Competency Based Worksheet
Class:- VIII Subject: Maths
Competencies
Knowledge of Concepts
Understanding the Concepts
Ability to compute
Problem Solving
Term 2 2024-2025
Chapters
Algebraic Expressions and Identities
Mensuration
Exponents and Powers
Direct and Inverse Proportions
Factorisation
Introduction to Graphs
From Term 1
Linear equations in one variable
Squares and square roots.
Algebraic Expressions and Identities
Mensuration
Direct and Inverse Proportions
Factorisation
Introduction to Graphs
Linear equations in one variable
Squares and square roots.
Exponents and Powers
Competency Based Worksheet
Class:- VIII Subject: Maths
NAME: _____________ Algebraic Expressions and Identities DATE: _____________
Competency : Knowledge of Concepts
Formulating Expressions in Daily Life
Rita decides to buy pencils and notebooks. She buys some pencils, each costing ₹2, and notebooks, each costing ₹15. Let the number of pencils be represented by x and the number of notebooks by y.
1.Write an expression for the total cost of the pencils.
(A) 2x+y (B) 2x (C) 15y (D) 2+x
2. Write an expression for the total cost of the notebooks.
(A) 15y (B) 2x (C) x+15 (D) 15x
3. Form an expression for the total amount Rita spends on pencils and notebooks combined.
(A) 2x+y (B) x+y (C) 2x+15y (D) 2x−y
Competency : Understanding the Concepts
Dimensions of a Rectangle
The length and breadth of a rectangle are represented by the expressions l=3x+2 and b=x+4, respectively, where x is a variable.
Answer the following questions based on this
1.What is the expression for the perimeter of the rectangle?
(a) 2(3x+2)+(x+4) (b) 2(3x+2+x+4) (c) 3x+2+x+43 (d) 3x+x+4
2. Simplify the expression for the perimeter of the rectangle.
(a) 8x+10 (b) 6x+12 (c) 4x+8 (d) 10x+6
3. What is the expression for the area of the rectangle?
(a) (3x+2)(x+4) (b) 3x+2+x+4 (c) 4x+8 (d) (3x+4)(x+2)
4.Expand the expression for the area of the rectangle.
(a) 3x²+12x+2x+8 (b) 3x²+14x+8 (c) 3x²+6x+8 (d) 2x²+14x+10
5. If x=2, what is the area of the rectangle?
(a) 32 (b) 48 (c) 56 (d) 64
Competency : Ability to Compute
Calculating Area of a Garden
Priya has a rectangular garden where the length is 3x+5 metres and the width is 2x+3 metres.
Questions:
1.Which expression represents the area of Priya’s garden?
a) 5x+8 b) 6x+15 c) (3x+5)(2x+3) d) (5x+8)(3x+2)
2. Expand (3x+5)(2x+3) to find the area in terms of x.
a) 6x²+15x+15 b) 6x²+19x+15 c) 6x²+21x+8 d) 6x²+11x+5
3. If x=4x = 4x=4, what is the area of the garden?
a) 180 sq. m b) 200 sq. m c) 210 sq. m d) 230 sq. m
4. If Priya doubles both the length and width of her garden, what will be the new area?
a) 4(6x²+19x+15) b) 2(3x+5)(2x+3) c) 2(6x²+19x+15) d) (3x+5)(2x+3)+20
Competency : Problem Solving
Calculating Costs for a School Event
The school is organising a science fair and needs to purchase supplies. The cost of buying x tables is ₹200 each, and y chairs are ₹100 each. They also need a projector, which costs ₹500.
Questions:
1.Which of the following expressions represents the total cost of the tables, chairs, and projector?
a) 200x+100y+500 b) 300x+100y+500 c) 200x+100y d) 100x+200y+500
2.If the school needs 5 tables and 10 chairs, what will be the total cost?
a) ₹2000 b) ₹3000 c) ₹4000 d) ₹4500
3.If the school decides to buy 2 extra tables and 5 extra chairs, which expression represents the new cost?
a) 200(x+2)+100(y+5)+500 b) 200(x+2)+100(y)+500
c) 200x+100(y+2)+500 d) 200(x+5)+100(y+2)+500
4. Suppose the budget for tables and chairs only is ₹3000. Which equation can help determine the maximum number of tables (x) if the school plans to buy 8 chairs?
a) 200x+800=3000 b) 200x+300y=3000
c) 300x+100y=3000 d) 200x+100y+500=3000
Competency Based Worksheet
Class:- VIII Subject: Maths
NAME: _____________ Mensuration DATE: _____________
Competency : Knowledge of Concepts
Water Storage Tank
A cylindrical water storage tank has a radius of 7 metres and a height of 10 metres.
