Let the fantastic wealth of resources below teach you how to Complete the Square.
Covers the whole of the National 5 Maths course
Created by an experienced maths teacher
Resources used with students studying Maths in Scottish Secondary Schools
Welcome to national5maths.co.uk
A sound understanding of Completing the Square is essential to ensure exam success.
Passing N5 Maths significantly increases your career opportunities by helping you gain a place on a college course, apprenticeship or even landing a job. A ‘good’ pass at N5 Maths will set you up well for the fast paced Higher Maths Course next year should you be interested. Please do your very best to keep on top of your studies.
For students looking for extra help with the N5 Maths course you may wish to consider subscribing to the fantastic additional exam focused resources available in the Online Study Pack.
To access a wealth of additional free resources by topic please either use the above Search Bar or click HERE selecting on the topic you wish to study.
We hope the resources on this website prove useful and wish you the very best of success with your N5 Maths course in 2023. Please find below:
1. About Completing the Square
2. Completing the Square – Worksheets
3. Quadratics – Videos, PowerPoints & Mind Maps
5. N5 Maths Exam Worksheets by Topic
6. Credit Maths Exam Worksheets by Topic
7. N5 Maths Exam Questions & Answers by Topic
8. N5 Maths 180 Booster Papers
9. N5 Maths Videos, PowerPoints, Mind Maps & Worksheets
10. N5 Maths SQA Past & Practice Papers
11. 100 N5 Maths Exam Questions & Answers
13. N5 Maths Exam Focused Homework
15. N5 Maths Further Revision Practice
16. Credit & Int 2 Maths SQA Papers
17. 100 N5 Maths Lesson Starter Questions
18. N5 Maths – Applications Unit Practice Assessment
19. N5 Maths – Expressions & Formulae Unit Practice Assessment
20. N5 Maths – Relationships Unit Practice Assessment
23. Maths Websites (Including Games/Puzzles)
24. Recommended National 5 Maths Books
25. N5 Maths Online Study Pack – Students looking for a ‘good’ Pass
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1. About Completing the Square
To learn about Completing the Square please click on the Completing the Square Theory link. Please also find in Sections 2 & 3 below videos, PowerPoints, mind maps and worksheets on this topic to help your understanding. The Essential Skills 2 worksheet, along with actual SQA Exam Questions, are highly recommended. Worksheets 1 & 2 are excellent resources to consolidate your learning.
If you would like more help understanding Completing the Square there are clear, easy to follow, step-by-step worked solutions to dozens of N5 Maths Past & Practice exam questions on all topics in the Online Study Pack. Please give yourself every opportunity for success, speak with your parents, and subscribe to the exam focused Online Study Pack today.
Completing the Square
An N5 Maths question on Completing the Square is shown below:
Express x² – 14x + 44 in the form (x – a)² + b
Source: N5 Specimen 2014, P1, Q3
Answer/Process
x² – 14x + 44
= (x – 7)² – 49 + 44 ⇒ Half (- 14 ⇒ – 7), Square (- 7² ⇒ 49) then Subtract (49 ⇒ – 49)
= (x – 7)² – 5 ⇒ Simplify
Notes
Completing the square involves changing the way a quadratic equation is written.
We complete the square to make it easier to draw parabolas (U-shaped curves).
Once the square has been completed, it is easy to extract information from the equation such as:
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2. Completing the Square – Worksheets
Thanks to the SQA and authors for making the excellent resources below freely available. Please use the below for revision prior to assessments, tests and the final exam. Clear, easy to follow, step-by-step worked solutions to the Essential Skills worksheet and N5 Maths exam questions below are available in the Online Study Pack.
