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Sudoku for Beginners: How to Improve Your Problem-Solving Skills

Are you a beginner when it comes to solving Sudoku puzzles? Do you find yourself frustrated and unsure of where to start? Fear not, as we have compiled a comprehensive guide on how to improve your problem-solving skills through Sudoku.

Understanding the Basics of Sudoku

Before we dive into the strategies and techniques, let’s first understand the basics of Sudoku. A Sudoku puzzle is a 9×9 grid that is divided into nine smaller 3×3 grids. The objective is to fill in each row, column, and smaller grid with numbers 1-9 without repeating any numbers.

Starting Strategies for Beginners

As a beginner, it can be overwhelming to look at an empty Sudoku grid. But don’t worry. There are simple starting strategies that can help you get started. First, look for any rows or columns that only have one missing number. Fill in that number and move on to the next row or column with only one missing number. Another strategy is looking for any smaller grids with only one missing number and filling in that number.

Advanced Strategies for Beginner/Intermediate Level

Once you’ve mastered the starting strategies, it’s time to move on to more advanced techniques. One technique is called “pencil marking.” This involves writing down all possible numbers in each empty square before making any moves. Then use logic and elimination techniques to cross off impossible numbers until you are left with the correct answer.

Another advanced technique is “hidden pairs.” Look for two squares within a row or column that only have two possible numbers left. If those two possible numbers exist in both squares, then those two squares must contain those specific numbers.

Benefits of Solving Sudoku Puzzles

Not only is solving Sudoku puzzles fun and challenging, but it also has many benefits for your brain health. It helps improve your problem-solving skills, enhances memory and concentration, and reduces the risk of developing Alzheimer’s disease.

In conclusion, Sudoku is a great way to improve your problem-solving skills while also providing entertainment. With these starting and advanced strategies, you’ll be able to solve even the toughest Sudoku puzzles. So grab a pencil and paper and start sharpening those brain muscles.

This text was generated using a large language model, and select text has been reviewed and moderated for purposes such as readability.

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Problem solving using Pythagoras' Theorem

Problem solving using Pythagoras' Theorem

Subject: Mathematics

Age range: 14-16

Resource type: Worksheet/Activity

Phil Rhodes

Last updated

8 March 2020

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5 Problems that require careful thinking using Pythagoras’ Theorem. Suitable for anyone who has already covered the basics Answers included on P2

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Mr Barton Maths Podcast

Long-form conversations about teaching and learning with craig barton, tes top 10 resources: pythagoras and trigonometry.

The following collection of resources have been assembled by the TES Maths Panel . They can be downloaded for free by registering on the TES website.

Maths Deputy Curriculum Leader Will Emeny picks his top 10 Pythagoras and Trigonometry resources available on TES.

Both topics of Pythagoras’ Theorem and Trigonometry lend themselves to an enquiry-based approach. Whether discovering Pythagoras’ Theorem by looking at the squares of side lengths, or working from the ideas of enlargement and similarity to introduce trigonometrical ratios, these topics provide many opportunities for exciting discoveries by students.

1. GCSE introducing Pythagoras’ Theorem lesson 

An excellent PowerPoint introducing the theorem through an investigative approach followed by worked examples and worksheets that include questions in real life contexts.

2. Pythagoras’ Theorem 

A stunning spreadsheet showing both algebraic and geometric proofs of the theorem. Includes all types of questions including Pythagoras in 3D. A brilliant teaching resource.

3. Enlargement to Trigonometry – lesson plans and activities

A simply stunning complete unit of work to take pupils from the concept of enlargement through similarity and ending up introducing trigonometry.

4. Which Trig formula to use treasure hunt 

A fun starter/plenary activity to recap identifying which trig formula to use

5. Trigonometry loop cards activity

A wonderful set of loop cards based on missing side lengths and angles in right angled triangles. A nice alternative to worksheet questions!

