Larbert High School

Faculty of Mathematics

SQA Higher Past Paper Questions (Ordered by Topic)

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

− +

+

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

Higher Past Paper Questions by Topic Straight Lines

Note: Some questions overlap 2 topic areas; these are in both topic sections.

2000

P1 Q

3

2001

P1 Q

1

2001

P1 Q

11

2001

P2 Q

7

2002

P1 Q

4

2002

P2 Q

1

2003

P1 Q

1

2004

P1 Q

1

2004

P2 Q

1

2006

P1 Q

1

2006

P2 Q

1

2007

P1 Q

1

2008

P1 Q

5

2008

P1 Q

7

2008

P2 Q

1

2009

P1 Q

5

2009

P1 Q

15

2009

P1 Q

21

2010

P1 Q

1

2010

P1 Q

8

2010

P1 Q

21

2010

P1 Q

23

2011

P1 Q

2

2011

P1 Q

8

2011

P1 Q

21

2012

P1 Q

4

2012

P1 Q

23

2013

P1 Q

5

2013

P2 Q

2

Higher Past Paper Questions by Topic

Functions and Graphs

Note: Some questions overlap 2 topic areas; these are in both topic sections.

2000

P1 Q

2

2000

P2 Q

3

2001

P1 Q

7

2001

P1 Q

10

2002

P1 Q

3

2003

P1 Q

9

2003

P2 Q

5

2004

P1 Q

4

2005

P1 Q

4

2006

P1 Q

3

2006

P2 Q

7

2007

P1 Q

3

2008

P1 Q

17

2008

P2 Q

20

2008

P2 Q

23

2009

P1 Q

10

2009

P1 Q

23

2009

P2 Q

2

2010

P1 Q

11

2010

P1 Q

13

2010

P1 Q

19

2010

P1 Q

20

2011

P1 Q

3

20

11

P1 Q

22

2011

P2 Q

2

2012

P1 Q

18

2012

P2 Q

1

2013

P1 Q

1

2013

P1 Q

11

Higher Past Paper Questions by Topic Differentiation

Note: Some questions overlap 2 topic areas; these are in both topic sections.

2000

P1 Q

2

2000

P1 Q

4

2000

P1 Q

8

2000

P2 Q

1

2000

P2 Q

6

2000

P2 Q

8

2001

P1 Q

6

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

2003

P1 Q

5

2003

P2 Q

4

2003

P2 Q

6

2003

P2 Q

8

2004

P1 Q

6

2004

P1 Q

8

2004

P1 Q

11

2004

P2 Q

5

2004

P2 Q

7

2004

P2 Q

9

2005

P1 Q

5

2005

P2 Q

6

2006

P1 Q

5

2006

P1 Q

3

2006

P2 Q

9

2006

P2 Q

12

2007

P1 Q

9

2007

P1 Q

10

2007

P2 Q

5

2007

P2 Q

6

2007

P2 Q

10

2008

P2 Q

15

2008

P2 Q

21

2008

P2 Q

22

2008

P2 Q

3

2008

P2 Q

6

2009

P1 Q

4

2009

P1 Q

8

2009

P1 Q

20

2009

P2 Q

1

2009

P2 Q

2

2010

P1 Q

12

2010

P1 Q

15

2010

P1 Q

17

2010

P2 Q

5

2011

P1 Q

4

2011

P1 Q

13

20

11

P1 Q

22

2012

P1 Q

2

2012

P1 Q

6

2012

P1 Q

8

2012

P1 Q

16

2012

P2 Q

3

2012

P2 Q

4

2013

P1 Q

2

2013

P1 Q

18

2013

P2 Q

3

2013

P2 Q

7

Higher Past Paper Questions by Topic

Recurrence Relations

Note: Some questions overlap 2 topic areas; these are in both topic sections.

2000

P1 Q

5

2001

P2 Q

3

2002

P2 Q

4

2003

P1 Q

4

2004

P2 Q

4

2005

P1 Q

6

2006

P1 Q

4

2007

P1 Q

7

2008

P1 Q

1

2008

P1 Q

4

2009

P1 Q

1

2009

P1 Q

6

2010

P1 Q

2

2010

P1 Q

7

2011

P2 Q

3

2012

P1 Q

1

2012

P2 Q

6

2013

P1 Q

8

2013

P2 Q

1

Higher Past Paper Questions by Topic Polynomials and Quadratics

Note: Some questions overlap 2 topic areas; these are in both topic sections.

