FPM Questions [7]

1.   Differentiate e3xcos 2x w.r.t. x. [3]

2.   In triangle PQR, PQ=4, QR=7.3 and RP = 5.9.
Find angle PRQ to 1d.p. Find the area of the triangle [3,3]

3.   Given y= 2 - 4/(x-3) (x<>3).
Find asymptotes [2] intercepts [2] Sketch the curve.[3]

4.  A particle moves along a straight line such that its velocity is given b
v= 2t
³ - 5t² - 18t, for t>=0. Find when the particle is at rest [3]
Find the distance travelled in the interval 0<t<3 [4]

5.   The sum to infinity of a convergent geometric series is 81x and the sum of the first three terms is 32x.
Find (possible values of) the common ratio. [4]
Given that the first term is positive, find the first term. [2]

6.   By writing values of sin 45º and sin 30º find the exact value of sin 15º and sin 75º (degrees understood). Write an expression for sin 2θ and hence the exact value of sin 37.5º.

7.    Given that tan θ is 2/7 and acute, find the exact value of sin2θ.

DJS 20130402


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