Expressions using Letter-Numbers - Practice Worksheet
Strengthen your foundation with key concepts and basic applications.
This worksheet covers essential long-answer questions to help you build confidence in Expressions using Letter-Numbers from Ganita Prakash for Class 7 (Mathematics).
Questions
Define letter-numbers and algebraic expressions. How are they used to solve real-life problems?
Letter-numbers are symbols, usually letters, that represent unknown values or quantities in algebra. For example, 'a' can stand for Aftab's age. Algebraic expressions combine these symbols with numerical coefficients and constants. They enable us to express mathematical relationships concisely. In real life, an expression like 's = a + 3' denotes Shabnam's age in relation to Aftab's. This concept is applied in various situations such as calculating ages, costs, and measurements.
Write an algebraic expression for the total cost of 'c' coconuts at ₹35 each and 'j' kg of jaggery at ₹60 per kg. Show how to evaluate it for specific values.
The expression for the total cost is: Total Cost = 35c + 60j. If 'c' is 10 and 'j' is 5, substituting these values gives: Total Cost = 35(10) + 60(5) = 350 + 300 = ₹650. This illustrates how different quantities affect the total cost.
Create an algebraic expression to find Aftab's age if Shabnam's age is 's'. Provide an example with a numerical solution.
Since Aftab is 3 years younger than Shabnam, we can express this as: Aftab's age 'a' = s - 3. If Shabnam's age 's' is 20, then substituting gives Aftab's age, a = 20 - 3 = 17 years. This expression helps us easily find Aftab's age when given Shabnam's age.
Explain how to derive a formula for calculating the perimeter of a rectangle with length 'l' and width 'w'.
The perimeter 'P' of a rectangle is calculated using the formula: P = 2(l + w). This means adding the lengths of all sides, which can be visualized as two times the sum of the length and the width. For example, if l = 5 cm and w = 3 cm, then P = 2(5 + 3) = 16 cm. This formula works for rectangles of any size.
Describe a scenario that can be modeled with the expression 10(x - y), and solve it for x = 15 and y = 5.
The expression 10(x - y) could represent the total earnings of a shopkeeper if they sell x items at ₹10 each and lose y items sold. Substituting the values gives: 10(15 - 5) = 10(10) = ₹100. This expression allows for quick adjustments in profit calculations based on inventory changes.
Using examples, explain how using variables helps express relationships between quantities in daily life.
Variables simplify complex relationships by allowing us to formulate expressions that adapt to different situations. For instance, if a school charges 'a' for registration and 'b' for materials, the total fee can be expressed as T = a + b. If the registration fee is ₹200 and materials are ₹300, substituting provides T = 200 + 300 = ₹500. This usage makes financial planning intuitive.
Write an expression to represent the total number of matchsticks used to create 'n' letter Ls, and evaluate it for n = 5.
Each letter 'L' requires 2 matchsticks, so the expression is: Total Matchsticks = 2n. For n = 5, substituting gives Total Matchsticks = 2(5) = 10. This showcases how expressions can quantify physical resources efficiently.
Explain how you can use the expression 4(q) to find the area of a square with side length 'q'. Calculate it for q = 7 cm.
Since the area of a square is given by the side length squared, the expression should be A = q². Thus, for q = 7 cm, A = 4(7) = 28 cm². This reveals how dimension relations are captured through expressions.
Formulate the relationship between the number of days 'd' and the total time in hours spent on studying, given that each day he studies for 'h' hours.
The total study time can be represented by the expression: Total Hours = d × h. If a student studies for 2 hours each day for 5 days, substituting gives: Total Hours = 5 × 2 = 10 hours. This method helps track time management effectively.
Expressions using Letter-Numbers - Mastery Worksheet
Advance your understanding through integrative and tricky questions.
This worksheet challenges you with deeper, multi-concept long-answer questions from Expressions using Letter-Numbers to prepare for higher-weightage questions in Class 7.
Questions
Consider Aftab's age 'a' and Shabnam's age 's' where s = a + 3. If Aftab's age increases to 25, what will be Shabnam's age? Explain the steps in your calculation and describe the relationship between their ages in detail.
Given s = a + 3, replacing a with 25 yields s = 25 + 3 = 28. Thus, Shabnam's age is 28. This shows that Shabnam is consistently 3 years older than Aftab.
Ketaki buys 'c' coconuts and 'j' kg of jaggery, and the costs are ₹35 per coconut and ₹60 per kg of jaggery. Write an algebraic expression for the total cost and evaluate it if c = 4 and j = 5.
The total cost expression is 35c + 60j. Substituting c = 4 and j = 5, the total cost becomes 35(4) + 60(5) = 140 + 300 = ₹440.
