1. Look at the pattern: 2, 4, 6, 8, ... What is the next number?
- A9
- B10
- C12
- D16
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Answer: B) 10
The numbers increase by 2 each time, so after 8 comes 8 + 2 = 10.
Class 6 Patterns and Rules — practice questions with answers
Algebra · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
2. A pattern is 2, 4, 8, 16, ... Each term is got by multiplying the previous one by 2. What is the next term?
- A64
- B32
- C35
- D29
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Answer: B) 32
Each term doubles: 16 × 2 = 32.
3. Squares of dots grow as 1, 4, 9, 16, ... (square numbers). What is the next term?
- A50
- B27
- C25
- D23
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Answer: C) 25
These are perfect squares: 1, 4, 9, 16, 25 (since 5 x 5 = 25).
4. Vijay multiplies 9 by counting numbers: 9 x 1 = 09, 9 x 2 = 18, 9 x 3 = 27, 9 x 4 = 36.
The tens digit goes up by 1 and the ones digit goes down by 1, and the digits of each product add to 9.
What is the ones digit of 9 x 7?
The tens digit goes up by 1 and the ones digit goes down by 1, and the digits of each product add to 9.
What is the ones digit of 9 x 7?
- A1
- B2
- C3
- D4
Show answer
Answer: C) 3
9 x 7 = 63. Its ones digit is 3 (and 6 + 3 = 9, matching the pattern).
5. Study this pattern of sums:
1 = 1
1 + 2 + 1 = 4
1 + 2 + 3 + 2 + 1 = 9
1 + 2 + 3 + 4 + 3 + 2 + 1 = 16
Using the pattern, what is the value of 1 + 2 + 3 + 4 + 5 + 6 + 5 + 4 + 3 + 2 + 1?
1 = 1
1 + 2 + 1 = 4
1 + 2 + 3 + 2 + 1 = 9
1 + 2 + 3 + 4 + 3 + 2 + 1 = 16
Using the pattern, what is the value of 1 + 2 + 3 + 4 + 5 + 6 + 5 + 4 + 3 + 2 + 1?
- A32
- B72
- C36
- D40
Show answer
Answer: C) 36
Each sum that peaks at n equals n x n. Here the peak is 6, so the sum is 6 x 6 = 36.
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