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Algebra Basics
Introduction to variables, expressions, and basic equations
Class VI
Mathematics
8 Questions
All Questions
8 questions available
MCQ
1 marks
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
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
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
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
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
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
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
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 ✓