15.1 Understanding Geometric Sequences Answers
Geometric Sequence
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A sound understanding of theGeometric Sequence is essential to ensure examination success.
Study at Avant-garde Higher Maths level will provide splendid preparation for your studies when at university. Some universities may require you to proceeds a pass at AH Maths to be accustomed onto the course of your choice. The AH Maths course is fast paced so delight exercise your very best to continue on top of your studies.
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We hope you find this website useful and wish you the very best of success with your AH Maths course in 2023. Please find below:
i. Nearly Geometric Sequences
2. Sequences & Serial – Examination Worksheet & Theory Guides
3. Sequences & Series – Recommended Text Book Questions
4. AH Maths By Exam Worksheets by Topic
v. AH Maths Past Paper Questions by Topic
6. AH Maths Past & Practice Examination Papers
7. AH Maths 2020 Specimen Exam Newspaper
8. AH Maths Prelim & Final Test Practice Papers
9. AH Maths Theory Guides
10. AH Maths Course Outline, Formulae Sheets & Bank check List
xi. Text Book Recommended Timings & Questions – Unit One
12. Text Book Recommended Timings & Questions – Unit 2
13. Text Book Recommended Timings & Questions – Unit Three
14. AH Maths Practice Unit Assessments – Solutions Included
15. AH Maths Video Links
xvi. AH Maths Recommended Text Book
17. Exam Focused Study Pack – Students looking for a 'proficient' Pass
Advanced Higher Maths Resources
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i. About Geometric Sequences
To learn about Geometric Sequences please click on any of the Theory Guide links in Section 2 below. For students working from the Maths In Activeness text book the recommended questions on this topic are given in Department three. Worksheets including actual SQA Exam Questions are highly recommended.
If you would like more than assistance understanding Geometric Sequences there are full, easy to follow, step-by-pace worked solutions to dozens of AH Maths Past & Practice exam questions on all topics in the AH Maths Online Report Pack. Too included in the Study Pack are full worked solutions to the recommended MIA text book questions. Please give yourself every opportunity for success, speak with your parents, and subscribe to the examination focused Online Written report Pack today.
Geometric Sequences
In a geometric series, consecutive terms modify by a abiding cistron:
a, ar, ar², …
The factor r is called thecommon ratio
The nth term of a geometric serial is:
Exam Formulae
In the AH Maths exam the below is given in the Test Formulae list:
Exam Question
Source: SQA AH Maths Newspaper 2012 Question two.
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two. Sequences & Serial – Test Worksheet & Theory Guides
Thanks to the SQA and authors for making the excellent AH Maths Worksheet & Theory Guides freely available for all to use. These will prove a fantastic resource in helping consolidate your understanding of AH Maths. Articulate, easy to follow, pace-by-step worked solutions to all SQA AH Maths Questions in the worksheet below are available in the Online Written report Pack.
| Worksheet/Theory Guides ____________________________ | Resources Link ____________________________________ | Answers ____________ |
| AH Maths Test Questions | Sequences & Series Exam Questions | Answers |
| AH Maths Formulae List | AH Maths Fomulae List | |
| Theory Guide 1 | Sequences & Series Theory Guide 1 | |
| Theory Guide 2 | Sequences & Series Theory Guide 2 | |
| Theory Guide 3 (HSN) | Sequences & Series HSN Summary Notes |
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iii. Sequences & Serial – Recommended Text Book Questions
Recommended questions from the Maths In Action (2nd Edition) by Edward Mullan text book are shown below. Articulate, easy to follow, step-past-step worked solutions to all questions below are available in theOnline Study Pack.
| Subtopic _______________________________ | Page Number _____________ | Exercise ______________ | Recommended Questions __________________________ | Worked Solutions ___________________ |
| Arithmetics Sequences | Page 151 | Exercise 9.1 | Q1a-f,2a-f,Q3,Q4,Q6 | In Online Study Pack |
| Finding Sum - Arithmetic Sequence | Page 153 | Practice nine.2 | Q1a,b,c,Q3a-d,Q4a,b,Q5a | In Online Study Pack |
| Geometric Sequence | Page 156 | Practise 9.3 | Q1a-due east,Q2,Q3,Q5 | In Online Study Pack |
| Finding Sum - Geometric Sequence | Page 159 | Practice 9.4 | Q1a-f,Q2a-d,Q3a-d,Q4 | In Online Study Pack |
| Finding Sum to Infinity | Page 162 | Exercise 9.5 | Q1,2,iii,4,6 | In Online Report Pack |
| Sigma Note | Page 168 | Exercise 10.1 | Q1a-east,Q2a-e | In Online Report Pack |
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iv. AH Maths Past Paper Exam Worksheets by Topic
Cheers to the SQA for making these bachelor. The worksheets by topic below are an first-class study resource since they are actual SQA by paper test questions. Articulate, piece of cake to follow, pace-by-footstep worked solutions to all SQA AH Maths Questions below are available in the Online Study Pack.
