JJC JC1 H2 Maths 2012 Promo Questions Uploaded 
2013 JC1 December Holiday Assignment
JJC 2012 H2 Mathematics Promotional Examination
1
−2
Expand ( k + y ) up to and including the term in y 2 , where k is a non-zero constant. State the range of values of y for which the expansion is valid.
[4]
In the expansion of ( k + x + 2 x 2 )
−2
in ascending powers of x, the coefficient of x 2 is zero. Find
the value of k.
2
The curve C has equation y =
[3]
2x + a
, where a is a positive constant. By rewriting the equation x−3 B
, where A and B are constants, state a sequence of geometrical transformations x−3 1 which transform the graph of y = to the graph of C.
[4]
x
as y = A +
Sketch C for the case where a = 3, giving the equations of any asymptotes and the coordinates of any points of intersection with the x- and y-axes.
3
[3]
The diagram below shows the curve with equation y = f(x ). y −1
O
1
x
−2
x = −1
x =1
On separate diagrams, sketch the curves with the following equations, making clear the main relevant features of the curves.
(i)
y=
1
,
f ( x)
[3]
(ii)
y = f '( x ).
[3]
2013 JC1 December Holiday Assignment
JJC 2012 H2 Mathematics Promotional Examination
4
A sequence of positive numbers u1 , u2 , u3 , … satisfies the recurrence relation un +1 =
3un + 20 un + 1
for n ≥ 1 .
(i)
Given that u1 = 3 , find u10 correct to 4 decimal places.
[1]
(ii)
Given that the sequence converges to L, find the exact value of L.
[2]
(iii)
Show that un ≥ 3 for all n ≥ 1 .
∞
Hence determine whether the series
∑u
r
is convergent.
[2]
r =1
5
The function f is defined by f : x
(i)
x+2
, for x ∈ » , x ≠ 1 . x −1
Find f 2 ( x ) and f 2012 ( x) .
The function g is defined by g : x
[3]
cos x , for 0 < x < 2π .
(ii)
Explain why the composite function fg exists.
[2]
(iii)
Define fg, giving its domain.
[2]
(iv)
Find the range of fg.
[1]
(i)
Prove by mathematical induction that
(ii)
Find
n
6
r ( r + 1)
∑
r =1
2
2n
∑
2
r ( r + 1) , giving the answer in the form
r = n +1
=
n(
JJC 2012 H2 Mathematics Promotional Examination
1
−2
Expand ( k + y ) up to and including the term in y 2 , where k is a non-zero constant. State the range of values of y for which the expansion is valid.
[4]
In the expansion of ( k + x + 2 x 2 )
−2
in ascending powers of x, the coefficient of x 2 is zero. Find
the value of k.
2
The curve C has equation y =
[3]
2x + a
, where a is a positive constant. By rewriting the equation x−3 B
, where A and B are constants, state a sequence of geometrical transformations x−3 1 which transform the graph of y = to the graph of C.
[4]
x
as y = A +
Sketch C for the case where a = 3, giving the equations of any asymptotes and the coordinates of any points of intersection with the x- and y-axes.
3
[3]
The diagram below shows the curve with equation y = f(x ). y −1
O
1
x
−2
x = −1
x =1
On separate diagrams, sketch the curves with the following equations, making clear the main relevant features of the curves.
(i)
y=
1
,
f ( x)
[3]
(ii)
y = f '( x ).
[3]
2013 JC1 December Holiday Assignment
JJC 2012 H2 Mathematics Promotional Examination
4
A sequence of positive numbers u1 , u2 , u3 , … satisfies the recurrence relation un +1 =
3un + 20 un + 1
for n ≥ 1 .
(i)
Given that u1 = 3 , find u10 correct to 4 decimal places.
[1]
(ii)
Given that the sequence converges to L, find the exact value of L.
[2]
(iii)
Show that un ≥ 3 for all n ≥ 1 .
∞
Hence determine whether the series
∑u
r
is convergent.
[2]
r =1
5
The function f is defined by f : x
(i)
x+2
, for x ∈ » , x ≠ 1 . x −1
Find f 2 ( x ) and f 2012 ( x) .
The function g is defined by g : x
[3]
cos x , for 0 < x < 2π .
(ii)
Explain why the composite function fg exists.
[2]
(iii)
Define fg, giving its domain.
[2]
(iv)
Find the range of fg.
[1]
(i)
Prove by mathematical induction that
(ii)
Find
n
6
r ( r + 1)
∑
r =1
2
2n
∑
2
r ( r + 1) , giving the answer in the form
r = n +1
=
n(