| N5 Maths Worksheets __________________________________ | Worksheet - Without Answers _______________________________________ | Worksheet - With Answers ______________________________ | Courtesy _________________________________________________ |
| Essential Skills 2 | Completing the Square | Answers | |
| N5 Exam Worksheet 1 - Recommended | Completing the Square | Answers Included on Worksheet | |
| N5 Exam Worksheet 2 | Completing the Square | Answers | |
| Credit Exam Worksheet | Quadratics including Completing the Square | Answers | |
| Worksheet 1 - Maths Scot | Completing the Square - Maths Scot | Answers | Maths Scot |
| Worksheet 2 | Completing the Square (With Theory) | On Worksheet | |
| Worksheet 3 | Completing the Square 1, With Answers | Answers | |
| Worksheet 4 | Completing the Square 2, With Answers | Answers | |
| Worksheet 5 | Completing the Square | Answers | Maths4Everyone.com kindly shared through TES website |
| Worksheet 6 | Completing the Square - Advanced | Answers | Maths4Everyone.com kindly shared through TES website |
| Worksheet 7 | Completing the Square - Question 3 | ||
| Worksheet 8 | Completing the Square | ||
| Worksheet 9 | Completing the Square & Sketching |
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3. Quadratics – Videos, PowerPoints & Mind Maps
Thanks to the authors for making the excellent resources below freely available. Please use the below for revision prior to assessments, tests and the final exam.
| YouKenMaths Video ________________________________ | Larbert Maths Video ____________________ | Maths 180 Videos _________________ | Mr Graham Maths Videos ______________________ | PowerPoints ___________________ | Mind Maps ______________________________ |
| N5 Exam Questions - Quadratic Formula | Completing the Square | Quadratics 1 | Quadratic Equations 1 | Factorising Quadratics | Quadratic Functions |
| Quadratics 2 | Quadratic Equations 2 | Quadratics | Quadratic Functions (PowerPoint) | ||
| Quadratics 3 | Sketching Quadratics | ||||
| Quadratics 4 | Quadratic Formula | ||||
| Quadratics 5 | Sketching Quadratics 2 |
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4. N5 Maths Essential Skills
Thanks to Mr G Rennie for making the excellent resources below freely available. The Essential Skills Worksheets can be used for general revision, homework, consolidation of a topic or preparation for assessments, tests and exams. Clear, easy to follow, step-by-step worked solutions to all 30 Essential Skills worksheets are available in the Online Study Pack.
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5. N5 Maths Exam Worksheets by Topic
Thanks to the SQA and authors for making the excellent resources below freely available. The worksheets by topic below are a fantastic study resource since they are actual SQA past paper exam questions. Clear, easy to follow, step-by-step worked solutions to all SQA N5 Maths Questions below are available in the Online Study Pack.
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6. Credit Maths Exam Worksheets by Topic
Thanks to the SQA and authors for making the excellent resources below freely available. In 2015 N5 Maths replaced Credit Maths. The Credit worksheets by topic below are a fantastic additional study resource.
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7. N5 Maths Exam Questions & Answers by Topic
Thanks to the SQA and authors for making the excellent resources below freely available. Questions & answers have been split up by topic for your ease of reference. Clear, easy to follow, step-by-step worked solutions to all N5 Maths Questions below are available in the Online Study Pack.
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8. N5 Maths 180 Booster Papers
Thanks to maths180.com for making the excellent resources below freely available. Please use the below for revision prior to assessments, tests and the final exam.
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9. N5 Maths Videos, PowerPoints, Mind Maps & Worksheets
Dozens of N5 Maths Videos, PowerPoints and Mind Maps provide quality lessons by topic. Also included are excellent revision worksheets, with actual SQA N5 Maths exam questions, to aid your understanding. Please click on our N5 Maths Videos & Worksheets dedicated page.
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10. N5 Maths SQA Past & Practice Papers
Thanks to the SQA and maths180.com for making the excellent resources below freely available. Clear, easy to follow, step-by-step worked solutions to all sixteen N5 Maths Past & Practice Papers below are available in the Online Study Pack.