| Number ______ | Topic ____________________________________________ | Answers _________ | Worked Solutions ___________________ |
| 1 | Binomial Theorem | Answers | In Online Study Pack |
| 2 | Circuitous Numbers | Answers | In Online Study Pack |
| iii | Differentiation | Answers | In Online Study Pack |
| iv | Differentiation (Farther) | Answers | In Online Study Pack |
| 5 | Differential Equations - Variables Separable | Answers | In Online Study Pack |
| half dozen | Differential Equations (Further) | Answers | In Online Study Pack |
| 7 | Functions & Graphs | Answers | In Online Study Pack |
| eight | Integration | Answers | In Online Study Pack |
| 9 | Integration (Further) | Answers | In Online Report Pack |
| x | Matrices | Answers | In Online Report Pack |
| 11 | Number Theory - Methods of Proof | Answers | In Online Study Pack |
| 12 | Number Theory (Further) - Euclidean & Number Bases | Answers | In Online Written report Pack |
| xiii | Partial Fractions | Answers | In Online Study Pack |
| 14 | Sequences & Series | Answers | In Online Study Pack |
| 15 | Sequences & Series - Maclaurin | Answers | In Online Study Pack |
| 16 | Systems of Equations | Answers | In Online Study Pack |
| 17 | Vectors | Answers | In Online Written report Pack |
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5. AH Maths Past Newspaper Questions by Topic
Thanks to the SQA for making these available. Questions and answers accept been split up by topic for your ease of reference. Articulate, easy to follow, step-by-step worked solutions to all SQA AH Maths questions below are bachelor in theOnline Report Pack.
| . Paper ___________ | . Marker ______ | Binomial Theorem ________ | Partial Fractions ________ | . Differentiation ___________ | Further Differentiation ___________ | . Integration ___________ | Farther Integration ____________ | Functions & Graphs ___________ | Systems of Equations ____________ | Complex Numbers __________ | Seq & Series _________ | Further Seq & Series ____________ | . Matrices _________ | . Vectors __________ | Methods of Proof __________ | Further No Theory ___________ | Differential Equations ____________ | Farther Differential Eqns _________________ |
| Specimen P1 | Marking | Q2 | Q4 | Q6 | Q8 | Q3 | Q5 | Q1 | Q7 | |||||||||
| Specimen P2 | Marking | Q3 | Q1 | Q2,4,8,10 | Q7 | Q11 | Q5 | Q13 | Q9 | Q6 | Q12 | |||||||
| 2019 | Marking | Q9 | Q4 | Q1a,b,6 | Q1c,five,10 | Q16b | Q16a | Q3 | Q18 | Q7,17 | Q2 | Q15 | Q11,14 | Q12 | Q13 | Q8 | ||
| 2018 | Marking | Q3 | Q2 | Q1b | Q1a,c,6,xiii | Q8 | Q15a | Q16a | Q4,ten | Q14 | Q17 | Q7,11 | Q16 | Q9,12 | Q5 | Q15b | ||
| 2017 | Mark | Q1 | Q2 | Q3 | Q11,xviii | Q16 | Q6 | Q12 | Q5 | Q17 | Q4,x | Q7 | Q15 | Q13 | Q8 | Q9 | Q14 | |
| 2016 | Mark | Q3 | Q13 | Q1a,b | Q1c,eleven | Q13 | Q9 | Q12 | Q4 | Q8 | Q2 | Q6 | Q7 | Q14 | Q5,10 | Q16 | Q15 | |
| 2015 | Marking | Q1,9 | Q2 | Q4,vi,8 | Q17 | Q10 | Q14 | Q13 | Q3 | Q5,11 | Q15 | Q12 | Q7 | Q18 | Q16 | |||
| 2014 | Marker | Q2 | 14b | Q1,13 | Q1,4,6 | Q10,12 | Q15 | Q11 | Q3 | Q16 | Q14 | Q9 | Q7 | Q5 | Q7 | Q8 | ||
| 2013 | Marker | Q1 | Q2 | Q11 | Q4,6 | Q8 | Q13 | Q7,10 | Q17 | Q3 | Q15 | Q9,12 | Q5 | Q16 | Q14 | |||
| 2012 | Marking | Q4 | 15a | Q1 | Q12,xiii | Q8 | Q11 | Q7 | Q14 | Q3,16b | Q2 | Q6 | Q9 | Q5 | 16a | Q10 | Q15 | |
| 2011 | Marking | Q2 | Q1 | 3b,vii | 3a | Q1,11a | Q1,eleven,16 | Q6 | Q10 | Q8,13 | Q5 | Q4 | Q15 | Q12 | Q9 | Q14 | ||
| 2010 | Marking | Q5 | Q1 | Q13 | Q15 | Q3,vii | Q10 | Q16 | Q2 | Q9 | Q4,14 | Q6 | Q8,12 | Q11 | ||||
| 2009 | Marking | Q8 | Q14 | Q1a | Q1b,11 | Q5,7 | Q9 | Q13 | 16a | Q6 | Q12 | Q14 | Q2 | Q16 | Q4 | Q10 | Q3 | Q15 |
| 2008 | Marking | Q8 | Q4 | Q10,xv | Q2,5 | Q4,9,10 | Q7 | Q3 | Q16 | Q1 | Q12 | Q6 | Q14 | Q11 | Q13 | |||
| 2007 | Mark | Q1 | Q4 | Q2 | Q13 | Q4,10 | Q4 | Q16 | Q3,11 | Q9 | Q6 | Q5 | Q15 | Q12 | Q7 | Q14 | Q8 | |
| Mixed | Mixed | Mixed | Mixed | Mixed | Mixed | Mixed | Mixed | Mixed | Mixed | Mixed | Mixed | Mixed | Mixed | Mixed | Mixed | Mixed |
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6. AH Maths Past & Practice Exam Papers
Thanks to the SQA for making these available. Clear, piece of cake to follow, footstep-past-footstep worked solutions to all SQA AH Maths questions below are available in theOnline Written report Pack.
