Week 3 | Maths4U

Week 3

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1. Year 6 - 1. Follow the family links

Foundation · Years 6–8Age Problems

Year 6 | Week 3 | Age problems

Year 6: Follow the family links - question, part 1

Prepared for the Maths4U Olympiad Club. English worksheet and source references.

2. Year 6 - 2. The same number of years passes

Foundation · Years 6–8Age Problems

Year 6 | Week 3 | Age problems

Year 6: The same number of years passes - question, part 1

Prepared for the Maths4U Olympiad Club. English worksheet and source references.

3. Year 6 - 3. One third and ten more

Foundation · Years 6–8Age Problems

Year 6 | Week 3 | Age problems

Year 6: One third and ten more - question, part 1

Prepared for the Maths4U Olympiad Club. English worksheet and source references.

4. Year 6 - 4. Three equal parts and one more

Foundation · Years 6–8Age Problems

Year 6 | Week 3 | Age problems

Year 6: Three equal parts and one more - question, part 1

Prepared for the Maths4U Olympiad Club. English worksheet and source references.

5. Year 6 - 5. A future total

Foundation · Years 6–8Age Problems

Year 6 | Week 3 | Age problems

Year 6: A future total - question, part 1

Prepared for the Maths4U Olympiad Club. English worksheet and source references.

6. Year 6 - 6. When will one be twice as old?

Foundation · Years 6–8Age Problems

Year 6 | Week 3 | Age problems

Year 6: When will one be twice as old? - question, part 1

Prepared for the Maths4U Olympiad Club. English worksheet and source references.

7. Year 6 - 7. Three brothers grow older

Foundation · Years 6–8Age Problems

Year 6 | Week 3 | Age problems

Year 6: Three brothers grow older - question, part 1

Prepared for the Maths4U Olympiad Club. English worksheet and source references.

8. Year 6 - 8. Two birthdays and a kitten

Foundation · Years 6–8Age Problems

Year 6 | Week 3 | Age problems

Year 6: Two birthdays and a kitten - question, part 1

Prepared for the Maths4U Olympiad Club. English worksheet and source references.

9. Year 6 - 9. A shared hundredth birthday total

Foundation · Years 6–8Age Problems

Year 6 | Week 3 | Age problems

Year 6: A shared hundredth birthday total - question, part 1

Prepared for the Maths4U Olympiad Club. English worksheet and source references.

10. Year 6 - 10. An elephant and a zebra

Foundation · Years 6–8Age Problems

Year 6 | Week 3 | Age problems

Year 6: An elephant and a zebra - question, part 1

Prepared for the Maths4U Olympiad Club. English worksheet and source references.

11. Year 6 - 11. Read the comparison carefully

Foundation · Years 6–8Age Problems

Year 6 | Week 3 | Age problems

Year 6: Read the comparison carefully - question, part 1

Prepared for the Maths4U Olympiad Club. English worksheet and source references.

12. Year 6 - 12. A mother and three children

Foundation · Years 6–8Age Problems

Year 6 | Week 3 | Age problems

Year 6: A mother and three children - question, part 1

Prepared for the Maths4U Olympiad Club. English worksheet and source references.

13. Year 6 - 13. Three different moments

Foundation · Years 6–8Age Problems

Year 6 | Week 3 | Age problems

Year 6: Three different moments - question, part 1

Prepared for the Maths4U Olympiad Club. English worksheet and source references.

14. Years 8-9 - 1. A mind-reading trick

Intermediate · Years 9–10Digits and Place Value

Years 8-9 | Week 3 | Digits and decimal notation

Years 8-9: A mind-reading trick - question, part 1

Prepared for the Maths4U Olympiad Club. English worksheet and source references.

15. Years 8-9 - 2. Four connected digits

Intermediate · Years 9–10Digits and Place Value

Years 8-9 | Week 3 | Digits and decimal notation

Years 8-9: Four connected digits - question, part 1

Prepared for the Maths4U Olympiad Club. English worksheet and source references.

16. Years 8-9 - 3. Append one digit

Intermediate · Years 9–10Digits and Place Value

Years 8-9 | Week 3 | Digits and decimal notation

Years 8-9: Append one digit - question, part 1

Prepared for the Maths4U Olympiad Club. English worksheet and source references.

17. Years 8-9 - 4. Add a number to its reversal

Intermediate · Years 9–10Digits and Place Value

Years 8-9 | Week 3 | Digits and decimal notation

Years 8-9: Add a number to its reversal - question, part 1

Prepared for the Maths4U Olympiad Club. English worksheet and source references.

18. Years 8-9 - 5. Recover the bicycle-lock code

Intermediate · Years 9–10Digits and Place Value

Years 8-9 | Week 3 | Digits and decimal notation

Years 8-9: Recover the bicycle-lock code - question, part 1

Prepared for the Maths4U Olympiad Club. English worksheet and source references.

