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Kalaimagal Academy

Grade 9 Mathematics Assessment

Chapter 2: Introduction to Linear Polynomials

Time Allowed: 1.5 Hours Maximum Marks: 40

General Instructions:

1. The question paper consists of four sections: A, B, C, and D.
2. Section A contains 5 Multiple Choice Questions carrying 1 mark each.
3. Section B contains 5 Very Short Answer Questions carrying 2 marks each.
4. Section C contains 3 Short Answer Questions carrying 3 marks each.
5. Section D contains 2 Long Answer Questions carrying 8 marks each.
6. All questions are compulsory. Internal choices are provided wherever applicable.

SECTION A — Multiple Choice Questions (1 mark each)

1. What is the degree of the polynomial \( 5y^3 + y^2 + 2y - 1 \)?

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(a) 1

(b) 2

(c) 3

(d) 0

2. What is the coefficient of \( x^3 \) in the polynomial \( x^4 - 3x^3 + 6x^2 - 2x + 7 \)?

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(a) 1

(b) -3

(c) 6

(d) -2

3. A straight line representing an equation of the form \( y = ax \) always passes through which point?

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(a) (1, 1)

(b) (0, 0)

(c) (0, a)

(d) (a, 0)

4. Which of the following represents a linear growth pattern?

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(a) A line with a negative slope

(b) A curve decreasing over time

(c) A line with a positive slope

(d) A constant horizontal line

5. What is the degree of a non-zero constant polynomial?

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(a) 0

(b) 1

(c) 2

(d) Not defined

SECTION B — Very Short Answer Questions (2 marks each)

6. Find the value of the linear polynomial \( 5x - 3 \) at \( x = -1 \).

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7. Find the constant term and the coefficient of \( z \) in the polynomial \( 4z^3 + 5z^2 - 11 \).

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8. The sum of two numbers is 64. One of the numbers is 10 more than the other. Form a linear equation and find the smaller number.

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9. A student has ₹500 in her savings bank account. She gets ₹150 every month as pocket money. Write a linear expression to represent the amount she will have in the \( n^{\text{th}} \) month.

[2]

10. Check whether the point \( (7, 15) \) lies on the line given by the linear equation \( y = 2x + 1 \). Justify your answer.

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SECTION C — Short Answer Questions (3 marks each)

11. The difference between two positive integers is 63. The ratio of the two integers is 2 : 5. Find the two integers.

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12. A mobile phone is bought for ₹10,000. Its value depreciates by ₹800 every year.

(i) Write an expression relating the value \( v \) and time \( t \) (in years).

(ii) Find the value of the phone after 3 years.

(iii) State whether this represents linear growth or linear decay.

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13. If the length of a rectangle is 3 cm more than twice its width, and its perimeter is 24 cm, find the dimensions (length and width) of the rectangle.

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SECTION D — Long Answer Questions (8 marks each)

14. Linear Relationships and Equations:
A gym charges a fixed monthly fee and an additional cost per hour for using the badminton court. A student observed that when she used the court for 10 hours, her bill was ₹800. When she used it for 15 hours, her bill was ₹1100. Let the monthly bill \( y \) depend on the hours of court usage \( x \) according to the linear relationship \( y = ax + b \).

(a) Set up two simultaneous linear equations using the given data. (2 marks)

(b) Solve the equations to find the values of \( a \) and \( b \). (3 marks)

(c) Interpret what the values \( a \) and \( b \) represent in this contextual scenario. (1 mark)

(d) Calculate the total bill if the court is used for 22 hours in a month. (2 marks)

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15. Patterns and Graphical Analysis:
Consider a growing pattern of tile stages where the number of square tiles \( y \) at stage \( x \) is given by the linear expression \( y = 2x - 1 \).

(a) Complete the following table for the given stages: (2 marks)

Stage (\(x\))	1	2	3	4	5
Tiles (\(y\))	1	?	?	7	?

(b) Find two specific points \( (x_1, y_1) \) and \( (x_2, y_2) \) on the coordinate plane from the table and write the steps to plot the line on a graph. (2 marks)

(c) Which stage of the pattern will contain exactly 47 square tiles? (2 marks)

(d) What is the slope of the line \( y = 2x - 1 \), and what does it signify regarding the sequence of tiles across consecutive stages? (2 marks)

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