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).
In today's blog, we attempt to tackle two fairly complex topics in the GCSE course. Firstly, we look at Estimating gradients.Calculating the average gradient from beginning to end does not give a good representation of what is happening in the graph. What can be done is to break the graph down into smaller sections and the average gradient of those are calculated to give a better idea of what is happening. Another method is to find the gradient at specific points on the graph, this involves constructing a series of tangents by eye and calculating the gradient at each point. This is where an estimate comes in because each tangent may vary slightly.
Secondly, we take a look at the area under a curve. The area under a velocity-time graph (most common question) will give you the distance that the object/particle has travelled. You will have to break the graph up into equal widths to give you a triangle and a series of trapezia. Calculate the area of each shape and that will tell the distance travelled.
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's focus in our countdown to exams is the topic of Translations and reflections of graphs. You will be given a function (graph) and be asked to manipulate the function and sketch a new graph sometimes labelling the key points on the graphs. Starting with translations, when you add to the function f(x)+a or f(x+a), this causes the graph to move up/down or left/right.
f(x)+a is a movement up/down by a units. f(x+a) is a movement left/right by a units (+=left, -=right).
Reflections are caused by making the function negative or the variable negative.
-f(x) is a reflection in the x axis (the outputs are reversed). f(-x) is a reflection in the y axis (the inputs are reversed)
On day 52 of the countdown, we approach the more complex topic of the Equation of a circle. There are a few areas of prior knowledge required to tackle the whole topic completely. You will need to be confident in calculating missing sides using Pythagoras' theorem (to find the radius), calculating the gradient (to find the equation of the radius and then the tangent). Knowledge of perpendicular lines will be required as well as memorising the general rule for the equation of a circle (x2+y2=r2)
In today's countdown, we take a look at the graphs of Reciprocal and Exponential functions. It is very important that you are able to distinguish between the shapes of the two graphs as you may be asked to fill in a table of values and plot the graph. If you know the shape, then you can check if your calculations are correct.
Make sure you know the key points of each graph and in an exam, check your answers so you do not lose simple marks.
Today we are looking the Equation of a straight line. Before we move onto the more complex straight line graphs, we must understand the equations of horizontal and vertical lines.
A horizontal line has the equation y =? where ? is the point the line crosses the y-axis. A vertical line has the equation x =? where ? is the point where the line crosses the x-axis.
All straight line graphs follow the general rule y = mx+c where m is the gradient (steepness) of the line and c is the y-intercept. You will need to be able to calculate gradients effectively and substitute into the general rule to find the y-intecept if you are given some coordinate points.
Here we take at look at the first 'Graph' section. We start off fairly simply looking at coordinates. A set of coordinates provides us with a set of instructions that indicate the position of a point or object. They normally occur in pairs (x,y) where the first number is your direction along and the second value is your direction up/down.
You will need to be able to plot coordinate points accurately for many types of question as well as being able to read the points off a graph as well.