19. Years 8-9 - 6. A password made from two digits

Intermediate · Years 9–10Digits and Place Value

Years 8-9 | Week 3 | Digits and decimal notation

Years 8-9: A password made from two digits - question, part 1

Prepared for the Maths4U Olympiad Club. English worksheet and source references.

20. Years 8-9 - 7. The two middle digits

Intermediate · Years 9–10Digits and Place Value

Years 8-9 | Week 3 | Digits and decimal notation

Years 8-9: The two middle digits - question, part 1

Prepared for the Maths4U Olympiad Club. English worksheet and source references.

21. Years 8-9 - 8. A letter sum

Intermediate · Years 9–10Digits and Place Value

Years 8-9 | Week 3 | Digits and decimal notation

Years 8-9: A letter sum - question, part 1

Prepared for the Maths4U Olympiad Club. English worksheet and source references.

22. Years 8-9 - 9. Build the longest digit chain

Intermediate · Years 9–10Digits and Place Value

Years 8-9 | Week 3 | Digits and decimal notation

Years 8-9: Build the longest digit chain - question, part 1

Prepared for the Maths4U Olympiad Club. English worksheet and source references.

23. Years 8-9 - 10. Reverse five digits and subtract

Intermediate · Years 9–10Digits and Place Value

Years 8-9 | Week 3 | Digits and decimal notation

Years 8-9: Reverse five digits and subtract - question, part 1

Prepared for the Maths4U Olympiad Club. English worksheet and source references.

24. Years 8-9 - 11. Only the final three digits matter

Intermediate · Years 9–10Digits and Place Value

Years 8-9 | Week 3 | Digits and decimal notation

Years 8-9: Only the final three digits matter - question, part 1

Prepared for the Maths4U Olympiad Club. English worksheet and source references.

25. Years 8-9 - 12. The smallest possible multiple

Intermediate · Years 9–10Digits and Place Value

Years 8-9 | Week 3 | Digits and decimal notation

Years 8-9: The smallest possible multiple - question, part 1

Prepared for the Maths4U Olympiad Club. English worksheet and source references.

26. Years 8-9 - 13. One hundred ones

Intermediate · Years 9–10Digits and Place Value

Years 8-9 | Week 3 | Digits and decimal notation

Years 8-9: One hundred ones - question, part 1

Prepared for the Maths4U Olympiad Club. English worksheet and source references.

27. Year 10 - 1. A quick start

Intermediate · Years 9–10Quadratic Equations

Year 10 | Week 3 | Quadratic equations

Year 10: A quick start - question, part 1

Prepared for the Maths4U Olympiad Club. English worksheet and source references.

28. Year 10 - 2. Keep both possibilities

Intermediate · Years 9–10Quadratic Equations

Year 10 | Week 3 | Quadratic equations

Year 10: Keep both possibilities - question, part 1

Prepared for the Maths4U Olympiad Club. English worksheet and source references.

29. Year 10 - 3. Two inputs, one output

Intermediate · Years 9–10Quadratic Equations

Year 10 | Week 3 | Quadratic equations

Year 10: Two inputs, one output - question, part 1

Prepared for the Maths4U Olympiad Club. English worksheet and source references.

30. Year 10 - 4. Doubling the roots

Intermediate · Years 9–10Quadratic Equations

Year 10 | Week 3 | Quadratic equations

Year 10: Doubling the roots - question, part 1

Prepared for the Maths4U Olympiad Club. English worksheet and source references.

31. Year 10 - 5. Find a quadratic inside a triangle

Intermediate · Years 9–10Quadratic Equations

Year 10 | Week 3 | Quadratic equations

Year 10: Find a quadratic inside a triangle - question, part 1

Prepared for the Maths4U Olympiad Club. English worksheet and source references.

32. Year 10 - 6. Three numbers, four roles

Intermediate · Years 9–10Quadratic Equations

Year 10 | Week 3 | Quadratic equations

Year 10: Three numbers, four roles - question, part 1

Prepared for the Maths4U Olympiad Club. English worksheet and source references.

33. Year 10 - 7. One root in each equation

Intermediate · Years 9–10Quadratic Equations

Year 10 | Week 3 | Quadratic equations

Year 10: One root in each equation - question, part 1

Prepared for the Maths4U Olympiad Club. English worksheet and source references.

34. Year 10 - 8. A discriminant without an equation

Intermediate · Years 9–10Quadratic Equations

Year 10 | Week 3 | Quadratic equations

Year 10: A discriminant without an equation - question, part 1

Prepared for the Maths4U Olympiad Club. English worksheet and source references.

35. Year 10 - 9. Cube the coefficients

Intermediate · Years 9–10Quadratic Equations

Year 10 | Week 3 | Quadratic equations

Year 10: Cube the coefficients - question, part 1

Prepared for the Maths4U Olympiad Club. English worksheet and source references.

