CBSE Class 6 Mathematics Patterns in Mathematics Practice Paper Worksheet Set 02

This is Class 6 Maths Ganita Prakash Chapter 1 Patterns in Mathematics Practice Paper 01, a 40-mark test of 20 questions in Sections A to E, given here with step-by-step answers. It checks how well you can continue number patterns such as 2, 8, 18, 32, …, find the rule in halving, doubling and tripling sequences, count the sides of many polygons, and use repeating colour patterns of tiles, stripes and banners to find totals and the colour at any position.

Section A: Multiple Choice Questions (1 Mark Each)

Section B: Short Answer Questions (2 Marks Each)

Question 11. Complete and explain: 5000, 2500, 1250, ____, ____.
Answer:
Rule: each term is half of the term before it (divide by 2).
Check: 5000 ÷ 2 = 2500 and 2500 ÷ 2 = 1250.
Next terms: 1250 ÷ 2 = 625 and 625 ÷ 2 = 312.5.
So the pattern is 5000, 2500, 1250, 625, 312.5.
In simple words: Keep halving: 1250 becomes 625, and 625 becomes 312.5.

Teacher's Note:
1. State the rule and check it on the given terms.
2. 312.5 means three hundred twelve and a half.

Question 12. Pattern: ◆ ● ◆◆ ●● ◆◆◆. Predict next two terms with explanation.
Answer:
The terms take turns: diamonds, then circles.
Each time the shape returns, it comes with one more symbol: ◆, ◆◆, ◆◆◆ and ●, ●●.
The next term is circles, one more than ●●: ●●●.
The term after that is diamonds, one more than ◆◆◆: ◆◆◆◆.
In simple words: Shapes alternate and grow by one, so ●●● comes next, then ◆◆◆◆.

Teacher's Note:
1. Two things change here: the shape and the count.
2. Give both terms, as the question asks for two.

Question 13. If 20 pentagons are arranged, find total sides. Explain.
Answer:
A pentagon has 5 sides.
Each pentagon adds 5 sides, so the totals go 5, 10, 15, 20, … (multiples of 5).
20 pentagons have 20 × 5 = 100 sides.
In simple words: 20 shapes with 5 sides each make 100 sides.

Teacher's Note:
1. Penta means five.
2. Write the multiplication in the explanation.

Question 14. Fill missing numbers: 4, 12, 36, ____, 324, ____.
Answer:
Rule: multiply by 3. Check: 4 × 3 = 12 and 12 × 3 = 36.
36 × 3 = 108, and 108 × 3 = 324 matches the given term.
324 × 3 = 972.
Missing numbers: 108 and 972.
In simple words: Multiply by 3 each time to get 108 and 972.

Teacher's Note:
1. Use the given 324 to check your first blank.
2. Divide 12 by 4 to spot the multiplier.

Section C: Short Answer Questions (3 Marks Each)

Question 15. A tile pattern uses 4 black tiles and 5 white tiles in repetition.
If 270 tiles are used, how many black tiles and white tiles were used?
Answer:
One repeating group has 4 + 5 = 9 tiles.
Number of groups = 270 ÷ 9 = 30.
Black tiles = 30 × 4 = 120.
White tiles = 30 × 5 = 150.
Check: 120 + 150 = 270.
In simple words: 270 tiles make 30 groups of 9, giving 120 black and 150 white tiles.

Teacher's Note:
1. Find the size of one repeating group first.
2. Always add your answers back to check the total.

Question 16. Multiply by 2, subtract 2. Starting at 6. Find first 6 terms.
Answer:
1st term = 6.
2nd term = 6 × 2 − 2 = 12 − 2 = 10.
3rd term = 10 × 2 − 2 = 20 − 2 = 18.
4th term = 18 × 2 − 2 = 36 − 2 = 34.
5th term = 34 × 2 − 2 = 68 − 2 = 66.
6th term = 66 × 2 − 2 = 132 − 2 = 130.
First 6 terms: 6, 10, 18, 34, 66, 130.
In simple words: Double the number and take away 2, again and again, starting from 6.