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11. 100 N5 Maths Exam Type Questions & Answers
Thanks to the SQA and authors for making the excellent resources below freely available. Please try to do as many questions as possible, checking your answers as you go. If stuck, always ask your teacher for help as soon as possible. Clear, easy to follow, step-by-step worked solutions to all 100 N5 Maths Questions below are available in the Online Study Pack.
| Exam Questions __________________________ | Answers ___________ | Worked Solutions ____________________ |
| Exam Ques 1 - 10 | Answers | In Online Study Pack |
| Exam Ques 11 - 20 | Answers | In Online Study Pack |
| Exam Ques 21 - 30 | Answers | In Online Study Pack |
| Exam Ques 31 - 40 | Answers | In Online Study Pack |
| Exam Ques 41 - 50 | Answers | In Online Study Pack |
| Exam Ques 51 - 60 | Answers | In Online Study Pack |
| Exam Ques 61 - 70 | Answers | In Online Study Pack |
| Exam Ques 71 - 80 | Answers | In Online Study Pack |
| Exam Ques 81 - 90 | Answers | In Online Study Pack |
| Exam Ques 91 - 100 | Answers | In Online Study Pack |
| Whole Booklet - With Answers | In Online Study Pack | |
| Whole Booklet - No Answers | In Online Study Pack |
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12. N5 Maths Exam Check Lists
Thanks to the SQA and authors for making the excellent resources below freely available. Please use the below for revision prior to assessments, tests and the final exam.
| Check List _____________________________________________ | Link _________ | Acknowledgements/Comments _____________________________________________________________________________ |
| Check List 1 - Linking TJ N5 Text Book to Past Papers | HERE | Excellent resource linking N5 TJ Book to Past Paper Questions - Thanks to CHS School |
| Check List 2 - N5 Learning | HERE | Courtesy of Zeta Maths |
| Check List 3 - Whole Course (By Unit) | HERE | Courtesy of Zeta Maths |
| Check List 4 - Expressions & Formulae | HERE | Courtesy of Zeta Maths |
| Check List 5 - Applications | HERE | Courtesy of Zeta Maths |
| Check List 6 - Relationships | HERE | Courtesy of Zeta Maths |
| Check List 7 - Facts NOT given in the N5 Maths Exam | HERE | Courtesy of Airdrie Academy Website |
| Check List 8 - Whole Course List of Topics | HERE | Excellent check list for teachers & pupils to help track course progress |
| Check List 9 - Whole Course | HERE | |
| N5 Maths Exam Formulae List | HERE | Courtesy of SQA |
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13. N5 Maths Exam Focused Homework
Thanks to the SQA and authors for making the excellent resources below freely available. The exercises below are a fantastic resource which can also be used for revision prior to assessments, tests and the final exam.
| Expressions & Formulae _____________________ | Relationships _______________________________ | Applications ___________________ | Mixed Questions ______________________________________ |
| Algebraic Fractions 1 | Equations & Inequalities | Fractions | Exam Revision 1 |
| Algebraic Fractions 2 | Functions | Compound Interest | Exam Revision 2 |
| Arcs & Sectors | Pythagoras | Percentages | Exam Revision 3 |
| Factorising | Quadratics | Reversing a % Change | Exam Revision 4 |
| Indices | Quadratic Equations | Statistics | Exam Revision 5 |
| Multiplying out Brackets | Quadratic Graphs | Trigonometry | Exam Revision 6 |
| Scientific Notation | Rearranging Formula | Vectors 1 | Exam Revision 7 |
| Surds & Indices | Similar Shapes 1 | Vectors 2 | Exam Revision 8 - Challenging Questions |
| Volume | Similar Shapes 2 | Exam Revision 9 - Challenging Questions | |
| Simultaneous Eqns 1 - N5 Exam | Exam Revision 10 - Challenging Questions | ||
| Simultaneous Eqns 2 | |||
| Simultaneous Eqns 3 | |||
| Straight Lines | |||
| Triangles in Circles | |||
| Trig Functions | |||
| Trig Graphs & Equations |
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14. N5 Maths Prelim Practice
Thanks to the SQA and authors for making the excellent resources below freely available. Please use the below for revision prior to assessments, tests and the final exam.