Questions:
What is the volume of the water tank?
a) 1540 cubic metres b) 1570 cubic metres
c) 1600 cubic metres d) 1620 cubic metres
2. If the tank is half-filled with water, what would be the volume of water in it?
a) 770 cubic metres b) 800 cubic metres
c) 850 cubic metres d) 880 cubic metres
3. What is the curved surface area of the tank?
a) 340 sq. metres b) 380 sq. metres
c) 420 sq. metres d) 440 sq. metres
4.If the tank is closed from the top, what would be the total surface area?
a) 480 sq. metres b) 510 sq. metres
c) 550 sq. metres d) 600 sq. metres
Competency : Understanding the Concepts
Building a Cylindrical Water Tank
A cylindrical water tank has a radius of 5 metres and a height of 8 metres. The tank needs to be painted on the outer surface, excluding the top and bottom.
Questions:
What is the curved surface area of the tank?
a) 240 sq. metres b) 250 sq. metres
c) 260 sq. metres d) 300 sq. metres
2. If the cost of painting is ₹15 per square metre, what will be the total cost to paint the tank?
a) ₹3500 b) ₹3600 c) ₹3700 d) ₹3800
3.If the height of the tank is increased by 50%, what will be the new curved surface area?
a) 320 sq. metres b) 340 sq. metres
c) 360 sq. metres d) 400 sq. metres
4.If the tank is open at the top, what would be the total surface area of the tank, including the bottom?
a) 240 sq. metres b) 300 sq. metres c) 320 sq. metres d) 400 sq. metres
Competency : Ability to Compute
A rectangular garden has a length of 25 metres and a width of 15 metres. The gardener needs to place a fence around the entire garden and plans to cover the garden with grass.
1. What is the perimeter of the garden?
(A) 80 metres (B) 70 metres (C) 100 metres (D) 50 metres
2.What is the area of the garden?
(A) 375 square metres (B) 400 square metres
(C) 325 square metres (D) 300 square metres
3.If the cost of fencing is 50 rupees per metre, what is the total cost of fencing?
(A) 3000 rupees (B) 4000 rupees (C) 2000 rupees (D) 2500 rupees
Competency : Problem Solving
Constructing a Rectangular Swimming Pool
A rectangular swimming pool has a length of 25 metres, a width of 10 metres, and a depth of 3 metres. It is to be fully filled with water.
Questions:
What is the volume of water needed to fill the swimming pool?
a) 500 cubic metres b) 650 cubic metres
c) 750 cubic metres d) 800 cubic metres
2. If the cost of filling water is ₹2 per cubic metre, what will be the total cost to fill the pool?
a) ₹1200 b) ₹1300 c) ₹1400 d) ₹1500
3.If the depth of the pool is reduced by 1 metre, what will be the new volume?
a) 500 cubic metres b) 600 cubic metres
c) 650 cubic metres d) 700 cubic metres
4. If the pool is to be tiled on the bottom and the four walls, what is the area that needs to be tiled?
a) 200 sq. metres b) 300 sq. metres c) 350 sq. metres d) 400 sq. metres
Competency Based Worksheet
Class:- VIII Subject: Maths
NAME: _____________ Direct and Inverse Proportions DATE: _____________
Competency : Knowledge of Concepts
A company has 5 workers who can complete a project in 12 days, working 8 hours per day. The company now needs to complete a similar project in 8 days. They plan to increase the number of workers while keeping the working hours the same.
1.If the project is to be completed in 8 days, how many workers are required?
(A) 8 workers (B) 6 workers (C) 7.5 workers (D) 7 workers
2.What type of proportion exists between the number of workers and the number of days to complete the project?
