We focus on the topic of Trigonometric graphs in today's countdown blog. You will be expected to recall the shapes of the three trigonometric functions and be able to highlight the key points (x-axis intercepts, Maximum and minimum turning points.). Note that the x-axis is measured in degrees and that the trigonometric graphs are periodical (they repeat every 360 degrees). You should then be able to read off the graphs to give the angles for specific sin/cos/tan values (notice the symmetry and that there will be more than one angle).
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 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.
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!