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Mathematics

Algebra Basics: Variables, Expressions, and Patterns — Practice Worksheet

Introductory Algebra (variables, expressions, properties, perimeters, and patterns)
Date: July 25, 2026  •  Questions: 40  •  Estimated time: 35 minutes
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____ / 100
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Instructions: Read each question carefully and answer to the best of your ability. Show all working for word problems.
1. A symbol like k used to represent a changing quantity is called a variable. (1 pt)
True
False
2. The expression 4 + x represents 4 multiplied by x. (1 pt)
True
False
3. In the expression 9p - 6, 9 is a coefficient. (1 pt)
True
False
4. The perimeter of a square with side s equals 2s. (1 pt)
True
False
5. If a = 3, then 2a + 1 equals 7. (1 pt)
True
False
6. The distributive property lets us rewrite 7(m + 2) as 7m + 14. (1 pt)
True
False
7. For whole-number n, the product 3n can be an even number only. (1 pt)
True
False
8. The expressions y + y + y and 3y are equivalent. (1 pt)
True
False
9. If each box has q pens, then 5 boxes contain q + 5 pens. (1 pt)
True
False
10. For any numbers a and b, a + b = b + a is an example of the associative property. (1 pt)
True
False

11. Which expression represents “12 more than a number t”? (2 pts)
A. t + 12
B. 12t
C. t - 12
D. 12 - t
12. “Subtract 9 from the product of m and n” is written as: (2 pts)
A. 9mn
B. mn - 9
C. m - 9n
D. 9 - mn
13. Which is equivalent to 6(x + 4)? (2 pts)
A. 6x + 24
B. 10x
C. 6x + 4
D. 24x
14. Find the value of 3x - 5 when x = 4. (2 pts)
A. 7
B. 12
C. -1
D. 17
15. Identify the property: (p + q) + r = p + (q + r). (2 pts)
A. Commutative of addition
B. Associative of addition
C. Distributive over addition
D. Additive identity
16. Perimeter of a rectangle with length L and breadth B is: (2 pts)
A. L + B
B. 2(L + B)
C. 4(L + B)
D. LB
17. If each packet holds 25 cookies, how many cookies are in k packets? (2 pts)
A. k + 25
B. 25 - k
C. 25k
D. 25/k
18. Which inequality represents “x is at least 7”? (2 pts)
A. x = 7
B. x > 7
C. x >= 7
D. x < 7
19. Which pair could represent two consecutive even integers? (2 pts)
A. 2n and 2n + 1
B. 2n and 2n + 2
C. n and n + 1
D. 2n - 1 and 2n + 1
20. If s is the side length of a square, which expression gives its area? (2 pts)
A. 4s
B. s + s
C. s^2
D. 2s

21. A number that does not change in value is called a   . (2 pts)
22. The expression for “7 multiplied by n” is   . (2 pts)
23. The coefficient of x in 5x + 2 is   . (2 pts)
24. The perimeter of a square with side a is   . (2 pts)
25. The expression “the sum of y and 11” can be written as   . (2 pts)
26. When like terms are combined, 4k + 3k becomes   . (2 pts)
27. If x = 2 and y = 3, then x + 2y equals   . (2 pts)
28. Using the distributive property, 9(t + 1) is rewritten as   . (2 pts)
29. “r exceeds s” can be expressed as   . (2 pts)
30. If each letter in a pattern uses 4 matchsticks, the total for n letters is   . (2 pts)

31. A student buys 3 notebooks at p rupees each and one pen for 12 rupees. Write an expression for the total cost and find the amount when p = 18. (5 pts)
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32. The side length of an equilateral triangle is x cm. Write a rule for its perimeter and evaluate it for x = 9 cm. (5 pts)
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33. There are b bags with 6 apples in each. If 4 apples are eaten, how many apples remain? Also find the number when b = 7. (5 pts)
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34. A taxi charges a base fare of 50 rupees plus 15 rupees per kilometer for d kilometers. Write the expression for the fare and compute it for d = 8. (5 pts)
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35. Let the smaller of two consecutive odd integers be 2n + 1. Their sum is 40. Find n and the two integers. (5 pts)
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36. A rectangular garden has width w meters and length that is 3 meters more than the width. Write the perimeter in terms of w and find it when w = 10. (5 pts)
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37. Evaluate 4a + 2(3a - 5) for a = 7, showing the use of the distributive property. (5 pts)
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38. A jar has 500 mL of juice. After pouring 4 glasses of g mL each, how much juice is left? Also find the amount left when g = 120. (5 pts)
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39. A pattern uses M(n) = 5n + 2 matchsticks for the nth figure. How many matchsticks are needed for the 12th figure? (5 pts)
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40. On a class trip, each of x students pays 320 rupees. The bus costs 4500 rupees. Write an expression for the money left after paying for the bus and evaluate it for x = 20. (5 pts)
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