(A) Direct Proportion (B) Inverse Proportion (C) No Proportion
(D) Both Direct and Inverse Proportion
3.If the company decides to add 3 more workers to the original team of 5, how many days would it take to complete the project?
(A) 7.5 days (B) 8 days (C) 9 days (D) 6 days
Competency : Understanding the Concepts
Buying Notebooks
A school is buying notebooks for students. The school calculates that if each notebook costs ₹20, they can purchase 50 notebooks within the budget. They wonder how many notebooks they can buy if the price per notebook changes.
Questions:
1.If the price per notebook decreases to ₹10, how many notebooks can the school buy with the same budget?
a) 50 b) 75 c) 100 d) 120
2.If the price per notebook increases to ₹25, how many notebooks can the school buy?
a) 30 b) 40 c) 50 d) 60
3.If the school buys 75 notebooks, what would be the cost per notebook?
a) ₹15 b) ₹13 c) ₹12 d) ₹10
4.What happens to the number of notebooks the school can buy if the price per notebook doubles?
a) It doubles. b) It halves. c) It remains the same. d) It increases slightly.
Competency : Ability to Compute
Fuel Consumption on a Road Trip
A car uses 10 litres of fuel to cover 100 kilometres. The driver wants to calculate the fuel needed for varying distances, assuming the car’s fuel efficiency remains constant.
Questions:
1.How much fuel will the car need to travel 250 kilometres?
a) 15 litres b) 20 litres c) 25 litres d) 30 litres
2.If the car has only 8 litres of fuel left, how far can it travel?
a) 60 kilometres b) 75 kilometres c) 80 kilometres d) 85 kilometres
If the driver wants to travel 400 kilometres, how much fuel will be required?
a) 35 litres b) 40 litres c) 45 litres d) 50 litres
3.Which of the following statements best describes the relationship between fuel consumption and distance travelled in this case?
a) Distance and fuel consumption are inversely proportional.
b) Distance and fuel consumption are directly proportional.
c) Fuel consumption decreases as distance increases.
d) Fuel consumption is unrelated to distance.
Competency : Problem Solving
Filling a Tank
A water tank can be filled by a pipe in 6 hours if the water flows at a rate of 10 litres per minute. The rate of water flow can be adjusted to fill the tank faster or slower.
Questions:
1.If the water flow rate is increased to 15 litres per minute, how long will it take to fill the tank?
a) 4 hours b) 5 hours c) 6 hours d) 8 hours
2.If the water flow rate is reduced to 5 litres per minute, how long will it take to fill the tank?
a) 8 hours b) 10 hours c) 12 hours d) 14 hours
3.How much time would it take to fill half of the tank at a rate of 10 litres per minute?
a) 2 hours b) 3 hours c) 4 hours d) 5 hours
4. What happens to the filling time if the flow rate is doubled?
a) The time required doubles. b) The time required halves.
c) The time required stays the same. d) It depends on the tank’s capacity.
Competency Based Worksheet
Class:- VIII Subject: Maths
NAME: _____________ Factorisation DATE: _____________
Competency : Knowledge of Concepts
Factorising Algebraic Expressions
A maths teacher gives students an expression to factorise: x²+7x+10, and asks them to identify the factors.
Questions:
1.Which of the following is the correct factorization of x²+7x+10?
a) (x+2)(x+5) b) (x+1)(x+10) c) (x+3)(x+4) d) (x+2)(x+7)
2.What are the values of the roots for the expression x²+7x+10=0?
a) x=−2 and x=−5 b) x=2 and x=5 c) x=−3 and x=−4 d) x=−1 and x=−10
3. If the teacher changes the expression to x²−7x+10, what would be the correct factorization?
a) (x+5)(x+2) b) (x−5)(x−2) c) (x+3)(x−4) d) (x+10)(x−1)
Competency : Understanding the Concepts
Ravi is learning about factorising expressions in his maths class. His teacher presents him with the expression 6x+9 and asks him to factorise it by finding the greatest common factor (GCF) of both terms.