| Year ____ | Paper Type _________________ | Exam Paper ______________ | Marking Scheme _________________ | Worked Solutions ___________________ |
| 2022 | Avant-garde College | Examination Paper | Marking Scheme | In Online Report Pack |
| 2019 | AH Specimen | Specimen | Marking Scheme | In Online Study Pack |
| 2019 | Advanced Higher | Exam Paper | Marking Scheme | In Online Study Pack |
| 2018 | Advanced Higher | Exam Newspaper | Mark Scheme | In Online Study Pack |
| 2017 | Avant-garde Higher | Exam Paper | Marking Scheme | In Online Study Pack |
| 2016 | Avant-garde Higher | Exam Paper | Marker Scheme | In Online Study Pack |
| 2016 | AH Specimen | Specimen | Marker Scheme | In Online Study Pack |
| 2016 | AH Exemplar | Exemplar | Marking Scheme | In Online Study Pack |
| 2015 | Advanced Higher | Exam Newspaper | Mark Scheme | In Online Report Pack |
| 2014 | Advanced College | Exam Newspaper | Marking Scheme | In Online Report Pack |
| 2013 | Advanced College | Exam Paper | Marking Scheme | In Online Study Pack |
| 2012 | Advanced Higher | Exam Paper | Marking Scheme | In Online Study Pack |
| 2011 | Advanced College | Exam Paper | Marking Scheme | In Online Written report Pack |
| 2010 | Advanced College | Exam Newspaper | Marking Scheme | In Online Report Pack |
| 2009 | Avant-garde College | Exam Newspaper | Marking Scheme | In Online Study Pack |
| 2008 | Advanced College | Exam Paper | Marker Scheme | In Online Study Pack |
| 2007 | Advanced Higher | Exam Paper | Mark Scheme | In Online Report Pack |
| 2006 | Avant-garde Higher | Test Paper | Marking Scheme | |
| 2005 | Advanced Higher | Exam Paper | Mark Scheme | |
| 2004 | Advanced Higher | Examination Paper | Marker Scheme | |
| 2003 | Advanced Higher | Exam Paper | Marker Scheme | |
| 2002 | Advanced Higher | Examination Paper | Marker Scheme | |
| 2001 | Advanced Higher | Exam Paper | Marking Scheme |
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7. AH Maths 2020 Specimen Examination Paper
Please detect below two Specimen Papers courtesy of the SQA. Clear, easy to follow, stride-by-footstep worked solutions to the SQA AH Maths Specimen Paper available in the Online Study Pack.
| . Date __________ | . Paper ___________ | . Marking ______ | Binomial Theorem ________ | Fractional Fractions ________ | . Differentiation ___________ | Further Differentiation ___________ | . Integration ___________ | Further Integration ____________ | Functions & Graphs ___________ | Systems of Equations ____________ | Complex Numbers __________ | Seq & Serial _________ | Further Seq & Series ____________ | . Matrices _________ | . Vectors __________ | Methods of Proof __________ | Further No Theory ___________ | Differential Equations ____________ | Further Differential Eqns _________________ |
| June 2019 | Specimen P1 | Marking | Q2 | Q4 | Q6 | Q8 | Q3 | Q5 | Q1 | Q7 | |||||||||
| June 2019 | Specimen P2 | Marking | Q3 | Q1 | Q2,4,8,10 | Q7 | Q11 | Q5 | Q13 | Q9 | Q6 | Q12 |
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8. AH Maths Prelim & Final Examination Do Papers
Thanks to the SQA and authors for making these freely bachelor. Please utilise regularly for revision prior to assessments, tests and the final examination. Articulate, easy to follow, step-by-step worked solutions to the starting time five Practice Papers below are available in theOnline Study Pack.
| AH Practice Exam Newspaper _____________________ | Marking ___________ | AH Practice Exam Newspaper _____________________ | Marking ___________ |
| Practice Exam Paper 1 | Here | Practice Exam Newspaper v | HERE |
| Practice Test Paper 2 | HERE | Practice Exam Paper half dozen | HERE |
| Practice Exam Newspaper 3 | Hither | Practice Exam Paper seven | HERE |
| Do Exam Paper 4 | HERE | Practice Exam Paper 8 | Here |
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9. AH Maths Theory Guides
Thanks to the authors for making the excellent AH Maths Theory Guides freely available for all to employ. These will prove a fantastic resource in helping consolidate your agreement of AH Maths.
Unit I
| Topic 1 ______________________ | Topic ii ___________________ | Topic three _____________________ | Topic four ___________________ | Topic 5 ___________________ | Topic six ___________________ |
| Partial Fractions 1 | Binomial 1 | Gaussian ane | Functions one | Differentiation ane | Integration 1 |
| Partial Fractions 2 | Binomial 2 | Gaussian 2 | Functions (HSN) | Differentiation 2 | Integration (HSN) |
| Partial Fractions (HSN) | Binomial (HSN) | Gaussian (HSN) | Differentiation (HSN) |
Unit of measurement Two
| Topic 1 ______________________ | Topic 2 ________________________ | Topic 3 ___________________ | Topic 4 ____________________ | Topic 5 _________________________ |
| Further Differentiation 1 | Further Integration 1 | Circuitous Numbers 1 | Sequences & Serial 1 | Methods of Proof |
| Farther Differentiation 2 | Further Integration 2 | Circuitous Numbers 2 | Sequences & Serial 2 | Proof by Induction |
| Differentiation (HSN) | Integration (HSN) | Complex Nos (HSN) | Seq & Series (HSN) | Methods of Proof (HSN) |
Unit Three
| Topic one ________________________ | Topic 2 _________________ | Topic 3 _____________________ | Topic 4 _____________________ | Topic 5 ______________________________ |
| Vectors ane | Matrices ane | Maclaurin Series ane | Differential Eqns i | Further Number Theory |
| Vectors 2 | Matrices 2 | MacLaurin Series 2 | Differential Eqns 2 | |
| Vectors iii | Matrices three | Maclaurin Series (HSN) | Differential Eqns (HSN) | |
| Vectors (HSN) | Matrices (HSN) |
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10. AH Maths Course Outline, Formulae Sheets & Check List
Thanks to the SQA and authors for making the excellent resource below freely available. These are fantastic check lists to assess your AH Maths noesis. Delight attempt to use these regularly for revision prior to tests, prelims and the terminal exam.
