Post on 02-Jun-2018
8/11/2019 Exam Questions Quadratics an Funtions (1)
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1. The diagram represents the graph of the function
f:x (xp)(x q).
x
y
C
21
2
(a) Write down the values ofpand q.
(b) The function has a minimum value at the point C. Find thexcoordinate of C.
(Total 4 marks)
2. The e!uationx2 2kx" 1 # $ has two distinct real roots. Find the set of all possible values of k.
(Total 6 marks)
3. (a) %&pressf (x)= x2 'x" 1 in the formf (x) # (xh)
2" k where h and kare to be
determined.
(b) *ence or otherwise write down the coordinates of the verte& of the parabola with
e!uationyx2 'x " 1.
(Total 4 marks)
4. (a) %&press + # 2x2 12x" 2, in the formy# 2(x c)
2" d.
The graph ofy#x2is transformed into the graph ofy# 2x
2 12x" 2, b+ the transformations
a vertical stretch with scale factor kfollowed by
a hori-ontal translation ofpunits followed by
a vertical translation of qunits.
(b) Write down the value of
(i) k
(ii) p
(iii) q.(Total 6 marks)
1
8/11/2019 Exam Questions Quadratics an Funtions (1)
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8/11/2019 Exam Questions Quadratics an Funtions (1)
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5. The diagram shows part of the graph ofy= a (x h)2+ k. The graph has its vertex at P,
and passes through the point A with coordinates (, !).
/
0
1 $ 1 x
y
2
1
(a) Write down the value of
(i) h
(ii) k.
(b) alculate the value of a.
(Total 6 marks)
6. The functionfis given b+f (x) #x2" x forx,.
(a) Writef (x) in the form (xa)
2
" b.
(b) Find the inverse functionf1
.
(c) 3tate the domain off1
.
(Total 6 marks)
7. Two functionsfg are defined as follows:
f:x ,x " 4g :x 2(1 x)
Find
(a) f1
(2)
(b) (g f )().
(Total 4 marks)
3
8/11/2019 Exam Questions Quadratics an Funtions (1)
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8. "et f (x) = 2x+ and g (x) = #x2 $.
Find
(a) f1
(x)
(b) (gf) (2)
(c) (fg) (x).
(Total 6 marks)
9. Three of the following diagrams 5 55 555 56 represent the graphs of
(a) y# , " cos 2x
(b) y# , cos (x" 2)
(c) y# 2 cosx" ,.
5dentif+ which diagram represents which graph.
x
1
2
1
2
3
2
y
2
1
1
2
x
1
2
1
2
3
2
y
,
2
1
,
y
x
(
2
1
2
1
2
3
2
x
1
2
1
2
3
2
4
(
,
2
1
y
5
5 5 5
5 5
5 6
(Total 4 marks)
4
8/11/2019 Exam Questions Quadratics an Funtions (1)
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10. 7etf(x) # ,(x" 1)2 12.
(a) 3how thatf(x) # ,x2" 'x .
(2)
(b) For the graph off
(i) write down the coordinates of the verte&
(ii) write down the equationof the a&is of s+mmetr+
(iii) write down theyintercept
(iv) find bothxintercepts.()
(c) !en"es8etch the graph off.(2)
(d) 7etg(x) #x2. The graph offma+ be obtained from the graph ofgb+ the two
transformations:
a stretch of scale factor tin theydirection
followed b+
a translation of
.
q
p
Find
q
p
and the value of t.(3)
(Total 1# marks)
5