1. What is the GCF of 6x and 9?
(A) 1 (B) 2 (C) 3 (D) 6
2. What is the factorised form of 6x+9?
(A) 3(2x+3) (B) 3(x+3) (C) 6(x+9) (D) 2(3x+9)
Competency : Ability to Compute
Product of Consecutive Integers
A teacher asks students to find the product of two consecutive integers, represented by the expression x(x+1), and then factorise it to make calculations easier.
Questions:
1.Factorise the expression x²+x
a) x(x+1) b) x²+1 c) x(x−1) d) x²−1
2.If x=7, find the product of two consecutive integers using the factorized expression.
a) 48 b) 54 c) 56 d) 7
3.Rewrite the product expression if x represents an even integer and factor it completely.
a) 2m(2m+1) for integer m b) x(x−1) c) 2m(m-1) for integer m d) None of the above
Competency : Problem Solving
Area of a Rectangle and Factorisation
A landscaper is creating a rectangular garden where the area is represented by the expression 3x²+12x square metres. The landscaper wants to determine the length and width to optimise the layout.
Questions:
1.Factorise the expression 3x²+12x to determine the possible dimensions of the garden.
a) 3(x+4) b) 3x(x+4) c) x(3x+12) d) 3x²(x+4)
2. If x=5 metres, what is the area of the garden?
a) 15 square metres b) 75 square metres
c) 105 square metres d) 90 square metres
3.If the landscaper decides to double the length, represented by x+4, what would be the new area in terms of x?
a) 3x(2x+8) b) 6x(x+4) c) 3x(x+8) d) 6x(x+8)
4.Which of the following best describes the factorization process used for the expression 3x²+12x?
a) Grouping method b) Taking out the common factor
c) Difference of squares d) None of the above
Competency Based Worksheet
Class:- VIII Subject: Maths
NAME: _____________ Introduction to Graphs DATE: _____________
Competency : Knowledge of Concepts
Distance vs. Time
Situation: A car travels a certain distance, and the distance covered over time is recorded as follows:
Based on this information, a distance-time graph is plotted.
Questions:
1.What does the slope of the distance-time graph represent?
a) Distance b) Time c) Speed d) Acceleration
2.What kind of line would you expect on a graph plotting this data?
a) Curved line b) Zigzag line c) Horizontal line d) Straight line
3.If the car continued at the same speed, how far would it travel in 7 hours?
a) 120 km b) 140 km c) 160 km d) 180 km
Competency : Understanding the Concepts
Athlete's Speed During a Race
An athlete's speed (in metres per second) is recorded at different intervals during a 100-metre race. The data is plotted on a graph with time (in seconds) on the x-axis and speed (in metres per second) on the y-axis. Initially, the athlete's speed increases, then it remains constant, and at the end, it decreases.
Questions:
1.What does a steep increase in speed at the beginning of the race suggest about the athlete’s performance?
a) The athlete is slowing down. b) The athlete is speeding up.
c) The athlete is running at a constant speed. d) The athlete has finished the race.
2.What does the flat portion of the graph in the middle of the race represent?
a) The athlete is accelerating. b) The athlete is running at a constant speed.
c) The athlete is decelerating. d) The athlete is resting.
3.What does the downward slope near the end of the race indicate about the athlete's speed?
a) The athlete is slowing down. b) The athlete is speeding up.
c) The athlete is running at a constant speed. d) The athlete has stopped.
Competency : Ability to Compute
School Admission Analysis
A school is analysing the number of students admitted over five years to understand trends. The following data represents the number of students admitted each year.
Based on this data, answer the following questions:
1.What type of graph would best represent this data for easy comparison over the years?
(a) Line Graph (b) Pie Chart (c) Bar Graph (d) Histogram
2.If the trend continues, how many students are expected to be admitted in 2024?
(a) 160 (b) 170 (c) 180 (d) 190
3.Which year showed the least number of admissions?
(a) 2019 (b) 2020 (c) 2021 (d) 2023
4.What is the total number of students admitted from 2019 to 2023?
(a) 700 (b) 740 (c) 750 (d) 800
5.In which year was the increase in admissions the highest as compared to the previous year?
(a) 2020 (b) 2021 (c) 2022 (d) 2023
Competency : Problem Solving
Weekly Temperature Trend
The table below shows the average temperature (in °C) recorded in a city over seven days of the week.
