Unsure about the Constraint Equation?

Unsure about the Constraint Equation?

Let the fantastic wealth of resources below teach you all about the Constraint Equation.

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Covers the whole of the AH Maths course

Created by an experienced maths teacher

Resources used with students in Scottish Secondary Schools

The Constraint Equation

Welcome to advancedhighermaths.co.uk

A sound understanding of the Constraint Equation is essential to ensure exam success.

Study at Advanced Higher Maths level will provide excellent preparation for your studies when at university. Some universities may require you to gain a pass at AH Maths to be accepted onto the course of your choice. The AH Maths course is fast paced so please do your very best to keep on top of your studies.

For students looking for extra help with the AH Maths course in 2020/21 you may wish to consider subscribing to the fantastic additional exam focused resources available in the Online Study Pack.

We hope you find this website useful and wish you the very best with your studies in 2020/21.

Please find below:

1. AH Maths Past Exam Worksheets by Topic

2. Links and Exam Formulae

3. Differentiation Resources

4. Further Differentiation Resources

5. MIA Text Book Questions – Differentiation

6. MIA Text Book Questions – Further Differentiation

7. About the Constraint Equation

8. AH Maths Past and Practice Papers

9. AH Maths Past Paper Questions by Topic

10. Recommended AH Book

11. Exam Focused Online Study Pack – For students looking for a ‘good’ Pass


Advanced Higher Maths Resources


1. AH Maths Past Paper Exam Worksheets by Topic

Thanks to the SQA for making these available. The worksheets by topic below are an excellent study resource since they are actual SQA past paper exam questions.

Clear, easy to follow, step-by-step worked solutions to all SQA Higher Maths Questions below are available in the Online Study Pack.

1Binomial TheoremAnswers
2Complex NumbersAnswers
4Differentiation (Further)Answers
5Differential Equations - Variables SeparableAnswers
6Differential Equations (Further)Answers
7Functions & GraphsAnswers
9Integration (Further)Answers
11Number Theory - Methods of ProofAnswers
12Number Theory (Further) - Euclidean & Number BasesAnswers
13Partial FractionsAnswers
14Sequences & SeriesAnswers
15 Sequences & Series - Maclaurin Answers
16Systems of EquationsAnswers


2. Links and Exam Formulae

AH Maths - Home Page LinkHERE
AH Maths - Whole Course LinkHERE
AH Maths - Exam Formula ListHERE
Higher Maths - Exam Formulae ListHERE
AH Maths - Complete Formula ListHERE
SQA Full Course Content and OutlineHERE


3. Differentiation Resources

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

Differentiation Theory Guide 1HERE
Differentiation Theory Guide 2HERE
Differentiation HSN Summary NotesHERE


4. Further Differentiation Resources

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

Further Differentiation Theory Guide 1HERE
Further Differentiation Theory Guide 2HERE
Further Differentiation HSN Summary NotesHERE


5. MIA Text Book Questions – Differentiation

Recommended questions from the Maths In Action (2nd Edition) by Edward Mullan text book are shown below.

Worked solutions to all questions below are available in the Online Study Pack.

Page Number
Recommended Questions
Derivative from First PrinciplesPage 45Exercise 4.1Q1,3,5,7
The Chain RulePage 48Exercise 4.3Q1a,d,2a,c,3b,4a,5a
The Product RulePage 51Exercise 4.5Q1a-h,Q2b,Q3a-l
The Quotient RulePage 52Exercise 4.6Q1,2,3,4
Differentiation - A Mixture!Page 53Exercise 4.7Q1,2,3,4,5
Sec, Cosec & CotPage 55Exercise 4.8Q1a,b,2a,c,d,3a,c,e,g
Exponential FunctionsPage 58Exercise 4.9Q1a,c,e,2a,3e,4a,b,5a,e
Logarithmic FunctionsPage 58Exercise 4.9Q1k,m,o,q,s,2f,g,3a,b,c,4d,e,5d
Nature & Sketching PolynomialsPage 70Exercise 5.5Q1a,b,c,2a,b
ConcavityPage 73Exercise 5.7Q5a,b,c,Q1a,b
ApplicationsPage 187Ex 11.1Q1a,b,e,f,2a,c,3a,c


6. MIA Text Book Questions – Further Differentiation

Recommended questions from the Maths In Action (2nd Edition) by Edward Mullan text book are shown below.

Worked solutions to all questions below are available in the Online Study Pack.

