Welcome to national5maths.co.uk
Please bookmark this excellent resource page for future reference.
Please find resources for all other Maths courses HERE.
To return to the Home Page please click HERE.
We hope you find this website useful and wish you all the very best with your studies in 2017/18.
Please find below:
2. AH Maths Theory Guides – Unit 1
3. AH Maths Text Book Worked Solutions – Unit 1
4. AH Maths Theory Guides – Unit 2
5. AH Maths Text Book Worked Solutions – Unit 2
6. AH Maths Theory Guides – Unit 3
7. AH Maths Text Book Worked Solutions – Unit 3
8. AH Maths Past & Practice Papers
9. AH Maths Past Paper Questions by Topic
10. AH Maths Theory – All Units
11. AH Maths Practice Unit Assessments (Solutions Included)
12. SQA & HeriotWatt University Course Notes
13. AH Maths Past Paper Video Solutions
1. AH Maths Couse Outline
The full AH Maths course outline, showing all topics, content and suggested timings is shown HERE.
2. AH Maths Theory Guides – Unit One
Thanks to the author(s) for making these available.
Topic 1 ___________________  Topic 2 _____________________  Topic 3 _____________________  Topic 4 __________________  Topic 5 ______________  Topic 6 ______________ 
Binomial 1  Partial Fractions 1  Differentiation 1  Integration 1  Functions 1  Gaussian 1 
Binomial 2  Partial Fractions 2  Differentiation 2  Integration (H.Watt)  Functions (H.Watt)  Gaussian 2 
Binomial (H.Watt)  Partial Fractions (H.Watt)  Differentiation (H.Watt)  Integration (HSN)  Functions (HSN)  Gaussian (H.Watt) 
Binomial (HSN)  Partial Fractions (HSN)  Differentiation (HSN)  Gaussian (HSN)  
Concavity (Maths Insight) 
3. AH Maths Text Book Worked Solutions – Unit One
The new MIA Text Book worked solutions below are courtesy of Robert Milton, Teacher of Mathematics.
Timings along with specific text book exercises and questions for Unit One are courtesy of Teejay Publishers HERE.
.
Topic ______________________  MIA Book (2nd Edition) Worked Solutions ____________________________________  MIA Book (2nd Edition) Worked Solutions ____________________________________ 
Binomial Theorem (4/5 Periods)  MIA Page 33 Ex 3.3 Ex3.3Q1a,b,c,2a,b,c,4a,b,c,d,5a,b,6a,7a,b,d (Combinations  nCr)  MIA Page 36 Ex 3.4 Ex3.4,Q1a,b,c,2a,i,ii,iii,iv,3ad,4af (Binomial Theorem  Expanding) 
MIA Page 38 Ex3,5 Ex3.5Q1a,b,c,4a,5a,6 (Finding Coefficients)  MIA Page 40 Ex 3.6 Ex3.6Q1a,b,c,d (Approximation eg 1.05^5 = ?) 

Partial Fractions (4/5 Periods)  MIA Page 23 Ex 2.2 Ex2.2Q1,5,12,18,19,22,25 (Type One)  MIA Page 24 Ex 2.3 Ex2.3Q1,3,5,10,14,18 (Type Two) 
MIA Page 25 Ex 2.4 Ex2.4Q1,5,7,9,11 (Type Three)  MIA Page 26 Ex 2.5 Ex2.5Q1a,b,e,j,l (Long Division) 

Differential Calculus (13/14 Periods)  MIA Page 45 Ex 4.1 Ex 4.1Q1,3,5,7 (Derivative from First Principles)  MIA Page 48 Ex 4.3 Ex4.3Q1a,d,2a,c,3b,4a,5a (The Chain Rule) 
MIA Page 51 Ex 4.5 Ex4.5Q1ah,Q2b,Q3al (The Product Rule)  MIA Page 55 Ex 4.8 (using Form List) Ex4.8Q1a,b,2a,c,d,3a,c,e,g (sec, cosec & cot) 

