Tag Archives: algebra

Hints and Tips

Here are a few articles to show how to tackle common problems in English, Maths, French, Verbal and Non-verbal Reasoning and photography.

General

Hints and tips

 

 

 

 

 

How do I know if my child will get a place?
This is the question I get asked the most as a tutor. And even if parents don’t ask it directly, I know that it’s always lurking in the background somewhere…! more

English

Hard and soft g and c

 

 

 

 

Pronunciation
English is a funny old language. It’s such a mishmash of imported words and complicated constructions that it was once described as having French vocabulary and German grammar! Unfortunately, that means the spelling and pronunciation of words are often different. Two of the letters that cause problems are c and g. more

 

 

 

 

 

 

Why I hate the Press!
I know why they do it (most of the time), but it’s still incredibly annoying and confusing. I’m talking about grammatical mistakes in the papers. more

 

 

 

 

 

Americanisms
In the words of Winston Churchill (or George Bernard Shaw or James Whistler or Oscar Wilde), Britain and America are “two nations divided by a single language”. Quite a few of my pupils live outside the United Kingdom and/or go to foreign schools but are applying to English schools at 11+ or 13+ level. One of the problems they face is the use of Americanisms. more

 

 

 

 

 

Colons and semicolons
Using colons and semicolons is often an easy way to get a tick in your homework, but it still involves taking a bit of a risk. If you get it right, you get the tick, but if you get it wrong, you’ll get a cross. This article will explain how to use both colons and semicolons so that you can be confident of getting far more ticks than crosses! more

 

 

 

 

 

 

Explaining humour
The ‘W’ words are useful if you’re trying to understand or summarise a story, but who, whom, who’s and whose tend to cause problems. Here’s a quick guide to what they all mean and how they can be used. more

Who-or-whom

Who or whom, who’s or whose?
The ‘W’ words are useful if you’re trying to understand or summarise a story, but whowhomwho’s and whose tend to cause problems. Here’s a quick guide to what they all mean and how they can be used. more

Could vs might

Could or might?
Could and might mean different things, but a lot of people use them both to mean the same thing. Here’s a quick guide to avoid any confusion. more

Homophones

Homophones
Homophones are words that sound the same even though they’re spelt differently and mean different things. Getting them right can be tricky, but it’s worth it in the end. more

Creating off-the-shelf characters
Common entrance exams have a time limit. If they didn’t, they’d be a lot easier! If you want to save time and improve your story, one thing you can do is to prepare three ‘off-the-shelf’ characters that you can choose from. more

Books
Children’s reading list
I’m often asked by parents what books their children should be reading. Here’s a list of my favourite books when I was a boy. Maybe a few of them might be worth ordering online…! more

John McEnroe
Describing feelings
In many 11+ and 13+ exams, you have to talk about feelings. Yes, I know that’s hard for most boys that age, but I thought it might help if I wrote down a list of adjectives that describe our emotions. Here we go… more

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How to write a letter
Writing a letter is not as easy as it might seem – especially if you have to do it during a Common Entrance exam! In this post, I’d like to explain the typical format of formal and casual letters and the decisions on wording that you’ll have to make… more

Grand Central
Descriptive writing
Exams at 11+ and 13+ level always let you tell a story in the writing section, but they sometimes provide a picture and simply ask you to describe it or to ‘write about it in any way you like’. Writing a description is obviously different from writing a story, so it’s worthwhile pointing out the differences and the similarities… more

SVO
What is a full sentence?
Teachers often tell pupils to use a ‘full sentence’ in their answers, but what is a full sentence? more

Apostrophe
It’s all about the apostrophe
The apostrophe is tricky. It means different things at different times. This article is meant to clear up any confusion and help you use apostrophes, which might mean you get straight As in your exams – or should that be A’s?! more

Keep calm and check your spelling
Spelling rules
The problem with the English is that we’ve invaded (and been invaded by) so many countries that our language has ended up with a mish-mash of spelling rules… more

 

 

 

 

 

 

 

Parts of speech
English exams often ask questions about the ‘parts of speech’. This is just a fancy term for all the different kinds of words, but they’re worth knowing just in case. Just watch out for words such as ‘jump’, which can be more than one part of speech! more

Letter N
Capital!
The three main things to check after writing anything are spelling, punctuation and capital letters, so when do you use capitals? more

speech marks
Speech marks
Speech marks, inverted commas, quotation marks, quote marks, quotes, 66 and 99 – does any other punctuation mark have so many names or cause so much confusion…?! more