Page Number
Recommended Questions
Inverse Trig Functions & Chain RulePage 85Exercise 6.2Q1a,b,c,Q2b,c,dQ3a,d
Inverse Trig Fns & Product/Quotient RulesPage 86Exercise 6.3Q2,Q3
Implicit & Explicit Functions - 1Page 89Exercise 6.4Q1,Q2
Implicit & Explicit Functions - 2Page 89Exercise 6.4Q5,Q9,Q4
Second Derivatives of Implicit FunctionsPage 90Exercise 6.5Q1a,d,f,k(i),6
Logarithmic DifferentiationPage 92Exercise 6.6Q1,Q2
Parametric EquationsPage 95Exercise 6.7Q1a,b,c
Parametric Eqns - Differentiation Page 96Exercise 6.8Q1,2,3
Parametric Eqns - Differentiation (Alternative)Page 96Exercise 6.8Q1(i)
Parametric Eqns - Differentiation (Alternative)Page 96Exercise 6.8Q1(ii),Q2,Q3
Applications of Further DifferentiationPage 193Exercise 11.2Q1,Q2,Q3


7. About The Constraint Equation

For a more detailed explanation, please first read the Theory Guides above.

Equations of the form: x = f(t) and y = g(t)

where t takes values in some interval, describe a curve/line in the xy-plane.

Consider a point moving in the x, y-plane.

Let (x, y) be the coordinates of the point at time t.

Therefore, both x and y are functions of t.

Suppose, for example x = 1 – t and y = 1 + 2t

At t = 2, x = 1 – 2 = – 1 and y = 1 + 4 = 5

Hence the coordinates at time t = 2 are (-1 , 5)

The equations of x and y in terms of t are known as parametric equations, t in known as the parameter.

An expression for dy/dx in terms of t can be found using the formula below:

It is also possible to eliminate the parameter from a pair of equations.

  • x = 1 – t              → (1)
  • y = 1 + 2t            → (2)

Multiplying equation (1) by 2 and adding gives

  • 2x + y = 3           → (3)

Equation (3) is referred to as the constraint equation of the function


8. AH Maths Past & Practice Papers

Thanks to the SQA for making these available.

Worked solutions to SQA Exam Questions available in the Online Study Pack.

Paper Type
Exam Paper
Marking Scheme
2019AH SpecimenSpecimenMarking Scheme
2019Advanced HigherExam PaperMarking Scheme
2018Advanced HigherExam PaperMarking Scheme
2017Advanced HigherExam PaperMarking Scheme
2016Advanced HigherExam PaperMarking Scheme
2016AH SpecimenSpecimenMarking Scheme
2016AH ExemplarExemplarMarking Scheme
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 HigherExam PaperMarking Scheme
2006Advanced HigherExam PaperMarking Scheme
2005Advanced HigherExam PaperMarking Scheme
2004Advanced HigherExam PaperMarking Scheme
2003Advanced HigherExam PaperMarking Scheme
2002Advanced HigherExam PaperMarking Scheme
2001Advanced HigherExam PaperMarking Scheme


9. AH Maths Past Paper Questions by Topic

Thanks to the SQA for making these available.

Questions and answers have been split up by topic for ease of reference.

Worked solutions to all SQA questions below available in the Online Study Pack.

Further Differentiation
& Graphs
Systems of
Seq &
Further Seq
& Series
of Proof
Further No
Differential Eqns
Specimen P1MarkingQ2Q4Q6Q8Q3Q5Q1Q7
Specimen P2MarkingQ3Q1Q2,4,8,10Q7Q11Q5Q13Q9Q6Q12


10. 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.


11. Exam focused Online Study Pack 

Through step-by-step worked solutions to exam questions available in the Online Study Pack we cover everything you need to know about the Constraint Equation to pass your final exam.

As well as students studying Advanced Higher Mathematics, the resources will benefit young adults studying A-Level Mathematics and undergraduates who need a little extra help. Particular benefit will be to students who have gained a ‘Conditional’ University place and are therefore required to pass in order to gain entry onto the course of their choice.

Subscribing to the Online Study Pack may therefore be one of your best ever investments. Please click Online Study Pack to view screenshots, examples and instructions on how to subscribe.

Please speak with your mum/dad and show them our fantastic website.

We hope the resources on this website prove useful and wish you the very best of success with your AH Maths course in 2020/21.

Get the Study Pack - just £9.99

Teachers click here >

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Not just Constraint Equation, but 70 other maths concepts covered in detail

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