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Class 6 Mathematics: Basic Algebra

Variables, constants, algebraic expressions, rule formulation from patterns, and elementary linear equations.

Class 6 Mathematics 5 Generated Practice Exercises NCERT Exercise Solutions

⚡ Key Formulas & Core Relations for Basic Algebra

Linear equation format: ax + b = c
Solution of equation: x = (c - b) / a (for a ≠ 0)
Perimeter rule for n-sided regular polygon: P = n × s

NCERT Textbook Exercise Solutions

1 Solutions
Exercise 11.5 - Q2

Textbook Exercise Problem

Check whether the value given in the brackets is a solution to the given equation: 7n + 5 = 19 (n = 2).

Step-by-Step Verified Solution:

  1. Step 1: Substitute n = 2 into LHS of the equation.
  2. Step 2: LHS = 7(2) + 5 = 14 + 5 = 19.
  3. Step 3: RHS is given as 19.
  4. Step 4: Since LHS = RHS = 19, n = 2 satisfies the equation.
Final Answer: Yes, n = 2 is a valid solution.
Key Concept / Exam Strategy: A value is a root/solution if and only if LHS evaluates identically to RHS upon substitution.

5 AI-Generated Chapter Exercises (Foundation to HOTS)

5 Problems with Full Steps
Generated Exercise #1 Foundation
Question: Write an algebraic expression for: "7 added to thrice of a number y".
Core Concept Tested: Translating verbal statements to algebraic expressions
Mentor Hint: Thrice of y is 3y; added to 7 gives 3y + 7.

Step-by-Step Solution:

  1. Step 1: Thrice of y means 3 × y = 3y.
  2. Step 2: Adding 7 yields 3y + 7.
Verified Answer: 3y + 7
Generated Exercise #2 Intermediate
Question: Solve the equation: 5m - 8 = 27.
Core Concept Tested: Transposition method in single-variable linear equations
Mentor Hint: Transpose -8 to RHS as +8, then divide by 5.

Step-by-Step Solution:

  1. Step 1: 5m = 27 + 8.
  2. Step 2: 5m = 35.
  3. Step 3: m = 35 / 5 = 7.
Verified Answer: m = 7
Generated Exercise #3 Intermediate
Question: Cadets are marching in a parade with 5 cadets in each row. Write the rule that gives the number of cadets for n rows.
Core Concept Tested: Pattern generalization using algebraic variables
Mentor Hint: Multiply cadets per row by number of rows.

Step-by-Step Solution:

  1. Step 1: For 1 row = 5 cadets.
  2. Step 2: For 2 rows = 5 × 2 = 10 cadets.
  3. Step 3: For n rows = 5 × n = 5n cadets.
Verified Answer: Total Cadets = 5n
Generated Exercise #4 JEE-NEET Foundation
Question: The present age of a father is 4 times the age of his son. If the sum of their ages is 50 years, find the present age of the son.
Core Concept Tested: Word problems on linear equations in one variable
Mentor Hint: Let son age be x, then father age is 4x. Their sum is 50.

Step-by-Step Solution:

  1. Step 1: Let son age = x years. Father age = 4x years.
  2. Step 2: Equation: x + 4x = 50 => 5x = 50.
  3. Step 3: x = 50 / 5 = 10 years.
Verified Answer: Son is 10 years old (Father is 40 years old)
Generated Exercise #5 Advanced HOTS
Question: If 2p/3 + 5 = 17, find the value of (p² - 4).
Core Concept Tested: Two-step equation solving followed by polynomial expression evaluation
Mentor Hint: Solve for p first, then substitute p into p² - 4.

Step-by-Step Solution:

  1. Step 1: 2p/3 = 17 - 5 = 12.
  2. Step 2: 2p = 12 × 3 = 36 => p = 36 / 2 = 18.
  3. Step 3: Evaluate p² - 4: (18)² - 4 = 324 - 4 = 320.
Verified Answer: 320