ASSERTION-REASONING WORKSHEET chapter1: Patterns in Mathematics Class: 6 | Based on NCERT Chapter 1 Concepts

 

ASSERTION-REASONING WORKSHEET

Chapter: Patterns in Mathematics FOR DOWNLOAD PDF CLICK HERE
Class: 6 | Based on NCERT Chapter 1 Concepts

✍🏽 Choose the correct option:
(A) Both Assertion and Reason are true, and Reason is the correct explanation.
(B) Both Assertion and Reason are true, but Reason is NOT the correct explanation.
(C) Assertion is true, but Reason is false.
(D) Assertion is false, but Reason is true.

Q1.Assertion (A): The sum of the first n odd numbers is always a perfect square.
Reason (R): The sum of the first n odd numbers equals n².
Option: ___

Q2.Assertion (A): The numbers 1, 4, 9, 16, 25... form an arithmetic sequence.
Reason (R): These numbers increase by the same difference each time.
Option: ___

Q3.Assertion (A): The pattern 1, 3, 6, 10, 15,... represents triangular numbers.
Reason (R): Each number in the pattern is the sum of the first n natural numbers.
Option: ___

Q4.Assertion (A): The number of dots in a triangle pattern (1 in 1st row, 2 in 2nd...) is a square number.
Reason (R): The sum of the first n natural numbers is n(n+1)/2.
Option: ___

Q5.Assertion (A): In a growing square pattern using odd numbers, each new layer adds an odd number of dots.
Reason (R): The area of a square increases by successive odd numbers.
Option: ___

Q6.Assertion (A): The pattern 2, 4, 8, 16, 32... is a geometric progression.
Reason (R): Each term is double the previous one.
Option: ___

Q7.Assertion (A): A palindromic number is a number that reads the same forward and backward.
Reason (R): All even numbers are palindromes.
Option: ___

Q8.Assertion (A): Squaring numbers like 11, 111, 1111 gives symmetric number patterns.
Reason (R): 111² = 12321, 1111² = 1234321.
Option: _

Q9.Assertion (A): The sum of any three consecutive odd numbers is divisible by 3.
Reason (R): Odd numbers follow the pattern 2n + 1.
Option: ___

Q10.Assertion (A): 1,4,9,16,25……….called square numbers.
Reason (R): When a multiplied number by itself is called a square number.

 Option: ___

Q11.

Assertion (A): The pattern 1, 3, 5, 7, 9… continues by adding 2 each time.

Reason (R): These are consecutive odd numbers.
Option: ___

Q12.

Assertion (A): The sequence 1, 4, 9, 16, 25… represents triangular numbers.

Reason (R): These are squares of natural numbers.
Option: ___

Q13.

Assertion (A): Every square number can be represented by a dot pattern forming a square.

Reason (R): Dot arrangements help in visualizing patterns in numbers.
Option: ___

Q14.

Assertion (A): The pattern 1, 3, 6, 10, 15, 21… is formed by adding 1, 2, 3, 4... successively.

Reason (R): This pattern forms triangular numbers.
Option: ___

Q15.

Assertion (A): A growing pattern can be represented using variables like n in algebra.

Reason (R): Algebra helps describe patterns using a rule or formula.
Option: ___

Q16.

Assertion (A): The 5th term of the pattern 2, 4, 6, 8, ... is 12.

Reason (R): This is an arithmetic sequence with common difference 2.
Option: ___

Q17.

Assertion (A): In a pattern of squares with increasing number of dots, the total number of dots in the nth square is n².

Reason (R): Square numbers grow by adding consecutive odd numbers.
Option: ___

Q18.

Assertion (A): Patterns are useful only in mathematics and not in nature.

Reason (R): Nature does not follow any fixed mathematical rules.
Option: ___

Q19.

Assertion (A): Recursive patterns are those in which the next term depends on the previous one.

Reason (R): For example, in the Fibonacci sequence, each term is the sum of two previous terms.
Option: ___

Q20.

Assertion (A): The pattern 2, 4, 8, 16, 32… is an example of geometric progression.

Reason (R): Each term is obtained by multiplying the previous term by 2.
Option: ___

CLICK HERE FOR ANSWER KEY

CBSE Worksheet: Class 6 Maths – Chapter: Patterns in Mathematics

 CBSE Worksheet: Class 6 Maths – Chapter: Patterns in Mathematics

Subject: Mathematics  Chapter: Patterns in Mathematics
Class: VI  Max Marks: 20  Time: 40 minutes
Name: ____________________  Roll No: ________  Date: __________

 Instructions:

• Use pencil and ruler for shapes.

• Show rough work where needed.

