AS PURE MATHS REVISION NOTES

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 =( )12( ) 25x = (52)x 3 QUADRATIC EQUATIONS AND GRAPHS Factorising identifying the roots of the equation ax2 + bc + c = 0 Look out f

Multiplying or Dividing by a negative value reverses the inequality Quadratic Inequality – always a good idea to sketch the graph! Solve 10 – 3x < 4 -3x < -6 x > 2 ... 9 POLYNOMIALS • A polynomial is an expression which can be written in the form ...

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