∑ DANEMATHICS
FREE CAPS MATHS RESOURCES
Grade 8 · Patterns
Extending Numeric & Geometric Patterns
MEMORANDUM
Name:
Class:
Date:
Mark
/ 18
Answer all questions. Show all your working — marks are awarded for method as well as the final answer. Teacher copy: accept any correct equivalent method.
- 1Write the next three terms: 6, 11, 16, 21, …(2)Difference +5 → 26, 31, 36✓✓ (2)
- 2Write the next three terms: 45, 38, 31, 24, …(2)Difference −7 → 17, 10, 3✓✓ (2)
- 3Write the next three terms: 3, 9, 27, 81, …(2)Ratio ×3 → 243, 729, 2187✓✓ (2)
- 4Write the next three terms: 160, 80, 40, 20, …(2)Ratio ÷2 → 10, 5, 2,5✓✓ (2)
- 5Write the next two terms: 1, 4, 9, 16, 25, …(2)Square numbers → 36, 49✓✓ (2)
- 6Write the next two terms: 1, 3, 6, 10, 15, …(2)Triangular; differences 2,3,4,5,6… → 21, 28✓✓ (2)
- 7Write the next two terms: 1, 1, 2, 3, 5, 8, …(2)Add the two before → 13, 21✓✓ (2)
- 8A pattern of tiles gives 5, 9, 13, … How many tiles in the 5th shape?(2)Difference +4 → 5, 9, 13, 17, 21 tiles✓✓ (2)
- 9Is 2, 6, 18, 54 a constant-difference or constant-ratio pattern? Give the value.(2)Constant ratio, ×3 (differences 4, 12, 36 are not constant)✓✓ (2)
TOTAL: 18 marks