Essay writing
Essay writing
There comes a point in everyone’s life when you have to undergo the ritual that marks the first, fateful step on the road to becoming an adult. It’s called ‘writing an essay’… more

Commas
Commas
If you had the chance to take a contract out on one punctuation mark, most people would probably choose the comma. Unfortunately, that’s not possible, although modern journalists are doing their best to make it into an optional extra… more

Poetic devices
Poetic devices
It’s important to be able to recognise and analyse poetic devices when studying literature at any level. Dylan Thomas is my favourite poet, and he uses so many that I decided to take most of my examples from his writings… more

Story mountains
Story mountains
Everyone needs a route map, whether it’s Hillary and Tenzing climbing Mount Everest or an English candidate writing a story. One of the ways of planning a story is to create a story mountain, with each stage of the tale labelled on the diagram… more

Remember the iceberg!
Remember the iceberg!
To pass Common Entrance, you have to be a scuba diver. Only a small part of any iceberg is visible above the waves, and only a small part of any answer to a question is visible in the text. To discover the rest, you have to ‘dive in’ deeper and deeper… more

Maths

Number triangle

 

 

 

 

 

 

 

Number Triangles

Number triangles are a useful way of working out how to rearrange a multiplication or division sum. This is important if you have to ‘fill in the gaps’, for example. more

Problem Questions

 

 

 

 

 

 

Problem Questions
‘Problem questions’ are often the most difficult in 11+ and 13+ Maths papers.
There are several different kinds, but they all have one thing in common: they all ‘hide’ the sums that you have to do.
That means the first thing you have to do is work out the actual calculations you’re being asked for. more

Value of pi

 

 

 

 

 

Rounding
Rounding is just a convenient way of keeping numbers simple. Nobody wants to have to remember all the decimals in 𝝅 (which is 3.1415926535897932384…), so people usually round it to 3.14 (or 22/7).

There are three ways of rounding numbers:

  • using a power of 10
  • using decimal places
  • using significant figures. more

 

Working out values from a pie chart

Working out values from a pie chart
This is a typical question from a Dulwich College 11+ Maths paper that asks you to work out various quantities from a pie chart. To answer questions like this, you have to be comfortable working with fractions and know that there are 360 degrees in a circle. more

Reflecting shapes in a mirror line

Reflecting shapes in a mirror line
This is a typical question from a Dulwich College 11+ Maths paper, and it asks you to draw a reflection of the triangle in the mirror line shown on the chart. more

SOHCAHTOA
SOHCAHTOA
SOHCAHTOA (pronounced ‘soccer-toe-uh’) is a useful ‘mnemonic’ to remember the definitions of sines, cosines and tangents. Amazingly, I was never taught this at school, so I just had to look up all the funny numbers in a big book of tables without understanding what they meant! more

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Long multiplication
You can use short multiplication if you’re multiplying one number by another that’s in your times tables (up to 12). However, if you want to multiply by a higher number, you need to use long multiplication. more

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How to add, subtract, multiply and divide
The most important things you need to do in Maths are to add, subtract, divide and multiply. If you’re doing an entrance exam, and there’s more than one mark for a question, it generally means that you have to show your working. more

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Long division
Long division is on the syllabus for both 11+ and 13+ exams, so it’s important to know when and how to do it… more

maths trick
Maths trick
Here’s a Maths trick a friend of mine saw on QI. Who knows? It might make addition and subtraction just a little bit more fun! more

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Simultaneous equations
Why do we have simultaneous equations? Well, there are two ways of looking at it… more

Prime factors
Prime factors
Prime factors have nothing to do with Optimus Prime – sadly – but they often crop up in Maths tests and can be used to find the Lowest Common Multiple or Highest Common Factor of two numbers… more

negative-numbers
Negative numbers
Working with negative numbers can be confusing, but a few simple rules can help you add, subtract, multiply and divide successfully… more

maths
Useful terms in Maths
Maths is complicated, but a good first step on the road to understanding it is to get to know the most useful terms. There are lists in the front of the Bond books, but here’s my own contribution. I hope it helps! more

algebra
Algebra
Algebra is supposed to make life easier. By learning a formula or an equation, you can solve any similar type of problem whatever the numbers involved. However, an awful lot of students find it difficult, because letters just don’t seem to ‘mean’ as much as numbers. Here, we’ll try to make life a bit easier… more

