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About Algebraic Expressions — Class 7 ICSE

Form, simplify, and evaluate algebraic expressions with multiple terms and variables. This topic is part of the ICSE Class 7 mathematics syllabus (chapter: Chapter 5). On this page you can practice 59 questions across three difficulty levels — 20 easy, 20 medium, and 19 hard — each with a visual step-by-step solution, plus a timed 35-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

What you'll learn in Algebraic Expressions

  • Introduction to Algebraic Expressions: The Language of Algebra
  • Components of Expressions: Terms, Coefficients, and Types
  • Like and Unlike Terms: Combining Expressions
  • Operations on Expressions: Multiplication and Evaluation
  • Summary and Next Steps: Mastering Algebraic Expressions

Interactive lesson · about 15 minutes · checkpoint question after every unit

Algebraic Expressions — solved examples for Class 7 ICSE

Example 1easy

Which of the following statements about algebraic expressions is TRUE?
  1. A)A) A constant can change its value.
  2. B)B) A variable has a fixed numerical value.
  3. C)C) In the expression 5x + 7, 'x' is a variable and '7' is a constant.
  4. D)D) Only letters of the alphabet can be variables.

Step-by-step solution

  1. Variables are symbols (usually letters) that represent unknown values that can change. Constants are numbers that have fixed numerical values.
  2. Option A is false because constants have fixed values. Option B is false because variables represent values that can change.
  3. Option D is false as symbols other than letters can sometimes represent variables, though letters are most common. Option C correctly identifies 'x' as a variable (unknown value) and '7' as a constant (fixed value).

Answer: C) In the expression 5x + 7, 'x' is a variable and '7' is a constant.

Example 2medium

In the algebraic expression `5x²y - 3xy + 7`, identify the constant term.
  1. A)A) 5
  2. B)B) -3
  3. C)C) 7
  4. D)D) xy

Step-by-step solution

  1. An algebraic expression consists of terms. Terms are separated by addition or subtraction signs.
  2. In the expression `5x²y - 3xy + 7`, the terms are `5x²y`, `-3xy`, and `7`.
  3. A constant term is a term that does not contain any variables. Out of the given terms, `7` is a pure number and does not have any variables associated with it.
  4. Therefore, the constant term is `7`.

Answer: C) 7

Example 3hard

Simplify the algebraic expression: 5x - [3y - {2x - (4y - x) + 7x} - 2y]
  1. A)15x - 4y
  2. B)-5x + 8y
  3. C)-5x + 4y
  4. D)15x - 5y

Step-by-step solution

  1. Simplify the innermost parenthesis (4y - x): 5x - [3y - {2x - 4y + x + 7x} - 2y]
  2. Combine like terms within the curly braces: 5x - [3y - {10x - 4y} - 2y]
  3. Remove the curly braces, distributing the negative sign: 5x - [3y - 10x + 4y - 2y]
  4. Combine like terms within the square bracket: 5x - [-10x + 5y]
  5. Remove the square bracket, distributing the negative sign: 5x + 10x - 5y = 15x - 5y

Answer: 15x - 5y

Practice questions on Algebraic Expressions

  1. Q1.easy

    In the algebraic expression `3x²y - 7xy + 5x - 2`, what is the coefficient of the term `xy`?
    1. A)A) 3
    2. B)B) -7
    3. C)C) 5
    4. D)D) -2
    Show answer

    Answer: B) -7

    Hint: Remember that the coefficient is the numerical factor, including its sign, that multiplies the variable part of a term.

  2. Q2.easy

    If 'p' represents the price of one chocolate bar, and 'q' represents the price of one juice box, which expression correctly represents the total cost of 4 chocolate bars and 3 juice boxes?
    1. A)A) 4p × 3q
    2. B)B) 4p + 3q
    3. C)C) p + q + 4 + 3
    4. D)D) 7pq
    Show answer

    Answer: B) 4p + 3q

    Hint: Think about how to find the cost of multiple items of the same type, and then how to find the total cost of different types of items.

  3. Q3.easy

    Which of the following pairs of terms are LIKE terms?
    1. A)A) `3x` and `3y`
    2. B)B) `5xy` and `5x`
    3. C)C) `7a²b` and `2ab²`
    4. D)D) `4p²q` and `-p²q`
    Show answer

    Answer: D) `4p²q` and `-p²q`

    Hint: Like terms must have exactly the same variable parts, including the same exponents for each variable.

  4. Q4.medium

    Which of the following algebraic expressions is a binomial?
    1. A)A) `3x²y`
    2. B)B) `a + b + c`
    3. C)C) `12`
    4. D)D) `4p - 7q`
    Show answer

    Answer: D) `4p - 7q`

    Hint: Recall the definition of a binomial: it's an algebraic expression with exactly two unlike terms.

  5. Q5.medium

    From the following terms, identify the pair of like terms: `(3x, 5y, -2x, 7xy)`
    1. A)A) `3x` and `-2x`
    2. B)B) `5y` and `7xy`
    3. C)C) `3x` and `5y`
    4. D)D) `-2x` and `7xy`
    Show answer

    Answer: A) `3x` and `-2x`

    Hint: Like terms are terms that have the same variables raised to the same powers. Only their numerical coefficients can be different.

  6. Q6.medium

    Simplify the algebraic expression: `(4a + 3b) + (2a - 5b)`
    1. A)A) `6a + 8b`
    2. B)B) `6a - 2b`
    3. C)C) `2a - 2b`
    4. D)D) `6a + 2b`
    Show answer

    Answer: B) `6a - 2b`

    Hint: Remember to combine only the like terms. Group the 'a' terms together and the 'b' terms together.

  7. Q7.hard

    A rectangular field has a length (L) which is 5 meters more than twice its width (W). If the width is represented by 'w' meters, and a 3-meter wide path is built *inside* the field along its perimeter, what is the area of the remaining field *without* the path?
    1. A)2w² + 5w - 12
    2. B)2w² - 13w + 6
    3. C)18w + 24
    4. D)12w - 12
    Show answer

    Answer: 2w² - 13w + 6

    Hint: First, express the original length in terms of 'w'. Then, calculate the new dimensions of the field after the path is built inside, and finally find its area.

  8. Q8.hard

    Consider two algebraic expressions, A and B. Which of the following statements is always true?
    1. A)The sum of A and B always has a greater degree than A or B.
    2. B)The difference between A and B (A - B) is always a binomial if A is a trinomial and B is a monomial.
    3. C)If A is a monomial and B is a monomial, then A × B is always a monomial.
    4. D)The value of A + B is always greater than the value of A when B is a positive constant.
    Show answer

    Answer: If A is a monomial and B is a monomial, then A × B is always a monomial.

    Hint: Test each statement with simple examples. Remember the definitions of monomial, binomial, trinomial, and degree.

  9. Q9.hard

    Rishabh was simplifying the expression 3(x + 2y) - 2(y - 3x) + 5x. His steps are:
    Step 1: 3x + 6y - 2y - 6x + 5x
    Step 2: 3x - 6x + 5x + 6y - 2y
    Step 3: (3 - 6 + 5)x + (6 - 2)y
    Step 4: 2x + 4y
    Which step contains the first error?
    1. A)Step 2
    2. B)Step 3
    3. C)Step 1
    4. D)Step 4
    Show answer

    Answer: Step 1

    Hint: Pay close attention to the distributive property, especially when a negative sign is outside a parenthesis.

These are 9 of the 59 questions available for Algebraic Expressions. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.