AM1 Algebraic Manipulation Expectations: All vocabulary words completed in your glossary (you can complete this digitally or in your theory book if you wish) All notes completed in theory book (an icon will be on each page to tell you which notes go in which book) Each exercise needs to have a heading and all questions numbered All work will be available via weebly if you need to catch up on missed or incomplete work All required questions must be completed, with required working, in workbook Extension questions are not compulsory, but are advisable to complete to improve your understanding of concepts

Why should I do extra hard questions? From the 2016 HSC Examination: Comments? The focus of this course is being able to read the questions and determine what is being asked for. There are frequently a large number of steps involved. More exposure to different levels of questions will prepare you more for the ‘final hurdle’

Vocabulary: Basic concepts: Add subtract and multiply algebraic terms Simplify algebraic expressions Substitute into expressions including formulae Solve linear equations involving two steps Vocabulary: algebraic expression axis common difference constant conversion dependent variable equation evaluate expand formulae function gradient independent variable intercept linear simplify solution point of intersection simultaneous linear equations stepwise linear function solve substitute y-intercept

Adding and Subtracting Terms When simplifying expressions, only like terms (those with exactly the same pronumeral part) can be added or subtracted. e.g. 3a + 4a = 7a, but 3a + 4b cannot be simplified. 1. 5a + 7a = 2. 13b - 4b = 3. 12ab + ab + 3ab = 4. 16xy - 4xy = 5. 7m - m = 6. 3a + 2a + 4b + 5b = 7. 7m + 3m + 5n - 2n = 8. 8a + 2b + 4a + 7b = 9. 10c + 5d - 2c - d = 10. 5a - 6b - 2a + 10b =

Multiplication of terms When multiplying pronumerals, remember that order is not important. However, the pronumerals in each term are usually written in alphabetical order. e.g. 6 x a = a x 6 = 6a, 3 x c x d = 3cd Also keep in mind that we usually leave out the x sign. e.g. 3 x a x b = 3ab It is also easier if you work out the sign (positive or negative), then multiply the numbers, then multiply the pronumerals. Simplify the following; 1. 4 x 3g = 2. 5 x 7h = 3. 9 x 4f = 4. 8 x 3df = 5. 5t x 4 = 6. 9k x 4f = 7. 9mn x 3mn = 8. 4de x 5 f = 9. 2a x 3b x 3c = 10. 5g x 6h x 2a =

Division of Terms The rules for division are the same as for multiplication, other than that order is important. e.g. 20ab ÷ 5a = 4b, 6a5x3 ÷2a2x = 3a3x2 20 a2b2 ÷ 10a = b) 45a4b6 ÷ 15ab = c) 6a3bc2 ÷ 11c =

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Grouping Symbols Examples of grouping symbols include parentheses ( ), brackets [ ], and braces { }. The expression 3(a+6) can be thought of as three groups of (a+6), or (a+6) + (a+6) + (a+6). When substituting into an expression with grouping symbols, remember to place a multiplication (x) sign next to the grouping symbols. For example, 4 ( n + 2 ) means 4 x ( n + 2 ) which gives 4 x n + 4 x 2 = 4n + 8 7 ( d - 4 ) means 7 x ( d - 4 ) which gives 7 x d - 7 x 4 = 7d - 28 a ( 2 + 6h ) means a x (2 + 6h) which gives a x 2 + a x 6h = 2a + 6ah

Match-Up! a) 5 ( d + 1 ) = b) 6 ( r + 1 ) = c) 4 ( z + 8) = d) 7 ( c - 5) = e) 5 ( v + 12) = f) 3 ( x - 7) = g) 2 ( 3x + 5) = h) x ( y + 3) = i) m ( n - 1) =

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Factorising Factorising is the opposite of expanding brackets. You need to find a common factor, then work out what you multiply it by to get each term in the original expression. e.g. 10x + 35 Look at the numbers, 10 and 35 can both be divided by 5, so it is a common factor. There is no common factor in the letters (pronumerals) in this question. Put the 5 at the front, open brackets and work out what you multiply 5 by to get 10x, write that inside the brackets. Do the same with 35. 10x + 35 = 5(2x + 7)

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Substitution Substitution is when you give a numerical value to a pronumeral, then evaluate the expression. e.g. if a=7, b=5 and c=-2, evaluate: 3a + 2b = 5(2a-c) = a2 + c2 =

Formulae A formula relates variables like length and area, speed and time, etc. To use a formula, decide what you need to find, and substitute in the information you have. Then simplify wherever possible. Check when you finish that you have answered the question carefully. e.g. if A = P(1+r)n find A given P=600, r=0.05 and n=3 A = 600 x (1 + 0.05)3 = 694.575

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Blood Alcohol Content Sometimes a formula is not exact. For example, BAC (blood alcohol content) can be affected by things such as your fitness level, whether you drink regularly and the state of your liver. An ESTIMATE of your BAC can be found using

How would you solve these linear equations?  

Solving two step equations: To solve a two step equation, we still work backwards, aiming for getting the variable by itself.

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