MIA Page 55 Ex 4.8 (Alternative) Ex4.8Q1a,b,2ah,3a,c,e,g (sec, cosec & cot)  MIA Page 58 Ex 4.9  exp ques Ex4.9Q1a,c,e,2a,3e,4a,b,5a,e (Exponential Functions) 

MIA Page 58 Ex4.9  ln ques Ex4.9Q1k,m,o,q,s,2f,g,3a,b,c,4d,e,5d (Logarithmic Functions)  MIA Page 60 Ex 4.10 Ex4.10 Q1a,b.2a,b,3a,6,7 (Higher Derivatives  f''(x)) 

MIA Page 70 Ex 5.5 Ex5.5Q1a,b,c2a,b (f''(x), Nature & Sketching Poly's)  MIA Page 73 Ex 5.7 Ex5.7Q5a,b,c,Q1a,b (Concavity) 

MIA Page 187 Ex 11.1 Ex11.1Q1a,b,e,f,2a,c,3a,c (Applications of Differential Calculus)  
Integral Calculus (10/11 Periods)  MIA Page 100 Ex 7.1 (2 Periods) Ex7.1Q1ai,2ai,3al,4af (Integration)  MIA Page 103 Ex 7.2 Ex7.2Q1a,c,e,g,i,k,m,o,q,s,u,w (Integration by Substitution) 
MIA Page 105 Ex 7.3  1 Ex7.3,Q2a,b,c,d,4a,b,c,d (Further Integration by Substitution  Using Exam Formula Sheet)  MIA Page 105 Ex 7.3  2 Ex7.3,Q6a,b,c,d (Further Integration by Substitution) 

MIA Page 105 Ex 7.3  3 Ex7.3,Q7a,b,c,d,e,f (Further Integration by Substitution  sin^m(x)cos^n(x))  MIA Page 105 Ex 7.3  4 Ex7.3,Q11a,b,c,d (Further Integration by Substitution  logs) 

MIA Page 107 Ex 7.4 Ex7.4Q1a,c,e,g,i,k (Substitution & Definite Integrals)  MIA Page 120 Ex 7.10 (2 Periods) Ex7.10Q3,6,7,11,12 (Area between curve & xaxis) (Area between curve & yaxis) (Volume  revolved around xaxis) 

MIA Page 187 Ex11.1  Applications Ex11.1Q4,14 (Applications of Integral Calculus)  
Functions & Graphs (6/7 Periods)  MIA Page 66 Ex 5.2 Ex5.2Q19 (Sketching Modulus Function y = x)  MIA Page 67 Ex 5.3 Ex5.3Q1a,c,e,g,i,2a,c,e,3 (Inverse Functions) 
MIA Page 74 Ex 5.8 Ex5.8Q1al (Odd & Even Functions)  MIA Page 75 Ex 5.9 Ex5.9Q1af (Vertical Asymptotes & Behaviour) 

MIA Page 76 Ex 5.10 Ex5.10Q1a,b,f,g,k,l (Horizontal & NonVertical Asymptotes)  MIA Page 77 Ex 5.11 (2 Periods) Ex5.11Q1a,c,e,i,k (Sketching Graphs) 

