larbert high school faculty of mathematics24453]higher_past...2009 p1 q15 2009 p1 q21 2010 p1 q1...
TRANSCRIPT
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Larbert High School
Faculty of Mathematics
SQA Higher Past Paper Questions (Ordered by Topic)
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FORMULAE LIST
Circle:
The equation 2 2 2 2 0x y gx fy c+ + + + = represents a circle centre ( , )g f− − and radius 2 2 .g f c+ −
The equation 2 2 2( ) ( )x a y b r− + − = represents a circle centre ( , )a b and radius r.
Scalar Product : . cos ,= θa b a b where θ is the angle between a and b.
or 1 1
1 1 2 2 3 3 2 2
3 3
. , where and .a b
a b a b a b a ba b
= + + = =
a b a b
Trigonometric formulae:
2 2
2
2
sin(A B) sin A cos B cos A sin Bcos(A B) cos A cos B sin A sin B
sin 2A 2sin A cos Acos 2A cos A sin A
2cos A 11 2sin A
± = ±± =
=
= −
= −
= −
Table of standard derivatives :
Table of standard integrals :
( )f x ( )f x′
sin
cos
ax
ax
cos
sin
a ax
a ax−
( )f x ( )f x dx∫ sin
cos
ax
ax
1 cos
1 sin
ax Ca
ax Ca
− +
+
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Contents
Straight Lines Page 5 Functions and Graphs Page 18 Differentiation Page 32 Recurrence Relations Page 51 Polynomials and Quadratics Page 57 Integration Page 75 Trigonometry Page 88 Circles Page 103 Vectors Page 114 The Wave Function Page 129 Logarithms and Exponentials Page 133
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Higher Past Paper Questions by Topic Straight Lines
Note: Some questions overlap 2 topic areas; these are in both topic sections.
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2000
P1 Q
3
2001
P1 Q
1
2001
P1 Q
11
2001
P2 Q
7
2002
P1 Q
4
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2002
P2 Q
1
2003
P1 Q
1
2004
P1 Q
1
2004
P2 Q
1
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2006
P1 Q
1
2006
P2 Q
1
2007
P1 Q
1
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2008
P1 Q
5
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2008
P1 Q
7
2008
P2 Q
1
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2009
P1 Q
5
2009
P1 Q
15
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2009
P1 Q
21
2010
P1 Q
1
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2010
P1 Q
8
2010
P1 Q
21
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2010
P1 Q
23
2011
P1 Q
2
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2011
P1 Q
8
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2011
P1 Q
21
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2012
P1 Q
4
2012
P1 Q
23
2013
P1 Q
5
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2013
P2 Q
2
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Higher Past Paper Questions by Topic
Functions and Graphs
Note: Some questions overlap 2 topic areas; these are in both topic sections.
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2000
P1 Q
2
2000
P2 Q
3
2001
P1 Q
7
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2001
P1 Q
10
2002
P1 Q
3
2003
P1 Q
9
2003
P2 Q
5
2004
P1 Q
4
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2005
P1 Q
4
2006
P1 Q
3
2006
P2 Q
7
2007
P1 Q
3
2008
P1 Q
17
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2008
P2 Q
20
2008
P2 Q
23
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2009
P1 Q
10
2009
P1 Q
23
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2009
P2 Q
2
2010
P1 Q
11
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2010
P1 Q
13
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2010
P1 Q
19
2010
P1 Q
20
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2011
P1 Q
3
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20
11
P1 Q
22
2011
P2 Q
2
2012
P1 Q
18
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2012
P2 Q
1
2013
P1 Q
1
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2013
P1 Q
11
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Higher Past Paper Questions by Topic Differentiation
Note: Some questions overlap 2 topic areas; these are in both topic sections.
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2000
P1 Q
2
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2000
P1 Q
4
2000
P1 Q
8
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2000
P2 Q
1
2000
P2 Q
6
2000
P2 Q
8
2001
P1 Q
6
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2001
P1 Q
9
2001
P2 Q
2
2001
P2 Q
11
2002
P1 Q
4
2002
P1 Q
6
2002
P1 Q
10
2002
P2 Q
6
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2003
P1 Q
5
2003
P2 Q
4
2003
P2 Q
6
2003
P2 Q
8
2004
P1 Q
6
2004
P1 Q
8
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2004
P1 Q
11
2004
P2 Q
5
2004
P2 Q
7
2004
P2 Q
9
2005
P1 Q
5
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2005
P2 Q
6
2006
P1 Q
5
2006
P1 Q
3
2006
P2 Q
9
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2006
P2 Q
12
2007
P1 Q
9
2007
P1 Q
10
2007
P2 Q
5
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2007
P2 Q
6
2007
P2 Q
10
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2008
P2 Q
15
2008
P2 Q
21
2008
P2 Q
22
2008
P2 Q
3
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2008
P2 Q
6
2009
P1 Q
4
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2009
P1 Q
8
2009
P1 Q
20
2009
P2 Q
1
2009
P2 Q
2
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2010
P1 Q
12
2010
P1 Q
15
2010
P1 Q
17
2010
P2 Q
5
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2011
P1 Q
4
2011
P1 Q
13
-
20
11
P1 Q
22
2012
P1 Q
2
2012
P1 Q
6
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2012
P1 Q
8
2012
P1 Q
16
2012
P2 Q
3
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2012
P2 Q
4
2013
P1 Q
2
2013
P1 Q
18
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2013
P2 Q
3
2013
P2 Q
7
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Higher Past Paper Questions by Topic
Recurrence Relations
Note: Some questions overlap 2 topic areas; these are in both topic sections.