Divisibility rules OK
Divisibility rules OK!
Times tables can be tricky, and there’s no substitute for learning them by heart. However, the divisibility rules can at least tell you whether an answer is definitely wrong. I’m a great believer in ‘sanity checking’ your work. Just ask yourself, “Is this crazy?” If it is, you’ll have to do the question again! more

Back-to-school-blackboard-chalk
Tips for the QTS numeracy test
The QTS numeracy and literacy tests are not very popular, but trainee teachers still have to pass them before they can start teaching in the state sector, so I thought I’d try and help out. There is always more than one way of doing a Maths question, but I hope I’ll demonstrate a few useful short cuts and describe when and how they should be used… more

Here be ratios
Ratios
Hundreds of years ago, it was traditional to put dragons on maps in places that were unknown, dangerous or poorly mapped. Ratios are one of those places… more

Fractions, decimals and percentages
Working with fractions
People don’t like fractions. I don’t know why. They’re difficult to begin with, I know, but a few simple rules will help you add, subtract, multiply and divide… more

Number sequences
Number sequences
Number sequences appear in Nature all over the place, from sunflowers to conch shells. They can also crop up either in Maths or Verbal Reasoning, and both are essential parts of 11+ and other school examinations… more

Fractions, decimals and percentages
Fractions, decimals and percentages
Pizzas are very useful, mathematically speaking. However much we hate fractions, we all know what half a pizza looks like, and that’s the point. Numbers don’t have any intrinsic meaning, and we can’t picture them unless they relate to something in the real world, so pizzas are just a useful way of illustrating fractions, decimals and percentages… more

Useful formulas
Useful formulas
What is a problem? A problem = a fact + a judgment. That is a simple formula that tells us something about the way the world works. Maths is full of formulas, and that can intimidate some people if they don’t understand them or can’t remember the right one to use… more

Short cuts
Short cuts
There is always more than one way of solving a Maths problem. That can be confusing, but it can also be an opportunity – if only you can find the right trade-off between speed and accuracy… more

French

French verbs
French regular verbs – present subjunctive tense
The subjunctive in French is generally used in the present tense after expressions such as ‘il faut que’ and certain verbs that also take the word ‘que’ after them. These are generally the ones that express feelings or doubts (eg craindre, vouloir), especially when two parts of a sentence have different subjects, eg ‘I want her to be happy’ becomes ‘Je veux qu’elle soit contente’. Verbs ending in -er or -re have one set of endings, but  -ir verbs have another… more

French verbs
Preceding Direct Objects in French
Forming the perfect (or pluperfect) tense in French is sometimes made harder than necessary by what’s called a Preceding Direct Object (or PDO). The object of a sentence is whatever ‘suffers the action of the verb’, eg the nail in ‘he hit the nail on the head’… more

French verbs
French regular verbs – conditional tense
The conditional tense in French is used to show that someone ‘would do’ or ‘would be doing’ something. All verbs end in -er, -re or -ir, and the endings are different (as shown here in red)… more

French verbs
French regular verbs – future tense
There is only one future tense in French, and it’s used to show that someone ‘will do’ or ‘will be doing’ something. Verbs end in -er, -re or -ir, but the endings are the same… more

French verbs
French regular verbs – past tense
Here are the basic forms of French regular verbs in the past tense, which include the perfect (or passé composé), pluperfect, imperfect and past historic (or passé simple). All verbs end in -er, -re or -ir, and there are different endings for each that are shown here in red… more

French verbs
Common French verbs – present tense
Language changes over time because people are lazy. They’d rather say something that’s easy than something that’s correct. That means the most common words change the most, and the verbs become ‘irregular’. In French, the ten most common verbs are ‘être’, ‘avoir’, ‘pouvoir’, ‘faire’, ‘mettre’, ‘dire’, ‘devoir’, ‘prendre’, ‘donner’ and ‘aller’, and they’re all irregular apart from ‘donner’… more

French verbs
French regular verbs – present tense
Nobody likes French verbs – not even the French! – but I thought I’d start by listing the most basic forms of the regular verbs in the present tense. All French verbs end in -er, -re or -ir, and there are different endings for each that are shown here in red… more

Learning the right words
Learning the right words
One of the frustrations about learning French is that you’re not given the words you really need to know. I studied French up to A-level, but I was sometimes at a complete loss when I went out with my French girlfriend and a few of her friends in Lyon. I was feeling suitably smug about following the whole conversation in French…until everyone started talking about chestnuts! more

