Today's blog looks at the topic of Using graphs to find solutions. You will normally come across this topic when you need to solve simultaneous equations graphically. With this topic it will be important to construct the graphs accurately to get the correct information (if they are already done for you, no problems!) You should be looking for the point of intersection as this will the point where x and y have the same value for each equation.
Today, we take a look at the topic of Functions. It is important to think of functions as a machine where a value is put into the function f(x) and an output is calculated. When using functions the key process is substituting the value into the function and yielding an output (imagine completing a table of values for a quadratic). You may be asked to calculate inverse functions which is the process of working backwards from the output to find the value of the number that has been put into the function. Composite functions is where you combine two or more functions to create a new (super) function.
In today's blog post, we focus on the topic of Algebraic fractions. In this higher level topic, it is important to remember the fundamentals of the operations involving fractions. If adding/subtracting, remember you need a common denominator so may have to multiply your fractions (with numbers or algebraic terms). When multiplying multiply across the numerators then multiply across the denominators (cross cancel where possible). When dividing remember to multiply by the reciprocal of the second fraction (keep change flip).
In today's blog post we cast our eye on Simultaneous equations. A simultaneous equation is where we have two equations containing different unknowns (normally x's and y's) and our job is to find the value of both of these letters. There are two ways to solve simultaneous equations; the first method is the elimination method. In this method the aim is to get one of your variables to have matching coefficients, we achieve this by multiplying one or both of the equations. When the are the same we simply add or subtract the equations to eliminate a variable. Solve the resultant equation to find the value of one variable. Remember to substitute this value into an equation to find the value of the second variable to get full marks.
The second method is the substitution method. In this method, the aim is to rearrange one of the equations so that a variable is equal to something. This something is then substituted into the other equation (this leaves one equation with one variable in it). Solve the resultant equation to find the value of one variable. Remember to substitute this value into an equation to find the value of the second variable to get full marks.
If there are quadratics present, be sure to use the substitution method.
In today's snapshot, we take a look at the topic of Inequalities. Many of the processes involving inequalities you should recognise from equations. In the case of inequalities, the = sign is replaced with four different symbols (<, >, ≤, ≥). You need to remember that inequalities show a range of values that your unknown might be (x) not just one specific value. You need to be able to represent inequalities on a number line deciding whether or not to fill the circle in. You solve and graph inequalities in the same way as an equation.
In today's blog post we are looking at the more complex topic of Completing the square and then using this information to solve quadratics. To complete the square you need to think about halving the coefficient of b, this will form the main part of your completed square. There will be another amount (half the coefficient of b then squared). This will need to be combined with your c value to create a number. From there you have a relatively straightforward equation to solve (remember you are looking for two answers).
Completing the square will also reveal the turning point of the quadratic graph if you were to plot it.
In today's blog, we take a look at solving quadratics using two methods. The first method to explore is solving by factorising. This means that we need to put the quadratic into double brackets and then solve to find values for x. If you end up with a quadratic that cannot be factorised then you will need to use the Quadratic formula method.
It is important to establish the values of a, b and c that are needed to substitute into the formula. You will need to memorise the formula as you will not be given this in the exam. Remember that when using the quadratic formula, you will need to do two calculations one where you ADD the square root and one where you SUBTRACT the square root.
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.
In today's revision countdown, we are taking a look at Factorising Quadratics. Remember, factorising is putting into brackets! It is important to remember the general structure of a quadratic as you may need to rearrange your expression/equation to create the general structure.
We start off by looking at simple quadratic expressions where the a value is equal to one. The key point to remember here is the 'Sum and Product rule' We finish off by looking to factorise quadratics where the a value is not equal to 1.
On day 14, we are still looking at the Algebra section paying attention to Linear Equations. Here we start with creating linear equations that will enable you to calculate the value of the unknown. Here you will need to utilise all you algebraic skills as you may be required to expand, factorise, collect like terms before attempting to solve the equation. Pay attention to the general order that you solve equations.
The difference between an expression and and equation is that an equation has an equal sign!
Surprise Surprise! Today we are focusing on the inverse of expanding, Factorising. Whenever you see this in a question, it means that you have to write the expression with brackets.
Here we take a look at how to factorise expressions by factoring out common factors (by dividing). We take you through two possible methods to do this.
On day 12 we take a look at Expanding brackets. It is important to state that this is the inverse of factorising and we take you through the process of expanding brackets by multiplication! Once the brackets have been expanded, it is essential to collect like terms and simplify your answer otherwise you will lose marks in a test.
Here we cover expanding single brackets and move onto double brackets. Note there is more than one method so make sure you get really comfortably with a method and get those marks!
Today we are looking at the topic of Laws of Indices. It is important to understand that an index might be referred to as a power (the little number in the upper right corner) and that the base is your key component. We take a look at the three basic laws of indices involving the multiplying, dividing and raising of the powers.
We then start to explore the advanced laws of indices which share close similarities with negative and fractional powers that were covered earlier.
Today we take a look at Formulae. There are many strands to Formulae that you need to be comfortable with. We take a look at creating a formula from some information given, paying particular attention to the operations that are involved.
You will be required to memorise formulae to help you solve problems and being able to substitute into a formula accurately is important in order to secure the right answer and marks.
There will be times that you will have to manipulate and rearrange the formula in order to work something else out. This is called changing the subject and is also the last thing we cover in this topic.
The focus for Day 9 is Algebraic notation and collecting like terms. Here we take an introductory look into Algebra and this will form the basis of all future algebraic manipulation. It will be important to know and understand the 'shortcuts' in algebraic notation. Using this knowledge, we are able to simplify expressions by collecting like terms together.
It is really important in this topic to pay attention to signs. Are you dealing with positives or negatives? If you gain a solid understanding of this topic it will help to enhance your Algebra skills and tackle more complex problems.