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2000
P1 Q
5
2001
P2 Q
3
2002
P2 Q
4
2003
P1 Q
4
2004
P2 Q
4
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2005
P1 Q
6
2006
P1 Q
4
2007
P1 Q
7
2008
P1 Q
1
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2008
P1 Q
4
2009
P1 Q
1
2009
P1 Q
6
2010
P1 Q
2
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2010
P1 Q
7
2011
P2 Q
3
2012
P1 Q
1
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2012
P2 Q
6
2013
P1 Q
8
2013
P2 Q
1
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Higher Past Paper Questions by Topic Polynomials and Quadratics
Note: Some questions overlap 2 topic areas; these are in both topic sections.
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2000
P2 Q
1
2000
P2 Q
4
2001
P1 Q
2
2001
P1 Q
4
2001
P2 Q
1
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2001
P2 Q
11
2002
P1 Q
7
2002
P2 Q
3
2002
P2 Q
5
2002
P2 Q
9
2003
P1 Q
2
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2003
P1 Q
7
2003
P1 Q
11
2003
P2 Q
1
2004
P1 Q
2
2004
P1 Q
8
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2004
P1 Q
11
2004
P2 Q
3
2005
P1 Q
8
2005
P2 Q
5
2005
P2 Q
11
2006
P1 Q
8
2006
P2 Q
2
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2006
P2 Q
3
2007
P1 Q
4
2007
P1 Q
8
2007
P2 Q
3
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2007
P2 Q
10
2008
P1 Q
10
2008
P1 Q
13
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2008
P2 Q
16
2008
P2 Q
21
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20
08
P2 Q
22
2008
P2 Q
4
2009
P1 Q
9
2009
P1 Q
12
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2009
P2 Q
3
2010
P1 Q
5
2010
P1 Q
6
2010
P1 Q
16
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2010
P1 Q
18
2010
P1 Q
22
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20
10
P2 Q
3
2011
P1 Q
5
2011
P1 Q
7
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2011
P1 Q
9
2011
P1 Q
17
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2011
P1 Q
18
2011
P2 Q
2
2011
P2 Q
4
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2011
P2 Q
7
2012
P1 Q
3
2012
P1 Q
13
2012
P1 Q
19
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2012
P1 Q
21
2013
P1 Q
3
2013
P1 Q
6
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2013
P1 Q
13
2013
P1 Q
17
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2013
P1 Q
19
2013
P1 Q
21
2013
P2 Q
3
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Higher Past Paper Questions by Topic
Integration
Note: Some questions overlap 2 topic areas; these are in both topic sections.
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2000
P1 Q
4
2000
P2 Q
4
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2000
P2 Q
10
2001
P2 Q
6
2001
P2 Q
8
2001
P2 Q
10
2002
P2 Q
5
2002
P2 Q
8
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2003
P1 Q
8
2003
P2 Q
3
2004
P1 Q
7
2004
P2 Q
11
2005
P2 Q
1
2005
P2 Q
5
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2006
P1 Q
6
2006
P2 Q
5
2007
P1 Q
8
2007
P2 Q
7
2008
P2 Q
7
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2008
P2 Q
14
2009
P1 Q
16
2009
P2 Q
5
-
2010
P1 Q
9
2010
P1 Q
14
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2010
P2 Q
6
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2011
P1 Q
11
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2011
P1 Q
16
2011
P2 Q
4
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2011
P2 Q
6
2012
P1 Q
11
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2012
P1 Q
14
2012
P1 Q
21
2013
P1 Q
7
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2013
P1 Q
16
2013
P2 Q
4
2013
P2 Q
6
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Higher Past Paper Questions by Topic Trigonometry
Note: Some questions overlap 2 topic areas; these are in both topic sections.
