mcq on algebraic expressions for class

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Important Algebra Questions with Step-

Important mcq on algebraic expressions for class 7

Below are 20 exam-style algebra questions with full step-by-step solutions written exactly as you would write them on paper. Squares are shown as x2, etc. Use this as a study sheet or paste directly into your website.

Quadratic Equations

1. Solve: x2 − 7x + 12 = 0

x2 − 7x + 12 = 0
(x − 3)(x − 4) = 0
So, x − 3 = 0 or x − 4 = 0
Therefore, x = 3 or x = 4

2. Solve: 2x2 − 3x − 2 = 0 (quadratic formula)

Given a = 2, b = −3, c = −2
x = [−b ± √(b2 − 4ac)] / (2a)
x = [3 ± √(9 − 4·2·(−2))] / (4)
x = [3 ± √(9 + 16)] / 4
x = [3 ± √25] / 4
Case 1: x = (3 + 5) / 4 = 8 / 4 = 2
Case 2: x = (3 − 5) / 4 = −2 / 4 = −1/2
Therefore, x = 2 or x = −1/2

3. Find roots of x2 + 4x + 4 = 0

x2 + 4x + 4 = 0
= (x + 2)(x + 2) = (x + 2)2
So, x + 2 = 0
Therefore, x = −2 (double root)

4. Solve: x2 − 9 = 0

x2 − 9 = 0
x2 = 9
x = ±3
Therefore, x = 3 or x = −3

5. Solve: x2 + 5x + 6 = 0

x2 + 5x + 6 = 0
= (x + 2)(x + 3) = 0
Therefore, x = −2 or x = −3

Linear Equations

6. Solve: 2x + 3 = 11

2x + 3 = 11
2x = 11 − 3 = 8
x = 8 / 2 = 4
Therefore, x = 4

7. Solve: 5x − 2 = 3x + 6

5x − 2 = 3x + 6
5x − 3x = 6 + 2
2x = 8
x = 8 / 2 = 4
Therefore, x = 4

8. Solve the system: 2x + 3y = 12 3x − y = 5

From 2nd: 3x − y = 5 ⇒ y = 3x − 5
Substitute in 1st: 2x + 3(3x − 5) = 12
2x + 9x − 15 = 12
11x − 15 = 12
11x = 27
x = 27 / 11
y = 3x − 5 = 3(27/11) − 5 = 81/11 − 55/11 = 26/11
Therefore, x = 27/11, y = 26/11

9. Solve: (x − 2)/3 = (x + 3)/5

5(x − 2) = 3(x + 3)
5x − 10 = 3x + 9
5x − 3x = 9 + 10
2x = 19
x = 19 / 2
Therefore, x = 19/2

10. Solve: 7x + 2 = 4x + 14

7x + 2 = 4x + 14
7x − 4x = 14 − 2
3x = 12
x = 12 / 3 = 4
Therefore, x = 4

Identities & Simplification

11. Prove: (x + y)2 = x2 + 2xy + y2

(x + y)2 = (x + y)(x + y)
= x·x + x·y + y·x + y·y
= x2 + xy + yx + y2
= x2 + 2xy + y2
Hence proved.

12. Simplify: (a + b)2 − (a − b)2

(a + b)2 = a2 + 2ab + b2
(a − b)2 = a2 − 2ab + b2
Subtract: (a2 + 2ab + b2) − (a2 − 2ab + b2)
= 4ab
Therefore, 4ab

13. Show: (x + 1)(x − 1) = x2 − 1

(x + 1)(x − 1) = x·x − x·1 + 1·x − 1·1
= x2 − x + x − 1
= x2 − 1
Hence proved.

14. Expand: (2x + 3y)2

Use (u + v)2 = u2 + 2uv + v2 with u = 2x, v = 3y
u2 = (2x)2 = 4x2
2uv = 2·(2x)·(3y) = 12xy
v2 = (3y)2 = 9y2
So, (2x + 3y)2 = 4x2 + 12xy + 9y2

15. If x + 1/x = 5, find x2 + 1/x2

(x + 1/x)2 = x2 + 2 + 1/x2
Given (x + 1/x) = 5 ⇒ (x + 1/x)2 = 25
So, x2 + 2 + 1/x2 = 25
x2 + 1/x2 = 25 − 2 = 23
Therefore, 23

Word Problems

16. A number exceeds its double by 9. Find the number.

Let the number = x
Statement: number exceeds its double by 9 ⇒ x = 2x + 9
x − 2x = 9 ⇒ −x = 9
x = −9
Therefore, x = −9
Note: If intended wording was “its double exceeds the number by 9”, equation would be 2x − x = 9 ⇒ x = 9.

