 35,000 = EBRTB0.8

750 + 35,000 = 35,750. This is the clients new basic rate tax threshold for 2011/12

4 You may need to work out an unknown value in one of the formulae in an equation.

If you were trying to find out the value of Z below, this could be done by manipulatingthe equation to get it to reads; Z =

Try reversing certain parts of the equation to get the Z on its own, as in the example. Forexample, a subtraction becomes an addition as its reversed. Similarly, multiplication

becomes division and a square number becomes a square root.


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Example from R02/J06.

To calculate the yield on a Gilt (your actual return on capital), you need to know theinterest rate (coupon) and the current trading (clean) price of the Gilt. The equation is:

Coupon x 100 = Yield %Clean price

So a coupon of 6% (i.e. 6 per 100) and clean price of 120 would give a yield of:

6 x 100 = 5%120

If you had to work out the clean price, but know the coupon (6%) and yield (5%), theformula would read:

6 x 100 = 5%Clean price

We need to rearrange the equation so that the clean price is on one side of the = and allthe numbers that we know are on the other.

To get rid of the 100 and the 6 (and so end up with Clean price = ):

Divide both sides of the equation by 100

6 = 5 aClean price 100

This boils down to 6 = 0.05Clean price

Multiply both sides by Clean price gives you:

6 = Clean price x 0.05

Divide both sides by 0.05 gives you:

6 = Clean price. The resulting answer gives you 120

0.05


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5 Calculation questions in J0 papers ask you to Calculate, showing all your workings .This is LITERALLY what you MUST do to have any chance of getting all the marksavailable in the question. Show all workings on your answer paper marks are oftenmissed because the workings havent been shown. Even if your final answer is wrong

you can usually pick up a lot of the marks available by showing the calculations donealong the way to get to your answer.

For example:Calculate, showing all your workings, the yield on a gilt with a coupon of 5% and acurrent clean price of 150 (2)

5 (1) x 100 = 4.55% (1)110

You can see that one mark was granted for the workings shown and one for the answer.

6 Double check your answer. Does it make sense? Is the decimal point in the right place?

7 If the answer is in multiple-choice format and you have no match in the answers given,check your formula is correct and work through it one more time.

4. Income tax

4A. Grossing up net income received(Topic covered in unit R03 Ch 1, J01 Ch 1)

HMRC income tax department always apply the appropriate rates of income tax to gross

income. This means that you need to be able to gross up any income received net of taxso that the correct rate of tax can be applied. Of course, income that is received where theinvestor has no personal tax liability should be completely ignored (for example, ISA incomeor VCT dividends).

The main culprits for grossing up in exams are dividends and interest.

Dividends are paid to the share holder net of 10% corporation tax. This tax eventuallyreaches HMRC and is credited against the years tax liability for the investor.

Interest from deposits or fixed interest based unit trusts or OEICs is paid net of basic rateincome tax at 20%. Just like the tax on dividends above, this tax is passed on to HMRC and

is credited against the years tax liability for the investor.

METHOD

income received x 100 = gross payment before tax(100 rate of interest deducted)

Example: Client receives 80 interest from a building society, received net of 20%.

80 x 100 = 100 gross interest before tax(100 20 = 80)


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Example question 4A1: Dividends

An investor receives a net dividend of 360. What is the gross amount of income subject totax?

Formula to use:Net amount x (100 / 90) (because it is a dividend, therefore net of 10% tax)

So the actual calculation is 360 x (100 / 90), but the worked example step by step (using abasic calculator) is shown below.

Step 1Always perform the calculations in brackets first, and show your workings, so

100 90 1.111

Step 2 360 1.111 400

Answer: The gross dividend is 400

Useful shortcut:A quick way is just to divide the net amount by 0.9, i.e.360 divided by 0.9 = 400

Example question 4A2: Interest

An investor receives a net interest payment of 400 into his savings account. What is thegross amount of interest?

Formula to use:Net amount x (100 / 80) (because it is an interest payment, therefore net of

20% tax)

The actual calculation is 400 x (100 / 80) but the worked example step by step (using abasic calculator) is shown below.


100 80 1.25

Step 2 400 1.25 500

Answer: The gross interest is 500

Useful shortcut:A quick way is just to divide the net amount by 0.8 i.e.400 divided by 0.8 = 500

In either example if the investor is a basic rate tax payer there is no further tax to pay, asHMRC has already banked the basic rate tax deducted at source. If the investor is a higheror additional rate tax payer you may be asked to calculate either:

The totaltax liability due on the income, OR

The extratax owed to HMRC on the income (to add to the amount already banked atsource).