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2000
P1 Q
1
2000
P2 Q
5
2001
P1 Q
5
2001
P1 Q
7
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2001
P2 Q
10
2002
P1 Q
5
2002
P1 Q
8
2002
P1 Q
9
2002
P2 Q
6
2003
P1 Q
10
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2003
P2 Q
2
2003
P2 Q
6
2003
P2 Q
10
2004
P1 Q
3
2005
P1 Q
9
2005
P2 Q
2
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2005
P2 Q
8
2006
P1 Q
7
2006
P2 Q
8
2007
P1 Q
6
2007
P1 Q
11
2007
P2 Q
1
2007
P2 Q
4
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2008
P1 Q
6
2008
P1 Q
9
2008
P2 Q
3
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2008
P2 Q
5
2009
P2 Q
7
2009
P1 Q
11
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2009
P1 Q
13
2009
P1 Q
14
2009
P1 Q
24
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2009
P2 Q
5
2010
P1 Q
4
2010
P1 Q
11
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2010
P1 Q
23
2010
P2 Q
2
2010
P2 Q
4
2011
P1 Q
10
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2011
P1 Q
12
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2011
P1 Q
20
2011
P1 Q
23
2012
P1 Q
5
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2012
P1 Q
9
2012
P1 Q
12
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2012
P2 Q
6
2013
P1 Q
4
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2013
P1 Q
9
2013
P1 Q
10
2013
P1 Q
15
2013
P2 Q
8
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Higher Past Paper Questions by Topic
Circles
Note: Some questions overlap 2 topic areas; these are in both topic sections.
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2000
P1 Q
6
2000
P2 Q
2
2001
P1 Q
11
2002
P1 Q
1
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2003
P1 Q
11
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2004
P2 Q
8
2005
P1 Q
2
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2005
P1 Q
11
2005
P2 Q
3
2006
P1 Q
2
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2006
P2 Q
4
2007
P1 Q
5
2007
P2 Q
5
-
2008
P1 Q
2
2008
P1 Q
5
-
2008
P2 Q
4
2009
P1 Q
2
2009
P1 Q
9
-
2009
P2 Q
4
2010
P1 Q
8
-
2010
P2 Q
3
2011
P1 Q
6
-
2011
P2 Q
7
2012
P2 Q
2
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2013
P1 Q
22
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Higher Past Paper Questions by Topic Vectors
Note: Some questions overlap 2 topic areas; these are in both topic sections.
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2000
P1 Q
7
2000
P2 Q
7
2000
P2 Q
9
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2001
P1 Q
3
2001
P2 Q
4
-
2002
P1 Q
2
2002
P2 Q
2
2003
P1 Q
3
2003
P1 Q
6
2003
P2 Q
9
2004
P1 Q
5
2004
P1 Q
10
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2004
P2 Q
2
2005
P1 Q
3
2005
P2 Q
4
2005
P2 Q
10
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2006
P1 Q
9
2006
P2 Q
6
2007
P1 Q
2
-
2007
P2 Q
1
2008
P1 Q
3
2008
P1 Q
11
-
2008
P1 Q
12
2008
P1 Q
18
-
2008
P2 Q
2
2009
P1 Q
3
2009
P1 Q
17
-
2009
P1 Q
22
2009
P2 Q
7
2010
P1 Q
3
-
2010
P1 Q
10
2010
P2 Q
1
-
2011
P1 Q
1
2011
P1 Q
14
-
2011
P1 Q
15
2011
P2 Q
1
2012
P1 Q
7
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2012
P1 Q
10
2012
P1 Q
15
-
2012
P1 Q
17
2012
P2 Q
5
2013
P1 Q
12
2013
P1 Q
14
2013
P1 Q
24
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Higher Past Paper Questions by Topic
The Wave Function
Note: Some questions overlap 2 topic areas; these are in both topic sections.
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2000
P1 Q
10
2001
P2 Q
5
2003
P2 Q
7
2004
P2 Q
6
2005
P1 Q
10
2006
P2 Q
10
2007
P1 Q
11
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2008
P2 Q
3
2009
P1 Q
13
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2010
P2 Q
2
2011
P2 Q
6
2012
P1 Q
22
2013
P1 Q
23
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Higher Past Paper Questions by Topic
Logarithms and Exponentials
Note: Some questions overlap 2 topic areas; these are in both topic sections.
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2000
P1 Q
9
2000
P2 Q
11
2001
P1 Q
8
2001
P1 Q
10
2001
P2 Q
9
2002
P1 Q
11
-
2002
P2 Q
7
2003
P1 Q
12
2003
P2 Q
11
2004
P1 Q
9
2004
P2 Q
10
2005
P1 Q
7
2005
P2 Q
7
2005
P2 Q
9
-
2006
P1 Q
10
2006
P2 Q
11
2007
P2 Q
8
2007
P2 Q
9
2007
P2 Q
11
-
2008
P2 Q
19
2008
P2 Q
20
-
2008
P2 Q
23
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2009
P1 Q
10
2009
P2 Q
3
-
2009
P2 Q
6
2010
P1 Q
19
2010
P2 Q
7
-
2011
P1 Q
19
-
2011
P2 Q
5
2012
P1 Q
20
2012
P2 Q
7
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2013
P1 Q
20
2013
P2 Q
5
2013
P2 Q
9
Higher Past Papers by topic