We have put together a list of the formulae required for the exam that you need to memorise. We have also put together a little list of tips to help with your exam preparation.
Today's topic that we are focusing on is Bearings. Bearings are used in navigation to identify (as a measure of turn) where the direction of one object is in relation to another. You need to remember that bearings are calculated from North, in a clockwise direction and given as a three digit value. Be careful with sentence structure as bearings are measured FROM the object (normally the second point in the question). When calculating more complex bearings knowledge of angles in parallel lines is useful (particularly co-interior angles). The harder questions will involve speed, time, perpendicular lines and maybe the use of Pythagoras' theorem and trigonometry.
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's topic in the countdown to exams is Vectors. Vectors describe a translation (a movement from one place to another) and can be written using vector notation (used to describe a translation). as we get more advanced, the coordinate grid is removed and the notation is given by bold letters (a, b, c) To go from one point to another, you will have to travel along vectors that you already know. If you travel with a vector it will be positive, if you travel against a vector, it will be negative.
In more advanced questions midpoints and ratios will be introduced and you may have to factorise your answers to prove that two vectors are parallel or collinear.
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 80 of our countdown to exams, we take a look at the topic of Circle theorems. There are 7 key circle theorems you need to be able to recall when faced with questions involving missing angles in circles. In order to secure full marks, you will need to justify your reasoning by stating one or more of the circle theorems (not just the shape) along with other angle facts you know (straight line, triangle, around point etc.).
Today we are taking a look at Frequency and Two-way tables. Frequency tables are created from raw data that have categorised, tallied and then totalled. We can use frequency tables to calculate relative frequencies which can be useful to describe proportions. If the sample is large enough, it can enable us to interpret them as probabilities. Two-way tables provide information about the frequency of two variables and the key to solving problems of this type is to pay attention to the totals column. This will enable you to complete a two-way table accurately and then use the information to calculate probabilities based on the data within the table.
Types of data and Sampling is the foci in today's countdown. You need to be able to recall the types of data and be able to categorise data when it is given to you. Note that there are several categories of data and your information may fit into two or more of these categories. The idea behind sampling is to get a selection of people that will accurately represent the whole population when statistical analysis is carried out. There are two types to be aware of, random (members given a number and then randomly chosen) and stratified (proportionate amount of each group is selected). When dealing with data collection it is always important to think about Bias and whether the data will be collected in a 'fair' manner.
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 post, we take a look at the Sine and Cosine rules. These rules are used when we are asked to find missing lengths or angles in non-right-angled triangles. The Sine rule is best used when you have an angle and its opposite length and the Cosine rule when you have two sides and the included angle. It is then a case of substituting know values into the formulae and rearranging to generate your answer.
You will not be given these formulae in the exam so makes sure you commit them to memory.
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)
In today's blog, we look at the topic of Rates of change. With linear functions (straight line graphs) the rate of change can be interpreted from the gradient of the function. It is interpreted as an amount of y per amount of x (e.g. Dollars per hour, Metres per second). When dealing with non-linear functions there are two rates of change you could calculate.
The average rate of change; here you create a chord between two intervals and then calculate the gradient of the cord and interpret as a rate of change. The disadvantage of this is that it doesn't truly reflect the nature of the graph.
The other rate of change is an instantaneous rate of change; here you are working out the rate of change at a specific point. Create a tangent at the point, calculate and interpret the gradient as a rate of change. This will give a more accurate representation of what is happening but more tangents will be required to deliver the bigger picture.
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).
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.
In today's blog, we extend to diagrams used in probability, these include; Venn diagrams and Probability trees.With Venn diagrams, we organise data into Sets which are then contained within overlapping circles. Only elements of data that share two properties are situated in the overlap. If asked to fill in a Venn diagram, try and start with the overlaps where possible. It is important to understand the key terms surround Venn diagrams such as Union, Intersection and Complement.
With probability trees, you will be looking at two or more events happening. Remember that the probability of each event must add up to one. When the events are combined, we multiply along the branches (do not simplify at this point) to calculate the probability that these events will happen. When answering a question you may need to find the combinations that satisfy the question and then add those probabilities together. Be aware of repeated events where something is NOT replaced. This will mean that the denominator will be reduced in the second event.
Today we shift our focus to the Statistics section and focus on the topic of Probability. Here we take an introductory look at probability and using a sample space diagram to identify the number of outcomes. You should know that all probabilities from an event add up to make 1. Take care when calculating probabilities as your answer can be in the form of fractions (simplify them), decimals, and percentages so you may need to convert between them. We cover the 'or' rule for mutually exclusive events and the 'and' rule for independent events.