Systems of Equations (4/5 Periods)  MIA Page 265 Ex 14.4 Ex14.4Q1,2  MIA Page 268 Ex 14.6 Ex14.6Q1a,b,c,2 
MIA Page 274 Ex 14.9 Ex14.9Q2a,b,c,d  
Revision (3 Periods)  
NAB (1 Period) 
4. AH Maths Theory Guides – Unit Two
Thanks to the author(s) for making these available.
Topic 1 ______________________  Topic 2 _____________________  Topic 3 ___________________  Topic 4 __________________  Topic 5 __________________________________ 
Further Differentiation 1  Further Integration 1  Complex Numbers 1  Seq & Series 1  Proof & Elementary No Theory 
Further Differentiation 2  Further Integration 2  Complex Numbers 2  Seq & Series 2  Proof by Induction 
Further Different'n (H.Watt)  Further Integration (H.Watt)  Complex Nos (H.Watt)  Seq & Series (H.Watt)  Proof & Elementary No Theory (H.Watt) 
Differentiation (HSN)  Integration (HSN)  Complex Nos (HSN)  Seq & Series (HSN)  Methods of Proof (HSN) 
5. AH Maths Text Book Worked Solutions – Unit Two
The new MIA Text Book worked solutions below are courtesy of Robert Milton, Teacher of Mathematics.
Timings along with specific text book exercises and questions for Unit Two are courtesy of Teejay Publishers HERE.
Topic ________________________  MIA Book (2nd Edition) Worked Solutions ____________________________________  MIA Book (2nd Edition) Worked Solutions ____________________________________ 
Further Differentiation (8/9 Periods)  MIA Page 85 Ex 6.2 Ex6.2Q1a,b,c,Q2b,c,dQ3a,d (Inverse Trig Functions & Chain Rule)  MIA Page 86 Ex6.3 Ex6.3Q2,Q3 (Inverse Trig Fns & Product/Quotient Rules) 
MIA Page 89 Ex 6.4  1 Ex6.4Q1,Q2 (Implicit & Explicit Functions  1)  MIA Page 89 Ex 6.4  2 Ex6.4Q5,Q9,Q4 (Implicit & Explicit Functions  2) 

MIA Page 90 Ex 6.5 Ex6.5Q1a,d,f,k(i),6 (Second Derivatives of Implicit Functions)  MIA Page 92 Ex 6.6 Ex6.6Q1,Q2 (Logarithmic Differentiation) 

MIA Page 95 Ex 6.7 Ex6.7Q1a,b,c (Parametric Equations)  MIA Page 96 Ex 6.8  1 Ex6.8Q1(i) (Parametric Equations  Differentiation  1) 

MIA Page 96 Ex 6.8  2 Ex6.2Q1(ii),Q2,Q3 (Parametric Equations  Differentiation  2)  MIA Page 193 Ex 11.2 Ex11.2Q1,Q2,Q3 (Applications of Further Differentiation) 

Further Integration (10/11 Periods)  MIA Page 111 Ex 7.6 Ex7.6Q1,2,3,4a,b (Integration using Inverse Trig Functions)  MIA Page 113 Ex 7.7 Ex7.7Q1a,b2a,b3a,b,4a,b5a,b6a,b (Integration using Partial Fractions) 
MIA Page 116 Ex 7.8  1 Ex7.8Q1al (Integration by Parts  1)  MIA Page 116 Ex 7.8  2 Ex7.8Q2a,c,d,e,f,g,h (Integration by Parts  2) 

MIA Page 116 Ex 7.8  3 Ex7.8Q5a,bQ6a,b (Integration by Parts  3)  MIA Page 118 Ex 7.9  1 Ex 7.9 Q1a,b,c,d (Integration by Parts  Special Cases  1) 

MIA Page 118 Ex 7.9  2 Ex7.9Q2a,b,c,d,e (Integration by Parts  Special Cases  2)  MIA Page 128 Ex 8.1  1 Ex8.1Q1aj (First Order Diff Eqns  General Soln) 

MIA Page 128 Ex 8.1  2 Ex8.1Q2ag (First Order Diff Eqns  Particular Soln)  MIA Page 131 Ex 8.2 Ex8.2Q2,4,5,6 (Differential Equations in Context) 

Complex Numbers (9/10 Periods)  MIA Page 207 Ex 12.1 Ex12.1Q1,2,3,6,7,8 (Arithmetic with Complex Numbers)  MIA Page 209 Ex 12.2 Ex12.2Q1a,b,c,2c,e,3a,b,f,5a,b (Division & Square Roots of Complex Nos) 
MIA Page 211 Ex 12.3 Ex12.3Q3a,b,d,e,f,6a,b,f,7a,b,c (Argand Diagrams)  MIA Page 215 Ex 12.5 Ex12.5Q1a,b,f,g (Multiplying/Dividing in Polar Form) 

MIA Page 218 Ex 12.6 Ex12.6Q1,2,3a,4g,h,i,j (De Moivre's Theorem)  MIA Page 224 Ex 12.8 (3 Periods) Ex12.8Q2a,d,3a,b,4,5,6a,b (Polynomials & Complex Numbers) 