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To work out the total liability on the gross income, you must know the rates of tax that apply.The following table will help. Lets stick with the gross dividend of 400 and gross interest of500:

4B. Percentages

Calculating a percentage of an amount is often an area where mistakes are made. Usually,decimal places are put in the wrong place but there are other pitfalls which are easilyavoided.

Even if you have a % button on a basic calculator it is worth checking through your answerto ensure it makes sense.

Example question 4B1: Basic percentage calculation

Find 25% of 500.

Formula to use:Amount x (percentage / 100)

The actual calculation is 500 x (25 / 100) but the worked example step by step (using a basiccalculator without using the % button) is shown below.

Step 1Always perform the calculations in brackets first and show your workings, so

25 100 0.25Step 2 500 0.25 125

Answer: The amount is 125

Useful shortcut:A quick way is just to multiply the amount by 0.25 (or if the percentagewere 17% then 0.17. If 50 percent, then 0.50 etc).

GROSS DIVIDEND OF 400 GROSS INTEREST OF 500Total liability Extra liability Total liability Extra Liability

Non tax payer 10% - 10.00 due NIL NIL due100 refund

NIL

Savings rate taxpayer

10% - 10.00 due NIL 10% - 50 due50 refund

NIL

Basic rate taxpayer

10% - 10.00 due NIL 20% - 100 due NIL

Higher rate taxpayer

32.5% - 130 due 22.5% - 90owed

40% - 200 due 20% - 100owed

Additional rate taxpayer

42.5% - 170 due 32.5% - 130owed

50% - 250 due 30% - 150owed


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Example question 4B2(i): Higher rate tax calculations on dividends

Using the previous example of the gross income received from dividends of 400, Calculate,showing all your workings, the extra amount of tax that the investor would pay if they were

a higher rate tax payer.

Formula to use for dividends: Gross amount x 22.5%

The actual calculation is 400 x (22.5 / 100) but the worked example step by step (using abasic calculator without using the % button) is shown below.


22.5 100 0.225

Step 2 400 0.225 90

Answer: The investor would have a further 90 dividend tax to pay

Example question 4B2(ii): Higher rate tax calculations on interest

Using the previous example of the gross amount received from an interest payment of 500,Calculate, showing all your workings, the extra amount of tax that the investor should payif they were a higher rate tax payer.

Formula to use for interest payments: Gross amount x 20%

The actual calculation is 500 x (20 / 100) but the worked example step by step (using a basiccalculator without using the % button) is shown below.


20 100 0.2

Step 2 500 0.2 100

Answer: The investor would have a further 100 savings tax to pay

4C. Chargeable gains within onshore insurance bonds(Topic covered in unit J01 Ch 5)

This is a very common type of calculation where many mistakes can be made. Generallyspeaking, onshore insurance bonds are deemed to have suffered basic rate tax at source.There are then three typical considerations for the investor.

1. Is the investor a basic rate tax payer and when the resulting chargeable gain is added toother taxable income is the total still belowthe higher rate tax threshold (35,000)?

2. Is the investor a basic rate tax payer and when the resulting chargeable gain is added toother taxable income is the total now abovethe higher rate tax threshold (35,000)?


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3. Is the investor already a higher rate tax payer or an additional rate tax payer?

If you apply certain principles to these types of calculations they are relativelystraightforward.

If 1. applies then there is no further tax to pay on the bond gain.

If 2. applies then we must do a top slicing calculation.

If 3. applies then the investor has a further 20% tax to pay (for a higher rate taxpayer) ofthe chargeable gain, or 30% if an additional rate taxpayer. (NB. Remember that it ispossible that if the gain is partially in higher rate and additional rate tax, then acombination of 20% and 30% will apply to the relevant parts of the gain to work out thetotal tax due).

Lets go through an example for each consideration.

Example question 4C1 Basic Rate Tax payer

An individual makes a chargeable gain on an insurance bond of 5,000. His taxable incomeis 15,000 per annum. Calculate, showing all your workings, any tax he must pay as aresult of encashing his bond.

Here, the total income (15,000 5,000 20,000) is clearly below the higher rate taxthreshold of 35,000, so there is no tax to pay and no calculation needed.

