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Introduction Quiz - CBSE Class 7 Mathematics

Free practice quiz: Introduction (CBSE Class 7 Mathematics). 30 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This CBSE Class 7 Mathematics practice quiz has 30 multiple-choice questions on Introduction, and 30 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

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Parts of an Algebraic Expression

  • A variable is a letter that can take different values. A constant is a fixed number with no variable.
  • Terms are the parts joined by + or -. The number multiplied with a variable is its coefficient.
  • If a term has no number in front, like m, its coefficient is 1.
Coefficient of a term
\[k\,x \;\Rightarrow\; k \text{ is the coefficient of } x\]
Constant term
\[\text{a term with no variable, e.g. } 6 \text{ in } p + 6\]

Common mistake: Calling the constant term the coefficient, or forgetting that a lone variable like y has coefficient 1, not 0.

Like Terms and Simplifying

  • Like terms have the same variables raised to the same powers. Only their coefficients may differ.
  • To simplify, add or subtract the coefficients of like terms. Combine constants separately.
  • To multiply a bracket by a number, multiply every term inside the bracket.
Combining like terms
\[a\,x + b\,x = (a+b)\,x\]
Subtracting like terms
\[a\,x - b\,x = (a-b)\,x\]
Distributive rule
\[k\,(m + n) = k\,m + k\,n\]

Common mistake: Adding unlike terms together, for example writing 6p + 2 as 8p, or treating p and p^2 as like terms.

Writing Expressions from Words

  • Sum means add, difference means subtract, product means multiply, and quotient means divide.
  • Twice means multiply by 2, thrice means multiply by 3. Increased by means add. Decreased by means subtract.
  • For differences and quotients, order matters. Read carefully which quantity comes first.
Sum and difference
\[m + n, \quad m - n\]
Product and quotient
\[m \times n = mn, \quad \frac{m}{n}\]
Thrice n subtracted from m
\[m - 3n\]

Common mistake: Reversing the order: 'n less than m' means m - n, not n - m.

Value of Expressions and Degree

  • To find the value, replace each variable with the given number and then calculate.
  • Follow the order of operations: powers first, then multiplication, then addition and subtraction.
  • The degree of a polynomial in one variable is the highest power of that variable. f(c) means put c in place of x.
Function notation
\[f(x) = p\,x + q \;\Rightarrow\; f(c) = p\,c + q\]
Power before multiplication
\[k\,x^{2} = k \times (x \times x)\]
Degree of a polynomial
\[\text{degree} = \text{highest power of } x\]

Common mistake: Squaring the coefficient too, i.e. treating k x^2 as (kx)^2, or adding the powers to find the degree.

Solving Simple Linear Equations

  • An equation says two sides are equal. Do the same operation on both sides to keep the balance.
  • Bring variable terms to one side and constants to the other, then divide by the coefficient.
Undo addition
\[x + p = q \;\Rightarrow\; x = q - p\]
Undo multiplication
\[k\,x = q \;\Rightarrow\; x = \frac{q}{k}\]
Variables on both sides
\[a\,x + b = c\,x + d \;\Rightarrow\; (a - c)\,x = d - b\]

Common mistake: Forgetting to change the sign when moving a term to the other side, e.g. keeping +p as +p.

Exam tips

Beta: made with AI and checked by a second AI. A teacher has not reviewed it yet.

Sample questions

  1. What is the value of the expression 3x + 2 for x = 1?

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    Answer: B. 5

    Substituting x = 1 into 3x + 2 gives 3(1) + 2 = 3 + 2 = 5.

  2. What is the degree of the polynomial 5x^3 + 4x^2 + 2?

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    Answer: A. 3

    The degree of a polynomial is the highest power of the variable. The highest power in 5x^3 is 3.

  3. What is the value of x in the equation 2x + 3 = 11?

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    Answer: C. 4

    Subtract 3 from both sides to get 2x = 8, then divide by 2; x = 4.

  4. Identify the like terms in the list: 3y, 5x, 7y, 9.

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    Answer: A. 3y and 7y

    Like terms have the same variable raised to the same power. Here, 3y and 7y both have the variable y.

  5. Which expression is equal to 15 - 5y?

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    Answer: A. 5(3 - y)

    The expression 5(3 - y) is equivalent to 15 - 5y using the distributive property.

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More questions in this quiz

Answers and explanations are in the full quiz.

  1. Identify the coefficient in the expression: 5x + 3.
  2. What is the variable in the expression: y - 7?
  3. What is the coefficient of x in the expression 4x + 7?
  4. Simplify the expression 2x + 3x.
  5. If a = 3, what is the value of 2a + 4?
  6. Which expression represents the sum of a and b?
  7. What do you call a term that does not contain a variable?
  8. If x = 2, what is the value of 4x^2 + 1?
  9. What is the combined like terms of the expression 7x + 3 - 2x + 4?
  10. What is the result of multiplying the expression (x + 1) by 3?
  11. If f(x) = 5x + 2, find f(3).
  12. If 3a + 2 = 14, what is the value of a?
  13. Which expression represents the difference of a and b?
  14. If 5x - 3 = 2x + 9, what is the value of x?
  15. What is the sum of 2x and 3x?
  16. If a = 2, what is the value of the expression 4a?
  17. What happens to an expression if you multiply it by 1?
  18. Find the expression for: 'a decreased by twice b'.
  19. The product of a number and 0 is:
  20. Choose the expression that accurately represents 'x divided by 5'.
  21. Find the expression for: 'twice the sum of x and 3'.
  22. If x = 3 and y = 4, evaluate the expression 2x + 3y.
  23. Find the like terms in the expression: 3x^2, 5xy, 7x^2, -2xy.
  24. If z = 5, what is the value of the expression 4z^2?
  25. Express 'thrice the difference between a and b' as an algebraic expression.

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