# Revision of Basic Algebra

May 19th, 2015
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Square of a sum: (A + B)2 = A2 +2AB + B2 Square of a difference: (A – B)2 = A2 – 2AB + B2 Difference of squares: (A + B)(A – B) = A2 - B2 Four methods of factoring: - Highest common factor

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MathematicsRevision of Basic AlgebraIndex lawsaxay = ax + y = ax y(ax)n = axn(ab)x = axbx = Square of a sum: (A + B)2 = A2 +2AB + B2Square of a difference: (A B)2 = A2 2AB + B2Difference of squares: (A + B)(A B) = A2 - B2Four methods of factoring:Highest common factor2 terms = Difference of squares3 terms = Quadratics4 + terms = GroupingFractions1. Factorise numerators and denominators2. Cancel common factorsCompounds Fractions:1. Find lowest common multiple of the denominators on the top and bottom2. Multiply top and bottom by this lowest common multipleSum of a cube: a3 + b3 = (a + b)(a2- ab + b2)Difference of a cube: a3- b3 = (a - b)(a2 + ab +b2)Completing the square: ax2 + bx + c = 0ax2 + bx = -cx2 + = - x2 + bx +()2 = - +()2(x +)2 = - +(x +)2 = x + = x + b = x = Converting a recurring decimal to a fractionConverting a recurring decimal to a fraction using a GPSurd rules:Miscellaneous rule:Real functionsA function is a relation that when a vertical line is drawn it will only cut in one place.Functions: y = f(x)Domain is set of x valuesRange is set of y values Circle: x2 + y2 = r2 Semi-circle: Shift right: Shift left: Shift up: Shift down:Even and reflects in y: Odd and reflects in x: Shifted circles: (x h)2 + (y k)2 = r2 (h,k) = centre of circleAbsolute values: y = |x a | is y = x a or y = -(x - a) a > 0Graphing regions:1. 2. Corners have closed

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