School Skills
Maths olympiad foundation, class 6 to 8
The thinking behind olympiad questions: number patterns, divisibility, fractions and ratios, geometry, counting, logic puzzles and how to show your working.
Suits: Students of class 6, 7 and 8
Duration, fees and batch timings are quoted by the head office or your centre.
The study book of this course
- Maths Olympiad Foundation (Class 6 to 8)
- Lessons
- 10
- Practice questions
- 40
- Free ebooks
- 0
About the course
What the maths olympiad foundation course is about
Olympiad questions do not ask for a method the student has memorised; they ask the student to find one. This course builds that habit on the maths of class 6 to 8: patterns, divisibility, fractions and ratio, simple algebra, geometry, counting and logic puzzles.
Every lesson of the study book works examples in full, shows how to write the working, and ends with problems to try. The last lesson is exam strategy: reading twice, estimating, checking and managing time. The practice tests in the student portal use the same style of question.
What you will practise
Drawn from the lessons of the study books below.
- 01
Tell an olympiad problem from a textbook sum, and write clear working
- 02
Continue and explain number patterns and sequences
- 03
Use divisibility rules, primes, HCF and LCM to solve problems
- 04
Work with fractions, decimals, percentages and ratio in word problems
- 05
Reason with angles, triangles, perimeter, area and symmetry
- 06
Count arrangements systematically and solve logic puzzles
What you will learn
10 lessons, 30 exercises
Every lesson of the study book that comes with this course in the student portal, with the key points of each lesson and exercises to try. Your centre gives you the syllabus, the duration and the fee.
Study book
Maths Olympiad Foundation (Class 6 to 8)
Build the thinking skills that olympiad-style maths rewards: number patterns, divisibility and primes, fractions and ratio, algebra and working backwards, geometry, counting, logic puzzles, speed and work sums, and a calm plan for the exam day.
1How olympiad questions differ and how to show working4 min read · 4 key points · 3 exercises
Key points
- Olympiad questions hide the method inside a story; your first job is to recognise the topic.
- Use the four steps: understand, plan, do, check.
- Write working one step per line with units, ending with the kind of answer the question asked for.
- Try small cases, draw diagrams and keep a mistakes notebook.
Try this
- Count how many times the digit 7 is written in the numbers from 1 to 100, showing your working in the two-part style used above.
- Take any five sums from your school textbook and rewrite each one as a short story question for a friend to solve.
- Start a mistakes notebook: solve ten questions from an old paper and record every wrong one with the correct method.
2Number patterns and sequences4 min read · 4 key points · 3 exercises
Key points
- Find the rule from the differences between neighbouring terms.
- For an add-the-same-number sequence, the nth term is (difference × n) plus or minus a fixed number.
- The nth triangular number is n(n + 1) ÷ 2 and the sum 1 to n is the same thing.
- Units digits of powers repeat in short cycles.
Try this
- Write the first ten terms of 5n + 2 and of n(n + 2), then find the 25th term of each.
- Find the sum of all whole numbers from 1 to 200 by pairing, and check with the formula.
- Work out the cycle of units digits for powers of 3 and 7, then find the units digit of 7 to the power 15.
3Divisibility, factors, primes, HCF and LCM5 min read · 4 key points · 3 exercises
Key points
- Learn the divisibility tests for 2 to 11; the digit-sum test covers 3 and 9.
- A prime has exactly two factors; test by dividing by primes up to the square root.
- HCF takes the lower power of each shared prime, LCM the higher; HCF × LCM = product of the two numbers.
- Sharing and tiling stories want HCF; repeating events and common multiples want LCM.
Try this
- Find the prime factorisation of 360, then count its factors without listing them, and check by listing.
- Three buses leave a stand every 15, 20 and 30 minutes starting together at 7 a.m. Find the next three times they leave together.
- List all numbers between 50 and 100 that look prime but are not, and show the factor pair for each.
4Fractions, decimals, percentages and ratio5 min read · 4 key points · 3 exercises
Key points
- Learn the fraction, decimal and percentage forms of the common parts by heart.
- Percentage change is always measured against the original amount.
- To share in a ratio, find one part by dividing the total by the sum of the parts.
- Cross-multiply to compare fractions quickly.
Try this
- A tank is 2/5 full. After 30 litres are added it is 3/4 full. Find the capacity of the tank, showing each step.
- A number is increased by 25 per cent and then decreased by 25 per cent; show that it ends 6.25 per cent below where it started.
- Divide Rs 900 among three friends in the ratio 2 : 3 : 4 and check that the shares add up.
5Algebra thinking: unknowns, equations and working backwards4 min read · 4 key points · 3 exercises
Key points
- Treat an equation like a balanced scale: do the same to both sides.
- For think-of-a-number puzzles, undo the steps in reverse order.
- Choose the simplest quantity as x, express the rest in terms of it, then write one linking sentence as an equation.
- Always check the answer in the words of the question.
Try this
- I think of a number, subtract 4, multiply by 3 and get 27. Find the number by working backwards and again by solving an equation.
- A father is 30 years older than his son; in 5 years he will be three times as old. Find both ages and check.
