Mastery

Patterns in Mathematics — Mastery

30 questions 30 min Full-chapter mastery

Q1. Mathematicians often think of mathematics as both an art and a science. The chapter gives one main reason. Which is it?
- A. Because mathematics uses colourful diagrams
- B. Because solving problems can win prizes
- C. Because mathematics is taught with paint and brushes
- D. Because the search for patterns and their explanations is a fun and creative endeavour
Q2. Mathematics aims not just to find what patterns exist but to do something more. What?
- A. To memorise the patterns for tests
- B. To draw the patterns neatly on paper
- C. To list the patterns alphabetically
- D. To find the explanations for why those patterns exist
Q3. One example each from physics and biology where understanding patterns helped humanity. Which pair is correct?
- A. Gravitation (from planetary motion) and disease diagnosis (from genomes)
- B. Newton's laws and the periodic table
- C. Quantum mechanics and DNA fingerprinting
- D. Theory of relativity and cell biology
Q4. A Class 6 teacher wants to introduce triangular numbers (1, 3, 6, 10, 15) for the first time. Which of these is the BEST first step?
- A. Write the formula n(n+1)/2 on the board and ask students to compute terms
- B. Ask students to memorise the first ten triangular numbers
- C. Show the dot-triangle pictures and ask students to draw the next two
- D. Test students with a quiz before any teaching
Q5. Ravi has written 1, 2, 4, 8, 16, 32. The next THREE terms in this pattern, taken from Table 1, are
- A. 48, 64, 80
- B. 40, 48, 56
- C. 63, 127, 255
- D. 64, 128, 256
Q6. Asked for the next term of 1, 3, 6, 10, 15, a student writes 20. Which response from the teacher is MOST diagnostic, in the spirit of the chapter?
- A. Mark it wrong and write 21 on the board
- B. Ask the student to copy the sequence ten times
- C. Ask the student to draw the dot-triangle pictures for 10 and 15 and to draw the next one
- D. Tell the student to memorise the triangular sequence
Q7. 36 can be drawn as a triangle and as a square. Which of these statements is also true, by extension of the chapter's reasoning?
- A. Every triangular number can be drawn as a square
- B. A number can be represented in different ways and play different roles depending on the context
- C. Triangular numbers and square numbers are the same sequence
- D. Only 36 has more than one geometric form
Q8. What is the 10th triangular number?
- A. 45
- B. 50
- C. 65
- D. 55
Q9. Which of the following is NOT a cube number from Table 1?
- A. 1
- B. 27
- C. 100
- D. 125
Q10. From the sequence 1, 3, 9, 27, 81, 243, 729, what is the 8th term?
- A. 2187
- B. 1024
- C. 1458
- D. 972
Q11. Q5 explains the Koch snowflake rule: each line segment is replaced by a small 'speed bump'. As a result of one such replacement, one line segment becomes how many segments?
- A. Two
- B. Three
- C. Five
- D. Four
Q12. Shape patterns can be in 1D, 2D or 3D — or even more dimensions. Which is a 3D example from Table 2 ?
- A. Regular triangle
- B. Cube numbers (1, 8, 27, 64, 125 shown as solid cubes)
- C. Square dot pattern of 25
- D. Hexagon
Q13. The word 'regular' (as in 'regular polygon') means
- A. The shape is drawn with a ruler
- B. The shape appears often in nature
- C. The shape has equal-length sides and equal angles
- D. The shape always has an even number of sides
Q14. If you draw the 6th triangular number as a dot triangle (as in Table 2), how many dots will be in the bottom row?
- A. 5
- B. 7
- C. 8
- D. 6
Q15. A student says, 'In every number sequence, you add the same number to get the next term.' Which is the best teacher response, in line with Chapter 1?
- A. Praise the rule and move on
- B. Tell the student to stop guessing and follow textbook rules
- C. Show Table 1 — sequences like 1, 3, 6, 10 (triangular) and 1, 2, 4, 8 (powers of 2) do NOT add a constant, and ask the student to find the actual rule