Example question 4C2 Basic Rate Tax payer close to higher rate threshold

An individual makes a chargeable gain on an insurance bond of 5,000 which he held for 5years. His taxable income is 34,600 per annum. Calculate any tax he must pay as a resultof encashing his bond.

(Note: Personal allowance has already been offset from income to provide taxable income)

The higher rate threshold for 2011/12 is 35,000.

Step 1

Some of the gain falls below the higher rate threshold and some of the gain isabove the threshold to work this out, subtract income from the higher rate

threshold, so 35,000 34,600 400. This portion of the gain needs nofurther tax paid on it.

Step 2Now top slice the total gain - divide the gain by the number of full years in force.

So, 5,000 5 1,000

Step 3As calculated earlier, 400 of this 1,000 does not need to be taxed. Therefore, theremaining 600 of eachtop slice must be taxed at 20%.


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Example question 4C3 To calculate any tax payable on top s licing

The individual in the previous example needs 600 of the amount of the top slice to be taxedat 20%, as it is above the higher rate threshold.

Formula to use:Amount of top slice above threshold x number of years in force x 20%

The actual calculation is 600 x 5 x (20 / 100) but the worked example step by step (using abasic calculator without using the % button) is shown below.

Step 1Always perform the calculations in brackets first and show your workings, so

20 100 0.2

Step 2 600 5 0.2 600

Answer: The income tax liability is 600.

Please note:Without top slicing, 4,600 of the gain would have been taxable at 20% i.e. taxof 920.

Example question 4C4 Higher Rate Tax payer

An individual makes a chargeable gain on an insurance bond of 5,000. Her taxable incomeis 50,000 per annum. Calculate,showing all your workings, any tax she must pay as aresult of encashing her bond.

Here the investor is already a higher rate tax payer before encashment of the bond, so shemust pay 20% tax on the gain.

Formula to use: Chargeable gain x 20%

The actual calculation is 5,000 x (20 / 100) but the worked example step by step (using abasic calculator without using the % button) is shown below.


20 100 0.2

Step 2 5,000 0.2 1,000

Answer: The income tax liability is 1,000.


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4D. Age allowances(Topic covered in unit R03 Ch 1, R02 Ch 6, R06 Appendix)

Golden rules

An age allowance for relevant incomes under 100,000 can never be reduced below thebasic personal allowance of 7,475

Age allowance applies for the entire tax year of attaining age 65 or 75

Any married couples allowance is a tax reducer, so only reduces a tax liability at the endof a calculation

Always check the tax tables provided to ensure you are using the correct allowance

Example question 4D1: Basic OOA calculation all allowance lost

Bob is 68. His income is 30,000 per annum. Calculate, showing all your workings, hispersonal allowance for 2011/12.

The age related personal allowance for 2011/12 is 9,940The minimum personal allowance for 2011/12 is 7,475The age allowance income limit for 2011/12 is 24,000For every 2 earned over the age allowance income limit (24,000) the personal allowanceis reduced by 1

Step 1

First, we need subtract the age allowance income limit from Bobs annual income,so:

30,000 24,000 6,000

Step 2We then divide this figure by 2, to show that this part of the personal allowance is

reduced by 1 for every 2 earned, so 6,000 2 3,000

Step 3Therefore the age related personal allowance of 9,940 is reduced by 3,000. So

9,940 3,000 = 6,940

This is below the minimum personal allowance so Bobs personal allowance will be 7,475 in2011/12.

Example question 4D2: Some allowance lost

Barbara is 67 and earns 25,000 per annum from her pension. Calculate, showing all yourworkings, her age related personal allowance in 2011/12.

The age related personal allowance for 2011/12 is 9,940The minimum personal allowance for 2011/12 is 7,475The age allowance income limit is 24,000 for 2011/12For every 2 earned over the age allowance income limit (24,000) the personal allowanceis reduced by 1

Step 1

First, we need subtract the age allowance income limit from Barbaras annual

income, so25,000 24,000 1,000


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Step 2We then divide this figure by 2, to show that this part of the personal allowance is

reduced by 1 for every 2 earned, so 1,000 2 500

Step 3Therefore the age related personal allowance of 9,940 is reduced by 500. So

9,940 500 = 9,440

This is above the minimum personal allowance, so Barbaras personal allowance will be9,440 in 2011/12.