| Title ____________________________________ | Link ___________ | Courtesy ___________________ |
| AH Maths Course Outline & Timings | Here | |
| SQA AH Maths Exam Formulae List | Hither | Courtesy of SQA |
| SQA College Maths Test Formulae Listing | HERE | Courtesy of SQA |
| SQA AH Maths Support Notes | Here | Courtesy of SQA |
| AH Maths Consummate Check Listing | HERE |
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11. Text Book Recommended Timings & Questions – Unit One
Course timings, along with specific text book exercises/questions for Unit Ane, courtesy of Teejay Publishers can exist found Here.
Fractional Fractions
Recommended questions from the Maths In Activeness (second Edition) past Edward Mullan Text Volume are shown below. Articulate, piece of cake to follow, step-past-stride worked solutions to all questions below are available in theOnline Study Pack.
| Subtopic _______________________________ | Page Number _____________ | Do _____________ | Recommended Questions _______________________ | Worked Solutions ___________________ |
| Blazon One - Partial Fractions | Page 23 | Practise 2.2 | Q1, 5, 12, 18, 19, 22, 25 | In Online Study Pack |
| Type Two - Partial Fractions | Page 24 | Practice 2.3 | Q1, iii, 5, ten, 14, xviii | In Online Study Pack |
| Blazon Three - Partial Fractions | Folio 25 | Exercise ii.4 | Q1, five, vii, 9, 11 | In Online Study Pack |
| Algebraic Long Segmentation Worksheet | Worksheet | Worked Solutions | ||
| Partial Fraction - Long Division | Page 26 | Exercise 2.5 | Q1 a, b, due east, j, fifty | In Online Study Pack |
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Binomial Theorem
Recommended questions from the Maths In Action (2nd Edition) by Edward Mullan Text Book are shown below. Clear, easy to follow, step-by-footstep worked solutions to all questions beneath are available in theOnline Study Pack.
| Subtopic ____________________________________ | Page Number _____________ | Exercise ___________ | Recommended Questions _______________________________ | Worked Solutions/Notes __________________________________________________________________________________ |
| Combinations nCr | Page 33 | Exercise 3.3 | Q1a,b,c,2a,b,c,4a-d,5a,b,6a,7a,b,d | In Online Study Pack |
| Expanding - Lesson one | Page 36 | Practise 3.4 | Q1a,b,c,2a,i,ii,3,iv | In Online Study Pack |
| Expanding - Lesson 2 | Page 36 | Exercise 3.four | Q3a-d,4a-f | THEORY - Questions 3 & 4 |
| Finding Coefficients | Folio 38 | Exercise three.v | Q1a,b,c,4a,5a,half dozen | In Online Study Pack |
| Approximation eg 1.05^5 = ? | Page forty | Exercise three.6 | Q1a,b,c,d | In Online Study Pack |
| Simplifying Full general Term (SQA Questions) | SQA Questions & Answers | Common SQA Binomial Questions non in AH Text Volume |
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Systems of Equations
Recommended questions from the Maths In Action (second Edition) past Edward Mullan Text Volume are shown below. Clear, piece of cake to follow, stride-by-pace worked solutions to all questions below are available in theOnline Study Pack.
| Subtopic ______________________________ | Page Number _____________ | Exercise _______________ | Recommended Questions _______________________ | Worked Solutions ___________________ |
| Gaussian Emptying | Page 265 | Exercise xiv.iv | Q1a,b,c,d,2a,b,c | In Online Written report Pack |
| Back-up & Inconsistency | Page 268 | Practice 14.vi | Q1a,b,c,2 | In Online Written report Pack |
| Redundancy SQA Question | 2016 Q4 (SQA) | In Online Written report Pack | ||
| Inconsistency SQA Question | 2017 Q5 (SQA) | In Online Study Pack | ||
| ILL Conditioning | Page 274 | Exercise xiv.ix | Q2a,b,c,d | In Online Study Pack |
| ILL Conditioning SQA Question | 2012 Q14c (SQA) | In Online Written report Pack |
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Functions & Graphs
Recommended questions from the Maths In Action (2nd Edition) by Edward Mullan Text Book are shown below. Clear, easy to follow, step-by-step worked solutions to all questions beneath are available in theOnline Study Pack.
