Ecz additional mathematics grade 12 2012 paper 2
A particle starts from rest at a point 0 and moves in a straight line with velocity
v m/s given by v = 6t – 3t2, where t is the time in seconds after the start.
Find
(a) the acceleration of the particle when it is next at instantaneous rest,
(b) the maximum velocity,
(c) the distance travelled to that position when the particle was next at
instantaneous rest.
12 Answer only one of the following alternatives:
EITHER
The curve y = e^x – 2 meets the x-axis at A and the y-axis at B.
(a) Find the coordinates of A and B.
(b) Sketch the graph of y = e^2x – 2 for the domain -1 < x < 1. [3] [3] Find the equation of the straight line which must be drawn on the graph of -2 to obtain a solution of the equation x = (c) y = e-2x InWf —72—2x—+3 JV [3] -2x (d) State the range of f: x —>e – 2.
OR
(a) Grace would like to give a sum of money to a charity each year for 10 years.
She decides to give $120 in the first year, and to increase her contribution
by $10 each year.
How much does she give in the last year?
(ii) How much does the charity receive from her altogether?