Non-verbal Reasoning

Non-verbal Reasoning
Non-verbal reasoning tests are commonly found in Common Entrance exams at 11+ and 13+ level, and they’re designed to test pupils’ logical reasoning skills using series of shapes or patterns. It’s been said that they were intended to be ‘tutor-proof’, but, of course, every kind of test can be made easier through proper preparation and coaching. more

Photography

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African field guide
Find an alphabetical list of the most common animals seen on safari in Africa, including mammals, reptiles and birds. more

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Basics of photography
Learn all about the basic aspects of photography, including types of camera, types of lenses, the Exposure Triangle (shutter speed, aperture and ISO), focus and other settings. more

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Game drives
Read all about the best gear, equipment to take with you on safari, learn the rules of composition and find out the best workflow for editing your wildlife images. more

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How to stand out from the herd
Read this quick guide to improve your wildlife shots by setting up something a little bit different, from slow pans to sunny silhouettes. more

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Introduction to Lightroom
Learn how to import, edit and organise your images in Lightroom, including the main features available in the Library and Develop modules and a summary of keyboard shortcuts. more

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Making money from photography
Find out how to start making money from your photography with this quick and easy guide to entering competitions, putting on exhibitions, selling through stock (and microstock) agencies and more. more

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Rules of composition
Find out the rules of composition to help you get the most out of your photography, including the Rule of Thirds, framing, point of view, symmetry and a whole lot more. more

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Safari pub quiz
Challenge your friends and family on their wildlife knowledge with this fun quiz. more

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Wildlife photography
Learn how to take great wildlife shots by preparing properly, taking the right equipment and getting to know the rules of composition. more

Verbal Reasoning

VRTypeO

Verbal Reasoning
Verbal Reasoning (VR) tests were invented to test pupils’ logic and language skills – although they do sometimes includes questions about numbers. In order to do well in a VR test, the most important thing is to be systematic, to have a plan for what to do if the question is hard. Here is a guide to the different kinds of problems and the best ways to approach them. more

Simultaneous Equations

Simultaneous equations help you work out two variables at once.

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Why do we have simultaneous equations? Well, there are two ways of looking at it.

  1. The first is that it solves a problem that seems insoluble: how do you work out two variables at once? For example, if x + y = 10, what are x and y? That’s an impossible question because x and y could literally be anything. If x was 2, then y would be 8, but if x was 100, then y would be -90, but if x was 0.5, then y would be 9.5 and so on.Simultaneous equations help us solve that problem by providing more data. Yes, we still can’t solve each equation individually, but having both of them allows us to solve for one variable and then the other.
  2. The second way of looking at simultaneous equations is to imagine that they describe two lines that meet. The x and y values are obviously different as you move along both lines, but they are identical at the point where they meet, and that is the answer to the question.

The next question is obviously ‘How do we solve simultaneous equations?’ The answer is simple in theory: you just have to add both equations together to eliminate one of the variables, at which point you can work out the second one and then put it back into one of the original equations to work out the first variable.

However, it gets more and more complicated as the numbers get less and less ‘convenient’, so let’s take three examples to illustrate the three different techniques you need to know.

Simple Addition and Subtraction

The first step in solving simultaneous equations is to try and eliminate one of the variables by adding or subtracting them, but you can only do that if the number of the variable is the same in both. In theory, you could choose the first or the second term, but I find the one in the middle is the easiest, eg

4x + 2y = 10

16x – 2y = 10

Here, the number of the variables in the middle of the equations is the same, so adding them together will make them disappear:

20x = 20

It’s then simple to divide both sides by 20 to work out x:

x = 1

Once you have one variable, you can simply plug it back into one of the original equations to work out the other one, eg

4x + 2y = 10

4 x 1 + 2y = 10

4 + 2y = 10

2y = 6

y = 3

Answer: x = 1, y = 3

Multiplying One Equation

If the number of variables in the middle is not the same, but one is a factor of the other, try multiplying one equation by whatever number is needed to make the number of the variables match, eg

4x + 2y = 10

7x + y = 10

Multiplying the second equation by 2 means the number of the y’s is the same:

4x + 2y = 10

14x + 2y = 20

The rest of the procedure is exactly the same, only this time we have to subtract rather than add the equations to begin with:

10x = 10

x = 1

The next part is exactly the same as the first example as we simply plug in x to find y:

4x + 2y = 10

4 x 1 + 2y = 10

4 + 2y = 10

2y = 6

y = 3

Answer: x = 1, y = 3

Multiplying Both Equations

If the number of variables in the middle is not the same, but neither is a factor of the other, find the lowest common multiple and multiply the two equations by whatever numbers are needed to reach it, eg

4x + 2y = 10

x + 3y = 10

The lowest common multiple of 2 and 3 is 6, which means we need to multiply the first equation by 3:

12x + 6y = 30

…and the second by 2:

2x + 6y = 20

As the number of variables in the middle is now the same, we can carry on as before by subtracting one from the other in order to find x:

10x = 10

x = 1

Again, the final part of the technique is exactly the same as we plug x into the first of the original equations:

4x + 2y = 10

4 x 1 + 2y = 10

4 + 2y = 10

2y = 6

y = 3

Answer: x = 1, y = 3

Practice Questions

Job done! Now, here are a few practice questions to help you learn the rules. Find x and y in the following pairs of simultaneous equations:

  1. 2x + 4y = 16
    4x – 4y = 8
  2. 3x + 2y = 12
    5x + 2y = 16
  3. 12x – 4y = 28
    3x – 2y = 5
  4. 2x – y = 12
    3x – 2y = 17
  5. 4x + 3y = 24
    5x – 2y = 7
  6. 4x + 3y = 31
    5x + 4y = 40
  7. x + 4y = 23
    5x – 2y = 5
  8. 4x + 3y = 37
    2x – 3y = -13
  9. 2x + 4y = 16
    3x – 5y = -9
  10. 2x + 4y = 20
    3x + 3y = 21

Algebra

Nothing makes the heart of a reluctant mathematician sink like an algebra question.algebra

Algebra is supposed to make life easier. By learning a formula or an equation, you can solve any similar type of problem whatever the numbers involved. However, an awful lot of students find it difficult, because letters just don’t seem to ‘mean’ as much as numbers. Here, we’ll try to make life a bit easier…

Gathering Terms

X’s and y’s look a bit meaningless, but that’s the point. They can stand for anything. The simplest form of question you’ll have to answer is one that involves gathering your terms. That just means counting how many variables or unknowns you have (like x and y). I like to think of them as pieces of fruit, so an expression like…

2x + 3y – x + y

…just means ‘take away one apple from two apples and add one banana to three more bananas’. That leaves you with one apple and four bananas, or x + 4y.

If it helps, you can arrange the expression with the first kind of variables (in alphabetical order) on the left and the second kind on the right like this:

2x – x + 3y + y

x + 4y

Just make sure you bring the operators with the variables that come after them so that you keep exactly the same operators, eg two plus signs and a minus sign in this case.

Here are a few practice questions:

  1. 3x + 4y – 2x + y
  2. 2m + 3n – m + 3n
  3. p + 2q + 3p – 3q
  4. 2a – 4b + a + 4b
  5. x + y – 2x + 2y

Multiplying out Brackets

This is one of the commonest types of question. All you need to do is write down the same expression without the brackets. To take a simple example:

2(x + 3)

In this case, all you need to do is multiply everything inside the brackets by the number outside, which is 2, but what do we do about the ‘+’ sign? We could just multiply 2 by x, write down ‘+’ and then multiply 2 by 3:

2x + 6

However, that gets us into trouble if we have to subtract one expression in brackets from another (see below for explanation) – so it’s better to think of the ‘+’ sign as belonging to the 3. In other words, you multiply 2 by x and then 2 by +3. Once you’ve done that, you just convert the ‘+’ sign back to an operator. It gives exactly the same result, but it will work ALL the time rather than just with simple sums!

Here are a few practice questions:

  1. 2(a + 5)
  2. 3(y + 2)
  3. 6(3 + b)
  4. 3(a – 3)
  5. 4(3 – p)

Solving for x

Another common type of question involves finding out what x stands for (or y or z or any other letter). The easiest way to look at this kind of equation is using fruit again. In the old days, scales in a grocery shop sometimes had a bowl on one side and a place to put weights on the other.

To weigh fruit, you just needed to make sure that the weights and the fruit balanced and then add up all the weights. The point is that every equation always has to balance – the very word ‘equation’ comes from ‘equal’ – so you have to make sure that anything you do to one side you also have to do to the other. Just remember the magic words: BOTH SIDES!