| Subtopic ______________________________ | Page Number _____________ | Exercise ___________ | Recommended Questions _______________________ | Worked Solutions ___________________ |
| Sketching Modulus Function y = |10| | Page 66 | Exercise five.2 | Q1-9 | In Online Study Pack |
| Inverse Functions | Page 67 | Do 5.3 | Q1a,c,eastward,g,i,2a,c,due east,3 | In Online Study Pack |
| Odd & Even Functions | Page 74 | Exercise 5.8 | Q3a-l | In Online Study Pack |
| Vertical Asymptotes & Behaviour | Folio 75 | Practise v.ix | Q1a-f | In Online Study Pack |
| Horizontal & Oblique Asymptotes | Page 76 | Exercise 5.ten | Q1a,b,f,g,thousand,l | In Online Study Pack |
| Sketching Graphs | Folio 77 | Exercise 5.11 | Q1a,c,due east,i,one thousand | In Online Study Pack |
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Differential Calculus
Recommended questions from the Maths In Action (2nd Edition) by Edward Mullan Text Book are shown below. Clear, piece of cake to follow, stride-past-footstep worked solutions to all questions below are bachelor in theOnline Study Pack.
| Subtopic ___________________________ | Page Number ____________ | Practice ___________ | Recommended Questions _______________________ | Worked Solutions ___________________ |
| Derivative from Start Principles | Page 45 | Practise 4.1 | Q1,iii,v,7 | In Online Written report Pack |
| The Chain Rule | Page 48 | Exercise 4.3 | Q1a,d,2a,c,3b,4a,5a | In Online Study Pack |
| The Production Rule | Folio 51 | Practice iv.5 | Q1a-h,Q2b,Q3a-l | In Online Report Pack |
| The Quotient Rule | Folio 52 | Practise 4.vi | Q1,2,3,4 | In Online Study Pack |
| Differentiation - A Mixture! | Page 53 | Exercise 4.7 | Q1,2,iii,four,5 | In Online Written report Pack |
| Sec, Cosec & Cot | Page 55 | Exercise 4.8 | Q1a,b,2a,c,d,3a,c,e,grand | In Online Written report Pack |
| Exponential Functions | Page 58 | Exercise 4.ix | Q1a,c,e,2a,3e,4a,b,5a,e | In Online Study Pack |
| Logarithmic Functions | Page 58 | Exercise 4.9 | Q1k,chiliad,o,q,south,2f,chiliad,3a,b,c,4d,east,5d | In Online Study Pack |
| Nature & Sketching Polynomials | Page 70 | Exercise five.5 | Q1a,b,c,2a,b | In Online Study Pack |
| Concavity | Folio 73 | Practise 5.vii | Q5a,b,c,Q1a,b | In Online Study Pack |
| Applications | Page 187 | Ex 11.ane | Q1a,b,eastward,f,2a,c,3a,c | In Online Study Pack |
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Integral Calculus
Recommended questions from the Maths In Action (2d Edition) past Edward Mullan Text Book are shown below. Clear, easy to follow, step-by-step worked solutions to all questions beneath are available in theOnline Report Pack.
| Subtopic ______________________________________ | Page No __________ | Practice ___________ | Recommended Questions _____________________ | Worked Solutions ___________________ |
| Integration (College Revision) | Folio 100 | Exercise vii.1 | Q1a-i,2a-i,3a-l,4a-f | In Online Study Pack |
| Integration by Commutation | Page 103 | Exercise 7.ii | Q1a,c,e,k,i,m,m,o,q,s,u,due west | In Online Report Pack |
| Integration past Exchange - Extra Revision! | Folio 103 | Exercise 7.2 | Q1b,d,f,h,j,l,due north,p,r,t,v,x | In Online Study Pack |
| Further Integration by Exchange | Page 105 | Practice 7.3 | Q2a,b,c,d,4a,b,c,d | In Online Study Pack |
| Farther Integration by Substitution | Page 105 | Exercise 7.3 | Q6a,b,c,d | In Online Report Pack |
| Further Int'n by Sub'n - sin^m(x), cos^n(10) | Folio 105 | Exercise seven.3 | Q7a,b,c,d,due east,f | In Online Study Pack |
| Further Integration by Exchange - logs | Page 105 | Exercise 7.three | Q11a,b,c,d | In Online Study Pack |
| Substitution & Definite Integrals | Page 107 | Practise 7.4 | Q1a,c,e,g,i,chiliad | In Online Study Pack |
| Area between bend & x-axis | Page 120 | Exercise 7.10 | Q1,3 | In Online Study Pack |
| Expanse between curve & y-centrality | Page 120 | Exercise seven.10 | Q6,7 | In Online Report Pack |
| Book - revolved effectually x-axis SQA Question | 2014 Q10 (SQA) | In Online Report Pack | ||
| Book - revolved effectually y-centrality SQA Question | 2017 Q16 (SQA) | In Online Study Pack | ||
| Book - revolved around x-centrality | Page 120 | Exercise 7.x | Q11,12 | In Online Written report Pack |
| Applications of Integral Calculus | Folio 187 | Exercise 11.one | Q4,14 | In Online Study Pack |
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12. Text Book Recommended Timings & Questions – Unit of measurement Two
Course timings, along with specific text book exercises/questions for Unit Ii, courtesy of Teejay Publishers tin can exist found Hither.