• Maintain clean and neat diagrams.

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Section A: Objective Type Questions (1 mark each)

Q1. Complete the pattern:
3, 6, 12, 24, ___, ___

Q2. Identify the rule in this number pattern:
100, 90, 80, 70, __, __

Q3. What comes next in this shape pattern?
🔷 🔶 🔷 🔶 🔷 ___ ___

Q4. Find the mirror image of the letter pair:
PQ

---

Section B: Short Answer Questions (2 marks each)

Q5. Draw the next two figures in the pattern:
⬛⬜⬛⬜⬛⬜ ⬜ ⬛

Q6. Create a number pattern where each number increases by 7. Write the first 5 terms.

Q7. A design uses this shape pattern:
🟦 🟩 🟨 🟦 🟩 🟨 …
Which shape will be in the 10th position?

---

Section C: Long Answer/Reasoning Questions (3 marks each)

Q8. Observe the staircase pattern:

• Step 1: 3 sticks

• Step 2: 5 sticks

• Step 3: 7 sticks

• Step 4: 9 sticks
  a) Write the number of sticks for Step 5 and Step 6.
  b) What is the rule in the pattern?

Q9. Create your own pattern using either numbers or shapes (draw at least 5 steps).
Explain the logic behind your pattern.

CBSE Worksheet2 - Answers

Q1. 3, 6, 12, 24, ___, ___

➡️ 48, 96 ✅

Q2. 100, 90, 80, 70, ___, ___

➡️ 60, 50 ✅

Q3. Shape Pattern

🔷 🔶 🔷 🔶 🔷 ___ ___
➡️ 🔶 🔷 ✅

Q4. Mirror Image of "PQ"

➡️ QP ✅

---

Q5. Pattern Drawing

⬛⬜⬛⬜⬛⬜ __ __
➡️ ⬜ ⬛ ✅

---

Q6. Add 7 Pattern

➡️ 7, 14, 21, 28, 35 ✅

---

Q7. 10th shape in 🟦 🟩 🟨 ...

➡️ 🟦 (10 ÷ 3 leaves remainder 1 → 🟦) ✅

---

Q8. Matchsticks

➡️ Step 5 = 11, Step 6 = 13 ✅
🧠 Odd numbers (Add 2)

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Q9. Own Pattern

🔵 🔵 🔵 🔵 🔵
➡️ Student-drawn, check for correct logic

 

Class 6 Maths Worksheet1: Patterns in Mathematics

Chapter: Patterns in Mathematics (NCERT)
Total Marks: 25 | Time: 40 Minutes
Name: _____________                                                                         Date: _____________

Section A: Number Patterns (1 mark each)

Q1. Write the next two numbers in the pattern:
2, 4, 8, 16, ___, ___

Q2. Fill in the blanks:
81, 72, 63, ___, ___

Q3. Write the rule for this pattern:
1, 4, 9, 16, 25, ...

Q4. Which number will come in the blank?
2, 6, 12, ___, 30

Q5. Write any one pattern you observe in the multiplication table of 5.

Section B: Shape Patterns (2 marks each)

Q6. Draw the next two shapes in the pattern:
🟦 🔺 🟦 🔺 🟦 🔺 __ __

Q7. Color the pattern:
⬜⬛⬜⬛⬜⬛⬜⬛
(Continue the pattern for 4 more boxes)

Q8. Which shape comes at the 10th position in this repeating pattern?
🔴🟢🔵🟣 (Hint: Repeats every 4)

OR

Look at the following pattern and find what comes next:

🔵🔵🟢🔵🔵🟢🔵🔵🟢 __ __

Section C: Symmetry & Mirror Patterns (3 marks each)

Q9. Complete the other half of the figure using symmetry:
(Provide half-image for student to complete — if you're printing, draw half a butterfly or star)

Q10. A pattern looks like this when seen in a mirror:
ABC ➞ CBA
Write how the word MATH will look in the mirror.

Section D: Creative Thinking (4 marks each)

Q11. Make your own pattern using numbers or shapes (draw at least 5 steps of the pattern).
Explain the rule you used.

Q12. A staircase is made with matchsticks like this:

• Step 1: 3 sticks

• Step 2: 5 sticks

• Step 3: 7 sticks

• ...
  How many sticks will Step 5 have?

Class 6 Maths – Chapter1: Patterns in Mathematics- Answer Key 

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✨ Section A: Number Patterns

Q1. Complete the pattern:

📘 2, 4, 8, 16, ___, ___
➡️ Answer: 32, 64
🧠 Rule: Multiply by 2

---

Q2. Fill in the blanks:

📘 81, 72, 63, ___, ___
➡️ Answer: 54, 45
🧠 Rule: Subtract 9

---

Q3. Pattern Rule:

📘 1, 4, 9, 16, 25...
➡️ Answer: Square numbers (1², 2², 3², …)

---

Q4. What comes next?