5. Capital gains tax calculations(Topic covered in unit R03 Ch 3, R06 Ch 2)

There are three steps that establish how much CGT is due. Always apply these in a strictorder:

1. Calculate the gain2. Deduct the annual exemption3. Apply the current CGT rate

The 2011/12 annual exemption is 10,600. The CGT rates on chargeable gains are:

18% for individuals who are non-taxpayers and basic rate taxpayers; and

28% for higher and additional rate taxpayers.

These figures are available in the tax tables provided in the exam. Always check you areusing information for the correct tax year relevant to your exam, unless otherwise

instructed.

Example question 5A1: CGT at basic rate

A private investor, who is a non-taxpayer for income tax purposes, makes an individual gainof 120,000. Calculate, showing all your workings, the amount of tax due on this gain.

Formula to use:(Gain annual exemption) x (18 / 100)

Step 1Always perform the calculations in brackets first and show your workings, so:

18 100 0.18

Step 2 Next, do the first part of the calculation, so 120,000 10,600 109,400Step 3 Finally, 109,900 0.18 19,692

Answer: The CGT liability is 19,692

Please note:A common error is to calculate 18% of the gain and then deduct the annualexemption, giving the wrong answer. Therefore the order in which you apply these steps iscritical to establishing the correct answer.


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Example question 5A2: CGT at higher rate

A private investor on higher rate tax makes an individual gain of 110,600. Calculate,showing all your workings, the amount of tax due on this gain.

Formula to use:(Gain annual exemption) x (28 / 100)


28 100 0.28

Step 2 Next, do the first part of the calculation, so 110,600 10,600 100,000

Step 3 Finally, 100,000 0.28 28,000

Answer: The CGT liability is 28,000

Finally on CGT, a split situation. If the tax payer is a marginal higher rate tax payer, thensome of the chargeable gain may be in the basic rate income tax band (so chargeable at18% CGT) and some of it in higher rate income tax band (so chargeable at 28% CGT).

For example, in 2011/12, Fred has a taxable income of 30,000 (after deductions andallowances, the amount now subject to income tax). He also has a chargeable gain to CGTof 10,000. All you need to do is calculate:

5,000 of the gain at 18% plus5,000 of the gain at 28%.

Have a quick practice using the method explained above, and you should get to a total CGT

bill of 2,300.

6. Inheritance tax calculations(Topic covered in unit R03 Ch 4, R06 Ch 4)

The difficulty with these type of calculations is when and how to apply the nil rate band(NRB). Often the NRB is incorrectly selected. So the golden rule here is to check your taxtables to ensure the correct NRB is used.

In 2011/12 the NRB is 325,000 and any part of a deceaseds estate above that threshold istaxed at 40%.

Example question 6A1: IHT after NRB deduction

A widower dies leaving an estate worth 600,000. His former spouse fully utilised her NRBwhen she died. Calculate,showing all your workings, the inheritance tax due.

Important: There is no NRB to transfer to the widower as it was utilised.

Step 1It is important to deduct the NRB first as this is exempt from tax. So:

600,000 325,000 275,000


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Step 2

275,000 is therefore chargeable at 40%. To calculate, use the percentageequation discussed earlier:

40 100 = 0.4

Step 3 275,000 0.4 = 110,000

Answer: The IHT liability is 110,000

The calculation becomes a little more complicated when some or all of a former spousesNRB is unused.

Example question 6A2: Inherited NRB from deceased spouse

A widower dies on 1stFebruary 2012 leaving an estate worth 1,000,000. His former spouse,

who died on 30 June 2008, used 156,000 of her NRB Calculate,showing all yourworkings, the inheritance tax due.

The NRB in 2008/09 was 312,000156,000 of that NRB was utilised at that timeTo calculate the percentage/proportion of NRB un-used on first death:

(312,000 - 156,000) x 100312,000

156,000 x 100 = 50%312,000

Therefore 50% is the uplift to the surviving spouses NRB at the date of his death.

The NRB in 2010 2012 is 325,00050% is 325,000 x (50 / 100) = 162,500

So the widowers NRB at death is now 325,000 + 162,500 = 487,500

Formula to useto calculate inheritance tax due: (Total estate total NRB) x 40%

Step 1 So, 1,000,000 487,500 512,500. This is the amount chargeable at

40%Step 2 To calculate, use the percentage equation discussed earlier: 40 100 = 0.4

Step 3 512,500 0.4 = 205,000

Answer: The IHT liability is 205,000


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7. Other

A. Future & present values(Topic covered in unit R02 Ch 4, R06 Ch 3)

You may be called up to calculate the future value of a sum of money given an investmentterm and compound rate of interest or return. This requirement is represented by that scaryformula:

FV = PV(1 + r)n

The good news is, you dont need to have a complex scientific calculator to carry outcalculations like this. First of all we need to break down each component in the formula.

