Larbert High School
Faculty of Mathematics
SQA Higher Past Paper Questions
(Ordered by Topic)
FORMULAE LIST
Circle:
The equation x 2 + y 2 + 2 gx + 2 fy + c =
0 represents a circle centre ( − g , − f ) and radius
The equation ( x − a)2 + ( y − b)2 =
r 2 represents a circle centre ( a , b) and radius r.
Scalar Product :
or
=
a.b
a b cos θ, where θ is the angle between a and b.
 a1 
 b1 
 
 
a . b = a1b1 + a2 b2 + a3 b3 , where a =  a2  and b =  b2  .
a 
b 
 3
 3
Trigonometric formulae:
sin(A
=
± B) sin A cos B ± cos A sin B
cos(A ± B) =
cos A cos B  sin A sin B
sin 2A = 2 sin A cos A
cos
=
2A cos 2 A − sin 2 A
= 2 cos 2 A − 1
= 1 − 2 sin 2 A
Table of standard derivatives :
f ( x)
f ′( x)
sin ax
a cos ax
cos ax
−a sin ax
Table of standard integrals :
f ( x)
∫ f (x) dx
sin ax
1
− cos ax + C
a
cos ax
1
sin ax + C
a
g2 + f 2 − c .
Contents
Straight Lines
Functions and Graphs
Differentiation
Recurrence Relations
Polynomials and Quadratics
Integration
Trigonometry
Circles
Vectors
The Wave Function
Logarithms and Exponentials
Page 5
Page 18
Page 32
Page 51
Page 57
Page 75
Page 88
Page 103
Page 114
Page 129
Page 133
Higher Past Paper Questions by Topic
Straight Lines
Note: Some questions overlap 2 topic areas; these are in both topic sections.
2001
P2 Q7
2002
P1 Q4
P1 Q11
2001
P1 Q1
2001
P1 Q3
2000
2004
P1 Q1
2004
P2 Q1
P1 Q1
2003
P2 Q1
2002
2006
P2 Q1
2007
P1 Q1
P1 Q1
2006
P1 Q5
2008
2008
P1 Q7
2008
P2 Q1
2009
P1 Q5
2009
P1 Q15
2009
P1 Q21
2010
P1 Q1
2010
P1 Q8
2010
P1 Q21
2010
P1 Q23
2011
P1 Q2
P1 Q8
2011
P1 Q21
2011
2012
P1 Q23
2013
P1 Q5
P1 Q4
2012
P2 Q2
2013
Higher Past Paper Questions by Topic
Functions and Graphs
Note: Some questions overlap 2 topic areas; these are in both topic sections.
2000
P2 Q3
2001
P1 Q7
P1 Q2
2000
2003
P2 Q5
2004
P1 Q4
P1 Q9
2003
P1 Q3
2002
P1 Q10
2001
2007
P1 Q3
2008
P1 Q17
P2 Q7
2006
P1 Q3
2006
P1 Q4
2005
2008
P2 Q20
2008
P2 Q23
2009
P1 Q10
2009
P1 Q23
2009
P2 Q2
2010
P1 Q11
P1 Q13
2010
2010
P1 Q19
2010
P1 Q20
P1 Q3
2011
2011
P2 Q2
2012
P1 Q18
P1 Q22
2011
2012
P2 Q1
2013
P1 Q1
P1 Q11
2013
Higher Past Paper Questions by Topic
Differentiation
Note: Some questions overlap 2 topic areas; these are in both topic sections.
P1 Q2
2000
2000
P1 Q4
2000
P1 Q8
2000
P2 Q8
2001
P1 Q6
P2 Q6
2000
P2 Q1
2000
2002
P1 Q10
2002
P2 Q6
P1 Q6
2002
P1 Q4
2002
P2 Q11
2001
P2 Q2
2001
P1 Q9
2001
2004
P1 Q6
2004
P1 Q8
P2 Q8
2003
P2 Q6
2003
P2 Q4
2003
P1 Q5
2003
2004
P2 Q9
2005
P1 Q5
P2 Q7
2004
P2 Q5
2004
P1 Q11
2004
2006
P1 Q3
2006
P2 Q9
P1 Q5
2006
P2 Q6
2005
2007
P1 Q10
2007
P2 Q5
P1 Q9
2007
P2 Q12
2006
2007
P2 Q6
2007
P2 Q10
2008
P2 Q22
2008
P2 Q3
P2 Q21
2008
P2 Q15
2008
2008
P2 Q6
2009
P1 Q4
2009
P2 Q1
2009
P2 Q2
P1 Q20
2009
P1 Q8
2009
2010
P1 Q17
2010
P2 Q5
P1 Q15
2010
P1 Q12
2010
2011
P1 Q4
2011
P1 Q13
2012
P1 Q2
2012
P1 Q6
P1 Q22
2011
2012
P1 Q16
2012
P2 Q3
P1 Q8
2012
2013
P1 Q2
2013
P1 Q18
P2 Q4
2012
2013
P2 Q3
2013
P2 Q7
Higher Past Paper Questions by Topic
Recurrence Relations
Note: Some questions overlap 2 topic areas; these are in both topic sections.