Further Differentiation
Recommended questions from the Maths In Action (2nd Edition) by Edward Mullan Text Book are shown below. Clear, easy to follow, step-by-step worked solutions to all questions below are bachelor in theOnline Written report Pack.
| Subtopic _______________________________________ | Page Number _____________ | Do ______________ | Recommended Questions _____________________ | Worked Solutions ___________________ |
| Inverse Trig Functions & Chain Rule | Page 85 | Exercise 6.two | Q1a,b,c,Q2b,c,dQ3a,d | In Online Study Pack |
| Inverse Trig Fns & Product/Quotient Rules | Page 86 | Practise 6.3 | Q2,Q3 | In Online Study Pack |
| Implicit & Explicit Functions - 1 | Page 89 | Exercise 6.4 | Q1,Q2 | In Online Report Pack |
| Implicit & Explicit Functions - 2 | Page 89 | Practise 6.iv | Q5,Q9,Q4 | In Online Study Pack |
| Second Derivatives of Implicit Functions | Page 90 | Exercise 6.5 | Q1a,d,f,k(i),vi | In Online Study Pack |
| Logarithmic Differentiation | Page 92 | Exercise six.half-dozen | Q1,Q2 | In Online Study Pack |
| Parametric Equations | Page 95 | Exercise six.7 | Q1a,b,c | In Online Study Pack |
| Parametric Eqns - Differentiation | Page 96 | Practise 6.8 | Q1,2,iii | In Online Study Pack |
| Parametric Eqns - Differentiation (Alternative) | Page 96 | Exercise 6.8 | Q1(i) | In Online Study Pack |
| Parametric Eqns - Differentiation (Alternative) | Page 96 | Do 6.eight | Q1(2),Q2,Q3 | In Online Report Pack |
| Applications of Farther Differentiation | Page 193 | Exercise 11.2 | Q1,Q2,Q3 | In Online Study Pack |
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Farther Integration
Recommended questions from the Maths In Action (2nd Edition) by Edward Mullan Text Volume shown below. Articulate, easy to follow, stride-past-stride worked solutions to all questions below are available in theOnline Study Pack.
| Subtopic ______________________________________ | Page No __________ | Practice _________________ | Recommended Questions __________________________ | Worked Solutions ___________________ |
| Integration using Inverse Trig Functions | Folio 111 | Exercise 7.half dozen | Q1,two,3,4a,b | In Online Report Pack |
| Integration using Partial Fractions | Page 113 | Exercise vii.7 | Q1a,b,2a,b,3a,b,4a,b,5a,b,6a,b | In Online Written report Pack |
| Integration by Parts - 1 | Folio 116 | Practise seven.viii | Q1a-l | In Online Study Pack |
| Integration by Parts - 2 | Folio 116 | Do 7.8 | Q2a,c,d,east,f,g,h | In Online Study Pack |
| Integration past Parts - three | Page 116 | Exercise 7.viii | Q5a,b,Q6a,b | In Online Study Pack |
| Integration by Parts - Special Cases - 1 | Folio 118 | Do 7.9 | Q1a,b,c,d | In Online Report Pack |
| Integration by Parts - Special Cases - two | Folio 118 | Do vii.9 | Q2a,b,c,d,due east | In Online Study Pack |
| Start Club Diff Eqns - General Soln | Page 128 | Exercise 8.ane | Q1a-j | In Online Report Pack |
| First Order Diff Eqns - Particular Soln | Folio 128 | Practice 8.1 | Q2a-m | In Online Report Pack |
| Differential Equations in Context | Page 131 | Exercise 8.2 | Q2,4,5,half-dozen | In Online Study Pack |
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Complex Numbers
Recommended questions from the Maths In Action (2nd Edition) by Edward Mullan Text Book are shown beneath. Clear, like shooting fish in a barrel to follow, step-by-step worked solutions to all questions beneath are available in theOnline Report Pack.
| Subtopic _________________________________ | Page Number _____________ | Practice ______________ | Recommended Questions _________________________ | Worked Solutions ___________________ |
| Arithmetic with Complex Numbers | Page 207 | Exercise 12.1 | Q1,2,3,6,7,8 | In Online Report Pack |
| Division & Square Roots of Complex Nos | Page 209 | Exercise 12.2 | Q1a,b,c,2c,east,3a,b,f,5a,b | In Online Study Pack |
| Argand Diagrams | Folio 211 | Exercise 12.3 | Q3a,b,d,e,f,i,6a,b,f,7a,b,c | In Online Report Pack |
| Multiplying/Dividing in Polar Form | Page 215 | Exercise 12.five | Q1a,b,f,thou | In Online Study Pack |
| De Moivre's Theorem | Page 218 | Practise 12.six | Q1,ii,3a,4g,h,i,j | In Online Study Pack |
| Polynomials & Complex Numbers | Folio 224 | Practice 12.8 | Q2a,d,3a,b,four,v,6a,b | In Online Report Pack |
| Loci on the Complex Airplane | Page 213 | Exercise 12.4 | Q1a,b,d,f,j,3a,b,4a,b,c | In Online Study Pack |
| Expanding Trig Formula | Page 219 | Practice 12.6 | Q5,6,7a | In Online Study Pack |
| Roots of a Circuitous Number | Page 222 | Exercise 12.7 | Q2a,b,c,d,e,f,1a(i) | In Online Study Pack |
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Sequences & Series, Sigma Notation
Recommended questions from the Maths In Action (2nd Edition) by Edward Mullan Text Book are shown below. Clear, easy to follow, pace-by-step worked solutions to all questions below are bachelor in theOnline Study Pack.
