Generated Aug 16, 2026 at 10:51 AM from manual-input
Download Worksheet PDF Download Answer Key
Home JSON
Home Download Worksheet PDF Download Answer Key JSON
Mathematics

Class 6 Algebra — Variables, Expressions, and Equations

Intro to Algebra: variables, expressions, equations, LHS/RHS, and simple properties
100 pts
40 questions • ~35 min
Aayush Nayak
6-B
Grade 6
YBIS
Home
Read each question carefully and answer to the best of your ability. Show all working for word problems.
1.
True / False In algebra, letters can stand for numbers whose values are not fixed.
1 pt
True
False
Answer: True
2.
True / False The expression 3k + 7 is an equation.
1 pt
True
False
Answer: False
3.
True / False In an equation, the equality sign separates the LHS and RHS.
1 pt
True
False
Answer: True
4.
True / False If a and b are numbers, then a + b is always equal to b + a.
1 pt
True
False
Answer: True
5.
True / False The number of days in a week is a variable.
1 pt
True
False
Answer: False
6.
True / False 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
Answer: True
7.
True / False The expression 2n has the same value no matter what n is.
1 pt
True
False
Answer: False
8.
True / False If each shape uses 5 matchsticks, then repeating it t times needs 5 + t matchsticks.
1 pt
True
False
Answer: False
9.
True / False If x = 3, then the value of 2x + 1 is 7.
1 pt
True
False
Answer: True
10.
True / False The two sides of an equation are called RHS and RHE.
1 pt
True
False
Answer: False
11.
Multiple Choice Which of the following is an equation?
2 pts
A. y + 8 = 20
B. 7p − 3
C. m/5
D. 9 + q
Answer: A. y + 8 = 20
12.
Multiple Choice 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
Answer: C. l, b and P
13.
Multiple Choice 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
Answer: A. Commutative property of addition
14.
Multiple Choice 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
Answer: A. 4n
15.
Multiple Choice For x = −2, what is the value of 5 − x?
2 pts
A. 3
B. 7
C. −7
D. −3
Answer: B. 7
16.
Multiple Choice 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.
Answer: A. For x = 4, 3x = 12, so x = 4 solves 3x = 12.
17.
Multiple Choice 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
Answer: A. 6 − t/2
18.
Multiple Choice Which value of y makes y + 5 = 2y − 1 true?
2 pts
A. 4
B. 5
C. 6
D. 7
Answer: C. 6
19.
Multiple Choice 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
Answer: A. LHS: 4p + 1, RHS: 13
20.
Multiple Choice 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
Answer: B. 2s
21.
Fill in the Blank In algebra, letters like x or y that can take different values are called _____.
2 pts
Answer: variables
22.
Fill in the Blank An equality such as 3k − 2 = 10 is called an _____.
2 pts
Answer: equation
23.
Fill in the Blank The side to the left of the equal sign is called the _____.
2 pts
Answer: LHS
24.
Fill in the Blank In the statement a + b = b + a, the property shown is the _____ property of addition.
2 pts
Answer: commutative
25.
Fill in the Blank To check if a number is a solution, we _____ it into the equation.
2 pts
Answer: substitute
26.
Fill in the Blank If each figure uses 3 matchsticks, then repeating the figure n times needs _____ matchsticks.
2 pts
Answer: 3n
27.
Fill in the Blank For x = 5, the value of 2x + 4 is _____.
2 pts
Answer: 14
28.
Fill in the Blank A quantity whose value does not change is a _____.
2 pts
Answer: constant
29.
Fill in the Blank Only when LHS equals RHS is a value said to _____ the equation.
2 pts
Answer: satisfy
30.
Fill in the Blank We can use any letter such as p, q, r to _____ a number whose value can change.
2 pts
Answer: represent
31.
Word Problem 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
Working:
Answer:
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 Find the number m if m − 5 = 11. Show your working.
5 pts
Working:
Answer:
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 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
Working:
Answer:
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 Evaluate the expression 4y + 9 when y = −3. Show your working.
5 pts
Working:
Answer:
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 Check whether x = 8 is a solution of the equation 3x + 1 = 25. Show your working.
5 pts
Working:
Answer:
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 Twice a number increased by 5 equals 21. Find the number. Show your working.
5 pts
Working:
Answer:
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 Solve for k: k/3 + 2 = 8. Show your working.
5 pts
Working:
Answer:
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 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
Working:
Answer:
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 The sum of two consecutive integers is 37. Find the two integers. Show your working.
5 pts
Working:
Answer:
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 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:
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
40
Total Questions
100
Total Points
~35
Minutes