Answer the following questions:
1.Which type of graph would best represent temperature changes over the week?
(a) Line Graph (b) Bar Graph (c) Pie Chart (d) Histogram
2.What is the difference in temperature between the hottest and coldest day of the week?
(a) 8°C (b) 6°C (c) 5°C (d) 4°C
3.If the temperature on Monday next week is expected to be 3°C higher than this Monday, what would it be?
(a) 24°C (b) 25°C (c) 26°C (d) 27°C
4.What is the average temperature over the seven days?
(a) 26°C (b) 27°C (c) 28°C (d) 25°C
5.If temperatures continue to rise by 1°C each day for the next seven days, what would the temperature be on Sunday next week?
(a) 26°C (b) 27°C (c) 28°C (d) 29°C
Competency Based Worksheet
Class:- VIII Subject: Maths
NAME: ____________ Linear equations in one variable DATE: _____________
Competency : Knowledge of Concepts
Pocket Money Distribution
Aman receives a monthly allowance of ₹600 from his parents. He spends part of it on snacks and saves the rest. Aman decides to spend half of his allowance and save the remaining amount. Let x be the amount he spends.
Questions:
1.Which of the following equations represents the amount Aman saves in terms of x?
a) x+2x=600 b) x+x2=600 c) x+(600−x)=600 d) x+600=600
2.If Aman spends half of his allowance, what equation represents this relationship?
a) x=300 b) x=600 c) x2=600 d) x+600=1200
3.How much does Aman save each month?
a) ₹300 b) ₹600 c) ₹200 d) ₹400
Competency : Understanding the Concepts
Buying Notebooks
A teacher buys notebooks for her students. Each notebook costs ₹25, and she has a budget of ₹500. Let x represent the number of notebooks she can buy.
Questions:
1.Which equation represents the number of notebooks the teacher can buy within her budget?
a) x+25=500 b) 25x=500 c) x/25=500 d) x=500+25
2. How many notebooks can the teacher buy with her budget?
a) 10 b) 15 c) 20 d) 25
3. If the cost of each notebook increased to ₹30, how many notebooks could she buy with the same budget?
a) 15 b) 12 c) 10 d) 25
Competency : Ability to Compute
Daily Wage Worker
A daily wage worker is paid ₹200 per day and receives a bonus of ₹25 for each hour of overtime. In one week, he worked 6 days and earned a total of ₹1800, including overtime. Let x represent the number of overtime hours he worked in that week.
Which equation represents the worker’s earnings for the week?
(a) 6×200+25x=1800 (b) 200x+25=1800
(c) 200+25x=1800 (d) 6×200+x=1800
What is the simplified form of the equation 6×200+25x=1800?
(a) 25x=600 (b) 1200+25x=1800 (c) 200x+25=1800 (d) x=600+1800
How many hours of overtime did the worker work?
a) 20 hours (b) 15 hours (c) 10 hours (d) 5 hours
If the worker worked 8 hours of overtime in the next week, what would his total earnings be?
(a) ₹1400 (b) ₹1600 (c) ₹1800 (d) ₹1800
If the overtime bonus was increased to ₹30 per hour, what would the worker earn for 10 hours of overtime?
(a) ₹1800 (b) ₹2000 (c) ₹2200 (d) ₹2400
Competency : Problem Solving
Monthly Savings Plan
Ananya decides to save a fixed amount every month. Her goal is to save ₹6000 by the end of the year. She has already saved ₹1500. Let x represent the amount she needs to save each remaining month to reach her goal.
1.Which equation represents the situation if there are 10 months left in the year?
(a) 10x+1500=6000 (b) x+1500=6000 (c) 10+1500x=6000 (d) x=6000−1500
2.What is the amount Ananya needs to save each month to reach her goal?
(a) ₹350 (b) ₹400 (c) ₹450 (d) ₹500
3.If Ananya could only save ₹400 each month, how much more would she need to reach her goal at the end of the year?
(a) ₹1000 (b) ₹500 (c) ₹1500 (d) ₹2000
4.If Ananya decided to save an additional ₹50 per month, what would be her new monthly savings?
(a) ₹450 (b) ₹500 (c) ₹550 (d) ₹600
5.If Ananya had already saved ₹2000 instead of ₹1500, how much would she need to save per month to meet her goal?