- A car park has cars and motorbikes, 25 vehicles and 70 wheels. Find the number of each using the all-one-kind method.
6Geometry: angles, triangles, perimeter, area and symmetry5 min read · 4 key points · 3 exercises
Key points
- Straight line 180°, round a point 360°, triangle 180°, quadrilateral 360°.
- The exterior angle of a triangle equals the sum of the two opposite interior angles.
- Rectangle area is l × b, triangle area is half base times height; a path inside a rectangle shrinks both lengths by twice its width.
- A square has 4 lines of symmetry, a rectangle 2, an equilateral triangle 3 and a cube has 6 faces, 12 edges and 8 vertices.
Try this
- Find the angle between the hands of a clock at 7 o'clock and at 10 o'clock, showing the 30° per hour rule.
- A rectangle is 15 cm by 8 cm; a square of the same perimeter is drawn. Which has the bigger area, and by how much?
- Draw a regular hexagon and mark all its lines of symmetry; state its order of rotational symmetry.
7Counting and arrangements4 min read · 4 key points · 3 exercises
Key points
- List possibilities in a fixed order so none are missed or counted twice.
- Choices made one after another multiply: a ways then b ways gives a × b ways.
- When order does not matter, as with handshakes, divide the ordered count by 2.
- If direct counting is hard, count the opposite and subtract from the total.
Try this
- List all the 2-digit numbers that can be made from the digits 2, 5, 7, 9 with no repeats, then confirm the count with the multiplication principle.
- Eight teams play a league where each team plays every other team once. Find the number of matches two different ways.
- A lunch menu has 3 rotis choices, 4 sabzi choices and 2 sweets. Find the number of different thalis if one of each is chosen, and if the sweet is optional.
8Logic puzzles and reasoning4 min read · 4 key points · 3 exercises
Key points
- Suppose one thing, follow it through and look for a contradiction.
- A grid of ticks and crosses solves who-owns-what puzzles cleanly.
- For odd-one-out, find the property shared by all the others and state it.
- Dividing into three groups makes a balance scale work hardest.
Try this
- Make up a two-person truth-teller and liar puzzle that has exactly one solution, and write out the full reasoning.
- Four students sit in a row with four clues about who sits next to whom; draw the grid and solve a puzzle from any practice book.
- Explain how to find one heavier coin among 27 using a balance three times only.
9Time, speed, distance and work5 min read · 4 key points · 3 exercises
Key points
- Distance = speed × time; keep units matching and convert km/h to m/s with 5/18.
- A train passing a pole covers its own length; passing a platform, its length plus the platform's.
- Average speed is total distance divided by total time.
- Turn work into fractions per day (or hour) and add them; drains subtract.
Try this
- A 150 m train at 54 km/h passes a 300 m bridge; convert the speed to m/s and find the time taken.
- Rekha walks 4 km at 4 km/h and runs 4 km back at 8 km/h; find her average speed and explain why it is not 6 km/h.
- Three taps fill a tank in 4, 6 and 12 hours; find how long all three take together, then how long if the 12-hour tap is actually a drain.
10Strategies for the exam day3 min read · 4 key points · 3 exercises
Key points
- Set a time budget per question and keep minutes back for checking.
- Do three passes: sure answers first, then skipped ones, then checking.
- Read every question twice and underline words such as least, not and altogether.
- Estimate first, then check by a different route and confirm you answered what was asked.
Try this
- Take a 30-question practice paper, allow 36 minutes, and record how long each pass took.
- Go through an old paper and underline the key words in every question before solving any of them.
- For ten solved questions, write a one-line estimate for each and compare it with the exact answer.
Glossary: 28 key terms of Maths Olympiad Foundation (Class 6 to 8)
- Sequence
- A list of numbers made by a rule.
- nth term
- A formula that gives any term of a sequence from its position n.
- Triangular number
- A number of the form n(n + 1) ÷ 2, such as 1, 3, 6, 10, 15.
- Square number
- A number made by multiplying a whole number by itself, such as 1, 4, 9, 16.
- Factor
- A number that divides another number exactly.
- Multiple
- The result of multiplying a number by a whole number.
- Prime
- A number with exactly two factors, 1 and itself.
- Prime factorisation
- Writing a number as a product of primes, for example 60 = 2 × 2 × 3 × 5.
- HCF
- Highest common factor: the largest number that divides two or more numbers.
- LCM
- Lowest common multiple: the smallest number that two or more numbers divide into.
- Remainder
- What is left over after dividing one whole number by another.
- Divisibility test
- A quick rule to tell whether a number divides by 2, 3, 4, 5, 9 and so on.
- Percentage
- A part out of 100.
- Ratio
- A comparison of two or more quantities by their parts, such as 3 : 5.
- Equation
- A statement that two expressions are equal, often containing an unknown.
- Unknown
- A number you do not know yet, usually written as a letter such as x.
- Working backwards
- Undoing each step of a puzzle in reverse order to find the start.
- Exterior angle
- The angle between one side of a triangle and the extension of the next side.
- Perimeter
- The total distance around the edge of a shape.
- Area
- The amount of surface inside a shape, measured in square units.
