AC9M10A01Year 10AlgebraPractised on site

AC9M10A01 — Year 10 Algebra

Official Curriculum Content Description:

expand, factorise and simplify expressions and solve equations algebraically, applying exponent laws involving products, quotients and powers of variables, and the distributive property

Worked Examples (3)

Example 1Solving Quadratics by Completing the Square
Write x2+2x+2x^2 + 2x + 2 in the form (x+a)2+b(x + a)^2 + b.
Correct Answer:(x+1)2+1(x + 1)^2 + 1
Worked Solution:
Identify b=2b = 2 and c=2c = 2: Half of bb is p=22=1p = \frac{2}{2} = 1. Subtract p2=1p^2 = 1 from c=2c = 2 to get q=2−1=1q = 2 - 1 = 1. =(x+1)2+1= (x + 1)^2 + 1.
Example 2Factorising Non-Monic Quadratics
Factorise 4x2−28x+494x^2 - 28x + 49.
Common mistake: Sign error in factorising non-monic quadratic
Correct Answer:(2x−7)(2x−7)(2x - 7)(2x - 7)
Worked Solution:
Factorise 4x2−28x+494x^2 - 28x + 49 by trial or grouping: Split the middle term or test factors of 4 and 49. =(2x−7)(2x−7)= (2x - 7)(2x - 7).
Example 3Solving Quadratic Equations by Factorising
Solve by factorising: x2+6x−16=0x^2 + 6x - 16 = 0.
Common mistake: Reporting only one solution to the quadratic equation
Correct Answer:x=−8x = -8 or x=2x = 2
Worked Solution:
Factorise into two brackets: (x+8)(x−2)=0(x + 8)(x - 2) = 0 Set each factor to zero to find the roots: x=−8x = -8 or x=2x = 2.

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