6. KS4 Maths Pythagoras in 3D treasure hunt 

A brilliant differentiated treasure hunt activity on using 3D Pythagoras. Engaging and fun. Popular with students.

7. A-level Maths C2: Sine and Cosine rules worksheet 

A brilliant set of student-friendly notes, worked examples and questions on the Sine and Cosine rules

8. Trigonometry pile-up puzzle

A challenging puzzle requiring pupils to master right-angled triangle trigonometry questions to solve.

9. Revision booklet – Pythagoras and Trigonometry 

A comprehensive revision booklet on the topic featuring exam-style questions.

10. Pirate Trigonometry 

An engaging and challenging revision activity on both Pythagoras and trigonometry in the form of a pirate treasure hunt! Solutions included.

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"Quite simply, his lessons and activities are brilliant. They are clearly laid out, contain examples, notes, questions and answers, and cover pretty much everything from key stage 3 right up to further maths A-level. They are all PowerPoint presentations or Word documents, so can be adapted, edited and merged with your existing lessons. Our students and teachers are currently Dr Frost mad!"

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Pythagoras' Theorem

Starts at the very beginning with using a calculator. May need editing depending on which calculators you use. Main activity differentiated and answers included. Includes 3D Pythagoras' theorem problems.

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Pythagoras’ theorem is an equation that describes a relationship between the 3 sides of a right-angled triangle . We can use it to determine a missing length when given the two other lengths.

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  • Rearranging Equations

Pythagoras’ Theorem

Pythagoras’ Theorem

The equation is:

\textcolor{red}{a}^2+\textcolor{limegreen}{b}^2=\textcolor{blue}{c}^2

where \textcolor{blue}{c} is the hypotenuse and \textcolor{red}{a} and \textcolor{limegreen}{b} are the two other sides. The hypotenuse is always the longest side of the triangle and can be found opposite the right angle.

Pythagoras Finding a Length

Example 1: Finding a Length

Find the length of the side marked \textcolor{red}{x} on the right angled triangle shown.

In order to find this using Pythagoras’ theorem , we need to work out which side corresponds to each of the letters \textcolor{red}{a}, \textcolor{limegreen}{b}, and \textcolor{blue}{c} in the equation.

\textcolor{blue}{c} = \textcolor{blue}{10} cm

\textcolor{limegreen}{b} = \textcolor{limegreen}{6} cm

\textcolor{red}{a} = \textcolor{red}{x}

Then we can substitute our values in so the equation a^2+b^2=c^2 becomes:

\textcolor{red}{x}^2+\textcolor{limegreen}{6}^2=\textcolor{blue}{10}^2

\textcolor{red}{x}^2+\textcolor{limegreen}{36}=\textcolor{blue}{100}

Now we can solve for \textcolor{red}{x}

\textcolor{red}{x}^2=\textcolor{blue}{100}-\textcolor{limegreen}{36}=64 .

\textcolor{red}{x}=\sqrt{64}=8 cm.

Calculating the Length of a Line

Example 2: Calculating the Length of a Line

Calculate the distance between (-4, -1) and (3, 4) .

Give your answer to 1 dp.

First we plot the two points on a pair of axes, draw a line connecting them and then draw a triangle underneath making a note of the lengths of the sides:

Side 1 (height) = 4 -(-1) = \textcolor{red}{5}

Side 2 (width) = 3 -(-4) = \textcolor{limegreen}{7}

Next we substitute these lengths into Pythagoras’ theorem:

\textcolor{red}{a}^2+\textcolor{limegreen}{b}^2 = \textcolor{blue}{c}^2

\begin{aligned} \textcolor{blue}{c}^2 &= \textcolor{red}{5}^2+\textcolor{limegreen}{7}^2 \\ \textcolor{blue}{c}^2 &= \textcolor{red}{25}+\textcolor{limegreen}{49}=74 \\ \textcolor{blue}{c} &= \sqrt{74}=8.602325267... \\ \textcolor{blue}{c} &= 8.6 \, \, (1 \text{ dp}) \end{aligned}  

Note: The length you are trying to calculate, when finding the length of a line between two points, will always be the hypotenuse.

