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Answer Key — Teacher Copy
Mathematics

Class 6 Algebra — Variables, Expressions, and Equations

Intro to Algebra: variables, expressions, equations, LHS/RHS, and simple properties
Date: August 16, 2026  •  40 questions  •  Total: 100 points
StudentAayush Nayak
Class6-B
GradeGrade 6
SchoolYBIS
1. True / False (1 pts)
In algebra, letters can stand for numbers whose values are not fixed.
✓ Answer
True
2. True / False (1 pts)
The expression 3k + 7 is an equation.
✓ Answer
False
3. True / False (1 pts)
In an equation, the equality sign separates the LHS and RHS.
✓ Answer
True
4. True / False (1 pts)
If a and b are numbers, then a + b is always equal to b + a.
✓ Answer
True
5. True / False (1 pts)
The number of days in a week is a variable.
✓ Answer
False
6. True / False (1 pts)
To check if a number is a solution of x − 4 = 9, we can substitute and see if both sides are equal.
✓ Answer
True
7. True / False (1 pts)
The expression 2n has the same value no matter what n is.
✓ Answer
False
8. True / False (1 pts)
If each shape uses 5 matchsticks, then repeating it t times needs 5 + t matchsticks.
✓ Answer
False
9. True / False (1 pts)
If x = 3, then the value of 2x + 1 is 7.
✓ Answer
True
10. True / False (1 pts)
The two sides of an equation are called RHS and RHE.
✓ Answer
False
11. Multiple Choice (2 pts)
Which of the following is an equation?
✓ Answer
A. y + 8 = 20
12. Multiple Choice (2 pts)
In the formula P = 2(l + b) for a rectangle, which of the following are variables?
✓ Answer
C. l, b and P
13. Multiple Choice (2 pts)
The statement a + b = b + a shows which property?
✓ Answer
A. Commutative property of addition
14. Multiple Choice (2 pts)
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?
✓ Answer
A. 4n
15. Multiple Choice (2 pts)
For x = −2, what is the value of 5 − x?
✓ Answer
B. 7
16. Multiple Choice (2 pts)
Which statement is true?
✓ Answer
A. For x = 4, 3x = 12, so x = 4 solves 3x = 12.
17. Multiple Choice (2 pts)
Which expression represents "six minus half of t"?
✓ Answer
A. 6 − t/2
18. Multiple Choice (2 pts)
Which value of y makes y + 5 = 2y − 1 true?
✓ Answer
C. 6
19. Multiple Choice (2 pts)
In the equation 4p + 1 = 13, which option correctly identifies the LHS and RHS?
✓ Answer
A. LHS: 4p + 1, RHS: 13
20. Multiple Choice (2 pts)
If s stands for any number, which of the following is always equal to s + s?
✓ Answer
B. 2s
21. Fill in the Blank (2 pts)
In algebra, letters like x or y that can take different values are called _____.
✓ Answer
variables
22. Fill in the Blank (2 pts)
An equality such as 3k − 2 = 10 is called an _____.
✓ Answer
equation
23. Fill in the Blank (2 pts)
The side to the left of the equal sign is called the _____.
✓ Answer
LHS
24. Fill in the Blank (2 pts)
In the statement a + b = b + a, the property shown is the _____ property of addition.
✓ Answer
commutative
25. Fill in the Blank (2 pts)
To check if a number is a solution, we _____ it into the equation.
✓ Answer
substitute
26. Fill in the Blank (2 pts)
If each figure uses 3 matchsticks, then repeating the figure n times needs _____ matchsticks.
✓ Answer
3n
27. Fill in the Blank (2 pts)
For x = 5, the value of 2x + 4 is _____.
✓ Answer
14
28. Fill in the Blank (2 pts)
A quantity whose value does not change is a _____.
✓ Answer
constant
29. Fill in the Blank (2 pts)
Only when LHS equals RHS is a value said to _____ the equation.
✓ Answer
satisfy
30. Fill in the Blank (2 pts)
We can use any letter such as p, q, r to _____ a number whose value can change.
✓ Answer
represent
31. Word Problem (5 pts)
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.
✎ Worked Solution
Step 1: Let T be the total number of matchsticks. T = 6t
Step 2: Substitute t = 9 into T = 6t
Step 3: T = 6 × 9 = 54
Answer: 54 matchsticks
32. Word Problem (5 pts)
Find the number m if m − 5 = 11. Show your working.
✎ Worked Solution
Step 1: m − 5 = 11
Step 2: Add 5 to both sides → m = 11 + 5
Step 3: m = 16
Answer: m = 16
33. Word Problem (5 pts)
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.
✎ Worked Solution
Step 1: P = 2(l + b)
Step 2: Substitute l = 13 and b = 9 → P = 2(13 + 9)
Step 3: P = 2(22) = 44
Answer: 44 cm
34. Word Problem (5 pts)
Evaluate the expression 4y + 9 when y = −3. Show your working.
✎ Worked Solution
Step 1: 4y + 9 with y = −3
Step 2: 4(−3) + 9 = −12 + 9
Step 3: −12 + 9 = −3
Answer: −3
35. Word Problem (5 pts)
Check whether x = 8 is a solution of the equation 3x + 1 = 25. Show your working.
✎ Worked Solution
Step 1: Compute LHS with x = 8 → 3(8) + 1 = 24 + 1 = 25
Step 2: RHS is 25
Step 3: LHS = RHS, so x = 8 satisfies the equation
Answer: Yes, x = 8 is a solution
36. Word Problem (5 pts)
Twice a number increased by 5 equals 21. Find the number. Show your working.
✎ Worked Solution
Step 1: Let the number be n. Then 2n + 5 = 21
Step 2: Subtract 5 from both sides → 2n = 16
Step 3: Divide both sides by 2 → n = 8
Answer: 8
37. Word Problem (5 pts)
Solve for k: k/3 + 2 = 8. Show your working.
✎ Worked Solution
Step 1: k/3 + 2 = 8
Step 2: Subtract 2 from both sides → k/3 = 6
Step 3: Multiply both sides by 3 → k = 18
Answer: k = 18
38. Word Problem (5 pts)
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.
✎ Worked Solution
Step 1: Total bottles B = 24p
Step 2: Substitute p = 11 → B = 24 × 11
Step 3: B = 264
Answer: 264 bottles
39. Word Problem (5 pts)
The sum of two consecutive integers is 37. Find the two integers. Show your working.
✎ Worked Solution
Step 1: Let the first integer be n, the next is n + 1
Step 2: n + (n + 1) = 37 → 2n + 1 = 37
Step 3: 2n = 36 → n = 18
Answer: 18 and 19
40. Word Problem (5 pts)
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.
✎ Worked Solution
Step 1: c = 12n + 15
Step 2: Substitute n = 5 → c = 12(5) + 15
Step 3: c = 60 + 15 = 75
Answer: Rs 75