This MCQ module is based on: Chapter 4 Exercises
TOPIC 15 OF 31
Chapter 4 Exercises
🎓 Class 7
Mathematics
CBSE
Theory
Ch 4 — Expressions Using Letter-Numbers
⏱ ~35 min
🌐 Language: [gtranslate]
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This mathematics assessment will be based on: Chapter 4 Exercises
Targeting Class 7 level in Algebra, with Basic difficulty.
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Chapter 4 — Exercises
Q1. Write algebraic expressions for: (a) 5 more than a number \(n\) (b) 4 less than a number \(n\) (c) 2 less than 13 times a number \(m\) (d) 13 less than 2 times a number \(m\).
(a) \(n+5\) (b) \(n-4\) (c) \(13m-2\) (d) \(2m-13\).
Q2. Describe in words: (a) \(8 \times x + 3 \times y\) (b) \(15 + j - 2 \times k\).
(a) Eight times a number x plus three times another number y. (b) Fifteen plus j minus twice k.
Q3. A snail climbs \(u\) cm by day and slips \(d\) cm by night (\(d < u\)). Write an expression for how far it has climbed from the starting point at the end of 10 days and 10 nights. What can we say about the snail's movement if \(d > u\)?
(a) Distance = \(10(u - d) = 10u - 10d\) cm. (b) If \(d > u\), the snail slips more than it climbs each cycle; it never reaches the top.
Q4. Radha cycles 5 km/day in week 1. Every week she increases by \(z\) km/day. How far has she cycled in 3 weeks?
\(7\cdot 5 + 7\cdot(5+z) + 7\cdot(5+2z) = 105 + 21z\) km.
Q5. In a figure path \(w + 2\) applied with operations ×3, +4, ×4 gives \(6w + 20\). Fill in expressions on alternate paths (example: start with different letter).
Sample: start \(3w\) → +3: \(3w+3\) → ×5: \(15w+15\) → −5: \(15w+10\). Many valid answers depending on the operations in the path.
Q6. A local train stops at 3 intermediate stations for 2 minutes each. Each leg takes \(t\) minutes and total journey = 45 min. Find \(t\).
\(4t + 6 = 45 \Rightarrow 4t = 39 \Rightarrow t = 9.75\) minutes.
Q7. Simplify: (a) \(7a + 5 - 3a + 2\) (b) \(12x - 4y + 3x + 9y\) (c) \(5p - (2p - 3) + 4\) (d) \(2(m + 3) + 3(m - 1)\).
(a) \(4a + 7\) (b) \(15x + 5y\) (c) \(3p + 7\) (d) \(5m + 3\).
Q8. The side of a regular pentagon is \((2x + 1)\). Write its perimeter.
Perimeter = \(5(2x+1) = 10x + 5\).
Q9. A rectangle has length \((3y+2)\) and breadth \((y-1)\). Find expressions for (i) perimeter (ii) area.
(i) Perimeter = \(2[(3y+2)+(y-1)] = 2(4y+1) = 8y+2\). (ii) Area = \((3y+2)(y-1) = 3y^2 - y - 2\).
Q10. Evaluate the expression \(4p^2 - 5q + 7\) for \(p = 2, q = 3\).
\(4(4) - 5(3) + 7 = 16 - 15 + 7 = 8\).
Q11. Observe the pattern: Step 4 has 17 squares, Step 10 has 41 squares, Step 50 has 201 squares. Write a general formula for Step \(n\). How does the formula change if we count vertices instead?
Number of squares: \(5 + (n-1) \times 4 = 4n + 1\). Number of vertices: \(16n + 4\).
Q12. Numbers are written in a 4-column grid (row 1: 1, 2, 3, 4; row 2: 5, 6, 7, 8; ...). (a) Expression for numbers in column 1, 2, 3, 4. (b) In which row and column does 124 appear? 147? 201? (c) General number at row \(r\), column \(c\)?
(a) Col 1: \(4(r-1)+1 = 4r-3\); Col 2: \(4r-2\); Col 3: \(4r-1\); Col 4: \(4r\). (b) 124: divide 124 by 4 → 31 exactly → row 31, column 4. 147: 147/4 = 36 remainder 3 → row 37, column 3. 201: 201/4 = 50 remainder 1 → row 51, column 1. (c) General: \(4(r-1)+c\).
Chapter Summary
Letter-Number
A letter used to represent a number. Also called a variable.
Algebraic Expression
Combination of numbers, letters, and operations. No equals sign.
Term & Coefficient
A term keeps its sign. Coefficient = the number part multiplying the letter.
Like & Unlike Terms
Like terms share the same letter-number part and can be combined.
Distributive Property
\(a(b+c) = ab + ac\). Multiplication distributes over addition.
Formula
Algebraic rule summarising a pattern or physical relation.
Key Terms
letter-number?, algebraic expression?, like terms?, coefficient?, distributive property?, formula?.
Capstone Activity: My Own Pattern
L3 ApplyMaterials: Matchsticks or pencil and paper.
Predict: Can you invent a pattern whose rule is \(5n+2\) and verify it works?
- Start with 7 matchsticks arranged in any shape (Step 1).
- Design a rule for how to add matchsticks so that Step 2 has 12, Step 3 has 17.
- Check: does Step \(n\) have \(5n+2\) matchsticks? Verify \(n=5\).
- Draw the first four steps.
One idea: a row of pentagons sharing a side — each new pentagon adds 4 matchsticks. Better yet, a row of open-top hexagons sharing a side. At Step 5 count: \(5 \times 5 + 2 = 27\).
