Class 7 Algebr a -
Inter national Level
Com pr ehensive Qu estion B ank w ith
Com plete Explanations
Pr epar ed for : International Curriculum Students
Gr ade Level: 7 (Ages 12-13)
Subject: Algebra
Date: March 2026
Intr oduction
This document contains a comprehensive collection of algebra problems designed for Class 7
students following international curricula such as IB MYP, Cambridge IGCSE, and IMO
preparation. Each question is followed by detailed step-by-step explanations to help students
understand the concepts thoroughly.
Section 1: Algebr aic Expr essions
Topic 1.1: Sim plifying Expr essions
Question 1: Simplify the expression: 5 x+ 3 x −2 x+7
Solution:
• Step 1: Identify like terms (terms with the same variable)
• Step 2: Combine the x terms: 5 x+ 3 x −2 x=6 x
• Step 3: Add the constant: 6 x +7
Answ er : 6 x +7
Explanation: Like terms are terms that have the same variable raised to the same power.
We can only add or subtract like terms. Here, 5 x , 3 x , and −2 x are like terms, so we combine
them by adding their coefficients: 5+3 −2=6.
,Question 2: Simplify: 3 a2 +5 a+ 2a 2 −3 a+4
Solution:
• Step 1: Group like terms: (3 a2 +2 a2 )+(5 a − 3 a)+ 4
• Step 2: Combine a 2 terms: 3 a2 +2 a2 =5 a2
• Step 3: Combine a terms: 5 a −3 a=2 a
• Step 4: Write the final expression: 5 a2 +2 a+ 4
Answ er : 5 a2 +2 a+ 4
Explanation: We must be careful to combine only like terms. a 2 terms are different from a
terms because they have different powers. Constants (numbers without variables) stand
alone.
Question 3: Simplify: 4 (2 x+ 3) −2( x −5)
Solution:
• Step 1: Use distributive property on first bracket: 4 ×2 x+ 4 ×3=8 x +12
• Step 2: Use distributive property on second bracket: −2 × x +(−2)×(−5)=−2 x+10
• Step 3: Combine the results: 8 x +12− 2 x +10
• Step 4: Group like terms: (8 x − 2 x )+(12+10)
• Step 5: Simplify: 6 x +22
Answ er : 6 x +22
Explanation: The distributive property states that a (b+c )=a b +a c . When we have a
negative sign before brackets, we must multiply each term inside by −1 , which changes the
signs.
Topic 1.2: Expan din g B r ackets
Question 4: Expand: 3(x +5)
Solution:
• Step 1: Multiply 3 by each term inside the brackets
• Step 2: 3 × x=3 x
• Step 3: 3 ×5=15
• Step 4: Combine: 3 x+ 15
, Answ er : 3 x+ 15
Explanation: Expanding brackets means removing the brackets by multiplying each term
inside by the term outside.
Question 5: Expand: −2(4 y −7)
Solution:
• Step 1: Multiply −2 by each term inside
• Step 2: −2 × 4 y=− 8 y
• Step 3: −2 ×(−7)=+ 14 (negative times negative equals positive)
• Step 4: Result: − 8 y +14
Answ er : − 8 y +14
Explanation: Remember that when multiplying two negative numbers, the result is
positive. So −2 ×(−7)=+ 14.
Question 6: Expand and simplify: 5(2 x +1)+3 ( x − 4)
Solution:
• Step 1: Expand first bracket: 5 ×2 x+ 5× 1=10 x+ 5
• Step 2: Expand second bracket: 3 × x +3 ×(− 4)=3 x − 12
• Step 3: Combine: 10 x+5+ 3 x −12
• Step 4: Group like terms: (10 x+ 3 x )+(5 −12)
• Step 5: Simplify: 13 x −7
Answ er : 13 x −7
Section 2: Solving Linear Equ ations
Topic 2.1: On e-Step Equ ations
Question 7: Solve: x +7=15
Solution:
• Step 1: Subtract 7 from both sides to isolate x
• Step 2: x +7 −7=15 −7
Inter national Level
Com pr ehensive Qu estion B ank w ith
Com plete Explanations
Pr epar ed for : International Curriculum Students
Gr ade Level: 7 (Ages 12-13)
Subject: Algebra
Date: March 2026
Intr oduction
This document contains a comprehensive collection of algebra problems designed for Class 7
students following international curricula such as IB MYP, Cambridge IGCSE, and IMO
preparation. Each question is followed by detailed step-by-step explanations to help students
understand the concepts thoroughly.