2000

P2 Q

1

2000

P2 Q

4

2001

P1 Q

2

2001

P1 Q

4

2001

P2 Q

1

2001

P2 Q

11

2002

P1 Q

7

2002

P2 Q

3

2002

P2 Q

5

2002

P2 Q

9

2003

P1 Q

2

2003

P1 Q

7

2003

P1 Q

11

2003

P2 Q

1

2004

P1 Q

2

2004

P1 Q

8

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

2006

P2 Q

3

2007

P1 Q

4

2007

P1 Q

8

2007

P2 Q

3

2007

P2 Q

10

2008

P1 Q

10

2008

P1 Q

13

2008

P2 Q

16

2008

P2 Q

21

20

08

P2 Q

22

2008

P2 Q

4

2009

P1 Q

9

2009

P1 Q

12

2009

P2 Q

3

2010

P1 Q

5

2010

P1 Q

6

2010

P1 Q

16

2010

P1 Q

18

2010

P1 Q

22

20

10

P2 Q

3

2011

P1 Q

5

2011

P1 Q

7

2011

P1 Q

9

2011

P1 Q

17

2011

P1 Q

18

2011

P2 Q

2

2011

P2 Q

4

2011

P2 Q

7

2012

P1 Q

3

2012

P1 Q

13

2012

P1 Q

19

2012

P1 Q

21

2013

P1 Q

3

2013

P1 Q

6

2013

P1 Q

13

2013

P1 Q

17

2013

P1 Q

19

2013

P1 Q

21

2013

P2 Q

3

Higher Past Paper Questions by Topic

Integration

Note: Some questions overlap 2 topic areas; these are in both topic sections.

2000

P1 Q

4

2000

P2 Q

4

2000

P2 Q

10

2001

P2 Q

6

2001

P2 Q

8

2001

P2 Q

10

2002

P2 Q

5

2002

P2 Q

8

2003

P1 Q

8

2003

P2 Q

3

2004

P1 Q

7

2004

P2 Q

11

2005

P2 Q

1

2005

P2 Q

5

2006

P1 Q

6

2006

P2 Q

5

2007

P1 Q

8

2007

P2 Q

7

2008

P2 Q

7

2008

P2 Q

14

2009

P1 Q

16

2009

P2 Q

5

2010

P1 Q

9

2010

P1 Q

14

2010

P2 Q

6

2011

P1 Q

11

2011

P1 Q

16

2011

P2 Q

4

2011

P2 Q

6

2012

P1 Q

11

2012

P1 Q

14

2012

P1 Q

21

2013

P1 Q

7

2013

P1 Q

16

2013

P2 Q

4

2013

P2 Q

6

Higher Past Paper Questions by Topic Trigonometry

Note: Some questions overlap 2 topic areas; these are in both topic sections.

2000

P1 Q

1

2000

P2 Q

5

2001

P1 Q

5

2001

P1 Q

7

2001

P2 Q

10

2002

P1 Q

5

2002

P1 Q

8

2002

P1 Q

9

2002

P2 Q

6

2003

P1 Q

10

2003

P2 Q

2

2003

P2 Q

6

2003

P2 Q

10

2004

P1 Q

3

2005

P1 Q

9

2005

P2 Q

2

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

2008

P1 Q

6

2008

P1 Q

9

2008

P2 Q

3

2008

P2 Q

5

2009

P2 Q

7

2009

P1 Q

11

2009

P1 Q

13

2009

P1 Q

14

2009

P1 Q

24

2009

P2 Q

5

2010

P1 Q

4

2010

P1 Q

11

2010

P1 Q

23

2010

P2 Q

2

2010

P2 Q

4

2011

P1 Q

10

2011

P1 Q

12

2011

P1 Q

20

2011

P1 Q

23

2012

P1 Q

5

2012

P1 Q

9

2012

P1 Q

12

2012

P2 Q

6

2013

P1 Q

4

2013

P1 Q

9

2013

P1 Q

10

2013

P1 Q

15

2013

P2 Q

8

Higher Past Paper Questions by Topic

Circles

Note: Some questions overlap 2 topic areas; these are in both topic sections.

2000

P1 Q

6

2000

P2 Q

2

2001

P1 Q

11

2002

P1 Q

1

2003

P1 Q

11

2004

P2 Q

8

2005

P1 Q

2

2005

P1 Q

11

2005

P2 Q

3

2006

P1 Q

2

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

2013

P1 Q

22

Higher Past Paper Questions by Topic Vectors

Note: Some questions overlap 2 topic areas; these are in both topic sections.

2000

P1 Q

7

2000

P2 Q

7

2000

P2 Q

9

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

2004

P2 Q

2

2005

P1 Q

3

2005

P2 Q

4

2005

P2 Q

10

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

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

Higher Past Paper Questions by Topic

The Wave Function

Note: Some questions overlap 2 topic areas; these are in both topic sections.

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

2008

P2 Q

3

2009

P1 Q

13

2010

P2 Q

2

2011

P2 Q

6

2012

P1 Q

22

2013

P1 Q

23

Higher Past Paper Questions by Topic

Logarithms and Exponentials

Note: Some questions overlap 2 topic areas; these are in both topic sections.

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

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

2013

P1 Q

20

2013

P2 Q

5

2013

P2 Q

9

Higher Past Papers by topic