Teacher's Note:
1. The starting number itself is the 1st term.
2. Multiply first, then subtract.

Question 17. Multiply by 3, subtract 1 pattern, starting from 2. Write the first 5 terms.
Answer:
1st term = 2.
2nd term = 2 × 3 − 1 = 6 − 1 = 5.
3rd term = 5 × 3 − 1 = 15 − 1 = 14.
4th term = 14 × 3 − 1 = 42 − 1 = 41.
5th term = 41 × 3 − 1 = 123 − 1 = 122.
First 5 terms: 2, 5, 14, 41, 122.
In simple words: Triple the number and take away 1, starting from 2.

Teacher's Note:
1. Count the starting number as the 1st term.
2. The jumps 3, 9, 27, 81 triple each time, a good check.

Section D: Long Answer Question (5 Marks)

Teacher's Note:
1. Check the rule on all three given steps.
2. The n × (n + 1) form lets you jump to any step quickly.
3. These numbers are double the triangular numbers.

Section E: Case Study Based Questions (4 Marks Each)

Question 19. In a newly constructed hotel, a painter was assigned to decorate its walls with 96 stripes in all, using a specific stripe pattern for aesthetic appeal. The stripes were to be painted in a repeating sequence of 2 blue stripes followed by 4 red stripes. The hotel owner wanted the pattern consistent throughout the building, making accurate pattern calculation essential for error-free decoration.
(a) How many blue stripes will be needed?
(b) How many red stripes will be needed?
(c) Which stripe color will be at 95th position?
(d) Why is pattern understanding important in such work?
Answer:
One repeating unit = 2 blue + 4 red = 6 stripes. Number of units = 96 ÷ 6 = 16.
(a) Blue stripes = 16 × 2 = 32.
(b) Red stripes = 16 × 4 = 64. (Check: 32 + 64 = 96.)
(c) 95 = 15 × 6 + 5. After 15 full units (90 stripes), the 95th stripe is the 5th stripe of the next unit.
In a unit, positions 1–2 are blue and 3–6 are red, so the 95th stripe is red.
(d) Knowing the pattern lets the painter buy the right amount of each paint and keep the order the same on every wall, so there are no mistakes to repaint.
In simple words: 96 stripes make 16 units of 6, so 32 blue and 64 red; the 95th is the 5th in a unit, which is red.

Teacher's Note:
1. Divide by the unit size and use the remainder for position questions.
2. Remainder 5 means the 5th place in the unit, not a full unit.

Question 20. During the annual school exhibition, coloured banners were arranged along the main walkway in a repeating sequence of 5 blue banners followed by 3 yellow banners. A total of 128 banners were used to decorate the area. Accurate pattern planning was important to maintain the sequence and aesthetic appeal of the event without any mismatch or confusion.
(a) How many blue banners were used in total?
(b) How many yellow banners were used in total?
(c) What colour banner will be at the 125th position?
(d) Why is pattern planning important in such decorations?
Answer:
One repeating unit = 5 blue + 3 yellow = 8 banners. Number of units = 128 ÷ 8 = 16.
(a) Blue banners = 16 × 5 = 80.
(b) Yellow banners = 16 × 3 = 48. (Check: 80 + 48 = 128.)
(c) 125 = 15 × 8 + 5. After 15 full units (120 banners), the 125th banner is the 5th of the next unit.
Positions 1–5 in a unit are blue, so the 125th banner is blue.
(d) Planning the pattern tells the organisers how many banners of each colour to arrange and keeps the sequence correct all along the walkway, so it looks neat and nothing has to be redone.
In simple words: 128 banners make 16 units of 8: 80 blue, 48 yellow; the 125th is the 5th in a unit, which is blue.

Teacher's Note:
1. The same method works for any repeating colour pattern.
2. Show the division with remainder clearly.