Maths Made Easy: Advanced, Ages 7-8 (Key Stage 2): Supports the National Curriculum, Maths Exercise Book (Made Easy Workbooks)
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Maths Made Easy: Advanced, Ages 7-8 (Key Stage 2): Supports the National Curriculum, Maths Exercise Book (Made Easy Workbooks)
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You should have seen some graph transformations before, such as translations and reflections – recall that reflections in the x-axis flip f(x) vertically and reflections in the y-axis flip f(x) horizontally. Here, we will also look at stretches. Step 1: Rearrange the linear equation to get one of the unknowns on its own and on one side of the equals sign. Question 3: Triangles BCA and BED are mathematically similar. Given that BC=4.4 cm, BA=3 cm, AD=3 cm, and AC=5 cm. From a humble beginnings of a dedicated individual adding free Maths content for all, to one of the country’s leading Maths, English and Science resources and a team committed to expanding on the good work, Maths Made Easy will continue to help more and more people find exceptional revision materials alongside expert private tutors.
begin{aligned}y&=2x-6\\ y&=\dfrac{1}{2}x+6 \\ \\ (y-y)&=(2x-\dfrac{1}{2}x)-6-6 \\ 0&= \dfrac{3}{2}x-12 \end{aligned} If we multiply the second equation by 2, we have two equations both with a 2x term, hence subtracting our new equation 2 from equation 1 we get,
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Learn an entire GCSE course for maths, English and science on the most comprehensive online learning Firstly, we will determine the scale factor that relates the side-lengths, dividing the larger by the smaller
AQA A Level Biology practice papers and mark schemes. A great way to practise for your A Level Biology exams. The profit from every set is reinvested into making free content on MME, which benefits millions of learners across the country. To do this we need to find two corresponding dimensions. For the example below we will use lengths. To do this, we’ll use a process called elimination– we’re going to eliminate one of the variables by subtracting one equation from the other. We will write one equation on top of the other and draw a line underneath, as with normal subtraction. Two shapes are said to be mathematically similar if all of the angles in the shapes are equal, but the shapes are not necessarily the same size. then there is a solution for us to find that works for both equations. These equations are called simultaneous for this reason.The coefficient of \dfrac{1}{2} before -f(x) means that the graph of -f(x) is squashed vertically by a factor of 2. b) Now we have the scale factor, we can apply it to the corresponding length to BE which is BC. Hence, we find that, If we multiply the first equation by 3, we have two equations both with a 3x term, hence subtracting our new equation 2 from equation 1 we get,
a) To work out the scale factor, SF, we need to divide the given side-length on the bigger shape by the corresponding side of the smaller shape. Doing so, we get, AQA A Level Physics practice papers and mark schemes. The best way to practise for your upcoming exams. The profit from every set is reinvested into making free content on MME, which benefits millions of learners across the country.
GCSE English Literature Practice Papers are great for your preparation leading up to your exams. These papers have been created by English content experts and examiners, to look and feel like the real exams! Step 2: Now we must get the coefficients to match, in this case we can multiply the first equation by 2 You can use the following table to find the corresponding measure of a mathematically similar shape. Simultaneous equations are multiple equations that share the same variables and which are all true at the same time. a) To work out the scale factor, SF, we need to divide the given side-length on the bigger shape by the corresponding side of the smaller shape. Doing so, we get
Question 5: The diagram shows two mathematically similar rectangles, ABEF and ACDF. Find the scale factor, giving your answer in surd form. Now, to get the area of the bigger shape, we must multiply the area of the smaller one by this scale factor. Doing so, we get
Split the transformation up into 2 parts – firstly sketch y=3f(x) which is a stretch vertically by a scale factor of 3 (multiply the y-coordinates by 3: begin{aligned} 2x Therefore, to find the area of the smaller shape, we need to divide the area of the bigger shape by the area scale factor: 16. Doing so, we get Now, if the scale factor for the side-lengths is \textcolor{red}{4}, then that means that the scale factor for the areas is: When an equation has 2 variables its much harder to solve, however, if you have 2 equations both with 2 variables, like
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