Competency-Based Questions
Scenario: Meera sells two types of tickets at her school fair: entry tickets (₹10) and game tickets (₹5). On a particular day she sold \(e\) entry and \(g\) game tickets. She also had to pay ₹150 as stall rent.
Q1. Write an expression for Meera's net profit.
L3 ApplyNet profit = \(10e + 5g - 150\).
Q2. For \(e=30, g=40\) analyse whether Meera profits or loses.
L4 AnalyseNet = 300 + 200 − 150 = ₹350 profit.
Q3. Evaluate: What minimum number of combined tickets (e+g) does Meera need to break even?
L5 EvaluateBreak-even depends on ticket mix. If all game tickets (₹5 each): 30 tickets. If all entry (₹10 each): 15 tickets. In general, need \(10e + 5g \geq 150\).
Q4. Design a new pricing: halve the entry ticket price and double the game ticket price. Write the new profit expression and compare to the old at \(e=30, g=40\).
L6 CreateNew profit = \(5e + 10g - 150\). For \(e=30, g=40\): \(150 + 400 - 150 = ₹400\). Higher than before (₹350), by ₹50.
Assertion–Reason Questions
A: For every \(n\), \(2(n+3) = 2n + 6\).
R: The distributive property states \(a(b+c) = ab + ac\).
R: The distributive property states \(a(b+c) = ab + ac\).
(a)
A: \(3x + 5x = 8x^2\).
R: Adding like terms adds the coefficients.
R: Adding like terms adds the coefficients.
(c) — A is false (\(3x + 5x = 8x\), not \(8x^2\)). R is true; it is applied incorrectly in A.
A: The expression \(4n + 1\) gives the number of squares at step \(n\) of the "+" cross pattern.
R: Each step adds 4 squares (one on each arm).
R: Each step adds 4 squares (one on each arm).
(a)
Frequently Asked Questions
What topics do Chapter 4 exercises cover?
Chapter 4 exercises cover translating word statements into expressions, identifying like terms, simplifying by combining like terms, applying the distributive property, and writing general formulas for number patterns. NCERT Class 7 Ganita Prakash gives comprehensive practice.
How to solve an expression simplification problem?
Step 1: Expand brackets using distributive property. Step 2: Group like terms. Step 3: Combine coefficients of like terms. Step 4: Write the simplified expression. NCERT Class 7 Chapter 4 exercises follow this sequence.
What is the summary of Class 7 Chapter 4?
Key ideas: letters can stand for numbers; expressions combine letters, numbers and operations; like terms share identical letter parts and can be combined; distributive property expands products over sums; patterns can be written with a general term. NCERT Class 7 Ganita Prakash Chapter 4.
Write 'five more than a number' as an expression.
Let the unknown number be x. 'Five more than x' is x + 5. If the number were named n, the expression would be n + 5. NCERT Class 7 Chapter 4 exercises include many such translations.
Why are Class 7 algebra exercises important?
These exercises build the foundation for solving equations, working with formulas, and all higher algebra. Without fluency in letter-number manipulation, Classes 8-10 maths become difficult. NCERT Class 7 Ganita Prakash Chapter 4 prepares students thoroughly.
How do you evaluate 3x + 2 at x = 4?
Substitute x = 4: 3(4) + 2 = 12 + 2 = 14. Always replace the letter everywhere it appears with the given value, then compute. NCERT Class 7 Chapter 4 exercises practise evaluation repeatedly.
Frequently Asked Questions — Expressions Using Letter-Numbers
What is Chapter 4 Exercises in NCERT Class 7 Mathematics?
Chapter 4 Exercises is a key concept covered in NCERT Class 7 Mathematics, Chapter 4: Expressions Using Letter-Numbers. This lesson builds the student's foundation in the chapter by explaining the core ideas with worked examples, definitions, and step-by-step methods aligned to the CBSE curriculum.
How do I solve problems on Chapter 4 Exercises step by step?
To solve problems on Chapter 4 Exercises, follow the NCERT method: identify the given quantities, choose the relevant formula or theorem, substitute values carefully, and simplify. Class 7 exercises gradually increase in difficulty — start with solved NCERT examples before attempting exercise questions, and always verify your answer by substitution or diagram.
What are the most important formulas for Chapter 4: Expressions Using Letter-Numbers?
The essential formulas of Chapter 4 (Expressions Using Letter-Numbers) are listed in the chapter summary and highlighted throughout the lesson in formula boxes. Memorise them and practise at least 2–3 problems per formula. CBSE board exams frequently test direct application as well as combined use of multiple formulas from this chapter.
Is Chapter 4 Exercises important for the Class 7 board exam?
Chapter 4 Exercises is part of the NCERT Class 7 Mathematics syllabus and appears in CBSE board exams. Questions typically include short-answer, long-answer, and competency-based items. Review the NCERT examples, exercise questions, and previous-year board problems on this topic to prepare confidently.
What mistakes should students avoid in Chapter 4 Exercises?
Common mistakes in Chapter 4 Exercises include skipping steps, misapplying formulas, sign errors, and losing track of units. Write each step clearly, double-check algebraic manipulations, and re-read the question after solving to verify that your answer matches what was asked.
Where can I find more NCERT practice questions on Chapter 4 Exercises?
End-of-chapter NCERT exercises for Chapter 4 Exercises cover all difficulty levels tested in CBSE exams. After completing them, try the examples again without looking at the solutions, attempt the NCERT Exemplar questions for Chapter 4, and solve at least one previous-year board paper to consolidate your understanding.
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