AS PURE MATHS REVISION NOTES

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AS pure MATHS REVISION NOTES 1 SURDS A root such as 3 that cannot be written exactly as a fraction is IRRATIONAL An expression that involves irrational roots is in SURD FORM 2 3 3 + 2 and 3 - 2 are CONJUGATE/COMPLEMENTARY surds needed to rationalise the denominator SIMPLIFYING = = RATIONALISING THE DENOMINATOR (removing the surd in the denominator) a + and a - are CONJUGATE/COMPLEMENTARY surds the product is always a rational number 2 INDICES Rules to learn = + =1 0=1 = 1 = ( ) = = Simplify 75 12 = 5 5 3 2 2 3 =5 3 2 3 = 3 3 Rationalise the denominator 22 3 =22 3 2+ 32+ 3 = 4+2 34+2 3 2 3 3 = 4+2 3 Multiply the numerator and denominator by the conjugate of the denominator Solve the equation 32 25 =15 (3 5)2 =(15)1 2 =1 =12 Simplify 2 ( )32+3( )12 ( )12(2 ( )+3) ( )12(2 2 2 +3) ( )32

www.mathsbox.org.uk 3 QUADRATIC EQUATIONS AND GRAPHS Factorising identifying the roots of the equation ax2 + bc + c = 0 • Look out for the difference of 2 squares x2 – a2= (x - a)(x + a) • Look out for the perfect square x2 + 2ax + a2 = (x + a)2 or x2 – 2ax + a2 = (x -a)2 • Look out for equations which can be transformed into quadratic equations

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