In today's topic, we look at Time and Money. You can be faced with questions involving time and converting time is an important skill to have when faced with some of the more obscure problem-solving questions. We also have a look at money as there have been money problems linked to probability and possible combination problems. Other common questions involve currency conversion where you either multiply or dived by the exchange rate.
In today's topic, we look at Units. Many of the questions you will face will include units of some descriptions so it important that you are able to convert between the different types of units (metric). This will involve multiplying or dividing your value by a power of 10 (10, 100, 1000 etc). When it comes to Area and Volume the conversion factors are squared and cubed respectively.
Today we focus our attention on the topic of Surds and rationalising the denominator. You need to understand that Surds are expressions that contain an irrational square root (meaning, if you square rooted the number, you would get a never ending decimal). There are some laws of Surds that you need to be aware of (much like the laws of indices). Some questions will ask you to change a root to the form a√b, to do this you need to find the largest square number that will go into the number and simplify form there.
When it comes to rationalising the denominator, the key principle here is removing the square root from the denominator so that we are left with a whole number. This is achieved by multiplying. Take care to notice the different methods used when dealing with simple and more complex problems.
On day 69 of our countdown, we focus on the topic of Standard Form. Standard form is a system of writing very large or very small numbers as a power of ten. Make sure you understand the basic structure of standard form (a number between 1 and 10 then times ten to a power --> a×10b). You will be asked to write numbers in standard form as well as carry out operations using standard form. If you are asked to add or subtract Standard form; take the numbers out of standard form, add/subtract them, convert back to standard form. When asked to multiply/divide standard form; calculate the numbers first, apply the laws of indices to the powers of ten. combine and convert to standard from if necessary.
On day 58, we take a look at Approximations and Error intervals. When approximating calculations we tend to round each of the numbers to one significant figure. This should then leave us with a simpler calculation to carry out. Approximating your answers is good practice (not just when asked to) so you know if your answer is in the right region and you haven't made any big mistakes.
With error intervals, we are looking to find out what the maximum and minimum value of a rounded number might be. For continuous values, we halve the accuracy level (rounded to) and add it on for the Upper bound and subtract for the Lower bound. You will need to be a bit more careful with discrete values (people on a bus for example)
For day 30 we are looking at the more complex topic of turning a recurring decimal into a fraction. Here we take a look at converting simple recurring decimals into fractions with denominators of 9/99/999 etc. We then extend onto more complex recurring decimals. The best approach to these questions is to take an algebraic approach and multiply the decimal to get yourself into a position where the recurring element can be eliminated.
Important to remember that a recurring decimal is a decimal number that will have a pattern of number/s repeating infinitely. The whole point of converting the recurring decimal into a fraction is so that it is easier to calculate with.
On day 29 we are taking a closer look at Converting fractions to decimals. Having a look at the table, there are some simple fraction to decimal conversions you should know. For more complex fractions, there are two methods to consider; the first is using a division method and the other is using an equivalent fraction method.
On day 28 we are taking a closer look at Converting decimals to fractions. Having a look at the table, there are some simple decimal to fraction conversions you should know. If in doubt, use place value to place your number over 10/100/1000 etc. and then look to simplify your answer.
On day 27 we continue calculating with fractions focusing on Multiplying and Dividing fractions. Unlike addition and subtraction there is no need to have a common denominator if we are asked to multiply/ divide fractions. All you need to do is multiply numerators, multiply denominators, simplify your answer. When dividing fractions you need to flip the second fraction and multiply. (Keep Change Flip)
Always look to see if you can cross cancel first. This will mean that you don't have to multiply large complicated numbers. When faced with mixed numbers, look to convert to improper fractions first.
Today we extend our fraction knowledge and look at calculating with fractions. The focus here will be Addition and Subtraction of fractions. In order to carry out these calculations, the denominators of your fractions need to be the same. This means that you will have to multiply one or both of the fractions to make equivalent fractions that have the same denominator.
Remember to simplify your answers where possible to secure full marks and remember how to convert between mixed and improper fractions.
On day 25, we turn our attention to Fractions. It is important to remember that fractions are 'part' of the 'whole'. The numerator is the top number (number of parts you are focusing on) and the denominator is the bottom number (total number of parts). To secure full marks you will have to make sure that your answers are in their simplest form and this is achieved by dividing the fraction to create an equivalent fraction with smaller numbers.
When you start calculating with fractions you will end up with combinations of improper fractions and mixed numbers. Being able to convert between these two formats will make calculations a lot easier.
Day 16 takes a look at Sequences. With sequences you will be required to know what is happening between each term in a sequence, using that information to carry on the sequence as well as find a general rule to find the value of any term in the sequence. We start off with simple sequences and the processes required to find the general rule (known as the nth term) and move onto the more advanced quadratic sequences.
Today we are looking at the topic of Powers and Roots. There are three areas to be aware of when dealing with powers. Here, we take you through positive powers, negative powers and fractional powers. If you ever end up dealing with negative fractional powers then look to deal with the negative element first then move onto the fractional part.
We also a take a look at roots today because they are closely linked to fractional powers. When dealing with questions involving this topic, you should be confident in knowing your square and cube numbers.
Today we are looking at the topics of Prime factor decomposition, HCF and LCM. We take a look at how to break down numbers into products of their primes and then use the information to calculate the HCF and LCM of two or more numbers.
It is important to be confident in breaking down numbers into a product of their primes as this provides the foundation for solving HCF and LCM problems. You may come across questions involving HCF and LCM that will not require you to carry out prime factor decomposition. These are normally involved in best buy problems.
Today we are looking at the topics of Prime numbers, factors and multiples. We take a look at the definitions and properties of prime numbers, factors and multiples.
An important topic when looking to solve problems involving Highest common factor and Lowest common multiple. It can also prove useful when you need to divide by a double digit number.
Today we are looking at the topic of BIDMAS. The set of rules required to solve calculations was developed to ensure there was some regularity when confronted with calculations containing a number of different operations.
An important topic when carrying out simple numerical problems but becomes crucial when starting to develop the skills required to solve algebraic problems. Don't forget to re-write your calculation at each stage so you can easily track what needs to be done next as you progress through the problem!
Today we are focusing on the topic of Multiplication and Division. It is important that you have a 'go-to' method whenever you are confronted with multiplication and division problems and here we look at some of the methods that are commonly used. We also take a look at the laws surrounding the multiplication and division of positive and negative numbers, a crucial area that many people make mistakes on when applying to algebra style questions.
The focus for Day 3 is Addition and Subtraction. As well as being able to use the appropriate method to add and subtract complex numbers, we explore the rules regarding the addition and subtraction of positive and negative numbers which is often an area where simple marks are lost in an exam.
Our focus today is on Rounding. Important to get right for questions which focus specifically on rounding, especially place value rounding. It is also important to avoid dropping careless marks by incorrectly rounding your final answers.
Today is the first day in our countdown to exams and we are focusing on Place Value and Numberlines. These are 2 topic areas of particular importance for foundation level students as they offer the opportunity to secure some key marks, potentially early on in the paper.