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Algebra Basics

Introduction to variables, expressions, and basic equations

Class VI
Mathematics
8 Questions
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All Questions

8 questions available

MCQ
1 marks
Question 1
What is the coefficient of x in the expression 5x + 3?

Options:

a) 5
b) 3
c) 8
d) x

Answer:

The coefficient is the number that multiplies the variable. In 5x + 3, the coefficient of x is 5.
MCQ
1 marks
Question 2
Simplify: 3x + 2x

Options:

a) 5x
b) 6x
c) 5x²
d) 5

Answer:

When adding like terms, add the coefficients: 3x + 2x = (3 + 2)x = 5x.
MCQ
1 marks
Question 3
If x = 4, what is the value of 2x + 1?

Options:

a) 7
b) 8
c) 9
d) 10

Answer:

Substitute x = 4 into 2x + 1: 2(4) + 1 = 8 + 1 = 9.
SHORT
2 marks
Question 4
Explain the difference between a variable and a constant with examples.

Answer:

Variable: A symbol that represents an unknown number and can change. Examples: x, y, a, b

Constant: A fixed number that does not change. Examples: 5, -3, 0.5, π

In the expression 3x + 7, x is a variable and 3, 7 are constants.
SHORT
2 marks
Question 5
What are like terms? Give three examples.

Answer:

Like terms are terms that have the same variable raised to the same power.

Examples:
1. 3x and 5x (both have variable x)
2. 2y² and -7y² (both have y²)
3. 4 and 9 (both are constants)

Like terms can be combined by adding or subtracting their coefficients.
SHORT
2 marks
Question 6
Solve for x: x + 5 = 12

Answer:

To solve x + 5 = 12:

Step 1: Subtract 5 from both sides
x + 5 - 5 = 12 - 5

Step 2: Simplify
x = 7

Check: 7 + 5 = 12 ✓
LONG
5 marks
Question 7
Explain the basic rules of algebra and demonstrate with examples.

Answer:

Basic Rules of Algebra:

1. Commutative Property:
   Addition: a + b = b + a
   Example: 3 + x = x + 3
   Multiplication: a × b = b × a
   Example: 4x = x × 4

2. Associative Property:
   Addition: (a + b) + c = a + (b + c)
   Example: (2 + x) + 3 = 2 + (x + 3)
   Multiplication: (a × b) × c = a × (b × c)
   Example: (2x) × 3 = 2 × (3x)

3. Distributive Property:
   a(b + c) = ab + ac
   Example: 3(x + 2) = 3x + 6

4. Identity Property:
   Addition: a + 0 = a
   Multiplication: a × 1 = a

5. Inverse Property:
   Addition: a + (-a) = 0
   Multiplication: a × (1/a) = 1 (when a ≠ 0)
LONG
5 marks
Question 8
Solve these equations step by step: (a) 2x + 3 = 11, (b) 5x - 7 = 18

Answer:

Solution:

(a) 2x + 3 = 11

Step 1: Subtract 3 from both sides
2x + 3 - 3 = 11 - 3
2x = 8

Step 2: Divide both sides by 2
2x ÷ 2 = 8 ÷ 2
x = 4

Check: 2(4) + 3 = 8 + 3 = 11 ✓

(b) 5x - 7 = 18

Step 1: Add 7 to both sides
5x - 7 + 7 = 18 + 7
5x = 25

Step 2: Divide both sides by 5
5x ÷ 5 = 25 ÷ 5
x = 5

Check: 5(5) - 7 = 25 - 7 = 18 ✓