17. Sum of two numbers is 27 and their difference is 5. Find the numbers.

Let numbers be x and y (x ≥ y)
x + y = 27
x − y = 5
Add: 2x = 32 ⇒ x = 16
Put back: 16 + y = 27 ⇒ y = 11
Therefore, numbers are 16 and 11

18. Father is 3 times as old as his son. After 10 years, father will be twice the son. Find their present ages.

Let son’s present age = s
Father’s present age = 3s
After 10 years: son = s + 10, father = 3s + 10
Given: 3s + 10 = 2(s + 10)
3s + 10 = 2s + 20
3s − 2s = 20 − 10 ⇒ s = 10
Father = 3s = 30
Therefore, son = 10 years, father = 30 years

19. The product of two consecutive integers is 156. Find the integers.

Let smaller integer = n, next = n + 1
n(n + 1) = 156
n2 + n − 156 = 0
Factor: (n − 12)(n + 13) = 0
So n = 12 or n = −13
If n = 12 ⇒ integers = 12 and 13
If n = −13 ⇒ integers = −13 and −12
Therefore, (12, 13) or (−13, −12)

20. Divide 600 into two parts such that one part is double the other.

Let smaller part = x, other part = 2x
x + 2x = 600
3x = 600 ⇒ x = 200
Other part = 2x = 400
Therefore, parts are 200 and 400

MCQ on Algebraic Expressions for Class 7

Here are 20 important Multiple Choice Questions (MCQs) on Algebraic Expressions for Class 7 with answers. Click on each question to reveal the correct answer.

Algebraic Expressions MCQs

  1. Which of the following is an algebraic expression?
    a) 45
    b) x + 5
    c) 1000
    d) 7 × 9

    Answer: b) x + 5

  2. In the expression 7x + 9, what is the coefficient of x?
    a) 7
    b) 9
    c) x
    d) 16

    Answer: a) 7

  3. Which of the following is a binomial?
    a) 2x
    b) 5y – 3
    c) x² + y² + z²
    d) 9

    Answer: b) 5y – 3

  4. The expression 3x² + 4x + 7 has how many terms?
    a) 1
    b) 2
    c) 3
    d) 4

    Answer: c) 3

  5. What is the degree of the expression 2x³ + 5x – 9?
    a) 1
    b) 2
    c) 3
    d) 4

    Answer: c) 3

  6. Which of these is a monomial?
    a) 7x
    b) x + y
    c) 3a + 2b
    d) a² + b²

    Answer: a) 7x

  7. What is the constant term in 4x² + 7x + 9?
    a) 4
    b) 7
    c) 9
    d) x

    Answer: c) 9

  8. The like terms in 3x + 5y + 7x are:
    a) 3x and 7x
    b) 5y and 7x
    c) 3x and 5y
    d) None

    Answer: a) 3x and 7x

  9. Which of these is a trinomial?
    a) x + 2
    b) x² + 3x + 4
    c) 7
    d) 2x

    Answer: b) x² + 3x + 4

  10. What is the coefficient of y in –8y?
    a) –8
    b) y
    c) 8
    d) –1

    Answer: a) –8

  11. Simplify: 3x + 4x.
    a) 12x
    b) 7x
    c) x
    d) 3x4x

    Answer: b) 7x

  12. Which expression represents “5 more than twice a number x”?
    a) 2x + 5
    b) x + 5
    c) 5x + 2
    d) 2x – 5

    Answer: a) 2x + 5

  13. What is the degree of 9a²b³?
    a) 2
    b) 3
    c) 5
    d) 6

    Answer: c) 5

  14. Which of these is not an algebraic expression?
    a) 7x – 3
    b) 2xy + 4
    c) 8 + 9
    d) x² + 1

    Answer: c) 8 + 9

  15. In the expression 2x² + 3xy – y², how many terms are there?
    a) 1
    b) 2
    c) 3
    d) 4

    Answer: c) 3

  16. Which of these is a polynomial?
    a) x² + 3/x
    b) √x + 2
    c) x³ – 2x² + 7
    d) 1/x

    Answer: c) x³ – 2x² + 7

  17. What is the constant in 12a – 4b + 7?
    a) 12
    b) –4
    c) 7
    d) a

    Answer: c) 7

  18. What is the coefficient of x² in 10x²y?
    a) 10y
    b) 10
    c) y
    d) x

    Answer: a) 10y

  19. The expression 2m + 3n – 5 is a:
    a) Monomial
    b) Binomial
    c) Trinomial
    d) Polynomial of 4 terms

    Answer: c) Trinomial

  20. If x = 2, what is the value of 3x + 4?
    a) 6
    b) 8
    c) 10
    d) 14

    Answer: d) 14

Why Practice Algebraic Expressions MCQs?

By solving these Class 7 Algebraic Expressions MCQs, students can strengthen their basics of algebra and prepare for exams. For more practice, visit our Math Quizzes Section.

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