Here are few short questions and answers for a quiz on algebraic expressions and formulas:
Q1: What is an algebraic expression?
Ans1: An algebraic expression is a combination of variables, constants, and operations (like addition, subtraction, multiplication, and division).
Q2: Differentiate between a constant and a variable.
Ans2: A constant is a fixed value, while a variable represents an unknown value and can change. For example, in (5x + 2), ‘5’ is a constant, and ‘x’ is a variable.
Q3: Differentiate between an equation and an expression.
Ans3: An expression is a mathematical phrase, while an equation is a statement asserting that two expressions are equal.
Q4: What is a polynomial?
Ans4: A polynomial is an algebraic expression with one or more terms, where each term consists of a variable raised to a non-negative integer power, multiplied by a coefficient.
Q5: What is a monomial?
Ans5: A monomial is an algebraic expression consisting of only one term, such as 3x or 4y^2.
Q6: Define a binomial.
Ans6: A binomial is an algebraic expression consisting of two terms, like (2x + 5) or (a – b).
Q7: What characterizes a trinomial?
Ans7: A trinomial is an algebraic expression with three terms, such as (2p + 3q – 7r) or (2a – 3b + 4).
Q8: Define the distributive property.
Ans8: The distributive property states that for any numbers a, b, and c, a. (b + c) = a. b + a .c.
Q9: How do you simplify the expression 3x + 2y – x + 4y?
Ans9: Combine like terms to get 2x + 6y.
Q10: What is the difference between an identity and an equation?
Ans10: An identity is true for all values of the variables, while an equation may be true only for specific values.
Q11: How do you factorize the expression x^2 – 9?
Ans11: x^2 – 9 can be factorized as (x + 3)(x – 3).
Q12: What is the zero product property?
Ans12: The zero product property states that if the product of two factors is zero, then at least one of the factors must be zero.
Q13: Solve for x in the equation 2(x – 5) = 3x + 4.
Ans13: x = -14, because 2(x – 5) = 3x + 4 simplifies to x = -14.
Q14: Simplify the expression (2x^2 + 4x) / 2.
Ans14: Simplifying, we get x^2 + 2x.
Q15: Factorize the expression x^2 + 6x + 9.
Ans15: The expression can be factorized as (x + 3)^2.
Q16: Solve for y in the equation 2y – 7 = 3.
Ans16: y = 5, because 2y – 7 = 3 simplifies to y = 5.
Q17: Find the value of ‘z’ in the equation (3z – 8 = 10).
Ans17: z = 6, because 3z – 8 = 10 simplifies to z = 6.
Q18: What is a quadratic expression?
A18: A quadratic expression is a second-degree polynomial, usually written in the form (ax^2 + bx + c), where ‘a’, ‘b’, and ‘c’ are constants.
Q19: Define a rational expression.
Ans19: A rational expression is the ratio of two polynomials, like {3x + 1}/{2x – 5}, where ‘x’ is not allowed to make the denominator zero.
Q20: What is an algebraic fraction?
Ans7: An algebraic fraction is a fraction where the numerator and/or denominator contains algebraic expressions, such as {x^2 + 1}/{x – 2}.
Frequently Asked Questions (FAQs):-
Q1: How do you solve a system of linear equations?
Ans: There are various methods, such as substitution, elimination, and matrix methods, to solve a system of linear equations.
Q2: What is the difference between an expression and a formula?
Ans: An expression is a mathematical phrase, while a formula is a specific type of equation that expresses a relationship between variables.
Q3: Can you provide an example of a quadratic expression?
Ans: Certainly, 3x^2 + 2x – 1 is an example of a quadratic expression.
Q4: How is a literal equation different from a regular equation?
Ans4: A literal equation contains one or more variables, whereas a regular equation typically involves only constants and numbers.
Q5: Give an example of a polynomial of degree zero.
Ans5: A constant term, such as ‘7’ or ‘-2’, is an example of a polynomial of degree zero.
Q6: What is an identity in terms of algebraic expressions?
Ans6: An identity is an equation that is true for all values of the variables, such as a^2 – b^2 = (a + b)(a – b).
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