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CHAPTER 4 — EXPRESSIONS USING LETTER-NUMBERS
Class VII Mathematics — NCERT Ganita Prakash 2024
Preeti Kushwah Classes — Unit Test — Set 1 (Foundation)
General Instructions:
1. All questions are compulsory.
2. Section A has 6 questions of 1 mark each.
3. Section B has 5 questions of 2 marks each.
4. Section C has 4 questions of 3 marks each.
5. Section D has 2 questions of 5 marks each.
6. Show all working clearly. Marks are awarded for steps.
1. All questions are compulsory.
2. Section A has 6 questions of 1 mark each.
3. Section B has 5 questions of 2 marks each.
4. Section C has 4 questions of 3 marks each.
5. Section D has 2 questions of 5 marks each.
6. Show all working clearly. Marks are awarded for steps.
Section A — (1 Mark Each) [6 × 1 = 6]
Q1.1
What is the coefficient of x in the expression 7x + 3?
Q2.1
Write an algebraic expression for: “5 more than a number n.”
Q3.1
In the expression 4y − 2, identify the variable and the constant term.
Q4.1
True or False: 3x and 3y are like terms. Justify your answer.
Q5.1
Find the value of 2x + 1 when x = 3.
Q6.1
Write the constant term in the expression 5a² − 9a + 4.
Section B — (2 Marks Each) [5 × 2 = 10]
Q7.2
Write algebraic expressions for the following:
(a) 4 less than twice a number m.
(b) The product of p and q, added to 7.
(a) 4 less than twice a number m.
(b) The product of p and q, added to 7.
Q8.2
From the terms 3x, 5y, 7x, 2y, 4x², identify which are like terms and which are unlike. Group the like terms together.
Q9.2
Add (3a + 2b) and (5a − b). Show your working using the column method.
Q10.2
Find the value of 3p − 2q when p = 4 and q = 5.
Q11.2
Write the formula for the perimeter of a rectangle with length l cm and breadth b cm. Use it to find the perimeter when l = 8.5 cm and b = 4.5 cm.
Section C — (3 Marks Each) [4 × 3 = 12]
Q12.3
Simplify by collecting like terms:
4x + 3y − 2x + 7y − 5
Show all steps clearly.
4x + 3y − 2x + 7y − 5
Show all steps clearly.
Q13.3
Subtract (2a + 3b − 1) from (5a − b + 4). Show step-by-step working.
Q14.3
Raju has n marbles. He gives 5 to his friend. His friend then gives him back 3 times the number Raju has now.
(a) Write an expression for the number of marbles Raju has after giving away 5. [1]
(b) Write an expression for the number the friend gives back. [1]
(c) Write the final expression for total marbles Raju has. Simplify it. [1]
(a) Write an expression for the number of marbles Raju has after giving away 5. [1]
(b) Write an expression for the number the friend gives back. [1]
(c) Write the final expression for total marbles Raju has. Simplify it. [1]
Q15.3
The length of a rectangle is (2x + 3) cm and its breadth is (x − 1) cm.
(a) Write an expression for its perimeter. [1]
(b) Simplify the expression. [1]
(c) Find the perimeter when x = 4. [1]
(a) Write an expression for its perimeter. [1]
(b) Simplify the expression. [1]
(c) Find the perimeter when x = 4. [1]
Section D — (5 Marks Each) [2 × 5 = 10]
Q16.5
A shopkeeper has p kg of rice in his store. He sells 12 kg on Monday, 8 kg on Tuesday, and receives a fresh stock of (2p − 5) kg on Wednesday.
(a) Write an expression for stock after Monday. [1]
(b) Write an expression for stock after Tuesday. [1]
(c) Write an expression for stock after Wednesday. Simplify. [1]
(d) Find the stock after Wednesday when p = 30. [1]
(e) If he wants the final stock to be at least 50 kg, what is the minimum value of p? [1]
(a) Write an expression for stock after Monday. [1]
(b) Write an expression for stock after Tuesday. [1]
(c) Write an expression for stock after Wednesday. Simplify. [1]
(d) Find the stock after Wednesday when p = 30. [1]
(e) If he wants the final stock to be at least 50 kg, what is the minimum value of p? [1]
Q17.5
Matchstick pattern — a row of squares sharing sides:
1 square uses 4 sticks; 2 squares use 7 sticks; 3 squares use 10 sticks.