FV = Future valuePV = Present value

r = rate of returnn = number of compounding periods (years)

Example question 7A1: Calculating the future value of an investment

Calculate, showing all your workingsthe future value of an initial investment of 5,000,assuming a return of 4% per annum compound over 5 years.

Formula to use to calculate the future value: FV = PV(1 + r)n

After replacing the letters with the right numbers, it will look like this:

FV = 5,000 x (1 + 4%)

5

Step 1Work out the part of the formula in brackets first. The 4% is achieved by the sum

4 100 0.04. Therefore 1 0.04 1.04. We next have 5,000 x (1.04)5

Step 2

To work out (1.04)5we simply multiply 1.04 by itself five times i.e.

1.04 1.04 1.04 1.04 1.04 = 1.21665(to five decimal places)

Step 3 The sum will now read 5,000 1.21665. This equals 6,083.25.

Answer: The future value (FV) = 6,083.25

The calculation becomes a little more difficult if you are asked to calculate the investmentannual rate of return, given the term and the start and end figures.

Example question 7A2: Calculating an annual rate of return

Calculate,showing all your workings, the annual rate of return of an investment of 8,000which returns 9,500 two years later.

Formula to use to calculate the future value: FV = PV(1 + r)n After replacing the letters withthe numbers you already know, it will look like this: 9,500 = 8,000 x (1 + r)2


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In this case you cannot do the calculation in brackets, because you dont know the value ofr. To work it out, if you remember from Chapter 2 the golden rules for calculations youneed to find out what r equals by neutralising some of the formula items as follows:

Step 1Divide both sides by 8,000. This leaves on the left hand side

9,500 8,000 1.1875

So, the equation now reads 1.1875 (1 r)2

Step 2

Next, neutralise the square from the end of the formula (the 2 after the bracket), byfinding the square Root of each side. So, the equation now looks like:

1.1875 (1 r), changing to 1.09 (1 r) once the square Root hasbeen calculated (use the square Root function ( on your calculator for this).

Step 3 Next, we subtract 1 from each side; 1.09 1 r

Step 4

1.09 1 0.09. We need to show this as a percentage to do this, simply

multiply it by 100. So 0.09 100 = 9%

Answer: The annual rate of return (r) = 9%

NOTE:It is a good idea to check your answer by putting 0.09 in as r in the formula.


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Calculations: a basic help guideNeed more help? Links to some useful free web resources*

http://www.bbc.co.uk/skillswise/maths A series of entry level factsheets, worksheets

and quizzes for adults.

http://www.mathcentre.ac.uk/ Varied help resources, including mobile phone downloadsand iPod segments.

http ://library.thinkquest.org/20991/prealg/eq.html Help on basic algebraic equations.

You Tube is a valuable resource there are lots of help videos which explain calculationsstep by step. Two examples are below:

http ://www.youtube.com/watch?v=9jhgbSOEa8k&feature=related

http ://www.youtube.com/watch?v=QgDMJuwpZZM&feature=channel

*The links for these sites are not under the control of CII. The CII shall not be responsible in any way for the content of suchwebsites. The CII provides such links only as a convenience and the inclusion of any link does not imply endorsement by CII ofthe content of such sites.
http://www.bbc.co.uk/skillswise/mathshttp://www.bbc.co.uk/skillswise/mathshttp://www.mathcentre.ac.uk/http://www.mathcentre.ac.uk/http://library.thinkquest.org/20991/prealg/eq.htmlhttp://library.thinkquest.org/20991/prealg/eq.htmlhttp://www.youtube.com/watch?v=9jhgbSOEa8k&feature=relatedhttp://www.youtube.com/watch?v=9jhgbSOEa8k&feature=relatedhttp://www.youtube.com/watch?v=QgDMJuwpZZM&feature=channelhttp://www.youtube.com/watch?v=QgDMJuwpZZM&feature=channelhttp://www.youtube.com/watch?v=QgDMJuwpZZM&feature=channelhttp://www.youtube.com/watch?v=9jhgbSOEa8k&feature=relatedhttp://library.thinkquest.org/20991/prealg/eq.htmlhttp://www.mathcentre.ac.uk/http://www.bbc.co.uk/skillswise/maths

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