| Name __________________________________________ | Paper ___________________________ | Paper/Answers ______________________________________________ | Answers _________ | Acknowledgements _________________________ |
| Prelim Revision Special | Questions Only, (X-Mas Theme) | Questions & Answers, (X-Mas Theme) | Answers | |
| N5 Prelim 1 | Paper 1 | Paper 2 | Answers | |
| N5 Prelim 2 | Paper 1 | Paper 2 | Answers | Courtesy of Larkhall Academy |
| N5 Prelim A - L Booklet | Prelim Papers A - L | Answers on Booklet | Courtesy of Larkhall Academy | |
| N5 Exam Papers A to F Booklet | Exam Papers A to F | Answers | Courtesy of Larkhall Academy | |
| N5 Exam Papers G to L Booklet | Exam Papers G to L | Answers | Courtesy of Larkhall Academy | |
| Prelim Revision Papers 1, 2 & 3 | Papers 1, 2 & 3 | |||
| 2022 SQA Adapted Papers (2014 -2019) | Whole Booket | Marking Scheme 2019, 2018, 2017, 2016, 2015, 2014 | ||
| 2022 P1 Essential Skills (Non-Calculator) | Paper 1 | Answers | ||
| 2022 P2 Essential Skills (Calculator) | Paper 2 | Answers | ||
| 2022 Essential Skills Additional Ques (Calculator) | Additional Questions | Answers | ||
| 2022 Essential Skills - Whole Paper | Whole Paper | Answers |
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15. N5 Maths Further Revision Practice
The excellent resources below are courtesy of Larkhall Academy. Please use the below for revision prior to assessments, tests and the final exam.
| N5 Exam Revision __________________________________ | Link ________________ | Acknowledgements _________________________ |
| N5 Maths 5 a Day Exam Preparation | 5 a Day, Answers | From TES Website |
| Applications Exam Questions | HERE | Courtesy of Larkhall Academy |
| Expressions & Formulae Exam Questions | HERE | Courtesy of Larkhall Academy |
| Relationships Exam Questions | HERE | Courtesy of Larkhall Academy |
| Credit Exam Questions by Topic Booklet | HERE | Courtesy of Larkhall Academy |
| Credit Exam Questions by Topic Answers | HERE | Courtesy of Larkhall Academy |
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16. Credit & Int 2 Maths SQA Papers
Thanks to the SQA for making the excellent resources below freely available. The SQA Past Papers below are a fantastic additional study resource.
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17. 100 N5 Maths Lesson Starters
Thanks to the authors for making the excellent resources below freely available.
The start of the lesson is important for setting the tone. This is the time during the lesson for practising, revisiting and developing further those aspects of mathematics which need a ‘little but often’ approach. Additional Lesson Starters for S1 & S2 can be found by clicking on the Free S1 & S2 Home Page HERE.
| ____________ | ____________ | ____________ | ____________ | ____________ | |||||
| Lesson Starter | 1 | Lesson Starter | 2 | Lesson Starter | 3 | Lesson Starter | 4 | Lesson Starter | 5 |
| Lesson Starter | 6 | Lesson Starter | 7 | Lesson Starter | 8 | Lesson Starter | 9 | Lesson Starter | 10 |
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| Lesson Starter | 96 | Lesson Starter | 97 | Lesson Starter | 98 | Lesson Starter | 99 | Lesson Starter | 100 |
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18. N5 Maths – Applications Unit Practice Assessment
Thanks to the authors for making the excellent resources below freely available.
| Applications _____________________ | Link ___________________________ | Acknowledgements __________________________ |
| Applications | Check List | Courtesy of Zeta Maths |
| Applications | Practice Booklet | Courtesy of Gryffe High School |
| Applications | Practice Booklet | Courtesy of Larkhall Academy |
| Applications | Practice Booklet - Answers | Courtesy of Larkhall Academy |
| Applications | Practice Test One | |
| Applications | Practice Test One - Solutions | |
| Applications | Practice Test Two | |
| Applications | Practice Test Two - Solutions | |
| Applications | Practice Test Three | |
| Applications | Exam Questions by Topic | Courtesy of Larkhall Academy |
| Outcome | 1.1 | |
| Outcome | 1.2 | |
| Outcome | 1.3 | |
| Outcome | 1.4 |
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19. N5 Maths – Expressions & Formulae Unit Practice Assessment
Thanks to the authors for making the excellent resources below freely available.