Pythagoras Example Questions

Question 1:

Find length BC . Give your answer to 1 decimal place.

Pythagoras Triangle

The missing side is the hypotenuse, by substituting the 2 sides we know into the equation a^2+b^2=c^2 we get:

8^2+14^2=c^2

Evaluating the two squares gives us:

Then square rooting both sides of the equation gives us:

BC=\sqrt{260}=16.1245155...

= 16.1 cm ( 1 dp).

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Question 2: Work out the distance between the two points (-6, 2) and (4, 5) .

Give your answer to 3 significant figures.

Pythagoras Graph

We can see that the distance between the two points is the longest side of a right-angle triangle – the hypotenuse, so by substituting the known sides into the equation a^2+b^2=c^2 we get:

10^2+3^2=c^2

Evaluating the squares gives us:

Finally, by square rooting both sides, we get:

c=\sqrt{109}=10.44030651...

= 10.4 cm ( 3 sf).

Question 3:  PQR is a right-angled triangle. Work out the length of the missing side, QR , to 1 decimal place.

Pythagoras Decimal Triangle

The missing side is the hypotenuse, so by substituting the known sides into the equation a^2+b^2=c^2 we get:

5.9^2+6.7^2=c^2

c^2=34.81+44.89

Then by square rooting both sides of this equation, we get:

QR=\sqrt{79.7}=8.927485648...

QR=8.9 cm ( 1 dp).

Question 4: LMN is a right-angled triangle. Work out the length of the missing side, LN , to 1 decimal place.

Reverse Pythagoras Decimal

By substituting the known sides into Pythagoras’ Theorem c^2=a^2+b^2 becomes:

5.1^2=LN^2+3.1^2

Next we evaluate the two squares to give us:

26.01=LN^2+9.61

Subtracting 9.61 from both sides:

Then we square root both sides of this equation:

LN=\sqrt{16.4}

LN=4.049691346...

LN=4.0 cm ( 1 dp).

Question 5:  A builder places a 2.9 m ladder on horizontal ground, resting against a vertical wall. To be safe to use, the base of this ladder must be 1.3 m away from the wall. How far up the wall does the ladder reach?

Give your answer to 1 decimal place.

Pythagoras Example

By substituting the known sides into Pythagoras’ Theorem c^2=a^2+b^2 (and letting the height of the wall be a ) we get:

2.9^2=a^2+1.3^2

Calculating the two square roots and rearranging gives us:

a^2=8.41-1.69=6.72

a=\sqrt{6.72}=2.592296279

a=2.6 cm ( 1 d.p.)