📘 2, 6, 12, ___, 30
➡️ Answer: 20
🧠 Rule: +4, +6, +8, …

---

Q5. Multiplication Pattern of 5

➡️ Answer Example: Ends in 5 or 0
💡 Extra Example: 5, 10, 15, 20, 25...

---

🔷 Section B: Shape Patterns

Q6. Draw next shapes:

📘 🟦 🔺 🟦 🔺 🟦 🔺 __ __
➡️ Answer: 🟦 🔺

---

Q7. Color pattern:

⬜⬛⬜⬛⬜⬛⬜⬛ ⬜⬛
➡️ Answer: ⬜ ⬛ (Alternates)

---

Q8. 10th position in pattern:

🔴 🟢 🔵 🟣 🔴 🟢 🔵 🟣 🔴 🟢
➡️ Answer: 🟢
🧠 Rule: Repeats every 4 items

OR

🔵🔵🟢🔵🔵🟢🔵🔵🟢 __ __

➡️ Answer: 🔵 🔵
🧠 Repeats every 3: 🔵🔵🟢

---

🔤 Section C: Mirror & Symmetry

Q9. Complete with Symmetry:

🦋 (Student completes drawing; check for mirror accuracy)

Q10. Mirror image of MATH

➡️ Answer: HTAM
📘 Each letter flips and order reverses

---

🎨 Section D: Creative Thinking

Q11. Make a pattern:

📘 Example Answer:
🔺 🔺🔺 🔺🔺🔺 🔺🔺🔺🔺 🔺🔺🔺🔺🔺
🧠 Rule: Add one 🔺 each step

---

Q12. Matchstick Staircase:

🪵 Step 1: 3 sticks
🪵 Step 2: 5 sticks
🪵 Step 3: 7 sticks
🪵 Step 4: 9 sticks
➡️ Step 5 = 11 sticks, Step 6 = 13 sticks
🧠 Rule: Add 2 each time (odd numbers)

---

patterns in Maths

🧠 Class 6 Quiz – Patterns in Mathematics

1. What comes next in the pattern: 2, 4, 8, 16, __?

2. Mirror image of "MATH" is:

3. Identify the 10th shape in 🔵🔵🟢 repeating pattern:
--Select-- 🔵 🟢 🔴

4. How many matchsticks in Step 6 (3, 5, 7, 9...)?

 SAT EXAM PREPARATION 2025-2026

Question:

There are 66 calories in 15 grams of grated Parmesan cheese, and 59% of those calories are from fat.
When measuring Parmesan cheese, 5 grams is equal to 1 tablespoon.

Which of the following is closest to the number of calories from fat per tablespoon of grated Parmesan cheese?

Options:

• A) 3

• B) 8

• C) 9

• D) 13

---

Solution:

Step 1: Calculate total fat calories in 15 grams

$$\text{Fat calories} = 59\% \text{ of } 66 = 0.59 \times 66 = 38.94 \approx 39 \text{ calories}$$

Step 2: Find fat calories per gram

$$\frac{39 \text{ calories}}{15 \text{ grams}} = 2.6 \text{ calories per gram}$$

Step 3: Find fat calories per 1 tablespoon (which is 5 grams)

$$2.6 \times 5 = 13 \text{ calories from fat per tablespoon}$$

---

✅ Correct Answer: D) 13

This is the closest value to the actual fat calories per tablespoon.

Question:

The base of a tree has 10 mushrooms growing from its roots.
The mushroom population doubles every 5 days.

What type of function best models the relationship between the mushroom population and time?

Options:

• A) Decreasing exponential

• B) Decreasing linear

• C) Increasing exponential

• D) Increasing linear

---

Solution:

Let’s understand what’s happening:

• The starting population is 10 mushrooms.

• The population doubles every 5 days, which means it multiplies by 2 repeatedly over time.

This is a classic example of exponential growth, where the population is increasing over time, not decreasing.

Why not linear?

• Linear growth adds a fixed amount each time.

• Exponential growth multiplies (like doubling), so the rate of increase itself increases over time.

---

✅ Correct Answer: C) Increasing exponential

---

Bonus (Equation form):

The function could be modeled as:

$$M(t)=10\cdot {\mathrm{2^}}^{t\mathrm{/}5}$$

Where:

• $M(t)$ is the number of mushrooms after $t$ days,

• 10 is the initial count,

• The exponent $t\mathrm{/}5$ reflects doubling every 5 days.