| Expressions & Formulae __________________________ | Title _______________________ | Acknowledgements ______________________________ |
| Expressions & Formulae | Check List | Courtesy of Zeta Maths |
| Expressions & Formulae | Practice Booklet | Courtesy of Gryffe High School |
| Expressions & Formulae | Practice Booklet - Part One | Courtesy of Larkhall Academy |
| Expressions & Formulae | Part One - Answers | Courtesy of Larkhall Academy |
| Expressions & Formulae | Practice Booklet - Part Two | Courtesy of Larkhall Academy |
| Expressions & Formulae | Part Two - Answers | Courtesy of Larkhall Academy |
| Expressions & Formulae | Practice Test One | |
| Expressions & Formulae | Practice Test One - Solutions | |
| Expressions & Formulae | Practice Test Two | |
| Expressions & Formulae | Practice Test Two - Solutions | |
| Expressions & Formulae | Practice Test Three | |
| Expressions & Formulae | Practice Test Four | |
| Expressions & Formulae | Exam Questions by Topic | Courtesy of Larkhall Academy |
| Outcome | 1.1 | |
| Outcome | 1.2 | |
| Ourcome | 1.3 | |
| Outcome | 1.4 |
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20. N5 Maths – Relationships Unit Practice Assessment
Thanks to the authors for making the excellent resources below freely available.
| Relationships __________________ | Title ______________________________ | Acknowledgements _____________________________ |
| Relationships | Check List | Courtesy of Zeta Maths |
| Relationships | Practice Booklet | Courtesy of Gryffe High School |
| Relationships | Practice Booklet - Part One | Courtesy of Larkhall Academy |
| Relationships | Part One - Answers | Courtesy of Larkhall Academy |
| Relationships | Practice Booklet - Part Two | Courtesy of Larkhall Academy |
| Relationships | Part Two - Answers (Diagrams) | Courtesy of Larkhall Academy |
| Relationships | Part Two - Answers | Courtesy of Larkhall Academy |
| Relationships | Practice Test One | |
| Relationships | Practice Test One - Solutions | |
| Relationships | Practice Test Two | |
| Relationships | Practice Test Three | |
| Relationships | Exam Questions by Topic | Courtesy of Larkhall Academy |
| Outcome | 1.1 | |
| Outcome | 1.2 | |
| Outcome | 1.3 | |
| Outcome | 1.4 |
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21. N5 Maths Mind Maps
Thanks to the authors for making these freely available. Mind Maps are an excellent diagrammatic way of organising key ideas or concepts from lessons/text books.
| Mind Map ____________ | Topic _________________________ | Mind Map ____________ | Topic _______________________________ |
| Mind Map 1 | Circles | Mind Map 12 | Quadratic Functions PowerPoint |
| Mind Map 2 | Circles PowerPoint | Mind Map 13 | Scientific Notation |
| Mind Map 3 | Comparing Data | Mind Map 14 | Scientific Notation PowerPoint |
| Mind Map 4 | Comparing Data PowerPoint | Mind Map 15 | Standard Deviation |
| Mind Map 5 | Factorising | Mind Map 16 | Standard Deviation PowerPoint |
| Mind Map 6 | Factorising PowerPoint | Mind Map 17 | Straight Lines |
| Mind Map 7 | Fractions | Mind Map 18 | Straight Lines PowerPoint |
| Mind Map 8 | Fractions PowerPoint | Mind Map 19 | Simultaneous Equations |
| Mind Map 9 | Percentages | Mind Map 20 | Simultaneous Equations PowerPoint |
| Mind Map 10 | Percentages PowerPoint | Mind Map 21 | Trig Functions & Equations |
| Mind Map 11 | Quadratic Functions | Mind Map 22 | Trig Functions & Equations PowerPoint |
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22. N5 Maths PowerPoints
Thanks to the authors for making the excellent resources below freely available.