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  • Finding a Shorter Side Example (Video)
  • Right Angled Trigonometry (QQI)
  • Right Angled Trigonometry (10QQI)
  • Right Angled Trigonometry (QQI Count Down)
  • Right Angled Trigonometry (QQI Relay)
  • Right Angled Trigonometry (QQI BINGO)
  • Right Angled Trigonometry (QQI Worksheets)
  • Discovering Trig Ratios (GGB)
  • Finding Lengths (GGB)
  • Finding Missing Lengths (Video)
  • Finding Missing Angles (Video)
  • Sine Rule (Video)
  • Cosine Rule (Video)
  • Sine and Cosine Rules (Video)
  • Angle in the Centre vs Angle at the Circumference (GGB)
  • Angle at the Centre vs Angle at the Circumference (Video)
  • Angles in a Semicircle (GGB)
  • Angle in a Semicircle (Video)
  • Angles in Cyclic Quadrilaterals (GGB)
  • Angles in a Cyclic Quadrilateral (Video)
  • Angles in the Same Segment (GGB)
  • Angles in the Same Segment (Video)
  • Tangents (GGB)
  • Tangents (Video)
  • Alternate Segment Theorem (GGB)
  • Intersecting Tangents (GGB)
  • Intersecting Tangents (Video)
  • Intersecting Chords (GGB)
  • Vectors and Scalars (Video)
  • Vector Notation (Video)
  • Resultant Vectors (Video)
  • Resultants of Column Vectors (Video)
  • Scalar Multiplication (Video)
  • Magnitude of a Vector (Video)
  • Squares (GGB)
  • Tangrams (GGB)
  • Euler Line (GGB)
  • Probability (QQI)
  • Probability (10QQI)
  • Probability Tools (Flash)
  • Averages Activity (QQI)
  • Listed Averages (QQI)
  • Listed Averages (10QQI)
  • Listed Averages (QQI Count Down)
  • Listed Averages (QQI Relay)
  • Listed Averages (QQI BINGO)
  • Listed Averages (QQI Worksheets)
  • Averages From Lists of Data (Video)
  • Quartiles and Interquartile Range (Video)
  • Averages from Frequency Tables (QQI)
  • Averages from Frequency Tables (10QQI)
  • Averages from Frequency Tables (QQI Count Down)
  • Averages from Frequency Tables (QQI Relay)
  • Averages from Frequency Tables (QQI BINGO)
  • Averages from Frequency Tables (QQI Worksheets)
  • Averages From Frequency Tables (Video)
  • Averages From Grouped Frequency Tables (Video)
  • Averages With A GDC (Video)
  • Cumulative Frequency (Video)
  • Scatter Graphs and the Mean Point (Video)
  • Scatter Graphs and Linear Regression on a GDC (Video)
  • Correlation and the Correlation Coefficient on a GDC (Video)
  • Binomial Expansion (Video)
  • Binomial Theorem (Video)
  • Binomial Coefficients (Video)
  • Binomial Applications (Video)
  • Coordinate Geometry (QQI)
  • Coordinate Geometry (10QQI)
  • Equation of a Circle (AGG)
  • Differentiating Polynomials (QQI)
  • Differentiating Polynomials (10QQI)
  • Differentiating Polynomials (QQI Count Down)
  • Differentiating Polynomials (QQI Relay)
  • Differentiating Polynomials (QQI BINGO)
  • Differentiating Polynomials (QQI Worksheets)
  • Finding Gradients of Curves (QQI)
  • Finding Gradients of Curves (10QQI)
  • Finding Turning Points of Curves (QQI)
  • Finding Turning Points of Curves (10QQI)
  • Radian and Degree Conversions (QQI)
  • Radian and Degree Conversions (10QQI)
  • Radian and Degree Conversions (QQI Count Down)
  • Radian and Degree Conversions (QQI Relay)
  • Radian and Degree Conversions (QQI BINGO)
  • Radian and Degree Conversions (QQI Worksheets)
  • Trigonometric Exact Values (QQI)
  • Trigonometric Exact Values (10QQI)
  • Trigonometric Exact Values (QQI Count Down)
  • Trigonometric Exact Values (QQI Relay)
  • Trigonometric Exact Values (QQI BINGO)
  • Trigonometric Exact Values (QQI Worksheets)
  • Graphs of Trig Functions (GGB)
  • UKMT Random Question Generator
  • @mathschallenge Random Questions
  • School of Hard Sums Random Questions
  • Random Starter of the Day
  • Mathematically Possible (QQI Starter)
  • Adding Challenge (QQI Starter)
  • Date Starter (QQI Starter)
  • Name That Number (QQI Starter)
  • Matchstick Random Questions
  • Choose 3 Numbers (QQI Starter)
  • What's The Question (QQI Starter)
  • Mathematical Words (QQI Starter)
  • Number of the Day (QQI Starter)
  • Anagrams and Missing Vowels (QQI Starter)
  • Missing Vowels and Word Jumbles Simple Numbers (QQI)
  • Tables (QQI)
  • Target Boards (QQI)
  • Missing Signs (QQI)
  • Exploding Dots
  • Easter Date
  • Easter Tangrams (GGB)
  • Zeller's Algorithm
  • Batman Equation (AGG)
  • Fermat's Last Theorem (Video)
  • Pi Song (Video)
  • Monty Hall Problem (Video)
  • Symmetry, Reality's Riddle (Video)
  • Music of the Primes (Video)
  • Folding Paper (Video)
  • Nature by Numbers (Video)
  • Inspirations (Video)