2003
P1 Q4
2004
P2 Q4
P2 Q4
2002
P2 Q3
2001
P1 Q5
2000
2007
P1 Q7
2008
P1 Q1
P1 Q4
2006
P1 Q6
2005
2009
P1 Q6
2010
P1 Q2
P1 Q1
2009
P1 Q4
2008
2011
P2 Q3
2012
P1 Q1
P1 Q7
2010
2013
P1 Q8
2013
P2 Q1
P2 Q6
2012
Higher Past Paper Questions by Topic
Polynomials and Quadratics
Note: Some questions overlap 2 topic areas; these are in both topic sections.
2001
P1 Q4
2001
P2 Q1
P1 Q2
2001
P2 Q4
2000
P2 Q1
2000
2002
P2 Q9
2003
P1 Q2
P2 Q5
2002
P2 Q3
2002
P1 Q7
2002
P2 Q11
2001
2004
P1 Q2
2004
P1 Q8
P2 Q1
2003
P1 Q11
2003
P1 Q7
2003
2006
P1 Q8
2006
P2 Q2
P2 Q11
2005
P2 Q5
2005
P1 Q8
2005
P2 Q3
2004
P1 Q11
2004
2007
P1 Q8
2007
P2 Q3
P1 Q4
2007
P2 Q3
2006
2008
P1 Q10
2008
P1 Q13
P2 Q10
2007
2008
P2 Q16
2008
P2 Q21
2009
P1 Q9
2009
P1 Q12
P2 Q4
2008
P2 Q22
2008
2010
P1 Q6
2010
P1 Q16
P1 Q5
2010
P2 Q3
2009
2010
P1 Q18
2010
P1 Q22
2011
P1 Q5
2011
P1 Q7
P2 Q3
2010
2011
P1 Q9
2011
P1 Q17
2011
P2 Q2
2011
P2 Q4
P1 Q18
2011
2012
P1 Q13
2012
P1 Q19
P1 Q3
2012
P2 Q7
2011
2013
P1 Q3
2013
P1 Q6
P1 Q21
2012
2013
P1 Q13
2013
P1 Q17
2013
P1 Q21
2013
P2 Q3
P1 Q19
2013
Higher Past Paper Questions by Topic
Integration
Note: Some questions overlap 2 topic areas; these are in both topic sections.
2000
P1 Q4
2000
P2 Q4
2002
P2 Q5
2002
P2 Q8
P2 Q10
2001
P2 Q8
2001
P2 Q6
2001
P2 Q10
2000
2005
P2 Q1
2005
P2 Q5
P2 Q11
2004
P1 Q7
2004
P2 Q3
2003
P1 Q8
2003
2007
P2 Q7
2008
P2 Q7
P1 Q8
2007
P2 Q5
2006
P1 Q6
2006
2009
P1 Q16
2009
P2 Q5
P2 Q14
2008
2010
P1 Q9
2010
P1 Q14
P2 Q6
2010
P1 Q11
2011
2011
P1 Q16
2011
P2 Q4
2011
P2 Q6
2012
P1 Q11
2012
P1 Q21
2013
P1 Q7
P1 Q14
2012
2013
P2 Q4
2013
P2 Q6
P1 Q16
2013
Higher Past Paper Questions by Topic
Trigonometry
Note: Some questions overlap 2 topic areas; these are in both topic sections.
