Free Advanced Higher Maths

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Please bookmark this excellent resource page for future reference.

Please find resources for all other Maths courses HERE.

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We hope you find this website useful and wish you all the very best with your studies in 2017/18.

Please find below:

1. AH Maths Course Outline

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 – 2017 SQA Paper Now Included!

9. AH Maths Past Paper Questions by Topic

10. AH Maths Theory – All Units

11. AH Maths Practice Unit Assessments (Solutions Included)

12. SQA & Heriot-Watt University Course Notes

13. AH Maths Past Paper Video Solutions

14. Recommended Text Books

 

Advanced Higher Maths Resources

 

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 1Partial Fractions 1Differentiation 1Integration 1Functions 1Gaussian 1
Binomial 2Partial Fractions 2Differentiation 2Integration (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.

Useful AH Maths Formulaes:

.

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,3a-d,4a-f
(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
Ex4.5Q1a-h,Q2b,Q3a-l
(The Product Rule)
MIA Page 52 Ex 4.6
Ex4.6Q1,2,3,4
(The Quotient Rule)
MIA Page 53 EX 4.7
Ex4.7Q1,2,3,4,5
(Differentiation - Mixture!)
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,2a-h,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)
Ex7.1Q1a-i,2a-i,3a-l,4a-f
(Integration)
MIA Page 103 Ex 7.2 - 1
Ex7.2Q1a,c,e,g,i,k,m,o,q,s,u,w
(Integration by Substitution)
MIA Page 103 Ex 7.2 - 2
Ex7.2Q1b,d,f,h,j,l,n,p,r,t,v,x
(Integration by Substitution - Extra Revision!)
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 & x-axis)
(Area between curve & y-axis)
(Volume - revolved around x-axis)
MIA Page 187 Ex11.1 - Applications
Ex11.1Q4,14
(Applications of Integral Calculus)
Functions & Graphs
(6/7 Periods)
MIA Page 66 Ex 5.2
Ex5.2Q1-9
(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
Ex5.8Q1a-l
(Odd & Even Functions)
MIA Page 75 Ex 5.9
Ex5.9Q1a-f
(Vertical Asymptotes & Behaviour)
MIA Page 76 Ex 5.10
Ex5.10Q1a,b,f,g,k,l
(Horizontal & Oblique 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
(Gaussian Elimination)
MIA Page 268 Ex 14.6
Ex14.6Q1a,b,c,2
(Redundancy & Inconsistency)
MIA Page 274 Ex 14.9
Ex 14.9
(Ill Conditioning)
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 1Further Integration 1Complex Numbers 1Seq & Series 1Proof & Elementary No Theory
Further Differentiation 2Further Integration 2Complex Numbers 2Seq & Series 2Proof 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.

Useful AH Maths Formulaes:

.

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
Ex7.8Q1a-l
(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
Ex8.1Q1a-j
(First Order Diff Eqns - General Soln)
MIA Page 128 Ex 8.1 - 2
Ex8.1Q2a-g
(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
Ex9.1Q1a-f,2a-f,Q3,Q4,Q6
(Arithmetic Sequences)
MIA Page 153 Ex 9.2
Ex9.2Q1a,b,c,Q3a-d,Q4a,b,Q5a
(Finding Sum - Arithmetic Sequence)
MIA Page 156 Ex 9.3
Ex9.3Q1a-e,Q2,Q3,Q5
(Geometric Sequence)
MIA Page 159 Ex 9.4
Ex9.4Q1a-f,Q2a-d,Q3a-d,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
Ex10.1Q1a-e,Q2a,b,c
(Sigma Notation)
Number Theory & Proof
(10/11 Periods)
Direct Proof (Ex 1 & Ex 2)Exercise 1 & 2 Handwritten Worked Solutions
Proof by Counter Example (Ex 3)Exercise 3 Typed Worked Solutions
Exercise 3 Handwritten Worked Solutions
Proof by Counter Example (Ex 4)Exercise 4 Typed Worked Solutions
Exercise 4 Handwritten Worked Solutions
Proof by Contradiction (Ex 5)Exercise 5 Typed Worked Solutions
Exercise 5 Handwritten Worked Solutions
Proof by Contrapositive (Ex 6)Exercise 6 Typed Worked Solutions
Exercise 6 Handwritten Worked Solutions
Proof by Induction (Ex 7)Exercise 7 Typed Worked Solutions
Exercise 7 Handwritten Worked Solutions

 

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 1Matrices 1Maclaurin Series 1Differential Eqns 13D Geometry
Vectors 2Matrices 2Maclaurin Series 2Differential Eqns 2Plane Notes
Vectors (H. Watt)Matrices 3Maclaurin Series (H.Watt)Differential Eqns (H.Watt)Further No Theory & Proofs (H.Watt)
Vectors (HSN)Matrices (H.Watt)Maclaurin Series (HSN)Differential Eqns (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.

Useful AH Maths Formulaes:

.