(a) How many sticks does 4 squares need? Complete the pattern for 5 squares too. [1]
(b) Find the rule (expression in n) for the number of sticks for n squares. [2]
(c) Use your expression to find the number of sticks for 15 squares. [1]
(d) If you have 100 sticks, how many complete squares can you make? [1]
1 square uses 4 sticks; 2 squares use 7 sticks; 3 squares use 10 sticks.
(a) How many sticks does 4 squares need? Complete the pattern for 5 squares too. [1]
(b) Find the rule (expression in n) for the number of sticks for n squares. [2]
(c) Use your expression to find the number of sticks for 15 squares. [1]
(d) If you have 100 sticks, how many complete squares can you make? [1]
Bonus Question (Optional) [2 Marks]
Q18.2
★ Fill in the □ to make each equation true:
(a) 3x + □ = 5x + 7 (find the missing expression) [1]
(b) □ − (2a − 3b) = 4a + b (find the missing expression) [1]
(a) 3x + □ = 5x + 7 (find the missing expression) [1]
(b) □ − (2a − 3b) = 4a + b (find the missing expression) [1]
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Answer Key & Detailed Solutions
Q1. [1 Mark]
In 7x + 3, the coefficient of x is 7.
Q2. [1 Mark]
“5 more than a number n” means add 5 to n.
Expression: n + 5
Expression: n + 5
Q3. [1 Mark]
In 4y − 2:
Variable: y
Constant term: −2
Variable: y
Constant term: −2
Q4. [1 Mark]
False. Like terms must have exactly the same variable(s) and powers. 3x has variable x and 3y has variable y — they are different variables, so they are unlike terms.
Q5. [1 Mark]
2x + 1 when x = 3:
= 2(3) + 1 = 6 + 1 = 7
= 2(3) + 1 = 6 + 1 = 7
Q6. [1 Mark]
In 5a² − 9a + 4, the term with no variable is 4.
∴ Constant term = 4
∴ Constant term = 4
Q7. [2 Marks]
(a) “4 less than twice a number m” = 2m − 4
Expression: 2m − 4
(b) “Product of p and q, added to 7” = pq + 7
Expression: pq + 7
Expression: 2m − 4
(b) “Product of p and q, added to 7” = pq + 7
Expression: pq + 7
Q8. [2 Marks]
Terms: 3x, 5y, 7x, 2y, 4x²
Like terms groups:
• x-terms: 3x and 7x (same variable x¹)
• y-terms: 5y and 2y (same variable y¹)
Unlike (stands alone): 4x² (has x², different power from 3x and 7x)
Like terms groups:
• x-terms: 3x and 7x (same variable x¹)
• y-terms: 5y and 2y (same variable y¹)
Unlike (stands alone): 4x² (has x², different power from 3x and 7x)
Q9. [2 Marks]
Column method:
3a + 2b
+ 5a − b
—————
a-terms: 3a + 5a = 8a
b-terms: 2b + (−b) = b
Answer: 8a + b
3a + 2b
+ 5a − b
—————
a-terms: 3a + 5a = 8a
b-terms: 2b + (−b) = b
Answer: 8a + b
Q10. [2 Marks]
3p − 2q when p = 4, q = 5:
= 3(4) − 2(5)
= 12 − 10
= 2
= 3(4) − 2(5)
= 12 − 10
= 2
Q11. [2 Marks]
Perimeter of rectangle: P = 2(l + b) = 2l + 2b
When l = 8.5 cm, b = 4.5 cm:
P = 2(8.5 + 4.5) = 2 × 13 = 26 cm
When l = 8.5 cm, b = 4.5 cm:
P = 2(8.5 + 4.5) = 2 × 13 = 26 cm
Q12. [3 Marks]
4x + 3y − 2x + 7y − 5
Step 1 — Group like terms: (4x − 2x) + (3y + 7y) + (−5)
Step 2 — Add x-terms: 4x − 2x = 2x
Step 3 — Add y-terms: 3y + 7y = 10y