P1 Q7
2001
2000
P2 Q5
2001
P1 Q5
P1 Q1
2000
2002
P2 Q6
2003
P1 Q10
P1 Q9
2002
P1 Q8
2002
P1 Q5
2002
P2 Q10
2001
2005
P1 Q9
2005
P2 Q2
P1 Q3
2004
P2 Q10
2003
P2 Q6
2003
P2 Q2
2003
2007
P2 Q1
2007
P2 Q4
P1 Q11
2007
P1 Q6
2007
P2 Q8
2006
P1 Q7
2006
P2 Q8
2005
2008
P1 Q9
2008
P2 Q3
P1 Q6
2008
2009
P2 Q7
2009
P1 Q11
P2 Q5
2008
2009
P1 Q14
2009
P1 Q24
P1 Q13
2009
2010
P1 Q4
2010
P1 Q11
P2 Q5
2009
2010
P2 Q4
2011
P1 Q10
P2 Q2
2010
P1 Q23
2010
P1 Q12
2011
2011
P1 Q23
2012
P1 Q5
P1 Q20
2011
2012
P1 Q9
2012
P1 Q12
2012
P2 Q6
2013
P1 Q4
2013
P1 Q15
2013
P2 Q8
P1 Q10
2013
P1 Q9
2013
Higher Past Paper Questions by Topic
Circles
Note: Some questions overlap 2 topic areas; these are in both topic sections.
2001
P1 Q11
2002
P1 Q1
P2 Q2
2000
P1 Q6
2000
P1 Q11
2003
2004
P2 Q8
2005
P1 Q2
2005
P2 Q3
2006
P1 Q2
P1 Q11
2005
2007
P1 Q5
2007
P2 Q5
P2 Q4
2006
2008
P1 Q2
2008
P1 Q5
2009
P1 Q2
2009
P1 Q9
P2 Q4
2008
2009
P2 Q4
2010
P1 Q8
2010
P2 Q3
2011
P1 Q6
2011
P2 Q7
2012
P2 Q2
P1 Q22
2013
Higher Past Paper Questions by Topic
Vectors
Note: Some questions overlap 2 topic areas; these are in both topic sections.
2000
P2 Q7
2000
P2 Q9
P1 Q7
2000
2001
P1 Q3
2001
P2 Q4
2004
P1 Q5
2004
P1 Q10
P2 Q9
2003
P1 Q6
2003
P1 Q3
2003
P2 Q2
2002
P1 Q2
2002
2005
P2 Q4
2005
P2 Q10
P1 Q3
2005
P2 Q2
2004
2006
P2 Q6
2007
P1 Q2
P1 Q9
2006
2008
P1 Q3
2008
P1 Q11
P2 Q1
2007
2008
P1 Q12
2008
P1 Q18
2009
P1 Q3
2009
P1 Q17
P2 Q2
2008
2009
P2 Q7
2010
P1 Q3
P1 Q22
2009
2010
P1 Q10
2010
P2 Q1
2011
P1 Q1
2011
P1 Q14
2011
P2 Q1
2012
P1 Q7
P1 Q15
2011
2012
P1 Q10
2012
P1 Q15
2013
P1 Q14
2013
P1 Q24
P1 Q12
2013
P2 Q5
2012
P1 Q17
2012
Higher Past Paper Questions by Topic
The Wave Function
Note: Some questions overlap 2 topic areas; these are in both topic sections.
2006
P2 Q10
2007
P1 Q11
P1 Q10
2005
P2 Q6
2004
P2 Q7
2003
P2 Q5
2001
P1 Q10
2000
2008
P2 Q3
2009
P1 Q13
2012
P1 Q22
2013
P1 Q23
P2 Q6
2011
P2 Q2
2010
Higher Past Paper Questions by Topic
Logarithms and Exponentials
Note: Some questions overlap 2 topic areas; these are in both topic sections.
2001
P2 Q9
2002
P1 Q11
P1 Q10
2001
P1 Q8
2001
P2 Q11
2000
P1 Q9
2000
2005
P2 Q7
2005
P2 Q9
P1 Q7
2005
P2 Q10
2004
P1 Q9
2004
P2 Q11
2003
P1 Q12
2003
P2 Q7
2002
2007
P2 Q9
2007
P2 Q11
P2 Q8
2007
P2 Q11
2006
P1 Q10
2006
2008
P2 Q19
2008
P2 Q20
P2 Q23
2008
2009
P1 Q10
2009
P2 Q3
2010
P1 Q19
2010
P2 Q7
P2 Q6
2009
P1 Q19
2011
2012
P1 Q20
2012
P2 Q7
P2 Q5
2011
2013
P2 Q5
2013
P2 Q9
P1 Q20
2013