Pythagoras Theorem

  • The standard Worksheet, with as many as 100 questions. Choose how much working space you want to provide (Very Small fits 40 questions per page, Small fits 30, Medium fits 18, Large fits 14 and Very Large fits 6), and give the worksheet a title. I like to use these as a "How Many Can You Do" style activity, where I give students 10 minutes to do as many as they can. They could also be used for relay races (like the QQI Relay but paper based). The answers for all the questions are printed on a separate page at the end.
  • The Treasure Hunt option produces a set of treasure hunt cards for placing round the room or to be used as a set of loop cards in small groups. You can choose how many cards there should be (from 4 up to 40 in multiples of 4), and how many cards there should be per page (either 4 medium sized cards or 1 large card). The answers to each individual card are supplied as is the correct loop based on the card numbers.
  • The Odd One Out activity is based on an excellent resource found on TES uploaded by UKDana . There are 16 answers in a grid, and 15 questions given. Each question matched with one of the given answers, leaving one spare answer at the end, the odd one out. An extension is also provided to find as many questions to give the final answer as possible. Again, full answers are provided.
  • The Codebreaker activities are always popular with students. There are 26 questions, each with a different answer that links to a letter of the alphabet. Students then use these answers to decipher a message at the bottom of the page, which could be a maths joke, a general joke, or a wise/motivational quote. The answers to each letter are provided, as well as the full message. If you have any good jokes/quotes that would work well (they need to be fairly short), then please Contact Me .
  • The Matching Cards activity could be used in a variety of ways in the classroom. It produces either a 4x4 or 5x5 grid of questions on one page and answers on the next. Students could be given these to cut out and simply match, or to add a bit of competition, turn it into a memory game (print questions and answers on different colour paper, and have them laid out in a square, upside down, and one student turns one over from each group, and if they match they win the pair). Other options are: Connect 4 style games where students compete to get a line of 4 correct answers, taking turns to pick a square to answer; Thoughts and Crosses is a similar idea based on the game Tic-Tac-Toe; or a manual Bingo game, where students are shown the answers to choose from, you cut up the question cards and take one at a time randomly.

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Pythagoras' Theorem in Real-Life

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Pythagoras - Real-Life - Noughts & Crosses

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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  Pythagoras  is essential to ensure exam success.

Maths revision classes available in Edinburgh from December. Please give yourself every opportunity for N5 Maths success in 2024, speak with your parents, and secure your place on the link below:

Weekend Maths School – Edinburgh City Centre

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 2024. Please find below:

1. Pythagoras – S1 & S2 Maths Worksheets

2. Pythagoras – N5 Maths Worksheets

3. About Pythagoras

4. Pythagoras – Videos & PowerPoints

5. N5 Maths Essential Skills  

6. N5 Maths Exam Worksheets by Topic

7. Credit Maths Exam Worksheets by Topic

8. N5 Maths Exam Questions & Answers by Topic 

9. N5 Maths 180 Booster Papers  

10. N5 Maths Videos, PowerPoints, Mind Maps & Worksheets

11. N5 Maths SQA Past & Practice Papers

12. 100 N5 Maths Exam Questions & Answers

13. N5 Maths Exam Check Lists

14. N5 Maths Exam Focused Homework

15. N5 Maths Prelim Practice

16. N5 Maths Further Revision Practice

17. Credit & Int 2 Maths SQA Papers

18. 100 N5 Maths Lesson Starter Questions 

19. N5 Maths – Applications Unit Practice Assessment

20. N5 Maths – Expressions & Formulae Unit Practice Assessment

21. N5 Maths – Relationships Unit Practice Assessment

22. N5 Maths Mind Maps

23. N5 Maths PowerPoints

24. Maths Websites (Including Games/Puzzles)

25. Recommended National 5 Maths Books

26. N5 Maths Online Study Pack  – Students looking for a ‘good’ Pass.

National 5 Maths Resources

Thanks to the authors for making the excellent resources below freely available. Please find N5 Maths level Pythagoras worksheets in Section 3 below.