36. Year 10 - 10. Compare two discriminants

Intermediate · Years 9–10Quadratic Equations

Year 10 | Week 3 | Quadratic equations

Year 10: Compare two discriminants - question, part 1

Prepared for the Maths4U Olympiad Club. English worksheet and source references.

37. Year 10 - 11. Integer roots give integer squares

Intermediate · Years 9–10Quadratic Equations

Year 10 | Week 3 | Quadratic equations

Year 10: Integer roots give integer squares - question, part 1

Prepared for the Maths4U Olympiad Club. English worksheet and source references.

38. Year 10 - 12. Count the possible quadratics

Intermediate · Years 9–10Quadratic Equations

Year 10 | Week 3 | Quadratic equations

Year 10: Count the possible quadratics - question, part 1

Prepared for the Maths4U Olympiad Club. English worksheet and source references.

39. Year 10 - 13. A quartic built from two quadratics

Intermediate · Years 9–10Quadratic Equations

Year 10 | Week 3 | Quadratic equations

Year 10: A quartic built from two quadratics - question, part 1

Prepared for the Maths4U Olympiad Club. English worksheet and source references.

40. Years 12-13 - 1. A fixed product

Advanced · Years 11–13Inequalities

Years 12-13 | Week 3 | AM-GM inequalities

Years 12-13: A fixed product - question, part 1

Prepared for the Maths4U Olympiad Club. English worksheet and source references.

41. Years 12-13 - 2. A coefficient hides an extra term

Advanced · Years 11–13Inequalities

Years 12-13 | Week 3 | AM-GM inequalities

Years 12-13: A coefficient hides an extra term - question, part 1

Prepared for the Maths4U Olympiad Club. English worksheet and source references.

42. Years 12-13 - 3. Four terms, with a sign check [Extension]

Advanced · Years 11–13Inequalities

Years 12-13 | Week 3 | AM-GM inequalities

Years 12-13: Four terms, with a sign check [Extension] - question, part 1

Prepared for the Maths4U Olympiad Club. English worksheet and source references.

43. Years 12-13 - 4. Split, apply, multiply

Advanced · Years 11–13Inequalities

Years 12-13 | Week 3 | AM-GM inequalities

Years 12-13: Split, apply, multiply - question, part 1

Prepared for the Maths4U Olympiad Club. English worksheet and source references.

44. Years 12-13 - 5. Six products and four variables

Advanced · Years 11–13Inequalities

Years 12-13 | Week 3 | AM-GM inequalities

Years 12-13: Six products and four variables - question, part 1

Prepared for the Maths4U Olympiad Club. English worksheet and source references.

45. Years 12-13 - 6. Two bounds meet

Advanced · Years 11–13Inequalities

Years 12-13 | Week 3 | AM-GM inequalities

Years 12-13: Two bounds meet - question, part 1

Prepared for the Maths4U Olympiad Club. English worksheet and source references.

46. Years 12-13 - 7. A coefficient controlled by its roots

Advanced · Years 11–13Inequalities

Years 12-13 | Week 3 | AM-GM inequalities

Years 12-13: A coefficient controlled by its roots - question, part 1

Prepared for the Maths4U Olympiad Club. English worksheet and source references.

47. Years 12-13 - 8. Combine two upper bounds

Advanced · Years 11–13Inequalities

Years 12-13 | Week 3 | AM-GM inequalities

Years 12-13: Combine two upper bounds - question, part 1

Prepared for the Maths4U Olympiad Club. English worksheet and source references.

48. Years 12-13 - 9. A product hidden in three fractions

Advanced · Years 11–13Inequalities

Years 12-13 | Week 3 | AM-GM inequalities

$Years 12-13: A product hidden in three fractions - question, part 1$

Prepared for the Maths4U Olympiad Club. English worksheet and source references.

49. Years 12-13 - 10. Build the algebraic bridge

Advanced · Years 11–13Inequalities

Years 12-13 | Week 3 | AM-GM inequalities

Years 12-13: Build the algebraic bridge - question, part 1

Prepared for the Maths4U Olympiad Club. English worksheet and source references.

50. Years 12-13 - 11. The USAMO target

Advanced · Years 11–13Inequalities

Years 12-13 | Week 3 | AM-GM inequalities

Years 12-13: The USAMO target - question, part 1

Prepared for the Maths4U Olympiad Club. English worksheet and source references.

51. Years 12-13 - 12. Choose larger expressions as the terms [Extension]

Advanced · Years 11–13Inequalities

Years 12-13 | Week 3 | AM-GM inequalities

Years 12-13: Choose larger expressions as the terms [Extension] - question, part 1

Prepared for the Maths4U Olympiad Club. English worksheet and source references.