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

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Q2. Fill in the blanks:

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

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Q3. Pattern Rule:

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

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Q4. What comes next?

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

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Q5. Multiplication Pattern of 5

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

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🔷 Section B: Shape Patterns

Q6. Draw next shapes:

📘 🟦 🔺 🟦 🔺 🟦 🔺 __ __
➡️ Answer: 🟦 🔺

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Q7. Color pattern:

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

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Q8. 10th position in pattern:

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

OR

🔵🔵🟢🔵🔵🟢🔵🔵🟢 __ __

➡️ Answer: 🔵 🔵
🧠 Repeats every 3: 🔵🔵🟢

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🔤 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

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🎨 Section D: Creative Thinking

Q11. Make a pattern:

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

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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)

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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

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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)

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

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✅ 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

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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.

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✅ Correct Answer: C) Increasing exponential

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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 $\mathrm{x\; ?}$

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  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) $5 + \sqrt{85}$

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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:

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

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✅ 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) $s = 8.05u^2 - 38.64u$

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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:

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

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✅ 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, $c = 0$

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At the maximum height:

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

When it hits the ground:

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

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From these conditions, solve the system of equations:

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

This gives:

$$b = 4.8a$$

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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:

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

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Thus, the equation is:

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

WORKSHEET ch1 class 6

WORKSHEET - Number pattern

1)  1,3,5,7, ________, ___________,  _______

Rule- ________________

2)  2,4,6,8,________, ___________,  _______

Rule- ________________

3) 24,34,44,54, ________, ___________,  _______

Rule- ________________

4) 3, 6,9,12,________, ___________,  _______

Rule- ________________

5) 35,40,45, ________, ___________,  _______

Rule- ________________

6) 11,22, 33, ________, ___________,  _______

Rule- ________________

7) 9,19,29, ________, ___________,  _______

Rule- ________________

WORKSHEET - Number pattern solutions

1)  1,3,5,7, ___9_____, ___11________,  ____13___
Rule- _________odd number_______

2)  2,4,6,8,____10____, ___12________,  _____14__
Rule- _____even number___________

3)  24,34,44,54, 64 ,74, 84
Rule: By adding 10-10 in each number

4) 36,9,12,15 18 21
Rule-By adding 3 in each number.

5) 35,40,45, 50,55,60
Rule: By adding 5-5 in each number.

6) 11,22, 33, 44, 55
Rule-By adding 11-11 in each number.

7)
9,19,29, 39 49,59

Rule: By adding 10-10. in each number.