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23. Maths Websites (Including Games/Puzzles)
Thanks to the authors for making the excellent resources below freely available.
| Website __________ | Website Name _________________________________ | Link _______ | Comment _____________________________ |
| Website 1 | Study Pack - National 5 Maths | Link | Highly Recommended |
| Website 2 | Study Pack - N5 Applications of Maths | Link | Highly Recommended |
| Website 3 | Study Pack - Higher Maths | Link | Highly Recommended |
| Website 4 | Study Pack - Advanced Higher Maths | Link | Highly Recommended |
| Website 5 | Advanced Higher Maths | Link | Highly Recommended |
| Website 6 | Activity Village | Link | |
| Website 7 | BGE Maths | Link | |
| Website 8 | BBC Games | Link | |
| Website 9 | Blooket | Link | |
| Website 10 | Cool Maths Games | Link | |
| Website 11 | Corbett Maths | Link | |
| Website 12 | CountOn Maths Games | Link | |
| Website 14 | DadsWorksheets.com | Link | |
| Website 15 | Dr Frost Maths | Link | |
| Website 16 | Don Steward Maths | Link | |
| Website 17 | Dot to Dot Precision Measure | Link | |
| Website 18 | Dynamic Maths | Link | |
| Website 19 | Future Learn | Link | |
| Website 20 | Fun Brain | Link | |
| Website 21 | GCSE Exam Boards - Important Info | Link | |
| Website 22 | Hegarty Maths | Link | |
| Website 23 | Higher Maths | Link | Highly Recommended |
| Website 24 | Maths Mutt | Link | Recommended |
| Website 25 | MathsGames.org | Link | |
| Website 26 | MathPlay.com - free online games | Link | |
| Website 27 | Mathsticks.com | Link | |
| Website 28 | Maths.scot | Link | |
| Website 29 | MathsIsFun.com | Link | |
| Website 30 | MathsDrills.com | Link | |
| Website 31 | MathsAid.com | Link | |
| Website 32 | Maths Starters | Link | |
| Website 33 | Maths Zone | Link | |
| Website 34 | Maths.bot.com - Create Worksheets | Link | |
| Website 35 | Mr Carter Maths - Bronze, Silver & Gold | Link | |
| Website 36 | Multiplication,com | Link | |
| Website 37 | National 5 Maths | Link | Highly Recommended |
| Website 38 | National 5 Applications of Maths | Link | Highly Recommended |
| Website 39 | National 5 Numeracy Unit | Link | Highly Recommended |
| Website 40 | National 3 Maths | Link | Highly Recommended |
| Website 41 | National 4 Maths | Link | Highly Recommended |
| Website 42 | NRich | Link | |
| Website 43 | Primary Games | Link | |
| Website 43 | Primary Interactive | Link | |
| Website 43 | Primary Resources | Link | |
| Website 44 | Resource Aholic | Link | |
| Website 45 | S1 & S2 Maths | Link | Highly Recommended |
| Website 46 | Sum Dog | Link | |
| Website 47 | Super Teacher Worksheets | Link | |
| Website 48 | Teacher Led | Link | |
| Website 49 | Top Marks | Link | |
| Website 50 | Work Sheets.com - Cross Number Puzzles | Link |
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24. Recommended N5 Maths Books
The highly recommended National 5 Maths books below can be used with students to compliment the material on this website. Click on the links below and order both books through amazon.co.uk.
TJ N5 Maths Text Book
This above can be used as a free-standing National 5 book for students, possibly in Secondary 4, 5 or 6, who have previously successfully completed a CfE Level 4 course, or equivalent.
N5 Maths Success Guide
National 5 Mathematics Success Guide provides easy-to-use and value-for-money revision for all abilities and learning styles. Guidance on how the new National 5 course and assessments are structured is included. All the popular features of this tried and trusted series are retained in the new National 5 Guides.
• Colourful double-page spreads aid both comprehensive and revision planning
• Topics are broken down into small, easily managed sections, complemented with lots of diagrams and illustrations to aid retention
• Quick Tests and Top Tips help keep students focused on the exam’s precise demands
• Revision checklists help students to manage and track their progress in the lead up to the exam
• A glossary present all of the key terms and definitions essential for the exam
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25. National 5 Maths 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 Completing the Square to pass your final exam.
For students looking for a ‘good’ pass at N5 Maths you may wish to consider subscribing to the fantastic additional exam focused resources available in the Online Study Pack. Subscribing could end up being one of your best ever investments.
Please give yourself every opportunity for success, speak with your parents, and subscribe to the exam focused Online Study Pack today.
We hope you find this website useful and wish you the very best of success with N5 Maths in 2023.
Topic Links
Free resources to dozens of National 5 Maths topics are available by clicking on any of the links to the right.
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