If Venkatalakshmi's flour mill takes a total time of 10 seconds to start and then takes 8 seconds to grind each kg of grain, write an expression for the time taken to grind 'y' kg. Then calculate this time for y = 3.
The time expression is 10 + 8y. For y = 3, the time is 10 + 8(3) = 10 + 24 = 34 seconds.
Radha cycles 5 km daily for the first week and increases her daily distance by 'z' km for each subsequent week. Write an expression for the total distance cycled after 3 weeks and evaluate it for z = 2.
The total distance is 5(7) + 7(1 + 2 + 3) = 35 + 21 = 56 km for z = 2. Hence, the expression encompasses her weekly increase.
A train travels a distance at a constant speed between three stations, stopping for 2 minutes each stop. Create an expression for the total time taken to travel 3 distances with time 't' when stopping.
The expression is 3t + 2(3) = 3t + 6 minutes. This explains how waiting time accumulates in transit.
A snail climbs 'u' cm during the day and slides down 'd' cm at night. After 10 days and nights, represent the total distance the snail covered. What if d > u?
The expression is 10(u - d) cm. If d > u, the snail would be further away from its starting point because it slides down more than it climbs up.
Construct an expression that represents the cost for 'x' Jowar rotis at ₹30 each and 'y' Pulaos at ₹20 each. Evaluate the expression for x = 4 and y = 5.
The expression is 30x + 20y. Evaluating it gives 30(4) + 20(5) = 120 + 100 = ₹220.
If two numbers 'a' and 'b' have a relationship such that one is always 2 less than twice the other, express this in terms of 'a' and 'b'. Solve this if a = 5.
The relationship can be expressed as b = 2a - 2. For a = 5, b = 2(5) - 2 = 10 - 2 = 8.
Abha's total amount spent for 'x' pens and 'y' notebooks can be expressed as 8x + 3y. If she buys 10 pens and 4 notebooks, find her total expense.
Substituting values gives 8(10) + 3(4) = 80 + 12 = ₹92.
Given the expression 5a + 3b - 2c, explain how to simplify it if a = 2, b = 3, and c = 1. What is the resultant value?
Substituting yields 5(2) + 3(3) - 2(1) = 10 + 9 - 2 = 17.
Expressions using Letter-Numbers - Challenge Worksheet
Push your limits with complex, exam-level long-form questions.
The final worksheet presents challenging long-answer questions that test your depth of understanding and exam-readiness for Expressions using Letter-Numbers in Class 7.
Questions
Evaluate the implications of describing Aftab and Shabnam's ages as algebraic expressions when dealing with aging and time. How could this help in understanding other real-life age-related problems?
Discuss how expressions provide a framework for generalizing age-related scenarios, making calculations more straightforward and better informing decisions.
Using the example of matchstick patterns, derive a formula for the total number of matchsticks required for any given number of patterns formed, and explain how this formula could be applied in architectural designs.
Analyze the relationship and derive the formula. Show applications in real-world contexts like construction planning.
Create a new real-life scenario where a formula similar to the costs of coconuts and jaggery is applicable. Formulate the algebraic expression to summarize this scenario.
Present a situation that requires summarizing costs using variables. Discuss the utility of formulas in budgeting.
If Radha cycles for a consistent increasing distance each week, formulate an expression to predict her total distance over a specified time. Justify how understanding this expression is beneficial for goal setting.
Construct the distance travelled expression. Discuss implications for personal fitness and planning.
Explore the significance of simplified expressions in problem-solving. Provide an example that requires simplification to effectively address a question.
Furnish an example where the simplification aids understanding and solution finding, analyzing the problem contextually.
Suppose we look at expressions representing time for Venkatalakshmi's mill. How can these expressions be modified to include factors like maintenance or downtime?
Evaluate potential variables affecting time. Suggest modifications to existing expressions to capture these nuances.
Discuss how the concept of letter-numbers in algebra can aid in predicting future events, such as population growth or financial forecasting.
Illustrate how algebraic expressions model trends and make future projections. Correlate this with statistical data.
How can exploring expressions related to geometry enhance our understanding of real-world shapes? Provide examples.
Discuss geometric applications of algebraic expressions. Use specific shape calculations as examples.
Critically analyze the statement 'Algebra is just a tool for calculations.' Do you agree or disagree? Support your view with examples.
Promote a discussion highlighting algebra's broader functions beyond mere calculations. Give concrete scenarios.
Consider the expressions for perimeters of different shapes. How might these expressions differ, and what implications does this have for real-world applications?
Contrast the perimeter expressions. Broaden the discussion on its significance in space planning and design.