MIA Page 213 Ex 12.4 Ex12.4Q1a,b,d,f,j,3a,b,4a,b,c (Loci on the Complex Plane)  MIA Page 219 Ex 12.6 Ex12.6Q5,6,7a (Expanding Trig Formula) 

MIA Page 222 Ex 12.7 Ex12.7Q2a,b,c,d,e,f,1a(i) (Roots of a Complex Number)  
Sequences & Series, Sigma Notation (7/8 Periods)  MIA Page 151 Ex 9.1 Ex9.1Q1af,2af,Q3,Q4,Q6 (Arithmetic Sequences)  MIA Page 153 Ex 9.2 Ex9.2Q1a,b,c,Q3ad,Q4a,b,Q5a (Finding Sum  Arithmetic Sequence) 
MIA Page 156 Ex 9.3 Ex9.3Q1ae,Q2,Q3,Q5 (Geometric Sequence)  MIA Page 159 Ex 9.4 Ex9.4Q1af,Q2ad,Q3ad,Q4 (Finding Sum  Geometric Sequence) 

MIA Page 162 Ex 9.5 Ex9.5Q1,2,3,4,6 (Finding Sum to Infinity)  MIA Page 168 Ex 10.1 Ex10.1Q1ae,Q2a,b,c (Sigma Notation) 