- D. Give the student more sums to practise without further explanation
Q16. The sum of the first 12 odd numbers (1 + 3 + 5 + … + 23) is
- A. 121
- B. 169
- C. 100
- D. 144
Q17. Two consecutive triangular numbers from Table 1 are 15 and 21. What is their sum, and which sequence does it belong to?
- A. 36 — even numbers
- B. 35 — odd numbers
- C. 42 — triangular numbers
- D. 36 — square numbers
Q18. How many dots are in the square arrangement for the 7th square number?
- A. 14
- B. 28
- C. 42
- D. 49
Q19. Cube numbers are visualised as actual solid cubes. Which statement is consistent with this picture?
- A. The cube number 8 is shown as a flat row of 8 dots
- B. The cube number 27 is a flat triangle of 27 dots
- C. The cube number 125 is a 6 × 6 × 6 stack of unit cubes
- D. The cube number 27 is a 3 × 3 × 3 stack of unit cubes
Q20. In Table 3 of Chapter 1, the stacked-triangles sequence is shown by progressively larger triangles each made of smaller triangles. Which is the correct description of the 3rd shape?
- A. An equilateral triangle made of 9 small triangles arranged in 3 rows
- B. An equilateral triangle made of 6 small triangles
- C. A pentagon made of 9 small triangles
- D. A square made of 9 small triangles
Q21. After students correctly write the next term of a sequence, the BEST follow-up prompt (in the spirit of finding explanations) is
- A. Now memorise the first ten terms for the test next week
- B. Move on to the next exercise immediately
- C. Test them with a tricky sequence to see who gets stuck
- D. Why does this pattern happen? Can you explain it with a picture?
Q22. Consider these claims about the pattern 1, 1 + 2, 1 + 2 + 4, 1 + 2 + 4 + 8, … : I. The cumulative sums are 1, 3, 7, 15, 31. II. Each sum is one less than the next power of 2. III. Adding 1 to each sum gives the powers of 2.
- A. I and II only
- B. II and III only
- C. I and III only
- D. All three
Q23. In the complete graph K7 (extending Table 3), how many lines join the 7 vertices?
- A. 15
- B. 20
- C. 28
- D. 21
Q24. What are the 11th and 12th square numbers, by extending Table 1's pattern?
- A. 121 and 144
- B. 100 and 121
- C. 144 and 169
- D. 110 and 132
Q25. Assertion (A): 1 + 3 + 5 + 7 + … (up to 100 terms) = 10000. Reason (R): The sum of the first n odd numbers equals n², so for n = 100 it is 100² = 10000.
- A. Both A and R are true, and R is the correct explanation of A.
- B. Both A and R are true, but R is NOT the correct explanation of A.
- C. A is true, R is false.
- D. A is false, R is true.
Q26. What is the 15th odd number, by extending the Table 1 sequence 1, 3, 5, 7, 9, … ?
- A. 27
- B. 30
- C. 31
- D. 29
Q27. A teacher wants to use Table 1 in class. Which of these classroom tasks BEST matches the chapter's instruction 'write the rule for forming the numbers in your own words'?
- A. Each student picks one sequence and writes its rule in plain language in their notebook
- B. The teacher reads every rule aloud while students listen
- C. Students copy the table verbatim with no discussion
- D. Students rank the sequences from easiest to hardest
Q28. Consider these statements: I. A regular polygon with 10 sides is called a decagon. II. The number of sides of regular polygons gives the counting numbers starting at 3. III. A regular polygon must always have an even number of sides.
- A. I and III only
- B. II and III only
- C. I only
- D. I and II only
Q29. Which of the following is NOT a hexagonal number?
- A. 1
- B. 7
- C. 27
- D. 19
Q30. Several places where patterns exist are listed. Which of the following groups is taken entirely from the list of everyday contexts?
- A. Volcanoes, earthquakes and tsunamis
- B. Nature, our homes and schools, motion of sun-moon-stars, weather patterns
- C. Chess, music and dance
- D. Mining, fishing and farming

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