class 9 maths Polynomial

 

Class 9 Sample Paper maths

 

Error and COrrection

Section A: Find and Correct the Errors

1. She don’t like to play football.

2. He are going to the market now.

3. The books is on the table.

4. I have saw that movie yesterday.

5. They enjoys the party very much.

6. Each of the boys have a pen.

7. There is many people in the hall.

8. The child cried because he losted his toy.

9. She can sings very well.

10. We was happy to see them.

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Section B: Correct the Passage
Identify and correct the errors in the following passage.

"Last weekend, me and my friends goes to the beach. We was very excited because it were a sunny day. We play volleyball and swimmed in the sea. Everyone enjoy the time and we eats ice cream before going back to home."

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Section C: Choose the Correct Option
Select the correct option to fix the error in each sentence.

1. He ___ (is/are) very intelligent.

2. They ___ (was/were) watching a movie last night.

3. She ___ (has/have) completed her homework.

4. The cat ___ (drink/drinks) milk every day.

5. We ___ (go/goes) to school by bus.

pattern - Class 6

 EASY

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Part 1: Number Patterns

1. Complete the sequences:

   a) 2, 4, 6, 8, ___, ___, ___

   b) 5, 10, 20, 40, ___, ___, ___

   c) 100, 90, 80, 70, ___, ___, ___

   d) 1, 4, 9, 16, ___, ___, ___

2. Find the rule and continue the pattern:

   a) 3, 6, 9, 12, ___, ___, ___ (Rule: ______________)

   b) 50, 45, 40, 35, ___, ___, ___ (Rule: ______________)

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Part 2: Shape Patterns

3. Draw the next shapes in the sequence:

   a) 🔺, 🔺🔺, 🔺🔺🔺, ___, ___

   b) ◼️, ⚫, ◼️, ⚫, ___, ___

   c) ★, ★★, ★★★, ★★★★, ___, ___

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Part 3: Word Patterns

4. Fill in the missing words:

   a) Cat, Dog, Cat, Dog, ___, ___

   b) Red, Blue, Green, Red, Blue, ___

   c) Run, Jump, Run, Jump, ___, ___

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DIFFICULT

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Part 1: Complex Number Patterns

1. Complete the sequences:

   a) 2, 6, 12, 20, 30, ___, ___

   b) 1, 3, 7, 15, 31, ___, ___

   c) 243, 81, 27, 9, ___, ___

   d) 2, 4, 12, 48, 240, ___, ___

2. Identify the rule and continue the pattern:

   a) 1, 4, 9, 16, 25, ___, ___ (Rule: ______________)

   b) 5, 11, 23, 47, 95, ___, ___ (Rule: ______________)

   c) 13, 21, 34, 55, ___, ___ (Rule: ______________)

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Part 2: Advanced Shape Patterns

3. Draw the next shapes in the sequence:

   a) 🔺, 🔺🔵, 🔺🔵🔷, 🔺🔵🔷🔸, ___, ___

   b) ◼️, ◼️⚫, ⚫◼️, ◼️⚫, ⚫◼️, ___, ___

   c) ★, ★★, ★★★, ★, ★★, ___, ___

4. Identify the rule and describe it in words:

   a) ◯, ◯◯, ◯, ◯◯◯, ◯, ◯◯◯◯, ___

   b) 🔵, 🔴, 🔵🔵, 🔴🔴, 🔵🔵🔵, ___, ___

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Part 3: Word & Logic Patterns

5. Complete the word sequences:

   a) Ant, Elephant, Bat, Dolphin, Cat, ___, ___
   (Hint: Look at the number of letters in each word.)

   b) Monday, Wednesday, Saturday, Tuesday, Thursday, ___, ___
   (Hint: Focus on the sequence of days in a hidden way.)

Operation with Square roots

Section 1: Addition and Subtraction of Square Roots

Simplify the following:

1. $\sqrt{16} + \sqrt{9}$
2. $\sqrt{25} + \sqrt{36}$
3. $\sqrt{49} - \sqrt{9}$
4. $\sqrt{100} - \sqrt{64}$
5. $\sqrt{81} + \sqrt{144}$

Section 2: Multiplication of Square Roots

Multiply and simplify:

6. $\sqrt{5} \times \sqrt{5}$
7. $\sqrt{2} \times \sqrt{8}$
8. $\sqrt{3} \times \sqrt{12}$
9. $2\sqrt{7} \times 3\sqrt{7}$
10. $4\sqrt{6} \times \sqrt{3}$

Section 3: Division of Square Roots

Divide and simplify:

11. $\frac{\sqrt{49}}{\sqrt{4}}$
12. $\frac{\sqrt{64}}{\sqrt{16}}$
13. $\frac{\sqrt{81}}{\sqrt{9}}$
14. $\frac{\sqrt{50}}{\sqrt{2}}$
15. $\frac{\sqrt{200}}{\sqrt{25}}$

Section 4: Mixed Operations with Square Roots

Simplify:

16. $\sqrt{9} + 2\sqrt{4} - \sqrt{1}$
17. $3\sqrt{2} + 2\sqrt{8} - \sqrt{18}$
18. $(2\sqrt{3} + \sqrt{12}) \times \sqrt{3}$
19. $\frac{\sqrt{32} + \sqrt{18}}{\sqrt{2}}$
20. $(5\sqrt{5} - 2\sqrt{20}) + (3\sqrt{45} - \sqrt{5})$

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factorisation- middle term split

Practice Problems:

1. $x^2 + 7x + 10$
2. $x^2 + 6x + 8$
3. $x^2 + 11x + 24$
4. $3x^2 + 10x + 7$
5. $2x^2 + 9x + 10$
6. $5x^2 + 13x + 6$
7. $4x^2 + 12x + 9$
8. $6x^2 + 17x + 12$
9. $2x^2 - 3x - 2$
10. $x^2 - 5x + 6$

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Challenge Problems:

1. $2x^2 + 15x + 25$
2. $3x^2 + 14x + 8$
3. $5x^2 - 19x + 12$
4. $6x^2 - 5x - 6$
5. $4x^2 + 20x + 25$

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Subject Verb Agreement

Part 1: Choose the correct verb

Choose the correct verb from the parentheses.

1. The dog (run / runs) around the yard every morning.
2. She (work / works) at the library every weekend.
3. The players (was / were) ready for the game.
4. Either the teacher or the students (has / have) the correct answer.
5. Neither the cat nor the dog (is / are) in the house.
6. My friends (like / likes) to play board games.
7. Each of the books (is / are) on the table.
8. The news (was / were) surprising to everyone.
9. Ten dollars (is / are) a fair price for this item.
10. Both of the children (want / wants) ice cream.

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Part 2: Fill in the blanks

Fill in the blanks with the correct form of the verb.

1. The boy _______ (play) soccer every afternoon.
2. They _______ (go) to the park on Sundays.
3. She _______ (study) hard for her exams.
4. Either Maria or John _______ (be) responsible for cleaning the room.
5. Nobody _______ (know) the answer to the question.
6. The committee _______ (meet) every month.
7. All of the cookies _______ (be) gone.
8. The flock of birds _______ (fly) over the lake.
9. There _______ (be) several apples on the counter.
10. The pair of shoes _______ (look) great on you.

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Part 3: Correct the mistakes

Each sentence below has a subject-verb agreement error. Rewrite the sentence correctly.

1. The group of students are going on a trip.
2. My brother and my sister likes to cook together.
3. There is many books on the shelf.
4. Either the teacher or the students has the key.
5. Everyone know the answer to the question.

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