- Line of symmetry
- A line along which a shape folds exactly onto itself.
- Multiplication principle
- If one choice has a ways and a second has b ways, together there are a × b ways.
- Factorial
- n! is the product 1 × 2 × ... × n, the number of ways to arrange n things in a row.
- Contradiction
- A result that cannot be true, showing that a supposition was wrong.
- Pigeonhole principle
- If more items are placed than there are boxes, some box holds at least two.
- Average speed
- Total distance divided by total time.
- Work rate
- The fraction of a job done in one unit of time.
- Estimate
- A rough answer found quickly to check the size of the exact answer.
Practice and study material
Study books and timed practice tests in the student portal
Students sign in to read the study books lesson by lesson, print them, mark lessons as done and test themselves with timed practice tests, every answer explained.
- 1study book
- 10lessons
- 40practice questions
- 28glossary terms
How the practice tests work
- Fresh questions each time
Up to 20 questions are picked at random from the subject’s question bank.
- One minute per question
A timer counts down. When it reaches zero, your answers are sent automatically.
- Move around freely
Skip a question, flag it, and come back to change your answer before you submit.
- Learn from every answer
At the end you see the right answer and an explanation for each question.
- Read, print and keep track
Each study book has its lessons, key points, exercises and a glossary. Print a lesson, or mark it as done.
Your centre gives you your login when you enrol.
Try 3 practice questions
Real questions from this course’s question banks. Pick an answer to see the explanation.
What is the 5th term of the sequence whose nth term is 2n + 3?
Show the answer
Answer: D. 13
2 × 5 + 3 = 13.
Which of these numbers is divisible by 9?
Show the answer
Answer: D. 7263
The digit sum of 7263 is 18, a multiple of 9; the others have digit sums of 10, 10 and 26.
Which list shows the first four square numbers?
Show the answer
Answer: B. 1, 4, 9, 16
1 × 1, 2 × 2, 3 × 3 and 4 × 4 give 1, 4, 9, 16.
Careers
Careers this course leads towards
The kind of work these skills are used for. Each guide explains what the job involves, the skills it asks for and how to get started.
Software developer
Writing, testing and fixing programs in languages such as C, C++, Java and Python.
Free calculators
Useful calculators
Free tools that go with this course. They work in your browser, on a phone or a computer.
Percentage and marks calculator
Work out the percentage of your marks in a test or across a whole marksheet.
How admission works
From your first question to your certificate.
The usual steps, at the head office in Delhi or at an authorised member centre.
- Who can join
- Students of class 6, 7 and 8
- Where
- The Delhi head office and authorised member centres.
- Fees and timings
- On WhatsApp at +91 97116 99511, or by phone on 011 2721 1512.
- 1
Ask about the course
Call or WhatsApp the head office, or visit your nearest member centre. Ask for the duration, the fee and the batch timings in writing.
- 2
Fill the admission form
Admission forms are supplied by the head office to every centre.
- 3
Learn in class
Attend your batch at the centre, with the course material and study notes, and sign in to the student portal for the study books and practice tests.
- 4
Take the exam
The institute prefers written exams, taken in front of a teacher.
- 5
Receive your certificate
Students who pass get a Gurukul Technicals Institute certificate and marksheet. Employers can verify it with the head office.
Who can join the maths olympiad foundation course?
Students of class 6, 7 and 8. Ask the head office or your nearest member centre which group your child should join, and what they already know will help them start in the right place.
Which olympiad does this prepare for?
The course covers the class 6 to 8 topics that school-level maths olympiads and talent searches in India draw on, rather than one exam’s syllabus. Check the organiser’s own notification for the exam you plan to take.
How long is the course and what is the fee?
Duration, fees and batch timings depend on the course and the centre. Ask the head office or your nearest member centre, and get the details in writing before you pay.
Where are the classes?
At the head office in Delhi (A-10, Chief Commissioner Colony, opposite Rana Pratap Bagh) and at authorised member centres. Call or WhatsApp the head office to find the nearest centre.
What do I need to use the study books and practice tests?
A phone or a computer with an internet connection, and the login your centre gives you at enrolment. The student portal opens in an ordinary web browser, so there is nothing to install. Student login.
How do the practice tests work?
Sign in to the student portal and choose a subject. Each test picks up to 20 questions at random from that subject’s question bank and gives you one minute per question, with a timer that sends your answers automatically when it reaches zero. You can skip a question, flag it and come back before you submit, and at the end you see the right answer and an explanation for every question. This course has 40 practice questions across 1 subject, and you can take the tests as often as you like.
Is there an exam and a certificate?
Yes. The institute prefers written exams, taken in front of a teacher. Students who pass receive a Gurukul Technicals Institute certificate and marksheet.
How is a Gurukul Technicals Institute certificate verified?
On the verify certificate page, anyone can enter a certificate number and check it against the institute’s online register, which covers certificates issued through the portal. For older certificates, or if there is any doubt, send a copy to the head office by email or WhatsApp; the reply comes within 2 working days.
Ready to start the maths olympiad foundation course?
Ask the head office for the duration, the fee, the batch timings and your nearest member centre.