An 'extra challenge' section involves applying the laws of indices to algebraic expressions. Following this, the chapter focusses on collecting terms, multiplying and dividing terms and expanding and factorising single brackets. This foundation chapter starts with a section on using algebra words (term, expression, etc.) and writing expressions and equations. Year 10 Foundation Chapter 2: Algebraic Expressions Finally, pupils solve quadratic equations using graphs of related functions. Pupils then study graphs of quadratic functions, looking at x- and y- intercepts and turning points. In this chapter, pupils solve quadratic equations by factorising, completing the square and using the formula. 1) x y A N B N' B' A' reflection across the x-axis 2) x y S JU N S' J' U' N' translation: 4 units right and 4 units up 3) x y L U' C' C U L' reflection across the y-axis 4) x y I R V I' R' V' rotation 180 about the origin 5) x y J W F J' W' F' translation: 4 units right and 1 unit. This chapter covers averages and range, stem-and-leaf diagrams, quartiles, box plots, cumultaive frequency diagrams, scatter graphs and probability (including tree diagrams). TRANSFORMATIONS Write a rule to describe each transformation. The following steps will help to ensure a correct solution.We have added three more textbook chapters / booklets of our GCSE series: Year 10 Higher Chapter 6: Statistics & Probability It is often necessary to perform trasnformations in a certain order to guarantee the arrival at the correct graph. Sometimes you must identify more than one transformation to describe a mapping. Sometimes there will be a single similarity transformation in the sequence. It can be thought of as sequence of transformations the image of the first transformation is used as the pre-image for the second and so on. Explain 2 Finding a Sequence of Similarity Transformations In order for two figures to be similar, there has to be some sequence of similarity transformations that maps one figure to the other. Expressions such as ( x + 3) and ( x - 4) can represent a horizontal shift, but expressions such as ( x 2 + 3) and ( x 3 - 4) cannot. Geometry CC WS 2.4 - Composition of transformations Combining two or more transformations to form a new transformation is called a composition of transformations. Remember that a horizontal shift is associated with a change in the x-coordinate value (expressed as a linear expression - x with a power of 1). The parentheses were done first, then any multiplication/division, followed by any addition/subtraction. This pattern is similar to order of operations. There was a pattern to the order in which this problem was analyzed ( horizontal shift - vertical stretch - vertical shift). Be sure to draw each new image in a new color. Directions: Graph the original coordinates. The subtraction of 1 indicated a vertical shift of one unit down. Showing top 8 worksheets in the category - Sequences Of Transformations. Compositions of Transformations A, also known as composition of transformations is a series of multiple transformations performed one after the other. The parent has a slope of 1, whereas this new function will have a slope of 2. The multiplication of 2 indicates a vertical stretch of 2, which will cause to line to rise twice as fast as the parent function. This is a horizontal shift of three units to the left from the parent function. It can be seen that the parentheses of the function have been replaced by x + 3,Īs in f ( x + 3) = x + 3. The parent function is f ( x) = x, a straight line. Vertically oriented transformations and horizontally oriented transformations to not affect one another.Ĭonsider the problem f ( x) = 2( x + 3) - 1.If two or more of the transformations have a horizontal effect on the graph, the order of those transformations will most likely affect the graph. If two or more of the transformations have a vertical effect on the graph, the order of those transformations will most likely affect the graph.
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