Advanced Algebraic Expressions
Class VII Mathematics - Complex Algebra & Equations
4
MCQ Questions
4
Short Questions
2
Long Questions
90
Minutes
100
Max Marks
Question Type:
Difficulty:
MCQ
Easy
Question 1
What is the coefficient of x² in the expression 3x³ - 5x² + 2x - 7?
A. 3
B. -5
C. 2
D. -7
Answer:
The coefficient of x² is -5. In an algebraic expression, the coefficient is the numerical factor of a term. Here, -5 is multiplied by x².
MCQ
Easy
Question 2
Which of the following is a binomial?
A. 2x³ + 3x² - x + 5
B. x² + 3x
C. 7x
D. x³ + 2x² - x + 4 - 2
Answer:
x² + 3x is a binomial because it has exactly two terms. A binomial is an algebraic expression with two terms connected by + or - signs.
MCQ
Medium
Question 3
If x = 2, what is the value of 3x² - 4x + 1?
A. 5
B. 7
C. 9
D. 11
Answer:
Substituting x = 2: 3(2)² - 4(2) + 1 = 3(4) - 8 + 1 = 12 - 8 + 1 = 5.
MCQ
Medium
Question 4
What is the degree of the polynomial 5x⁴ - 3x² + 7x - 2?
A. 2
B. 3
C. 4
D. 5
Answer:
The degree of a polynomial is the highest power of the variable. Here, the highest power of x is 4, so the degree is 4.
SHORT
Easy
Question 5
Add the following algebraic expressions: (3x² + 2x - 5) + (x² - 4x + 3)
Answer:
To add algebraic expressions, we combine like terms:
(3x² + 2x - 5) + (x² - 4x + 3)
= 3x² + x² + 2x - 4x - 5 + 3
= 4x² - 2x - 2
Therefore, the sum is 4x² - 2x - 2.
SHORT
Medium
Question 6
Subtract (2x² - 3x + 1) from (5x² + x - 4)
Answer:
To subtract, we change the signs of the second expression and add:
(5x² + x - 4) - (2x² - 3x + 1)
= 5x² + x - 4 - 2x² + 3x - 1
= 5x² - 2x² + x + 3x - 4 - 1
= 3x² + 4x - 5
Therefore, the result is 3x² + 4x - 5.
SHORT
Medium
Question 7
Multiply: 3x(2x² - 4x + 5)
Answer:
Using the distributive property:
3x(2x² - 4x + 5)
= 3x × 2x² - 3x × 4x + 3x × 5
= 6x³ - 12x² + 15x
Therefore, the product is 6x³ - 12x² + 15x.
SHORT
Medium
Question 8
Factorize: x² + 7x + 12
Answer:
To factorize x² + 7x + 12, we need two numbers that multiply to 12 and add to 7.
These numbers are 3 and 4 (since 3 × 4 = 12 and 3 + 4 = 7).
Therefore: x² + 7x + 12 = (x + 3)(x + 4)
Verification: (x + 3)(x + 4) = x² + 4x + 3x + 12 = x² + 7x + 12 ✓
LONG
Hard
Question 9
Solve the equation 3(x + 2) - 2(x - 1) = 15 and verify your answer.
Answer:
Step 1: Expand the brackets
3(x + 2) - 2(x - 1) = 15
3x + 6 - 2x + 2 = 15
Step 2: Combine like terms
3x - 2x + 6 + 2 = 15
x + 8 = 15
Step 3: Solve for x
x = 15 - 8
x = 7
Step 4: Verification
Substitute x = 7 in the original equation:
LHS = 3(7 + 2) - 2(7 - 1)
= 3(9) - 2(6)
= 27 - 12
= 15
RHS = 15
Since LHS = RHS, our answer x = 7 is correct.
LONG
Hard
Question 10
A rectangular garden has length (2x + 3) meters and width (x - 1) meters. If the perimeter is 28 meters, find the value of x and the dimensions of the garden.
Answer:
Given information:
- Length = (2x + 3) meters
- Width = (x - 1) meters
- Perimeter = 28 meters
Step 1: Write the perimeter formula
Perimeter = 2(Length + Width)
28 = 2[(2x + 3) + (x - 1)]
Step 2: Simplify inside the brackets
28 = 2[2x + 3 + x - 1]
28 = 2[3x + 2]
28 = 6x + 4
Step 3: Solve for x
28 - 4 = 6x
24 = 6x
x = 4
Step 4: Find the dimensions
Length = 2x + 3 = 2(4) + 3 = 8 + 3 = 11 meters
Width = x - 1 = 4 - 1 = 3 meters
Step 5: Verification
Perimeter = 2(11 + 3) = 2(14) = 28 meters ✓
Therefore, x = 4, length = 11 meters, and width = 3 meters.