Step 4 — Constant stays: −5
Answer: 2x + 10y − 5
Step 1 — Group like terms: (4x − 2x) + (3y + 7y) + (−5)
Step 2 — Add x-terms: 4x − 2x = 2x
Step 3 — Add y-terms: 3y + 7y = 10y
Step 4 — Constant stays: −5
Answer: 2x + 10y − 5
Q13. [3 Marks]
Subtract (2a + 3b − 1) from (5a − b + 4):
Step 1: Write the subtraction:
(5a − b + 4) − (2a + 3b − 1)
Step 2: Change signs of ALL terms in the subtracted expression:
= 5a − b + 4 − 2a − 3b + 1
Step 3: Group like terms:
= (5a − 2a) + (−b − 3b) + (4 + 1)
= 3a − 4b + 5
Step 1: Write the subtraction:
(5a − b + 4) − (2a + 3b − 1)
Step 2: Change signs of ALL terms in the subtracted expression:
= 5a − b + 4 − 2a − 3b + 1
Step 3: Group like terms:
= (5a − 2a) + (−b − 3b) + (4 + 1)
= 3a − 4b + 5
Q14. [3 Marks]
(a) After giving away 5: n − 5
(b) Friend gives back 3 times of (n−5): 3(n − 5) = 3n − 15
(c) Total marbles Raju has = marbles he kept + marbles friend gave back:
= (n − 5) + 3(n − 5)
= n − 5 + 3n − 15
= 4n − 20
(b) Friend gives back 3 times of (n−5): 3(n − 5) = 3n − 15
(c) Total marbles Raju has = marbles he kept + marbles friend gave back:
= (n − 5) + 3(n − 5)
= n − 5 + 3n − 15
= 4n − 20
Q15. [3 Marks]
Length = (2x + 3) cm, Breadth = (x − 1) cm
(a) Perimeter = 2[length + breadth]
P = 2[(2x + 3) + (x − 1)]
(b) Simplify: 2[2x + 3 + x − 1] = 2[3x + 2] = 6x + 4
(c) When x = 4: P = 6(4) + 4 = 24 + 4 = 28 cm
(a) Perimeter = 2[length + breadth]
P = 2[(2x + 3) + (x − 1)]
(b) Simplify: 2[2x + 3 + x − 1] = 2[3x + 2] = 6x + 4
(c) When x = 4: P = 6(4) + 4 = 24 + 4 = 28 cm
Q16. [5 Marks]
(a) After Monday (sold 12 kg): p − 12
(b) After Tuesday (sold 8 more kg): p − 12 − 8 = p − 20
(c) After Wednesday (received 2p−5 kg):
(p − 20) + (2p − 5) = p − 20 + 2p − 5 = 3p − 25
(d) When p = 30: 3(30) − 25 = 90 − 25 = 65 kg
(e) 3p − 25 ≥ 50
3p ≥ 75
p ≥ 25
Minimum value of p = 25 kg
(b) After Tuesday (sold 8 more kg): p − 12 − 8 = p − 20
(c) After Wednesday (received 2p−5 kg):
(p − 20) + (2p − 5) = p − 20 + 2p − 5 = 3p − 25
(d) When p = 30: 3(30) − 25 = 90 − 25 = 65 kg
(e) 3p − 25 ≥ 50
3p ≥ 75
p ≥ 25
Minimum value of p = 25 kg
Q17. [5 Marks]
(a) Pattern: 4, 7, 10, 13, 16 (add 3 each time)
4 squares: 13 sticks; 5 squares: 16 sticks
(b) First term = 4, common difference = 3
For n squares: 4 + (n−1)×3 = 4 + 3n − 3 = 3n + 1
Verify: n=1: 4✓ n=2: 7✓ n=3: 10✓
(c) For 15 squares: 3(15) + 1 = 45 + 1 = 46 sticks
(d) 3n + 1 ≤ 100 → 3n ≤ 99 → n ≤ 33
33 complete squares
4 squares: 13 sticks; 5 squares: 16 sticks
(b) First term = 4, common difference = 3
For n squares: 4 + (n−1)×3 = 4 + 3n − 3 = 3n + 1
Verify: n=1: 4✓ n=2: 7✓ n=3: 10✓
(c) For 15 squares: 3(15) + 1 = 45 + 1 = 46 sticks
(d) 3n + 1 ≤ 100 → 3n ≤ 99 → n ≤ 33
33 complete squares
Q18. [Bonus — 2 Marks]
(a) 3x + □ = 5x + 7
□ = 5x + 7 − 3x = 2x + 7
(b) □ − (2a − 3b) = 4a + b
□ = (4a + b) + (2a − 3b)
= 4a + b + 2a − 3b
= 6a − 2b
□ = 5x + 7 − 3x = 2x + 7
(b) □ − (2a − 3b) = 4a + b
□ = (4a + b) + (2a − 3b)
= 4a + b + 2a − 3b
= 6a − 2b