r,-l1 r.: ,
a G*odq I a- Mn:z &o ta
Inthediagram,thegraphs of f(x) = ox? * bx* candg(x):p, + q:rerepresented.
y = -l is an aqmptote to g(x).
/(x) passes through the origin The turning point of /(x) is (2;3) which is atso the point of intersection
between g(x) and f (x).
(a) Determine the equation of f (x) in the form ! = axz * bx *c t3l
(bJ Determine the equarion of g@). (3)
[c) Give the range of g(x). (1)
(d) Determine tlre coordinates of the turning point of f (x) if it undergoes a transformation of
f(x+4)+s (2)
I
(1) Give the equation of an asymptote of.;t. (1)
(2) Determine the coordinates of pointAn the point where the straight line g(x) = - x + 4
intercepts the hlryerbola. (4)
(3) Give the equation of h if ll is the translation of ;[ by,two units to the left (1)
(4) .r forwhich f(x) > S@)
Determinetherraluesof (2)
(E-> C:rtre or.\ e-1.^-e1.,-^. oF ql\ o,=-i* oF =t"^'*"-\ og h(rc-)
, Qu.esLrs.n 3
The graph of f(x) = log, x and h(x) = -3 aregivenbelow:
i
(11 Determine the coordinates oft
(D (1)
(iD (2)
(z) Use the graph to solve for r if log, r > - 3 (2)
3
(3) Determine the equation of f -' (x) in the form f -1(r) : (2)
t4l Determine the new equation of f (x) , it f (x) is reflected about the z-axis. (1)
+
Events A and B are mutually exclusive. It is given drat:
. P(B):2P(A)
. P(A or B) : 0,57
(-r)
Calculate P(B).
Two identical bags are filled with balls. Bag A contains 3 pink and 2 yellow balls'
L[
Bag B contains S pinf< and 4 yellow balls. It is equally likely that Bag A or Bag B
is
chosen- Each ball has an egual chance ofbeing chosen from the bag- A bag is chosen
at random and a ball is then chosen at randorn from the bag'
. t Represent the information by meal]s of a tree diagram- clearly indicate the
pr-obabiliry associated with each branch of the tree diagram and write
(4)
down all the outcomes.
.2 what is the probabilify that a yellow ball will be chosen from Bag A? (1)
.3 Wrat is the probability that a pink ball u'ill be chosen? (3)
a G*odq I a- Mn:z &o ta
Inthediagram,thegraphs of f(x) = ox? * bx* candg(x):p, + q:rerepresented.
y = -l is an aqmptote to g(x).
/(x) passes through the origin The turning point of /(x) is (2;3) which is atso the point of intersection
between g(x) and f (x).
(a) Determine the equation of f (x) in the form ! = axz * bx *c t3l
(bJ Determine the equarion of g@). (3)
[c) Give the range of g(x). (1)
(d) Determine tlre coordinates of the turning point of f (x) if it undergoes a transformation of
f(x+4)+s (2)
I
(1) Give the equation of an asymptote of.;t. (1)
(2) Determine the coordinates of pointAn the point where the straight line g(x) = - x + 4
intercepts the hlryerbola. (4)
(3) Give the equation of h if ll is the translation of ;[ by,two units to the left (1)
(4) .r forwhich f(x) > S@)
Determinetherraluesof (2)
(E-> C:rtre or.\ e-1.^-e1.,-^. oF ql\ o,=-i* oF =t"^'*"-\ og h(rc-)
, Qu.esLrs.n 3
The graph of f(x) = log, x and h(x) = -3 aregivenbelow:
i
(11 Determine the coordinates oft
(D (1)
(iD (2)
(z) Use the graph to solve for r if log, r > - 3 (2)
3
(3) Determine the equation of f -' (x) in the form f -1(r) : (2)
t4l Determine the new equation of f (x) , it f (x) is reflected about the z-axis. (1)
+
Events A and B are mutually exclusive. It is given drat:
. P(B):2P(A)
. P(A or B) : 0,57
(-r)
Calculate P(B).
Two identical bags are filled with balls. Bag A contains 3 pink and 2 yellow balls'
L[
Bag B contains S pinf< and 4 yellow balls. It is equally likely that Bag A or Bag B
is
chosen- Each ball has an egual chance ofbeing chosen from the bag- A bag is chosen
at random and a ball is then chosen at randorn from the bag'
. t Represent the information by meal]s of a tree diagram- clearly indicate the
pr-obabiliry associated with each branch of the tree diagram and write
(4)
down all the outcomes.
.2 what is the probabilify that a yellow ball will be chosen from Bag A? (1)
.3 Wrat is the probability that a pink ball u'ill be chosen? (3)
