Let the fantastic wealth of resources below teach you all about Parametric Differentiation ...

Covers the whole of the AH Maths course

Created by an experienced maths teacher

Resources used with students in Scottish Secondary Schools

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A sound understanding of Parametric Differentiation is essential to ensure exam success.

Please find resources for all other Maths courses HERE.

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Please find below:

3. Further Differentiation Resources

4. MIA Text Book Questions – Differentiation

5. MIA Text Book Questions – Further Differentiation

6. About Parametric Differentiation

7. AH Maths Past and Practice Papers

8. AH Maths Past Paper Questions by Topic

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

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**1. Links and Exam Formulae
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AH Maths - Home Page Link | HERE |

AH Maths - Whole Course Link | HERE |

AH Maths - Exam Formula List | HERE |

Higher Maths - Exam Formulae List | HERE |

AH Maths - Complete Formula List | HERE |

SQA Full Course Content and Outline | HERE |

**2. Differentiation Resources**

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

Differentiation Theory Guide 1 | HERE |

Differentiation Theory Guide 2 | HERE |

Differentiation HSN Summary Notes | HERE |

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**3. Further Differentiation Resources**

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

Further Differentiation Theory Guide 1 | HERE |

Further Differentiation Theory Guide 2 | HERE |

Further Differentiation HSN Summary Notes | HERE |

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**4. MIA Text Book Questions – Differentiation**

Recommended questions from the new MIA Text Book are shown below.

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

Subtopic ___________________________ | Page Number ____________ | Exercise ___________ | Questions ____________________________ | Worked Solutions _______________ |

Derivative from First Principles | Page 45 | Exercise 4.1 | Q1,3,5,7 | HERE |

The Chain Rule | Page 48 | Exercise 4.3 | Q1a,d,2a,c,3b,4a,5a | HERE |

The Product Rule | Page 51 | Exercise 4.5 | Q1a-h,Q2b,Q3a-l | HERE |

The Quotient Rule | Page 52 | Exercise 4.6 | Q1,2,3,4 | HERE |

Differentiation - A Mixture! | Page 53 | Exercise 4.7 | Q1,2,3,4,5 | HERE |

Sec, Cosec & Cot | Page 55 | Exercise 4.8 | Q1a,b,2a,c,d,3a,c,e,g | HERE |

Exponential Functions | Page 58 | Exercise 4.9 | Q1a,c,e,2a,3e,4a,b,5a,e | HERE |

Logarithmic Functions | Page 58 | Exercise 4.9 | Q1k,m,o,q,s,2f,g,3a,b,c,4d,e,5d | HERE |

Nature & Sketching Polynomials | Page 70 | Exercise 5.5 | Q1a,b,c,2a,b | HERE |

Concavity | Page 73 | Exercise 5.7 | Q5a,b,c,Q1a,b | HERE |

Applications | Page 187 | Ex 11.1 | Q1a,b,e,f,2a,c,3a,c | HERE |

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**5. MIA Text Book Questions – Further Differentiation **

Recommended questions from the new MIA Text Book are shown below.

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

Subtopic _______________________________________ | Page Number _____________ | Exercise ___________ | Questions ___________________ | Worked Solutions _______________ |

Inverse Trig Functions & Chain Rule | Page 85 | Exercise 6.2 | Q1a,b,c,Q2b,c,dQ3a,d | HERE |

Inverse Trig Fns & Product/Quotient Rules | Page 86 | Exercise 6.3 | Q2,Q3 | HERE |

Implicit & Explicit Functions - 1 | Page 89 | Exercise 6.4 | Q1,Q2 | HERE |

Implicit & Explicit Functions - 2 | Page 89 | Exercise 6.4 | Q5,Q9,Q4 | HERE |

Second Derivatives of Implicit Functions | Page 90 | Exercise 6.5 | Q1a,d,f,k(i),6 | HERE |

Logarithmic Differentiation | Page 92 | Exercise 6.6 | Q1,Q2 | HERE |

Parametric Equations | Page 95 | Exercise 6.7 | Q1a,b,c | HERE |

Parametric Eqns - Differentiation | Page 96 | Exercise 6.8 | Q1,2,3 | HERE |

Parametric Eqns - Differentiation (Alternative) | Page 96 | Exercise 6.8 | Q1(i) | HERE |

Parametric Eqns - Differentiation (Alternative) | Page 96 | Exercise 6.8 | Q1(ii),Q2,Q3 | HERE |

Applications of Further Differentiation | Page 193 | Exercise 11.2 | Q1,Q2,Q3 | HERE |

**6. About Parametric Differentiation**

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 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 = t³ and y = 5t

At t = 2, x = 2³ = 8 and y = 5 × 2 = 10

Hence the coordinates at time t = 2 are **(8 , 10)**

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:

**Example**

**7. 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.

Year _____ | Paper Type _________________ | Exam Paper ______________ | Marking Scheme _________________ |

2018 | Advanced Higher | Exam Paper | Marking Scheme |

2017 | Advanced Higher | 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 |

**8. 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.

**9. 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.

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**10. 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 Parametric Differentiation 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.

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We hope the resources on this website prove useful and wish you the very best of success with your AH Maths course in 2018/19.

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Topic Links

Free resources to dozens of AH Maths topics are available by clicking on any of the links to the right