Number Theory & Proof (10/11 Periods)  Direct Proof (Ex 1 & Ex 2)  Exercise 1 & 2 Worked Solutions 
Proof by Counter Example (Ex 3)  Exercise 3 Worked Solutions  
Proof by Counter Example (Ex 4)  Exercise 4 Worked Solutions  
Ex 5 & Ex 6  Proof by Contradiction & Contrapositive  Solutions to Proof by Contradiction & Contrapositive coming soon!  
Ex 7  Proof by Induction  Solutions to Proof by Induction coming soon! 
6. AH Maths Theory Guides – Unit Three
Thanks to the author(s) for making these available.
Topic 1 ________________________  Topic 2 _________________  Topic 3 _____________________  Topic 4 _____________________  Topic 5 ______________________________ 
Vectors 1  Matrices 1  Maclaurin Series 1  Differential Eqns 1  3D Geometry 
Vectors 2  Matrices 2  Maclaurin Series 2  Differential Eqns 2  Plane Notes 
Vectors (HSN)  Matrices 3  Maclaurin Series (H.Watt)  Differential Eqns (H.Watt)  Further No Theory & Proofs (H.Watt) 
Vectors (H.Watt)  Matrices (H.Watt)  Maclaurin Series (HSN)  Differential Eqns (HSN)  
Plane Transformations (HSN)  Matrices ( HSN) 
7. AH Maths Text Book Worked Solutions – Unit Three
The new MIA Text Book worked solutions below are courtesy of Robert Milton, Teacher of Mathematics.
Timings along with specific text book exercises and questions for Unit Three are courtesy of Teejay Publishers HERE.
Available Soon!
8. AH Maths Past & Practice Papers
Thanks to the SQA for making these available.
Year _____  Paper Type _________________  Exam Paper ______________  Marking Scheme _________________ 
2016  Advanced Higher  Exam Paper  Marking Scheme 
2016  AH Specimen  Specimen  
2016  AH Exemplar  Exemplar  Exemplar Guidance 
2015  Advanced Higher  Exam Paper  Marking Scheme 
2014  Advanced Higher  Exam Paper  Marking Scheme 
2013  Advanced Higher  Exam Paper  Marking Scheme 
2012  Advanced Higher  Exam Paper  Marking Scheme 
2011  Advanced Higher  Exam Paper  Marking Scheme 
2010  Advanced Higher  Exam Paper  Marking Scheme 
2009  Advanced Higher  Exam Paper  Marking Scheme 
2008  Advanced Higher  Exam Paper  Marking Scheme 
2007  Advanced Higher  Exam Paper  Marking Scheme 
2006  Advanced Higher  Exam Paper  Marking Scheme 
2005  Advanced Higher  Exam Paper  Marking Scheme 
2004  Advanced Higher  Exam Paper  Marking Scheme 
2003  Advanced Higher  Exam Paper  Marking Scheme 
2002  Advanced Higher  Exam Paper  Marking Scheme 
2001  Advanced Higher  Exam Paper 
9. AH Maths Past Paper Questions by Topic
Topic ________  Topic Name ___________________________  Topic ________  Topic Name ___________________________ 
Topic 1  Binomial Theorem  Topic 9  Integration 
Topic 2  Complex Numbers  Topic 10  Matrices 
Topic 3  Differential Equations  Topic 11  Partial Fractions 
Topic 4  Differentiation  Topic 12  Proof 
Topic 5  Further Differential Equations  Topic 13  Properties of Functions 
Topic 6  Further Differentiation  Topic 14  Sequences & Series 
Topic 7  Further Number Theory  Topic 15  Systems of Equations 
Topic 8  Further Sequences & Series  Topic 16  Vectors 
10. AH Maths Theory – All Units
Thanks to the author(s) for making these available.
Topic _______  Topic Name ____________________________  Topic _______  Topic Name ____________________________ 
Topic 1  Binomial Theorem (HSN)  Topic 15  Integration (HSN) 
Topic 2  Binomial Theorem  Topic 16  Iterative Schemes (HSN) 
Topic 3  Complex Numbers (HSN)  Topic 17  Matrices (HSN) 
Topic 4  Complex Numbers  Topic 18  Matrices 
Topic 5  Differentiation (HSN)  Topic 19  Methods of Proof (HSN) 
Topic 6  Differentiation  Topic 20  Partial Fractions (HSN) 
Topic 7  Further Differentiation  Topic 21  Partial Fractions 
Topic 8  Differential Eqns  Topic 22  Properties of Functions 
Topic 9  Further Differential Equations  Topic 23  Sequences & Series (HSN) 
Topic 10  Further Number Theory  Topic 24  Sequences & Series 
Topic 11  Functions (HSN)  Topic 25  Transformations of the Plane (HSN) 
Topic 12  Gaussian Elimination (HSN)  Topic 26  Vectors (HSN) 
Topic 13  Gaussian Elimination  Topic 27  Vectors 
Topic 14  HSN AH Notes  Topic 28  Whole Course  Revision 
11. AH Maths Practice Unit Assessments (Solutions Included)
All practice assessments below are courtesy of maths777.weebly.com
Methods in Algebra & Calculus __________________________  Applications of Algebra & Calculus ____________________________  Geometry, Proof & Systems of Eqns ______________________________ 
Practice One  Practice One  Practice One 
Practice Two  Practice Two  Practice Two 
Practice Three  Practice Three  Practice Three 
12. SQA & HeriotWatt University Course Notes
13. AH Maths Past Paper Video Solutions:
14. Recommended Text Books
All three books below are highly recommended.
Be fully prepared for 2017/18, click on the links below and order through amazon.co.uk today.
.
AH Maths Text Book – Maths In Action (2nd Edition) by Edward Mullan
A fully revised course for the new Curriculum for Excellence examination that is designed to fully support the course’s new structure and unit assessment. A part of the highly regarded Maths in Action series, it provides students with a familiar, clear and carefully structured learning experience that encourages them to build confidence and understanding.
AH Maths Study Guide – BrightRed
A brand new CfE Advanced Higher Mathematics Study Guide has been written specifically for the new CfE Advanced Higher Course by the authors of our bestselling Advanced Higher Mathematics Revision Guide. The title features fullcolour double spreads and all the essential course information to support students with the new qualification from 2015.
AH Maths – Practice Papers for SQA Exams
This book sets out to familiarise the student with exam layouts, timing and question style. The questions are supported with fully worked answers that clearly explain how to understand and tackle each question, how to reach the right answer and how to maximise marks in the final exam.
Covers most Maths topics in Secondary High Schools
Created by an experienced maths teacher
Resources used with students studying Maths in Scottish Secondary Schools