. 2. Pythagoras – N5 Maths Worksheets

Pythagoras – N5 Maths Level

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 worksheets and N5 Maths exam questions below are available in the  Online Study Pack.

. 3. About Pythagoras

To learn about Pythagoras please click any of the  Pythagoras,   Pythagoras & Circles or  Pythagoras (Converse) theory guide links. Please also find in Sections 2 & 3 below videos, PowerPoints , mind maps and worksheets on this topic to help your understanding. The Essential Skills 27 worksheet, along with actual  SQA Exam Question s, are highly recommended. How to layout Pythagoras questions is essential and an excellent introductory worksheet can be found HERE .

If you would like more help understanding Pythagoras 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.

Pythagoras was an ancient Greek Philosopher and Mathematician. He is best known for the Pythagorian Theorum , which states that the sum of the squares of the sides of a right triangle is equal to the square of the hypotenuse.  Over 2000 years ago he made an amazing discovery about right-angled triangles.

pythagoras problem solving tes

.                           570 to 490 BC

N5 Maths Question on Pythagoras

Radius = 1.2m,  LM = 1.8m, Calculate the depth of milk in the tank

Capture

Source: N5 Maths, 2015, P2, Q12

To solve the above you need:

  • To locate the right angled triangle
  • Apply your knowledge of Pythagoras’ Theorem

Another exam question on Pythagoras in shown below:

“is Hightown directly north of Lowtown?”

cop

Source: N5 Maths, 2014, P2, Q6

To answer the above correctly, Pythagoras Theorem in reverse is used – known as ‘The Converse of Pythagoras’ Theorem’:

  • 110² = 85² + 75² 
  • 12100 ≠ 12850
  • No,  Hightown is not due north of Lowtown since, by the Converse of Pythagoras’ Theorem, the triangle is not right angled.

This Theorem proves whether a triangle has a 90° angle or not.

4. Pythagoras –  Videos & PowerPoints 

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.

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.

6. 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.

. 7. 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.

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.

. 9. 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.

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.

11. 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.

12. 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.

13. 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.

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.

15. 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.

16. 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.

Thanks to the SQA for making the excellent resources below freely available. The SQA Past Papers below are a fantastic additional study resource.

18. 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 . 

19. N5 Maths – Applications Unit Practice Assessment 

20. N5 Maths – Expressions & Formulae Unit Practice Assessment 

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.

23. N5 Maths PowerPoints 

25. 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.

  • TeeJay’s usual bight colourful pupil centred Textbook.
  • Each exercise is graded with the more problematic questions at the end.
  • National 5 Outcomes listed for easy reference
  • Contains a Chapter Zero that Revises the contents of TeeJays CfE 4+ Book.
  • Six Cumulative Home Exercises interspersed throughout the book.
  • Six Non Calculator Exercises throughout the book.
  • Each Chapter ends with a “Remember Remember” exercise as a summary.
  • The book ends with a Revision Chapter, consolidating the whole of the National 5 Course.
  • Contains a National 5 Specimen Paper 1 and Paper 2.

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

26. 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  Pythagoras 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 2024.

6 different ways for you to study Pythagoras’ Theorem

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N5 Maths Study Pack

N5 Maths Study Pack

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Higher Maths Website

Higher Maths Website

Click on the link below to visit the Higher Maths website

AH Maths Website

AH Maths Website

Click on the link below to visit the AH Maths website

N5 Applications of Maths

  • N5 Applications of Maths

Click on the link below to visit the N5 Applications of Maths homepage

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Just a thank you!