| Subtopic _______________________________ | Page Number _____________ | Exercise ______________ | Recommended Questions __________________________ | Worked Solutions ___________________ |
| Arithmetic Sequences | Page 151 | Practice 9.1 | Q1a-f,2a-f,Q3,Q4,Q6 | In Online Study Pack |
| Finding Sum - Arithmetic Sequence | Page 153 | Exercise 9.ii | Q1a,b,c,Q3a-d,Q4a,b,Q5a | In Online Study Pack |
| Geometric Sequence | Page 156 | Practise 9.3 | Q1a-e,Q2,Q3,Q5 | In Online Study Pack |
| Finding Sum - Geometric Sequence | Folio 159 | Exercise 9.four | Q1a-f,Q2a-d,Q3a-d,Q4 | In Online Report Pack |
| Finding Sum to Infinity | Page 162 | Exercise nine.5 | Q1,2,3,4,6 | In Online Study Pack |
| Sigma Notation | Page 168 | Exercise 10.ane | Q1a-e,Q2a-eastward | In Online Written report Pack |
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Number Theory & Proof
| Topic _______________________________ | Lessons __________ | Questions _________ | Typed Solutions _______________ | Handwritten Solutions ______________________ | Exam Questions - Worked Solutions in Online Study Pack ______________________________________________________ |
| Straight Proof | Lesson 1 | Ex 1 & 2 | Ex 1 & 2 Handwritten Solns | 2018-Q9,2015-Q12, 2010-Q8a | |
| Proof by Counterexample | Lesson two | Ex 3 | Ex 3 Typed Solns | Ex iii Handwritten Solns | 2016-Q10, 2013-Q12, 2008-Q11 |
| Proof by Counterexample | Ex 4 | Ex four Typed Solns | Ex four Handwritten Solns | 2016-Q10, 2013-Q12, 2008-Q11 | |
| Proof by Contradiction | Lesson iii | Ex five | Ex 5 Typed Solns | Ex v Handwritten Solns | 2010-Q12 |
| Proof past Contrapositive | Lesson 4 | Ex vi | Ex 6 Typed Solns | Ex vi Handwritten Solns | 2017-Q13 |
| Proof by Induction | Lesson 5 | Ex 7 | Ex 7 Typed Solns | Ex vii Handwritten Solns | 2014-Q7,2013-Q9,2012-Q16a,2011-Q12,2010-Q8b,2009-Q4,2007-Q12 |
| Proof by Consecration - Sigma Notation | Lesson half-dozen | Ex 8 | Ex 8 Typed Solns | Ex viii Handwritten Solns | 2018-Q12,2016-Q5, 2013-Q9,2009-Q4 |
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xiii. Text Volume Recommended Timings & Questions – Unit of measurement Three
Course timings, along with specific text book exercises/questions for Unit Iii, courtesy of Teejay Publishers can be found HERE.
Vectors
Recommended questions from the Maths In Action (2nd Edition) by Edward Mullan Text Book are shown below. Clear, easy to follow, stride-by-step worked solutions to all questions below are available in theOnline Written report Pack.
| Subtopic __________________________________ | Folio Number _____________ | Do ______________ | Recommended Questions ________________________ | Lesson/Notes _________________ | Worked Solutions ___________________ |
| Higher Revision On Vectors | Page 282 | Practice 15.one | Q6,seven,8 | In Online Study Pack | |
| The Vector Product - 1 | Folio 286 | Do 15.three | Q1,2a,b,5,vii,8a,b,x | Lesson 1 | In Online Written report Pack |
| The Vector Product - 2 | Page 286 | Exercise 15.3 | Q3,4,6,12 | Lesson two | In Online Study Pack |
| The Equations of a Line | Page 298 | Do 15.8 | Q1a,b,2a,3a,c,e,5 | Lesson three | In Online Study Pack |
| Vector Equation of a Straight Line | Page 298 | Exercise fifteen.9 | Q2 | Lesson iii | In Online Study Pack |
| The Equation of a Aeroplane | Page 291 | Practice 15.5 | Q1a,b,c,d,2a,b,3,4a,c,9,x | Lesson iv | In Online Written report Pack |
| Angle Between 2 Planes | Page 293 | Exercise fifteen.six | Q1,two,three | Lesson v | In Online Study Pack |
| Intersection of Line & Plane | Folio 300 | Exercise 15.10 | Q1a,b,c,2a,b,3,4a | Lesson 6 | In Online Study Pack |
| Intersection of 2 Lines | Page 302 | Exercise 15.xi | Q1,2 | Lesson 7 | In Online Study Pack |
| Intersection of 2 Planes using Gaussian | Page 303 | Exercise fifteen.12 | Q1,2 | Lesson viii | In Online Written report Pack |
| Intersection of 2 Planes - Alternative | Folio 303 | Exercise 15.12 | Q1,two | In Online Report Pack | |
| Intersection of 3 Planes | Page 307 | Practice 15.3 | Q1a,c,2a,c | Lesson 9 | In Online Study Pack |
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Matrices
Recommended questions from the Maths In Action (2nd Edition) past Edward Mullan Text Volume are shown below. Clear, easy to follow, step-past-step worked solutions to all questions below are available in theOnline Study Pack.
