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Algebra Basics Worksheet
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Algebra Basics Worksheet
📚 Part 1: Key Terms and Concepts
Key definitions:
Variable: A letter or symbol that represents an unknown or changing number.
Formula: A rule written using symbols and operations to show how quantities are related.
Term: A single number, variable, or product of numbers and variables.
Expression: A combination of numbers, variables, and operations without an equals sign.
Equation: A mathematical statement showing that two expressions are equal, using an equals sign.
1. Match each algebra term with its correct definition:
Variable
Expression
Equation
Term
A mathematical statement with an equals sign
A letter that represents an unknown number
A combination of numbers, variables and operations
A single number, variable, or product of numbers and variables
2. Which of these are variables?
x
5
y
+
a
3. How many terms are in the expression 3x + 7 - 2y?
2 terms
3 terms
4 terms
5 terms
4. Which of these is an equation?
4x + 3
2y - 7 = 11
5a + 2b - 1
x + y
13. Identify the variable in the expression 8n + 3.
14. Identify the coefficient of x in the expression 12x - 5.
15. Identify the constant in the expression 7p + 9.
16. How many terms are in the expression 4a + 3b - 6?
17. Which expression has exactly two terms?
5x + 2
3a + 4b - 1
9
x + y + z
18. Is 6m + 2 = 20 an expression or an equation? Explain briefly.
✏️ Part 2: Writing Expressions and Equations
5. Write an expression for "5 more than a number x":
6. Write an expression for "3 times a number y, minus 8":
7. The cost of hiring a car is $50 plus $25 per day. Write a formula for the total cost (C) after d days:
8. A rectangle has length (x + 4) metres and width 6 metres. Write an expression for its perimeter:
19. Write an expression for "7 less than a number n".
20. Write an expression for "twice a number t plus 5".
21. Write an expression for "the sum of a and 14".
22. Write an expression for "the difference between 20 and q".
23. Write an equation for "a number r increased by 9 is 16".
24. The formula for the perimeter of a rectangle is P = 2l + 2w. Find P when l = 8 cm and w = 3 cm.
25. The formula for the area of a rectangle is A = lw. Write the formula using length l and width w, then find the area when l = 7 m and w = 4 m.
26. A taxi fare is $4 plus $2 for each kilometre k. Write a formula for the total fare F.
27. A cinema ticket costs $9. Write a formula for the cost C of buying n tickets.
🔢 Part 3: Simplifying Expressions
28. Simplify: 3x + 5x
29. Simplify: 9a - 4a
30. Simplify: 6y + 2 + 3y
31. Simplify: 8m + 5 - 3m + 2
32. Simplify: 4p + 7q + 2p
33. Simplify: 10b - 3 + 2b + 8
34. Simplify: 5(x + 2) by expanding the brackets.
35. Simplify: 3(2n + 4).
36. Simplify: 2r + 3s + 5r - s.
🧮 Part 4: Solving Simple Equations
9. Solve: x + 7 = 15
10. Solve: 3y = 21
11. Solve: 2x + 5 = 17
12. If the perimeter of a square is 4x + 8 = 28 centimetres, find the value of x and the length of each side:
37. Solve: a - 6 = 11
38. Solve: b + 13 = 25
39. Solve: 5c = 35
40. Solve: d ÷ 4 = 6
41. Solve: 4m + 3 = 19
42. Solve: 7n - 5 = 30
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