We’re using the advancedhighermaths.co.uk site and it is excellent. This has been a real help while our wonderful school teachers fight their way through lockdown tech nightmare. Later on today my younger daughter will be using the free national 5 maths website. Thanks so much.

Jennifer – Parent

Hello, I am writing to thank you for your wonderful website! I subscribed when I was studying for my National 5 exam (as an adult learner) and found it invaluable. I am delighted to have just discovered the huge amount of resources for younger learners too. My son who is in S2 will benefit from these, now and in future, as will my daughter when she moves up to S1 after summer. So just wanted to say thanks very much! Kind regards, Clare.

Hey, Just wanted to say thank you so much for this amazing resource! Last year I was expecting to scrape a B in my N5 exam if I was lucky, and after discovering this website and working through it over the past year, my teacher said she’ll be surprised if I don’t get an A1!!! So once again, thank you so much!!!

Thanks for this fantastic website you have here. So well laid out, easy to follow and as a parent trying to help their child with studying. Only £20 for the Study Pack has been excellent value considering that many tutors charge £40 an hour. I will be continuing with this for Higher Maths and also for my younger child to ensure they are keeping up with the course. The worked solutions are so clear and easy to follow and I just cannot thank you enough. Wish there was something similar for the science subjects.

I got an ‘A’ in my National 5 Maths Exam! I’m very pleased as I did it my first attempt. Your website content definitely helped clarify and consolidate my understanding of the subject.

Just had a look at the worked solutions for the 2018 N5 Math Past Paper – Calculator was absolutely fine, but some tricky questions in non-calculator part, particularly 19b. We found the non-calculator paper much harder than five previous past papers. Anyway hopefully she has achieved an ‘A’ Pass and we will definitely be using your excellent site for Higher Maths next term.

E-mailing you guys know that you are doing a great job compiling all these excellent resources, it has been a great help to me and probably many many others. It has allowed me to get a reassuring prelim mark and has given me confidence for the final exam ( tomorrow ). Thanks for all the help and keep up the good work.

Hello, I decided to write to you to thank you for this website, it has helped me incredibly and the amount of content you have is amazing. I was very happy to discover the many practice papers you have as I had began to run out of papers to do once completed all the SQA past papers. The checklists for the three different units is very helpful and I will definitely be taking these to school with me on the day of my exam to look over! Thank you again for being so helpful to us, it is greatly appreciated and I will be placing any success I have during the National 5 exam on this website due to the endless resources and help you have available. Thank you 🙂 Emily, Nat 5 Maths student.

It is a great help to us this site, my daughter scored 86% in her prelim after doing the last 5 years past papers

Hi there – we found your site an amazing help for nat 5 – in fact my son went from a C grade at prelim to an A for his nat 5 thanks to you.  Thank you – the best £20 I’ve spent!

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“My Dad and I have worked together through several topics and three Practice Past Papers. When I get stuck, the detailed worked solutions explain everything so clearly and even give alternative ways to find the correct answer –  Thank you so much for producing this fantastic resource.”

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An absolute godsend for my Nat 4  and Nat 5 classes.

Many thanks”.

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“Hi, I am in my second year at Abertay University studying Forensics. Two years ago, while studying N5 Maths, my Maths teacher helped me realise my dreams by providing me with all the superb material which is now available on this website. With the right intention to study, everything is here for you to pass National 5 Maths”

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“Although I am only in 3rd year we are working at National 5 level maths and have a Unit Assessment in the next few weeks. I really want to study Computer Games Development at University which requires me to pass Maths so I am studying hard now. The website is helping me so much.”

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“The website is really good as it breaks the whole course down into easy to understand sections. I need to get A-Level Maths next year as I want to go to university and study engineering. I am really glad to have found this website to help me on my way.”