There are three main types of operation you need to do in the following order:

  1. Multiplying out any brackets
  2. Adding or subtracting from BOTH SIDES
  3. Multiplying or dividing BOTH SIDES

Once you’ve multiplied out any brackets (see above), what you want to do is to simplify the equation by removing one expression at a time until you end up with something that says x = The Answer. It’s easier to start with adding and subtracting and then multiply or divide afterwards (followed by any square roots). To take the same example as before:

2(x + 3) = 8

Multiplying out the brackets gives us:

2x + 6 = 8

Subtracting 6 from BOTH SIDES gives us:

2x = 2

Dividing BOTH SIDES by 2 gives us the final answer:

x = 1

Simple!

Here are a few practice questions:

  1. b + 5 = 9
  2. 3y = 9
  3. 6(4 + c) = 36
  4. 3(a – 2) = 24
  5. 4(3 – p) = -8

Multiplying Two Expressions in Brackets (‘FOIL’ Method)

When you have to multiply something in brackets by something else in brackets, you should use what’s called the ‘FOIL’ method. FOIL is an acronym that stands for:

First
Outside
Inside
Last

This is simply a good way to remember the order in which to multiply the terms, so we start with the first terms in each bracket, then move on to the outside terms in the whole expression, then the terms in the middle and finally the last terms in each bracket.

Just make sure that you use the same trick we saw earlier, combining the operators with the numbers and letters before multiplying them together. For example:

(a + 1)(a + 2)

First we multiply the first terms in each bracket:

a x a

…then the outside terms:

a x +2

…then the inside terms:

+1 x a

…and finally the last terms in each bracket:

+1 x +2

Put it all together and simplify:

(a + 1)(a + 2)

= a² + 2a + a + 2

=a² + 3a + 2

Here are a few practice questions:

  1. (a + 1)(b + 2)
  2. (a – 1)(a + 2)
  3. (b + 1)(a – 2)
  4. (p – 1)(q + 2)
  5. (y + 1)(y – 3)

Factorising Quadratics (‘Product and Sum’ Method)

This is just the opposite of multiplying two expressions in brackets. Normally, factorisation involves finding the Highest Common Factor (or HCF) and putting that outside a set of brackets containing the rest of the terms, but some expressions can’t be solved that way, eg a² + 3a + 2 (from the previous example).

There is no combination of numbers and/or letters that goes evenly into a², 3a and 2, so we have to factorise using two sets of brackets. To do this, we use the ‘product and sum’ method.

This simply means that we need to find a pair of numbers whose product equals the last number and whose sum equals the multiple of a. In this case, it’s 1 and 2 as +1 x +2 = +2 and +1 + +2 = +3.

The first term in each bracket is just going to be a as a x a = a². Hence, factorising a² + 3a + 2 gives (a + 1)(a + 2). You can check it by using the FOIL method (see above) to multiply out the brackets:

(a + 1)(a + 2)

= a² + 2a + a + 2

=a² + 3a + 2

Subtracting One Expression from Another*

Here’s the reason why we don’t just write down operators as we come across them. Here’s a simple expression we need to simplify:

20 – 4(x – 3) = 16

If we use the ‘wrong’ method, then we get the following answer:

20 – 4(x – 3) = 16

20 – 4x – 12 = 16

8 – 4x = 16

4x = -8

x = -2

Now, if we plug our answer for x back into the original equation, it doesn’t balance:

20 – 4(-2 – 3) = 16

20 – 4 x -5 = 16

20 – -20 = 16

40 = 16!!

That’s why we have to use the other method, treating the operator as a negative or positive sign to be added to the number before we multiply it by whatever’s outside the brackets:

20 – 4(x – 3) = 16

20 – 4x + 12 = 16

32 – 4x = 16

4x = 16

x = 4

That makes much more sense, as we can see:

20 – 4(4 – 3) = 16

20 – 4 x 1 = 16

20 – 4 = 16

16 = 16

Thank Goodness for that!

Here are a few practice questions:

  1. 30 – 3(p – 1) = 0
  2. 20 – 3(a – 3) = 5
  3. 12 – 4(x – 2) = 4
  4. 24 – 6(x – 3) = 6
  5. 0 – 6(x – 2) = -12

Other Tips to Remember

  • If you have just one variable, leave out the number 1, eg 1x is just written as x.
  • When you have to multiply a number by a letter, leave out the times sign, eg 2 x p is written as 2p.
  • The squared symbol only relates to the number or letter immediately before it, eg 3m² means 3 x m x m, NOT (3 x m) x (3 x m).