Patterns in Mathematics — Quiz

Q1. Patterns occur in everything we do. Which of these is NOT given as an example of an everyday context in which patterns appear?

• A. The motion of the sun, moon and stars
• B. Shopping and cooking
• C. Throwing a ball and playing games
• D. Solving simultaneous linear equations

Q2. Ravi looks at the first row of Table 1 — 1, 1, 1, 1, 1, 1, 1, … . What is this sequence called?

• A. Counting numbers
• B. All 1's
• C. Triangular numbers
• D. Virahānka numbers

Q3. Priya writes the rule 'start from 2 and add 2 each time'. Which sequence in Table 1 does this rule generate?

• A. 1, 3, 5, 7, 9, …
• B. 2, 4, 6, 8, 10, 12, …
• C. 1, 2, 4, 8, 16, …
• D. 1, 3, 6, 10, 15, …

Q4. 36 is both a triangular number and a square number. Which of the following best explains why this is interesting?

• A. Because 36 is even
• B. Because 36 has many factors
• C. Because the same 36 dots can be arranged as both a triangle and a square
• D. Because 36 is the product of 6 and 6

Q5. The hexagonal numbers are 1, 7, 19, 37, … . The successive gaps are 6, 12, 18, … . What is the next hexagonal number after 37?

• A. 55
• B. 61
• C. 49
• D. 57

Q6. Consider the pattern 1 = 1, 1 + 3 = 4, 1 + 3 + 5 = 9, 1 + 3 + 5 + 7 = 16, … . What is the sum 1 + 3 + 5 + 7 + 9?

• A. 20
• B. 23
• C. 25
• D. 30

Q7. Using the pattern, what is the sum of the first 10 odd numbers (1 + 3 + 5 + … + 19)?

• A. 100
• B. 90
• C. 121
• D. 81

Q8. Given that 1 + 2 + 1 = 4, 1 + 2 + 3 + 2 + 1 = 9, 1 + 2 + 3 + 4 + 3 + 2 + 1 = 16. What is 1 + 2 + 3 + 4 + 5 + 4 + 3 + 2 + 1?

• A. 20
• B. 30
• C. 25
• D. 21

Q9. Q5 asks: what happens when you add two consecutive triangular numbers? Take 1 + 3, 3 + 6, 6 + 10, 10 + 15, …. Which sequence do you get?

• A. Counting numbers 2, 3, 4, 5, …
• B. Powers of 2 — 2, 4, 8, 16, …
• C. Cube numbers 1, 8, 27, 64, …
• D. Square numbers 4, 9, 16, 25, …

Q10. Q6 asks: start adding powers of 2 from 1 — 1, 1 + 2, 1 + 2 + 4, 1 + 2 + 4 + 8, …. The sums are 1, 3, 7, 15, 31, …. Add 1 to each. What sequence do you get?

• A. Triangular numbers
• B. Powers of 2
• C. Square numbers
• D. Cube numbers

Q11. In Table 3 of Chapter 1, the shapes labelled K2, K3, K4, K5, K6 belong to which sequence of shapes?

• A. Regular polygons
• B. Stacked squares
• C. Complete graphs
• D. Koch snowflake

Q12. Count the number of lines in each complete graph K2, K3, K4, K5, K6 in Table 3. Which number sequence do you get?

• A. 1, 3, 6, 10, 15 — triangular numbers
• B. 2, 4, 6, 8, 10 — even numbers
• C. 1, 4, 9, 16, 25 — square numbers
• D. 1, 2, 4, 8, 16 — powers of 2

Q13. Count the number of small squares in each shape of the stacked-squares sequence in Table 3 (1, then 2×2, 3×3, 4×4, 5×5). Which sequence do you get?

• A. Triangular numbers 1, 3, 6, 10, 15
• B. Square numbers 1, 4, 9, 16, 25
• C. Counting numbers 1, 2, 3, 4, 5
• D. Powers of 2 — 1, 2, 4, 8, 16

Q14. For the regular polygons in Table 3, what is the relation between the number of sides and the number of corners (vertices)?

• A. Corners are always one more than sides
• B. Corners are equal to the number of sides
• C. Corners are always twice the sides
• D. Corners are one less than the sides

Q15. Asha sees the sequence 2, 4, 8, 16, 32, 64. Which of the following best describes the rule for this sequence?

• A. Every term is two more than the previous one
• B. Every term is twice the previous one — these are powers of 2 from 2¹ onwards
• C. Every term is the sum of the previous two
• D. Every term is the square of its position