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P2 practice paper 20021121

P2 TEST    Surds indices and logarithms  220021009  DJS

No Calculators. Your working is crucial to the marking.

1    Simplify  a) ⁴√256     b)  64 ^3/2     c)  343  ^-1/3

2    Simplify  a)         5      .      b)      4 - √5
                            2√7+√3              2√5 +8

3    Solve         a)  log₉ x = 5     b)  log_x 9 = 5     c)   log_a (a³) = a

…. and do these differentiations, simplifying your answers as appropriate..

4   d  ( 3x^-5)             d  ( e^5x²)           d  ( 2x³ – 16) ^{–7 / 4}
     dx                       dx                      dx

5   d  ( 3x^-2 + 5x^-3) ^-2/3         d  (5x^-2 e^x³)         d  ( 2x² – 6x + 5)
     dx                                   dx                         dx(     x ^{– 3}       )

6   Find the stationary values and inflexions of the curve  

y = 12x⁵ – 15 x⁴ -20x³ +30x² – 10  and determine their type.