S4 (4.2) Algebraic Fractions.notebook September 03, 2015
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1 Daily Practice (b) 24k 20 (e) x = m (g) 45 = 90% = 1% = 100%
2 Daily Practice Q1. Simplify m 7 m 3 Q2. State the gradient of the line joining (-5, 2) and (3, 7) Q3. Simplify Q4. Simplify Simplifying Algebraic Fractions L.I: Today we will be learning how to simplify algebraic fractions. How do you simplify a fraction? S.C: We will be able to simplify an algebraic fraction using our knowledge of factorising and simplifying. How do you simplify a fraction in the form? Homework Due! Simplifying Algebraic Fractions Same process as simplifying regular fractions First fully factorise numerator & denominator where possible. Divide top and bottom by a common factor (otherwise known as cancelling) Examples: Simplify the following (a) (b) (c)
3 Daily Practice Q1. Calculate the magnitude of the vector Q2. State the equation of the line joining (-2, 3) and (5, -4) Q3. Calculate the area of the hexagon shown, given the diagonals are 40cm Daily Practice Q Mutliply out and simplify x x x Q Calculate the original cost of a bike that is now &' in the sale with L.I: Today we will be continuing to learn how to simplify algebraic fractions. () off Q Calculate the angle at the centre given that the area is (+cm 8cm Factorising Factorising is the reverse process of multiplying out brackets. There are three main types: L.I: Today we will be revising over factorising. 1. Taking out a common factor. 2. Difference of 2 squares. (Two terms that are squares with a minus inbetween E.g. of the form x 2 - y 2 ) 3. Trinomials i.e. in the form ax 2 + bx + c You should always look to take out a common factor first where possible. Then you may need to use methods 2 or 3 also.
4 Factorising Examples: Common factor Factorise (i) 3x 2 h + 6xh (ii) 21abc + 12bc 2 Factorising Examples: Difference of two squares Factorise (i) 25 - y 2 (ii) 49a 2 b 2-100c 2 (iii) 50x 2-2 Factorising Examples: Trinomials Factorise (i) x 2-15x + 56 (ii) 2a 2 + 9a - 5 (iii) 6a 2 + 7a y x 2-25x 24ab 2-16b
5 x 2-25 b ax 2 - ab 2 81x 2-25h 2 x 3-25x x 2 + 4x + 3
6 x 2 + 8x + 15 x 2-6x - 72 x 2-19x x 2 + 7x + 3 5x 2-8x x 2-13x + 4
7 12x x x 2-12x + 9 6x 2-27x x 2 + 6x - 10 Daily Practice x 2-2x - 144
8 Adding/Subtracting Algebraic Fractions L.I: Today we will be learning how to add/subtract algebraic fractions. How do you add two fractions together? S.C: We will be able to add/subtract algebraic fractions. What if the fractions had algebraic terms? Adding/Subtracting Algebraic Fractions Same process as adding/subtracting regular fractions. Find a common denominator Convert the fractions so that they have the same denominator Add/subtract them. Adding/Subtracting Algebraic Fractions Examples: Express as single fractions (a) (b) n 0 Simplify where possible (at the end). (c) b 0 Daily Practice Q1. Multiply out and simplify (2x + 4)(x 2 + 3x - 5) Q2. Factorise x 2 + x - 2 Q3.State the equation of the line that passes through (0, 4) and (3, 1) L.I: Today we will be continuing to practise adding and subtracting fractions. Q4. State the magnitude of the vector
9 Adding/Subtracting Algebraic Fractions Express as single fractions in their simplest form Express as a single fraction in its simplest form (d) k 0 Daily Practice Q1. Calculate the volume of the cone shown to 3 s.f. 8cm Q2. Multiply out and simplify (3x + 1) 2 Q3. Factorise 3x 2 - x cm Today we will be continuing to practise adding and subtrcating algebraic fractions. Q4. Simplify Adding/Subtracting Algebraic Fractions (1) x 0, 1 (2) x -4, 5 Page 55
10 Daily Practice Q1. A farmer has five crates of carrots, each weigh 17kg, 16kg, 19kg, 18kg and 20kg. Calculate the mean and standard deviation of the crates The farmer says that they should have a mean weight of 18kg and a maximum standard deviation of 1.5kg. Do the farmer's crates fall within these guidelines? L.I: Today we will be learning how to muliply and divide algebraic fractions. S.C: We will be able to multiply and divide algebraic fractions and simplify our answers when possible. Daily Practice Q1. Find the original value of a car that has depreciated by 15% and is now valued at Q2. State the equation of the line joining (2, 5) and (4, -8) Q3. Simplify Today we will be learning how to divide algebraic fractions. Homework Online due Q4. Simplify Multiplying/Dividing Algebraic Fractions Follow the same process as multiplying and dividing regular fractions. Simplify where possible. You may be able to cancel terms before you multiply to make it easier. Multiplying/Dividing Algebraic Fractions (iii) Examples: (i) (ii) Nat 5 Pack 1- Unit EF (complete).pdf
11 Success? I can add and subtract algebraic fractions. I can multiply & divide algebraic fractions and simplify where possible. Daily Practice Q1. Calculate the area of the minor sector shown cm Q2. Factorise 15x 2-5xy Q3. Multiply out and simplify (3m - 1)(2m + 4) L.I: Today we will be learning how to complete Exam style questions on Algebraic Fractions. Homework Due Monday. Q4. Simplify 2014 N5 Non -Calculator 2014 Intermediate 2 Calculator
12 Daily Practice Q1. Multiply out and simplify (3x - 1)(x + 4) Q2. Factorise x 2 + 3x - 18 Q3. Multiply out and simplify 2x 2 (x 3 - x -3 ) Today we will be continuing to practise questions on algebraic fractions. Q4. Write as a single fraction x Intermediate 2 Non - Calculator 2012 Intermediate 2 Calculator 2013 Intermediate 2 Calculator 2011 Intermediate 2 Calculator 2010 Intermediate 2 Non - Calculator
13 Daily Practice Q1. Multiply out and simplify (3x - 4)(2x 2 + x - 5) Q2. Simplify Q3. Calculate the value of 2a + 3b where and Q4. Write as a single fraction Today we will be continuing to practise mixed algebraic fractions. Homework Due Monday!
14 Daily Practice Q1. Multiply out and simplify (3x - 1) 2 Q2. Factorise x 2-11x + 24 Q3. Calculate the volume of a cone with diameter of base 16cm and height 12cm to 2 s.f. Q4. Simplify fully Today we will be marking homework. Homework Due Today
15 Daily Practice Questions Mental Mathematics Today we will be completing a check-up on algebraic fractions.
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