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Mathematics

Class 6 Algebra — Variables, Expressions, and Equations

Intro to Algebra: variables, expressions, equations, LHS/RHS, and simple properties
Date: August 16, 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. In algebra, letters can stand for numbers whose values are not fixed. (1 pt)
True
False
2. The expression 3k + 7 is an equation. (1 pt)
True
False
3. In an equation, the equality sign separates the LHS and RHS. (1 pt)
True
False
4. If a and b are numbers, then a + b is always equal to b + a. (1 pt)
True
False
5. The number of days in a week is a variable. (1 pt)
True
False
6. To check if a number is a solution of x − 4 = 9, we can substitute and see if both sides are equal. (1 pt)
True
False
7. The expression 2n has the same value no matter what n is. (1 pt)
True
False
8. If each shape uses 5 matchsticks, then repeating it t times needs 5 + t matchsticks. (1 pt)
True
False
9. If x = 3, then the value of 2x + 1 is 7. (1 pt)
True
False
10. The two sides of an equation are called RHS and RHE. (1 pt)
True
False

11. Which of the following is an equation? (2 pts)
A. y + 8 = 20
B. 7p − 3
C. m/5
D. 9 + q
12. In the formula P = 2(l + b) for a rectangle, which of the following are variables? (2 pts)
A. Only P
B. l and b only
C. l, b and P
D. None of these
13. The statement a + b = b + a shows which property? (2 pts)
A. Commutative property of addition
B. Distributive property
C. Associative property of subtraction
D. Identity property of multiplication
14. If n stands for the number of times a design is repeated and each design uses 4 sticks, which expression gives the total sticks needed? (2 pts)
A. 4n
B. n + 4
C. n − 4
D. 4 − n
15. For x = −2, what is the value of 5 − x? (2 pts)
A. 3
B. 7
C. −7
D. −3
16. Which statement is true? (2 pts)
A. For x = 4, 3x = 12, so x = 4 solves 3x = 12.
B. The expression r + 9 has an LHS and RHS.
C. If k = 2, then k + 1 = 4.
D. The number of sides of a triangle is a variable.
17. Which expression represents "six minus half of t"? (2 pts)
A. 6 − t/2
B. (6 − t)/2
C. t/2 − 6
D. 6t/2
18. Which value of y makes y + 5 = 2y − 1 true? (2 pts)
A. 4
B. 5
C. 6
D. 7
19. In the equation 4p + 1 = 13, which option correctly identifies the LHS and RHS? (2 pts)
A. LHS: 4p + 1, RHS: 13
B. LHS: 13, RHS: 4p + 1
C. LHS: p, RHS: 13
D. LHS: 4, RHS: p + 1
20. If s stands for any number, which of the following is always equal to s + s? (2 pts)
A. s^2
B. 2s
C. s/2
D. s − s

21. In algebra, letters like x or y that can take different values are called   . (2 pts)
22. An equality such as 3k − 2 = 10 is called an   . (2 pts)
23. The side to the left of the equal sign is called the   . (2 pts)
24. In the statement a + b = b + a, the property shown is the   property of addition. (2 pts)
25. To check if a number is a solution, we   it into the equation. (2 pts)
26. If each figure uses 3 matchsticks, then repeating the figure n times needs   matchsticks. (2 pts)
27. For x = 5, the value of 2x + 4 is   . (2 pts)
28. A quantity whose value does not change is a   . (2 pts)
29. Only when LHS equals RHS is a value said to   the equation. (2 pts)
30. We can use any letter such as p, q, r to   a number whose value can change. (2 pts)

31. A scout badge requires 6 matchsticks. Write an expression for the number of matchsticks needed for t badges. Then find how many matchsticks are needed for 9 badges. Show your working. (5 pts)
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Answer:
32. Find the number m if m − 5 = 11. Show your working. (5 pts)
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33. The perimeter P of a rectangle is given by P = 2(l + b). If l = 13 cm and b = 9 cm, find P. Show your working. (5 pts)
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34. Evaluate the expression 4y + 9 when y = −3. Show your working. (5 pts)
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35. Check whether x = 8 is a solution of the equation 3x + 1 = 25. Show your working. (5 pts)
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36. Twice a number increased by 5 equals 21. Find the number. Show your working. (5 pts)
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37. Solve for k: k/3 + 2 = 8. Show your working. (5 pts)
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38. Each crate holds 24 bottles. Write an expression for the total bottles in p crates and find the total for p = 11. Show your working. (5 pts)
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39. The sum of two consecutive integers is 37. Find the two integers. Show your working. (5 pts)
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40. The total cost c (in rupees) of buying n notebooks is given by c = 12n + 15, where 15 is a fixed delivery fee. Find c when n = 5. Show your working. (5 pts)
Working:
Answer: