Easy Level Worksheet
Part A: Subjective Questions - Very Short Answer (1 Mark Each)
Note: Answer each question carefully. Show all your work and explain your reasoning.
In this easy level, we'll learn the basics of algebraic expressions, variables, constants, and simple operations.
Let's start with the fundamental concepts of algebra!
1. Define an algebraic expression.
An algebraic expression is a mathematical phrase containing
Perfect! An algebraic expression combines numbers, variables, and operations like +, –, ×, ÷.
2. What is a variable?
A variable is a
Excellent! Variables like x, y, z can take different values.
3. What is a constant?
A constant is a
Examples of constants:
Great! Constants have fixed numerical values.
4. Write the algebraic expression for: "5 added to x".
Expression:
Correct! "Added to" means addition (+).
5. Write the algebraic expression for: "3 subtracted from y".
Expression:
Perfect! "Subtracted from" means we subtract 3 from y.
6. What are the terms in 7x + 5?
Term 1:
Term 2:
Number of terms:
Excellent! Terms are separated by + or – signs.
7. Identify the coefficient of x in 8x + 3.
Coefficient of x =
Correct! The coefficient is the number multiplying the variable.
8. Write the like terms in: 4x, 7y, –3x, 9.
Like terms:
Perfect! Like terms have the same variable with the same power.
9. Simplify: 3x + 2x.
3x + 2x =
Great! Add the coefficients: 3 + 2 = 5.
10. Identify the number of terms in 5x + 3y – 4.
Number of terms =
The terms are:
Excellent! Count all parts separated by + or – signs.
Drag each item to its correct category:
Part A: Section B – Short Answer Questions (2 Marks Each)
1. Write an algebraic expression for: (a) The sum of twice a number and 7. (b) 5 subtracted from thrice a number.
(a) Let the number be
Twice the number =
Expression =
Perfect! "Twice" means multiply by 2, then add 7.
(b) Let the number be
Thrice the number =
Expression =
Excellent! "Thrice" means multiply by 3, then subtract 5.
2. Simplify: 2x + 5 + 3x + 7.
Combine like terms with x: 2x + 3x =
Combine constants: 5 + 7 =
Simplified expression =
Great! Group like terms together and simplify.
3. Add: (4x + 3) and (5x + 2).
(4x + 3) + (5x + 2)
Combine x terms: 4x + 5x =
Combine constants: 3 + 2 =
Result =
Perfect! Add like terms separately.
4. Subtract: (3x + 2y) from (7x + 5y).
(7x + 5y) – (3x + 2y)
Subtract x terms: 7x – 3x =
Subtract y terms: 5y – 2y =
Result =
Excellent! Remember to subtract each like term.
5. Find the value of 2x + 3 when x = 4.
Substitute x =
2(4) + 3 =
=
Great! Substitute and calculate step by step.
6. Identify constants, variables, and coefficients in: 5x² + 3x + 2.
Variables:
Coefficients:
Constant:
Perfect! You've identified all components correctly.
7. Write the expression for: (a) Perimeter of a square = 4a (b) Perimeter of rectangle = 2(l + b)
(a) If side = a, Perimeter =
Correct! Square has 4 equal sides.
(b) If length = l, breadth = b
Perimeter =
Excellent! Rectangle has 2 lengths and 2 breadths.
8. Simplify: (x + 5) + (x + 3).
Remove brackets: x + 5 + x + 3
Combine x terms: x + x =
Combine constants: 5 + 3 =
Result =
Great! Combine like terms after removing brackets.
9. Write all like and unlike terms in: 4x, 7, 8y, –2x, 9.
Like terms:
Like terms:
Unlike term:
Perfect! Like terms have the same variable.
10. Simplify: 6x – 3x + 2y – y.
Combine x terms: 6x – 3x =
Combine y terms: 2y – y =
Result =
Excellent! Always combine like terms separately.
Part B: Objective Questions - Test Your Knowledge!
Answer these multiple choice questions:
6. Like terms in 3x, 4y, 5x are:
(a) 3x and 4y (b) 4y and 5x (c) 3x and 5x (d) All different
Correct! 3x and 5x are like terms because they have the same variable x.
7. Coefficient of y in 7y + 8 is:
(a) 7 (b) 8 (c) y (d) 15
Perfect! The coefficient is the number multiplied with the variable.
8. The degree of 5x² + 3x + 2 is:
(a) 1 (b) 2 (c) 3 (d) 0
Correct! The degree is the highest power of the variable, which is 2.
9. Simplify: 4x + 6x = ?
(a) 10x (b) 2x (c) 12x (d) 8x
Excellent! 4 + 6 = 10, so 4x + 6x = 10x.
10. The number of terms in x² + 3x + 5 is:
(a) 2 (b) 3 (c) 4 (d) 1
Perfect! The three terms are: x², 3x, and 5.
🎉 Fantastic Work! You've Mastered Basic Algebraic Expressions!
Here's what you learned:
Fundamental Concepts:
Algebraic Expression:
- A combination of variables, constants, and operations
- Example: 3x + 5, 2y – 7, 4a + 3b
Variable:
- A symbol (usually a letter) representing an unknown value
- Can take different values
- Examples: x, y, z, a, b
Constant:
- A fixed value that doesn't change
- Numbers like 5, –3, 0, 7.5
Coefficient:
- The number multiplied with a variable
- In 5x, the coefficient is 5
- In –3y, the coefficient is –3
Terms in Expressions:
- Parts of an expression separated by + or – signs
- Example: In 4x + 3y – 2
- Term 1: 4x
- Term 2: 3y
- Term 3: –2
- Each term can be a constant, variable, or both
Like Terms:
- Terms with the SAME variable raised to the SAME power
- Examples:
- 3x and 5x are like terms
- 2y and –7y are like terms
- 4x² and 6x² are like terms
- Unlike terms: 3x and 5y (different variables)
Basic Operations:
Addition:
- Combine like terms
- (3x + 4) + (2x + 5) = 5x + 9
Subtraction:
- Remove brackets and change signs
- (5x + 3) – (2x + 1) = 5x + 3 – 2x – 1 = 3x + 2
Simplification:
- Group like terms together
- Add or subtract coefficients
- Keep the variable part unchanged
Writing Expressions:
- "Sum" → addition (+)
- "Difference" → subtraction (–)
- "Product" → multiplication (×)
- "Twice" → multiply by 2
- "Thrice" → multiply by 3
- "More than" → add
- "Less than" → subtract
Substitution:
- Replace variable with given value
- Example: If x = 3, find 2x + 5
- 2(3) + 5 = 6 + 5 = 11
- Always follow order of operations
Common Mistakes to Avoid:
- Don't add unlike terms (3x + 2y ≠ 5xy)
- Remember signs when subtracting
- Coefficient of x is 1 (not 0)
- Keep track of negative signs
Algebraic expressions are the foundation of algebra - master these basics for success in mathematics!