Algebra Class 10 Quiz

Constants and Variables

• Constant: A fixed numerical value that doesn't change (e.g., 5, -3, 1.2).
• Variable (Literal/Pronumeral): A symbol (letter) representing an unknown number (e.g., x, y, a).

Uses of Variables

• Variables represent different types of numbers in real-world situations:
  • Whole numbers (e.g., number of students in a class, represented by 'n').
  • Fractions (e.g., distance traveled in half a day, represented by 'd/2').
  • Decimals (e.g., weight of a fruit, represented by 'x kg').
  • Percentages (e.g., discount on a product, represented by 'p%').

Algebraic Expressions with Monomials

• Monomial: An algebraic expression with just one term (e.g., 3x, -5a, 7m).
• Example: If bus fare is $x, traveling 3 times costs 3x.

Terms in an Expression

• Term: A single number, variable, or their product (e.g., 4x, -2y, 3).
• Number of Terms: Count separate parts before simplifying.
• Example: 5x + 3y - 2 has 3 terms (5x, 3y, -2).

Solving Equations

• Balancing: Keep both equation sides equal by performing the same operation on both sides.
• Example: x + 3 = 7 becomes x = 4 (subtracting 3 from both sides).
• Transposition: Move terms to the other side by changing the sign.
• Example: 2x - 3 = 9 becomes 2x = 12 (add 3 to both sides) and then x = 6 (divide both sides by 2).

Coefficients

• Numerical Coefficient: The number multiplying the variable (e.g., in 7x, the coefficient is 7).
• Coefficient: Can include variables, like 3xy (coefficient of x is 3y).

Finding Factors

• Factors: Numbers/variables that multiply to form a term.
• Example: 12xy
• Factors: 12, x, y
• Further breakdown: 12 = 2 x 2 x 3, so factors are 2, 2, 3, x, y.

Like and Unlike Terms

• Like Terms: Have the same variables and exponents (e.g., 3x and 5x).
• Unlike Terms: Have different variables or powers (e.g., 2x and 4y).

Simplifying by Collecting Like Terms

• Add or subtract only like terms.
• Example: 3x + 2x - 5y + y = (3x + 2x) + (-5y + y) = 5x - 4y.

Multiplying Monomials

• Multiply coefficients and variables separately.
• Example: (2x) * (-3y) = -6xy

Substituting in Expressions

• Replace variables with given values and find the solution.
• Example: If x= 2, find the value of 3x + 2 = 3(2)+2=8

Converting Statements to Expressions

• Translate word problems into algebraic expressions.
• Example: "A number n increased by 5" = n + 5.
• Example: "Twice a number x minus 3" = 2x - 3

Exam Tips

• Identify like terms before simplifying.
• Balance equations step-by-step.
• Be mindful of negatives in substitutions.
• Break monomials into factors for better simplification.