Section 1: Algebr aic Expr essions
Topic 1.1: Sim plifying Expr essions
Question 1: Simplify the expression: 5 x+ 3 x −2 x+7
Solution:
• Step 1: Identify like terms (terms with the same variable)
• Step 2: Combine the x terms: 5 x+ 3 x −2 x=6 x
• Step 3: Add the constant: 6 x +7
Answ er : 6 x +7
Explanation: Like terms are terms that have the same variable raised to the same power.
We can only add or subtract like terms. Here, 5 x , 3 x , and −2 x are like terms, so we combine
them by adding their coefficients: 5+3 −2=6.
,Question 2: Simplify: 3 a2 +5 a+ 2a 2 −3 a+4
Solution:
• Step 1: Group like terms: (3 a2 +2 a2 )+(5 a − 3 a)+ 4
• Step 2: Combine a 2 terms: 3 a2 +2 a2 =5 a2
• Step 3: Combine a terms: 5 a −3 a=2 a
• Step 4: Write the final expression: 5 a2 +2 a+ 4
Answ er : 5 a2 +2 a+ 4
Explanation: We must be careful to combine only like terms. a 2 terms are different from a
terms because they have different powers. Constants (numbers without variables) stand
alone.
Question 3: Simplify: 4 (2 x+ 3) −2( x −5)
Solution:
• Step 1: Use distributive property on first bracket: 4 ×2 x+ 4 ×3=8 x +12
• Step 2: Use distributive property on second bracket: −2 × x +(−2)×(−5)=−2 x+10
• Step 3: Combine the results: 8 x +12− 2 x +10
• Step 4: Group like terms: (8 x − 2 x )+(12+10)
• Step 5: Simplify: 6 x +22
Answ er : 6 x +22
Explanation: The distributive property states that a (b+c )=a b +a c . When we have a
negative sign before brackets, we must multiply each term inside by −1 , which changes the
signs.
Topic 1.2: Expan din g B r ackets
Question 4: Expand: 3(x +5)
Solution:
• Step 1: Multiply 3 by each term inside the brackets
• Step 2: 3 × x=3 x
• Step 3: 3 ×5=15
• Step 4: Combine: 3 x+ 15
, Answ er : 3 x+ 15
Explanation: Expanding brackets means removing the brackets by multiplying each term
inside by the term outside.
Question 5: Expand: −2(4 y −7)
Solution:
• Step 1: Multiply −2 by each term inside
• Step 2: −2 × 4 y=− 8 y
• Step 3: −2 ×(−7)=+ 14 (negative times negative equals positive)
• Step 4: Result: − 8 y +14
Answ er : − 8 y +14
Explanation: Remember that when multiplying two negative numbers, the result is
positive. So −2 ×(−7)=+ 14.
Question 6: Expand and simplify: 5(2 x +1)+3 ( x − 4)
Solution:
• Step 1: Expand first bracket: 5 ×2 x+ 5× 1=10 x+ 5
• Step 2: Expand second bracket: 3 × x +3 ×(− 4)=3 x − 12
• Step 3: Combine: 10 x+5+ 3 x −12
• Step 4: Group like terms: (10 x+ 3 x )+(5 −12)
• Step 5: Simplify: 13 x −7
Answ er : 13 x −7
Section 2: Solving Linear Equ ations
Topic 2.1: On e-Step Equ ations
Question 7: Solve: x +7=15
Solution:
• Step 1: Subtract 7 from both sides to isolate x
• Step 2: x +7 −7=15 −7