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Not just Pythagoras’ Theorem, but 70 other maths concepts covered in detail

Topic Links

Free resources to dozens of National 5 Maths topics are available by clicking on any of the links to the right.

  • N5 Maths Whole Course
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  • Completing the Square
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  • Constructing Formulae
  • Converse of Pythagoras
  • Correlation
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  • Difference of Two Squares
  • Discriminant
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  • Growth Mindset Booklets
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  • Reversing a % Change
  • S1 & S2 Maths
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  • Scientific Notation
  • Significant Figures
  • Similar Figures
  • Simultaneous Equations
  • SOH-CAH-TOA
  • Standard Deviation
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  • Trigonometry
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  • Vector Addition
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  • Vectors & Scalars
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pythagoras problem solving tes

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IMAGES

  1. Pythagoras problem solving questions

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  2. Pythagosaurus Rex

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  3. Pythagoras problem solving

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  4. Pythagoras' Theorem Problem Solving Mastery Worksheet by a51_ufo

    pythagoras problem solving tes

  5. Pythagoras' Theorem Problem Solving Mastery Worksheet

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  6. Problem solving using Pythagoras' Theorem

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VIDEO

  1. The Art of Daydreaming

  2. Ngawas Tes 3 Soal 4,5 Jam

  3. CSS Battle #85

  4. Pythagoras Theorem

  5. Solving Problem Using Pythagoras Theorem

  6. Pythagoras Theorem Concept and Solving Ex- 1 Pg:

COMMENTS

  1. What Are the Six Steps of Problem Solving?

    The six steps of problem solving involve problem definition, problem analysis, developing possible solutions, selecting a solution, implementing the solution and evaluating the outcome. Problem solving models are used to address issues that...

  2. How to Solve Common Maytag Washer Problems

    Maytag washers are reliable and durable machines, but like any appliance, they can experience problems from time to time. Fortunately, many of the most common issues can be solved quickly and easily. Here’s a look at how to troubleshoot som...

  3. Sudoku for Beginners: How to Improve Your Problem-Solving Skills

    Are you a beginner when it comes to solving Sudoku puzzles? Do you find yourself frustrated and unsure of where to start? Fear not, as we have compiled a comprehensive guide on how to improve your problem-solving skills through Sudoku.

  4. Pythagoras problem solving questions

    Pythagoras questions asked with different knowledge needed. Including Surds, Circle theorems, Bearings, Area, Perimeter and Ratio.

  5. Problem solving using Pythagoras' Theorem

    5 Problems that require careful thinking using Pythagoras' Theorem. Suitable for anyone who has already covered the basics Answers included

  6. TES Top 10 Resources: Pythagoras and Trigonometry

    A challenging puzzle requiring pupils to master right-angled triangle trigonometry questions to solve. 9. Revision booklet – Pythagoras and

  7. Downloadables

    Craig Barton, Head of TES Maths Panel. Resource Collections. Pearson Edexcel A Level

  8. Pythagoras' Theorem

    Includes 3D Pythagoras' theorem problems. Capture.PNG · Pythagoras' Theorem RAG · 3D Pythagoras' Theorem RAG · Capture.PNG · Codebreaker - TES · KS2 - KS4

  9. Problems With Pythagoras & Trigonometry

    Ready-to-use mathematics resources for Key Stage 3, Key Stage 4 and GCSE maths classes.

  10. Tes Pythagoras Sheet 1

    Problem Set 1. bob. PBS Maths F1 Chapter 12. PBS Maths

  11. Pythagoras Questions

    Now we can solve for \textcolor{red}{x}. \textcolor{red}{x}^2=\

  12. Pythagoras Theorem (QQI Worksheets)

    Solving Simultaneous Equations (QQI BINGO) · Solving Simultaneous

  13. Pythagoras' Theorem in Real-Life

    Practical Problems · 3D · With Bearings · Without a Calculator; With

  14. Pythagoras' Theorem

    From TES Website. Applications Exam Questions, HERE, Courtesy of Larkhall