  Question:
  

  Given the quadratic equation:

  $$x^2 + bx + c = 0$$

  where $b$ and $c$ are constants.

  If:

  $$\frac{-b+\sqrt{b^2-4c}}{2}=18\text{and}\frac{-b-\sqrt{b^2-4c}}{2}=10$$

  what is one possible value of $\mathrm{x\; ?}$

  ---

  Solution:

  These two expressions are the quadratic formula results for the roots of the equation:

  $$x = \frac{-b \pm \sqrt{b^2 - 4c}}{2}$$So, the two solutions are:

  $$x_1 = 18, \quad x_2 = 10$$
  

  Thus, one possible value of x is:

  ✅ Answer: $\boxed{10}$ or $\boxed{18}$

  
  

Question:

Solve:

$$3y^2 - 4 = 5y + 1$$

Which of the following is a solution to the equation above?

Options:
A) $\frac{5 - \sqrt{85}}{6}$
B) $\frac{5 - \sqrt{85}}{3}$
C) 5
D) $5 + \sqrt{85}$

---

Solution:

Step 1: Start with the given equation

$$3y^2 - 4 = 5y + 1$$

Step 2: Move all terms to one side to set the equation to 0

$$3y^2 - 5y - 5 = 0$$

Now we solve this quadratic using the quadratic formula:

$$y = \frac{-(-5) \pm \sqrt{(-5)^2 - 4(3)(-5)}}{2(3)}$$ $$= \frac{5 \pm \sqrt{25 + 60}}{6} = \frac{5 \pm \sqrt{85}}{6}$$

So the two solutions are:

$$y = \frac{5 + \sqrt{85}}{6} \quad \text{or} \quad y = \frac{5 - \sqrt{85}}{6}$$

---

✅ Correct Answer: A) $\frac{5 - \sqrt{85}}{6}$

Here is the question text and a full step-by-step solution based on the image:

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Question:

A rocket is launched vertically from ground level. The rocket reaches a maximum height of 46.36 meters above the ground after 2.4 seconds, and falls back to the ground after 4.8 seconds.

Which equation best represents the height $s$, in meters, of the rocket $u$ seconds after it is launched?

Options:

• A) $s = -8.05u^2 + 38.64u$

• B) $s = -4.8u^2 + 46.36u$

• C) $s = -u^2 + 46.36$

• D) $s = 8.05u^2 - 38.64u$

---

Solution:

We are told:

• The rocket starts at ground level → initial height = 0

• Maximum height is 46.36 meters at u = 2.4 seconds

• It returns to ground at u = 4.8 seconds

• So the vertex of the parabola is at $u = 2.4$, and the parabola opens downward

General form of a quadratic equation:

$$s = au^2 + bu + c$$

Since it starts at ground level: $c = 0$

Let’s use the vertex form:

$$s = a(u - h)^2 + k$$

Where:

• $h = 2.4$ (time of max height)

• $k = 46.36$ (maximum height)

$$s = a(u - 2.4)^2 + 46.36$$

We also know that at $u = 0$, $s = 0$ (ground level). Plug into the equation:

$$0 = a(0 - 2.4)^2 + 46.36 \Rightarrow 0 = a(5.76) + 46.36 \Rightarrow a = -\frac{46.36}{5.76} \approx -8.05$$

Now plug $a$ into the standard form:

$$s = -8.05u^2 + (2 \cdot 8.05 \cdot 2.4)u = -8.05u^2 + 38.64u$$

---

✅ Correct Answer: A) $s = -8.05u^2 + 38.64u$

• The rocket is launched from ground level, so the initial height is $0$.

• Using the general form of a quadratic equation for height,

  $$s(t) = -au^2 + bu + c$$

• Since the initial height is 0, $c = 0$

---

At the maximum height:

$$s(2.4) = -a(2.4)^2 + 2.4b = 46.36$$

When it hits the ground:

$$s(4.8) = -a(4.8)^2 + 4.8b = 0$$

---

From these conditions, solve the system of equations:

$$-23.04a + 4.8b = 0 \quad \text{(1)}$$

This gives:

$$b = 4.8a$$

---

Substitute $b = 4.8a$ into:

$$-a(2.4)^2 + 2.4(4.8a) = 46.36 \Rightarrow -5.76a + 11.52a = 46.36 \Rightarrow 5.76a = 46.36 \Rightarrow a = 8.05$$

Then:

$$b = 4.8 \times 8.05 = 38.64$$

---

Thus, the equation is:

$$s(u)=-8.05u^2+38.64u$$