Class 10 Exam > Class 10 Notes > Mathematics (Maths) Class 10 > Unit Test: Polynomials
Unit Test: Polynomials | Mathematics (Maths) Class 10 PDF Download
Time: 1 hour
M.M. 30
Attempt all questions.
- Question numbers 1 to 5 carry 1 mark each.
- Question numbers 6 to 8 carry 2 marks each.
- Question numbers 9 to 11 carry 3 marks each.
- Question number 12 & 13 carry 5 marks each.
Q1: Which of the following is NOT a polynomial? (1 Mark)
(a) 2x + 3y
(b) 4x2 - 7x + 1
(c) √2x + 1
(d) x3 - 5x2 + 4x - 7
Q2: If a polynomial has exactly three terms, what is it called? (1 Mark)
(a) Monomial
(b) Binomial
(c) Trinomial
(d) Polynomial
Q3: What is the degree of the polynomial 2x3 - 5x2 + 7x - 9? (1 Mark)
(a) 2
(b) 3
(c) 4
(d) 1
Q4: State whether the following statement is True or False: "A polynomial of degree 0 is called a constant polynomial." (1 Mark)
Q5: Identify the coefficients of the following polynomial: 3x2 - 8x + 5. (1 Mark)
Q6: Find the value of 'k' in the polynomial x2 - kx + 9, if one of its zeros is 3. (2 Marks)
Q7: Factorize the polynomial completely: 2x3 - 8x2 + 4x. (2 Marks)
Q8: If (x + 2) is a factor of the polynomial 2x3 + kx2 - 4x + 16, find the value of 'k'. (2 Marks)
Q9: If the sum of the zeroes of the polynomial x2 - kx + 15 is 5, find the value of 'k'. (3 Marks)
Q10: The area of a rectangular garden is given by the polynomial 2x2 + 7x - 15. Find the dimensions of the garden if its length is 2 units more than its breadth. (3 Marks)
Q11: Find the value of 'p' for which (2p - 1) is a factor of the polynomial 4p3 - 6p2 + 3p - 1. (3 Marks)
Q12: Explain the Remainder Theorem and how it can be used to find the remainder of a polynomial division. (5 Marks)
Q13: Explain the Factor Theorem and how it can be used to determine whether a given expression is a factor of a polynomial. (5 Marks)
You can find the solutions of this Unit Test here: Unit Test (Solutions): Polynomials
The document Unit Test: Polynomials | Mathematics (Maths) Class 10 is a part of the Class 10 Course Mathematics (Maths) Class 10.
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FAQs on Unit Test: Polynomials - Mathematics (Maths) Class 10
| 1. What is a polynomial? |  |
Ans. A polynomial is a mathematical expression that consists of variables (also known as indeterminates) raised to whole number powers, along with coefficients. The general form of a polynomial in one variable x is given by a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where the a's are constants (coefficients), and n is a non-negative integer representing the degree of the polynomial.
| 2. How do you add and subtract polynomials? | |
Ans. To add or subtract polynomials, you combine like terms, which are terms that have the same variable raised to the same power. For example, to add (3x^2 + 2x + 1) and (4x^2 + 3), you combine the coefficients of like terms: (3 + 4)x^2 + 2x + (1 + 3) = 7x^2 + 2x + 4.
| 3. What is the degree of a polynomial, and why is it important? | |
Ans. The degree of a polynomial is the highest power of the variable in the expression. It is important because it determines the polynomial's behavior, such as the number of roots it can have and its end behavior as x approaches positive or negative infinity. For example, a polynomial of degree 2 is a quadratic, which typically has a parabolic shape.
| 4. Can polynomials be factored, and if so, how? | |
Ans. Yes, polynomials can often be factored into simpler expressions, which can help in solving equations or simplifying expressions. Common methods of factoring include taking out the greatest common factor, using the difference of squares, applying the quadratic formula for quadratics, or using factoring by grouping. Each method depends on the structure of the polynomial.
| 5. What is the difference between a polynomial and a rational function? | |
Ans. A polynomial is an expression that consists solely of variables raised to non-negative integer powers and their coefficients, while a rational function is a ratio of two polynomials. For example, f(x) = (2x^2 + 3)/(x - 1) is a rational function because it is the quotient of the polynomial 2x^2 + 3 and the polynomial x - 1.
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