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.
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.
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.).
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.
Get those Compasses ready as we look at Bisectors and Loci today. You will sometimes be asked to construct perpendicular bisectors; either through a line segment, from a particular point or through a particular point. In each case, you will need to have a line segment to bisect. Remember you need to keep all of your construction markings in. We also take a look at bisecting an angle where a set of intersecting arcs need to be created inside the angle.
Loci are a series of points that satisfy a particular condition (a set distance from a point/line). In some questions, you will be asked to shade in regions based on the loci you have constructed.
On day 61, we focus our attention on the Congruence criteria for triangles. There will be questions that ask you to state why two triangles are identical. Here you will need to examine the side lengths and angles of the triangle and see which of the four categories they fit into. Side, Side, Side (SSS), Side, Angle, Side (SAS), Angle, Side, Angle (ASA), Right Angle, Hypotenuse, Side (RHS).
You may have to flip/rotate the triangles in your head (or use tracing paper) to see if they match up and identify which criterion to use.
Today we look at the popular topic of Transformations. There are four types of transformations to be aware of 1) Reflections (flipping a shape) 2) Rotations (turning a shape) 3) Translations (sliding a shape) and 4) Enlargements (altering the lengths of a shape). With each type of transformation, there are certain statements that need to be mentioned in order to secure full marks. A good indicator of how many things you need to state can be seen by the number of marks on offer.
A little tip: Ask for tracing paper with any transformation question so you can double check by tracing the shape and seeing if it matches up!
In today's blog, we are taking a look at Similarity and Congruence. Starting with congruence, the key thing to remember is that congruent shapes are IDENTICAL all sides are the same length and all angles are the same. The shapes may have been altered slightly so you might have to rotate, flip them so that they match up.
With similar shapes, it is important to understand that all angles remain the same and it is the side lengths that have been altered (essentially, similar shapes are ENLARGEMENTS of each other). You will have to calculate the scale factor in order to find missing values between the shapes.
When confronted with area and volume problems of similar shapes you must square or cube the scale factor to get the correct answer.
In this blog, we take a look at the volume of shapes. Volume is the space taken up by a 3D object and there are a few 3D-shapes you should be aware of. When it comes to calculating volume, you will need to establish if the shape is a prism ( the same area running the length of the shape) or a pyramid (faces meeting at a point). To calculate the volume of a prism you need to calculate the area of the face (that extends the whole depth of the shape) and multiply it by the depth. To calculate the volume of a pyramid, multiply the area of the base by the height then divide it by 3.
That last thing we look at is Spheres. You will be given the formula for this so there is no need to memorise it. Just remember to substitute the radius into the formula to get your answer.
In this quick countdown, we take a look at all the definitions of the parts of the circle. These will become useful when dealing with circle theorems, area problems involving circles and the equation of a circle. Make sure you are confident in the terms and where they are situated on a circle.
In today's countdown, we take a look at the more Advanced areas that you will come across. We start off with a Parallelogram which is base times height (perpendicular). Just imagine a 'tilted' rectangle. The formula for the trapezium is more complex but just follow the three steps of 1) Add the parallel sides, 2)Halve it, 3)Multiply by height (perpendicular). You might be required to use this formula to find the area under a graph as well as just a shape.
We finish off with the sine rule to find the area of a triangle when you have two sides and the included angle (no height). All area formulae need to be memorised so make sure you can recall them all.
Today our focus is on Perimeter and Area. The Perimeter of a shape is the distance around a shape and will require you to add up all of the side lengths together. You may have to deal with numbers and algebraic terms so make sure you are confident in collecting like terms. You also need to be aware of the properties of shapes so you can fill in missing lengths because they are equal etc.
Area is the space inside a 2D-shape. It is normally calculated by multiplying two lengths together (a horizontal and a vertical length).
You must take care of the units you have been given in the question and convert them all to the same if required. You are not given any formula for an area so make sure memorise them all.
Today we delve a little deeper into the topic of trigonometry, focusing on SohCahToa (mnemonic for the trig functions). You will use this when finding missing angles or side lengths in right angled triangles. The first step will be to accurately label the triangle with Opposite, Adjacent and Hypotenuse. We then have to decide which trig ratio to use to solve the problem.
You could use the formula triangles to instruct you or you could substitute values into the function and rearrange to solve.
Today, we are looking at the Trigonometry Ratios. Trigonometry is usually used to calculate missing side lengths and angles in right-angled triangles. There are three functions you need to aware of; the Sine, Cosine and Tangent Functions and these are related to the lengths of the key terms of the right-angled triangle (Opposite, Adjacent and Hypotenuse). They are simply one side of a right-angled triangle divided by another and will have a specific value dependent upon the angle marked theta (or x).
You are required to know the specific values for each function when given an angle. It will be important to remember the three tables provided in this snapshot.
Today, we are looking at Pythagoras' Theorem. When you have a right angled triangle and you know two of the lengths, you can use Pythagoras' theorem to work out the third and final side. Important to note that it ONLY works for a right angled triangle.
Solving questions using Pythagoras' theorem is a three stage process that may alter slightly depending if you need to find the hypotenuse or a shorter side. There will some questions where Pythagoras' theorem will be required as well as trigonometry in more complex questions.
For day 42, we are focusing on angles in parallel lines. It is fairly straight forward to calculate the angles on a straight line as we can use the vertically opposite angles reasoning or angles in a straight line reasoning.
When you want to compare one angle on one parallel line to another angle on a different parallel line there are three types of angle reasoning you will need to state. (Alternate, Corresponding, Co-Interior)
On day 41, we start by taking a look at calculating the missing angle in triangles (add up to 180 degrees). It is important to aware of the Isosceles and Equilateral triangles as they have very specific angle properties. We then move onto angles in polygons which can be found by using a special formula. If in doubt, use the fact that the number of triangles in a shape is always two less than the number of sides.
If in doubt, use the fact that the number of triangles in a shape is always two less than the number of sides.
You will have to be able to calculate the exterior angle of a shape as well (all exterior angles make 360 degrees, Interior + Exterior = 180 degrees)
On day 40, we turn our attention to Angle facts. An angle is a measure of turn and is measured in degrees. You should be able to classify the different types of angles based on their size and use that information to be able to calculate missing angles in straight lines and around a point. Calculating missing angles is achieved by subtracting angles you already know.
We are taking a look at 3D - Shapes today and how they are classified. We will take a look at Prisms, Pyramids and Spheres. Being able to identify the 3D - Shape will help with more complex problems involving calculating the the volume of the shape as well as the surface area. We can also classify these shapes according to the number of faces, edges and vertices (corners) it has.
Polygons is today's focus on Day 38 in our countdown to exams. You will need to be able to give the names of many sided shapes and use this information to calculate the angles inside these more complex shapes. You may also have to state whether the shape is concave or convex as well as regular and irregular.