Topic

________________________
MIA Book (2nd Edition)
Worked Solutions
____________________________________
MIA Book (2nd Edition)
Worked Solutions
____________________________________
Vectors
(13 Periods)
MIA Page 282 Ex 15.1
Ex15.1Q6,7,8
(Higher Revision On Vectors)
MIA Page 286 Ex 15.3 - 1
Ex15.3Q1,2a,b,5,7,8a,b,10
(The Vector Product - 1)
MIA Page 286 Ex 15.3 - 2
Ex15.3Q3,4,6,12
(The Vector Product - 2)
MIA Page 296 Ex 15.8
Ex15.8Q1a,b,2a,3a,c,e,5
(The Equations of a Line)
MIA Page 298 Ex 15.9
Ex15.9Q2
(Vector Equation of a Straight Line)
MIA Page 291 Ex 15.5
Ex15.5Q1a,b,c,d,2a,b,3,4a,c,9,10
(The Equation of a Plane)
MIA Page 293 Ex15.6
Ex15.6Q1,2,3
(Angle Between 2 Planes)
MIA Page 300 Ex15.10
Ex15.10Q1a,b,c,2a,b3,4a
(Intersection of Line & Plane)
MIA Page 302 Ex 15,11
Ex 15.11 Q1,2
(Intersection of 2 Lines)
MIA Page 303 Ex 15.12 - 1
Ex15.12Q1,2
(Intersection of 2 Planes using Gaussian)
MIA Page 303 Ex 15.12 - 2
Ex15.12Q1,2
(Intersection of 2 Planes - Alternative)
MIA Page 307 Ex 15.3
Ex 15.3Q1a,c,2a,c
(Intersection of 3 Planes)
Matrices
(7 Periods)
MIA Page 231 Ex 13.1
Ex13.1Q1,2,3a,4a,c,e,i,p,t,7a,f,9,10
(Basic Properties & Operations of Matrices)
MIA Page 235 Ex 13.3
Ex13.3Q1a,c,2a,c,k,m,o,3a,4,5a,c
(Matrix Multiplication)
MIA Page 236 Ex 13.4
Ex13.4Q6a,b,7a,b,8a
(Properties of Matrix Multiplication)
MIA Page 240 Ex 13.6
Ex13.6Q1a,b,d,h
(Determinant of a 2 x 2 Matrix)
Further Sequences & Series
(4 Periods)
Solutions Coming Soon!
Further Differential Equations
(5/6 Periods)
Solutions Coming Soon!
Further No Theory & Proofs
(4 Periods)
Solutions Coming Soon!

 

8. AH Maths Past & Practice Papers

Thanks to the SQA for making these available.

Year
_____
Paper Type
_________________
Exam Paper
______________
Marking Scheme
_________________
2017Advanced HigherExam PaperMarking Scheme
2016Advanced HigherExam PaperMarking Scheme
2016AH SpecimenSpecimen
2016AH ExemplarExemplarExemplar Guidance
2015Advanced HigherExam PaperMarking Scheme
2014Advanced HigherExam PaperMarking Scheme
2013Advanced HigherExam PaperMarking Scheme
2012Advanced HigherExam PaperMarking Scheme
2011Advanced HigherExam PaperMarking Scheme
2010Advanced HigherExam PaperMarking Scheme
2009Advanced HigherExam PaperMarking Scheme
2008Advanced HigherExam PaperMarking Scheme
2007Advanced Higher Exam PaperMarking Scheme
2006Advanced HigherExam PaperMarking Scheme
2005Advanced HigherExam PaperMarking Scheme
2004Advanced HigherExam PaperMarking Scheme
2003Advanced HigherExam PaperMarking Scheme
2002Advanced HigherExam PaperMarking Scheme
2001Advanced HigherExam Paper

 

9. AH Maths Past Paper Questions by Topic

Topic
________
Topic Name
___________________________
Topic
________
Topic Name
___________________________
Topic 1Binomial TheoremTopic 9Integration
Topic 2Complex NumbersTopic 10Matrices
Topic 3Differential EquationsTopic 11Partial Fractions
Topic 4DifferentiationTopic 12Proof
Topic 5Further Differential EquationsTopic 13Properties of Functions
Topic 6Further DifferentiationTopic 14Sequences & Series
Topic 7Further Number TheoryTopic 15Systems of Equations
Topic 8Further Sequences & SeriesTopic 16Vectors

 

10. AH Maths Theory – All Units

Thanks to the author(s) for making these available.

Topic
_______
Topic Name
____________________________
Topic
_______
Topic Name
____________________________
Topic 1Binomial Theorem (HSN)Topic 15Integration (HSN)
Topic 2Binomial TheoremTopic 16Iterative Schemes (HSN)
Topic 3Complex Numbers (HSN)Topic 17Matrices (HSN)
Topic 4Complex NumbersTopic 18Matrices
Topic 5Differentiation (HSN)Topic 19Methods of Proof (HSN)
Topic 6DifferentiationTopic 20Partial Fractions (HSN)
Topic 7Further DifferentiationTopic 21Partial Fractions
Topic 8Differential EqnsTopic 22Properties of Functions
Topic 9Further Differential EquationsTopic 23Sequences & Series (HSN)
Topic 10Further Number TheoryTopic 24Sequences & Series
Topic 11Functions (HSN)Topic 25Transformations of the Plane (HSN)
Topic 12Gaussian Elimination (HSN)Topic 26Vectors (HSN)
Topic 13Gaussian EliminationTopic 27Vectors
Topic 14HSN AH NotesTopic 28Whole 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 OnePractice OnePractice One
Practice TwoPractice TwoPractice Two
Practice ThreePractice ThreePractice Three

 

12.  SQA & Heriot-Watt University Course Notes

AH_Unit_1_(SQA)AH_Unit_1_Supp_Notes_(SQA)AH_Unit_1_Study_Guide_(H.Watt)AH_Unit_1_Tutor_Notes_(H.Watt)
AH Unit 2 (SQA)AH Unit 2 Supp Notes (SQA)AH Unit 2 Study Guide (H.Watt)AH Unit 2 Tutor Notes (H,Watt)
AH Unit 3 (SQA)AH Unit 1 Supp Notes (SQA)AH Unit 3 Study Guide (H.Watt)AH Unit 3 Tutor Notes (H.Watt)

 

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 full-colour 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

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Resources used with students studying Maths in Scottish Secondary Schools

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