AP Class 9 FA1 Maths Question Paper 2023

**Introduction **

In the academic journey of a student, assessments play a crucial role in evaluating their understanding and knowledge of different subjects. The Formative Assessment 1 (FA1) for Mathematics in Andhra Pradesh’s Class 9 for the year 2023 is an important milestone for students. This article aims to provide a comprehensive guide to help students prepare effectively for the FA1 Maths examination. We will cover various topics, study tips, and strategies to excel in the assessment.

**1. Understanding the FA1 Maths Assessment**

At the beginning of the academic year, students in Class 9 will encounter the Formative Assessment 1 (FA1) in Mathematics. This assessment is designed to gauge students’ progress, understanding, and application of mathematical concepts.

**3. Preparing Effectively for FA1 Maths**

Scoring well in FA1 Maths requires dedicated preparation. Here are some tips to help students prepare effectively:

3.1. Understand the Syllabus

Having a clear understanding of the syllabus and topics that will be assessed is the first step towards effective preparation.

3.2. Create a Study Schedule

Organize your study time by creating a study schedule that allocates sufficient time for each topic, ensuring comprehensive coverage.

3.3. Practice Regularly

Consistent practice is essential for improving mathematical skills. Solve a variety of problems and exercises to reinforce your understanding.

3.4. Seek Clarification

If you encounter any doubts or difficulties while studying, don’t hesitate to seek clarification from your teachers or peers.

3.5. Utilize Resources

Leverage textbooks, reference materials, online resources, and educational videos to enhance your learning experience.

**FORMATIVE ASSESSMENT-1 (2023-24)**

MATHEMATICS

(English Medium)

1. Write any three rational numbers.

2. Find the degree of 3x ⁶ +6y ³ -7

3. Express 3.28 in the Simplest form of p/q

4. Find the value of the Polynomial 4x ² -5x+3, When x = 0.

5. Represent 5/3 and -5/3 on the Number line.

6. Find the remainder when x ³ +1 devided by (x+1)

Answer

1. Three rational numbers are:

a) 1/2

b) -3/4

c) 5/7

2. The degree of a polynomial is the highest power of the variable present in the expression. In the given polynomial 3x⁶ + 6y³ – 7, the highest power of any variable is 6 (in the term 3x⁶). Therefore, the degree of the polynomial is 6.

3. To express 3.28 in the simplest form of p/q (where p and q are integers with no common factors other than 1), we can consider 3.28 as 328/100:

3.28 = 328/100

4. To find the value of the polynomial 4x² – 5x + 3 when x = 0, we substitute x with 0 in the expression:

4(0)² – 5(0) + 3 = 0 – 0 + 3 = 3

5. Representing 5/3 and -5/3 on the number line:

-5/3 <–o——-o——–o—> 5/3

-2 -1 0 1 2

6. To find the remainder when x³ + 1 is divided by (x + 1), we use the remainder theorem. The remainder is the value of the polynomial when x = -1.

So, when x = -1:

(-1)³ + 1 = -1 + 1 = 0

Hence, the remainder is 0.

7. Rationalise the denominator of 1/(7 + 4√3))

Solution – 1 / (7 + 4√3)

Multiply numerator and denominator by the conjugate of (7 + 4√3), which is (7 – 4√3):

(1 / (7 + 4√3)) × ((7 – 4√3) / (7 – 4√3))

Now, use the difference of squares formula (a² – b² = (a + b)(a – b)) to simplify the denominator:

[(1 * (7 – 4√3)) / ((7 + 4√3) * (7 – 4√3))]

Simplify the denominator further:

(7 – 4√3) * (7 + 4√3) = 7² – (4√3)² = 49 – 48 = 1

So the expression becomes:

1 / 1

And the rationalized form is:

1

IV. ANSWER THE FOLLOWING QUESTIONS.

8. When a polynomial 2x³ +3x²+ax+b is divided by (x – 2) leaves remainder 2, and (x – 2) leaves remainder 2, and (x + 2) leaves remainder -2 Find a and b.

Solution –

When the polynomial is divided by (x – 2), it leaves a remainder of 2:

Using the Remainder Theorem, if we substitute x = 2 into the polynomial, the result should be equal to the remainder (which is 2):

2(2)³ + 3(2)² + a(2) + b = 2

Simplify and solve for a and b:

16 + 12 + 2a + b = 2

28 + 2a + b = 2

2a + b = 2 – 28

2a + b = -26 ….(i)

When the polynomial is divided by (x + 2), it leaves a remainder of -2:

Using the Remainder Theorem, if we substitute x = -2 into the polynomial, the result should be equal to the remainder (which is -2):

2(-2)³ + 3(-2)² + a(-2) + b = -2

Simplify and solve for a and b:

-16 + 12 – 2a + b = -2

-4 – 2a + b = -2

-2a + b = -2 + 4

-2a + b = 2 ….(ii)

Now, we have a system of two equations (i) and (ii). Let’s solve for a and b:

(i) + (ii):

2a + b – 2a + b = -26 + 2

2b = -24

b = -12

Now, substitute the value of b back into equation (i):

2a + (-12) = -26

2a = -26 + 12

2a = -14

a = -7

So, the values of a and b are a = -7 and b = -12.

Or

If ‘a’ and ‘b’ are rational numbers, find the value of ‘a’ and ‘b’ in the equation:

√3 + √2 / √3 – √2 = a + b√6

To find the values of a and b, we need to rationalize the denominator of the fraction on the left-hand side. We do this by multiplying both the numerator and the denominator by the conjugate of the denominator, which is (√3 + √2):

(√3 + √2) / (√3 – √2) × (√3 + √2) / (√3 + √2)

Now, let’s simplify the expression:

= (√3 + √2)(√3 + √2) / ((√3)² – (√2)²)

= (√3 + √2)(√3 + √2) / (3 – 2)

= (√3 + √2)(√3 + √2)

= (√3)(√3) + (√3)(√2) + (√2)(√3) + (√2)(√2)

= 3 + √6 + √6 + 2

= 5 + 2√6

Now, comparing this with a + b√6, we can find the values of a and b:

a = 5

b = 2

So, the values of ‘a’ and ‘b’ in the equation are a = 5 and b = 2.

4. Tips for Answering FA1 Maths Questions

To excel in the FA1 Maths examination, consider these helpful tips while answering questions:

4.1. Read Carefully

Carefully read each question and ensure you understand what is being asked before attempting an answer.

4.2. Show Your Work

In mathematical problems, showing your work and step-by-step solutions can earn you partial credits even if the final answer is incorrect.

4.3. Time Management

Manage your time wisely during the examination. Allocate appropriate time to each question and avoid spending too much time on a single question.

5. Test Taking Strategies

When taking the FA1 Maths examination, employ these strategies for a smoother experience:

5.1. Start with Easy Questions

Begin with the questions that you find easier to solve. This will boost your confidence and save time for more challenging questions.

5.2. Review Your Answers

Once you have finished answering all the questions, take some time to review your answers. Correct any mistakes you might have made.

6. Conclusion

The Formative Assessment 1 (FA1) in Mathematics for Class 9 is an important evaluation of students’ knowledge and understanding of mathematical concepts. By following a systematic study plan, practicing regularly, and employing effective test-taking strategies, students can excel in the examination.