| Subtopic __________________________________ | Page Number _____________ | Exercise ______________ | Recommended Questions ____________________________ | Worked Solutions ___________________ |
| Basic Properties & Operations of Matrices | Folio 231 | Exercise 13.1 | Q1,ii,3a,4a,c,east,i,p,t,7a,f,9,x | In Online Study Pack |
| Matrix Multiplication | Page 235 | Exercise 13.3 | Q1a,c,2a,c,k,yard,o,3a,4,5a,c | In Online Study Pack |
| Backdrop of Matrix Multiplication | Page 236 | Exercise 13.4 | Q6a,b,7a,b,8a | In Online Study Pack |
| Determinant of a 2 10 2 Matrix | Page 240 | Exercise 13.half-dozen | Q1a,b,d,h | In Online Report Pack |
| Determinant of a 3 x 3 Matrix | Page 247 | Exercise 13.ix | Q4a,b,c,d,5a,b | In Online Report Pack |
| Inverse of a 2 x 2 Matrix | Page 243 | Practice 13.seven | Q1,2,4,8,9a,b,c | In Online Study Pack |
| Inverse of a 3 x 3 Matrix | Page 275 | Exercise 14.10 | Q1a,b,c,d | In Online Study Pack |
| Transformation Matrices | Page 251 | Exercise xiii.10 | Q1,2,5 | In Online Study Pack |
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Further Sequences & Series (Maclaurin Series)
Recommended questions from the Maths In Action (2nd Edition) by Edward Mullan Text Volume are shown below. Articulate, piece of cake to follow, step-by-step worked solutions to all questions below are available in theOnline Written report Pack.
| Subtopic ________________________________ | Page Number _____________ | Practise ______________ | Recommended Questions _______________________ | Worked Solutions ___________________ |
| Maclaurin Series for f(x) | Page 179 | Do 10.5 | Q1a,b,c,d,3a,b | In Online Written report Pack |
| Maclaurin Serial - Composite Functions | Page 182 | Exercise 10.7 | Q1a,f,2a,3a,6a,7a,8a,b | In Online Study Pack |
| Maclaurin Series - SQA Questions | SQA Questions & Answers | In Online Written report Pack |
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Further Differential Equations
Recommended questions from the Maths In Action (2d Edition) by Edward Mullan Text Volume are shown below. Articulate, easy to follow, pace-by-step worked solutions to all questions beneath are available in theOnline Written report Pack.
| Subtopic __________________________________ | Page Number _____________ | Exercise ______________ | Recommended Questions ________________________ | Worked Solutions ___________________ |
| 1st Lodge Linear Differential Equations | Folio 136 | Do 8.3 | Q1a,b,2a,3a,b | In Online Written report Pack |
| 2nd Order Differential Equations (Roots Existent & Distinct) | Page 140 | Practice 8.4 | Q1a,b,c,2a,b | In Online Report Pack |
| 2nd Social club Differential Equations (Roots Existent & Coincident) | Page 141 | Exercise 8.5 | Q1a,b,c,2a,b | In Online Written report Pack |
| 2d Order Differential Equations (Roots Not Real) | Page 142 | Exercise eight.6 | Q1a,b,c,2a,b | In Online Study Pack |
| Non-Homogeneous Differential Equations (Finding Full general Solution) | Page 146 | Exercise 8.9 | Q1a,b,c | In Online Study Pack |
| Not-Homogeneous Differential Equations (Finding Item Solution) | Page 146 | Exercise 8.nine | Q2a,b,c | In Online Study Pack |
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Further Number Theory & Proof
Recommended questions from the Maths In Action (2nd Edition) past Edward Mullan Text Book are shown below. Clear, easy to follow, pace-past-step worked solutions to all questions below are available in theOnline Study Pack.
| Subtopic _______________________________________ | Folio Number _____________ | Exercise _________ | Recommended Questions _________________________ | Worked Solutions ___________________ |
| Finding the Greatest Mutual Divisor (GCD) | Page 318 | Ex 16.three | Q1a,c,e,one thousand,i | In Online Written report Pack |
| Expressing GCD in the grade xa + yb = d | Folio 320 | Ex 16.4 | Q1,2,3,four | In Online Report Pack |
| Number Bases | Page 322 | Ex 16.5 | Q1a-d,2a-f | In Online Written report Pack |
| Further Number Theory - SQA Questions | SQA Questions & Answers | In Online Study Pack |
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fourteen. AH Maths Practice Unit Assessments – Solutions Included
Thanks to maths777 for making the excellent resource freely available for all to use. This will bear witness a fantastic resource in helping you prepare for assessments, tests and the concluding exam.
| Methods in Algebra & Calculus __________________________ | Applications of Algebra & Calculus ____________________________ | Geometry, Proof & Systems of Equations ____________________________________ |
| Practise i | Practice 1 | Practise 1 |
| Practice 2 | Exercise 2 | Practice 2 |
| Practice 3 | Do 3 | Practice 3 |
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fifteen. AH Maths Video Links
Please click DLB Maths to view AH Maths Past Paper video solutions. There are also many videos showing worked examples by topic on the St Andrews Stand up Maths YouTube Channel link. Both video links are excellent resources in helping you prepare for assessments, tests and the terminal exam.
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xvi. AH Maths Text Book – Maths In Action (2nd Edition) by Edward Mullan
A fully revised class for the new Curriculum for Excellence examination that is designed to fully support the class's new structure and unit assessment. A part of the highly regarded Maths in Action serial, it provides students with a familiar, clear and advisedly structured learning feel that encourages them to build conviction and understanding.
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17. Avant-garde College Maths Online Report Pack
Through step-by-step worked solutions to exam questions and recommended MIA text book questions available in the Online Study Pack we cover everything y'all need to know about theGeometric Sequence to pass your last exam.
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Non simply Geometric Sequence, but 70 other maths concepts covered in detail
15.1 Understanding Geometric Sequences Answers,
Source: https://www.advancedhighermaths.co.uk/geometric-sequence/
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