(a) ₹400 (b) ₹350 (c) ₹450 (d) ₹500
Competency Based Worksheet
Class:- VIII Subject: Maths
NAME: ____________ Exponents and Powers DATE: _____________
Competency : Knowledge of Concepts
Light Intensity and Distance
Light intensity III from a source diminishes as we move away from the source. This relationship can be described by the inverse square law, where I ∝ 1d², where d is the distance from the light source.
Questions:
1.If the distance from the light source doubles, by what factor does the light intensity change?
a) 2 times b) 4 times c) 0.5 times d) 0.25 times
2.If the initial intensity at 1 metre from the source is 100 units, what will the intensity be at 3 metres?
a) 33.33 units b) 11.11 units c) 9.1 units d) 1 unit
3.If the intensity at 5 metres is 4 units, what is the intensity at 1 metre?
a) 20 units b) 100 units c) 25 units d) 125 units
Competency : Understanding the Concepts
Scientific Notation of Distances in Space
The distance between Earth and the nearest star (Proxima Centauri) is approximately 4.22 light years, or 3.995×1013 kilometres.
Questions:
1.What does 1013 represent this distance?
a) 10,000 kilometres b) 100,000 kilometres
c) 1,000,000 kilometres d) 10 trillion kilometres
2. If the distance were written as 4×1013 km for simplicity, what is the percent error introduced in this approximation?
a) 0.1% b) 0.25% c) 0.5% d) 1%
3.Which of the following distances is correctly written in scientific notation?
a) 50000=5× 104 b) 0.0003=3×10-4 c) 70=7×101 d) All of the above
Competency : Ability to Compute
Growth of Investment
An investment scheme promises to double the initial amount every year. If the initial investment is ₹500, find the value of the investment over time.
1.What will be the expression for the value of the investment after t years?
(a) 500×t2 (b) 500+2t (c) 500×2t (d) 500×t
2.What will be the value of the investment after 3 years?
(a) ₹1000 (b) ₹2000 (c) ₹3000 (d) ₹4000
3. If the investment period is extended to 5 years, what will be the value of the investment?
(a) ₹10,000 (b) ₹12,000 (c) ₹16,000 (d) ₹18,000
4. If another person invests ₹1000 under the same scheme, what will be the difference in the investment values between this person and the first investor after 4 years?
(a) ₹2000 (b) ₹4000 (c) ₹5000 (d) ₹6000
5.What will be the value of an initial investment of ₹750 after 6 years under this scheme?
(a) ₹12,000 (b) ₹24,000 (c) ₹36,000 (d) ₹48,000
Competency : Problem Solving
Calculating the Population of Bacteria
A scientist is observing a bacterial culture in a petri dish. The initial number of bacteria is 500, and the population doubles every hour.
1.What is the expression for the population of bacteria after t hours?
(a) 500×2 (b) 500×t² (c) 500×2t (d) 500+2t
2.What will be the population after 3 hours?
(a) 2000 (b) 3000 (c) 4000 (d) 5000
3.If the scientist observes the culture for 5 hours, how many times will the population have increased?
(a) 5 times (b) 8 times (c) 16 times (d) 32 times
4. What will be the population after 7 hours?
(a) 32,000 (b) 64,000 (c) 128,000 (d) 256,000
5. If the scientist needs a population of at least 1,000,000 bacteria, after how many hours will this population be reached?
(a) 8 hours (b) 9 hours (c) 10 hours (d) 11 hours
Competency Based Worksheet
Class:- VIII Subject: Maths
NAME: ____________ Squares and square roots DATE: _____________
Competency : Knowledge of Concepts
Finding Square Roots by Estimation
Ravi wants to estimate the square root of 50 without using a calculator. He knows that 7²=49and 8²=64
Questions:
1.Between which two integers does the square root of 50 lie?
a) 6 and 7 b) 7 and 8 c) 8 and 9 d) 5 and 6
2. Which of the following is the best approximation of 50\sqrt{50}50 from the choices below?
a) 7.0 b) 7.1 c) 7.5 d) 7.2
3. What would be the square root of 48, estimated using similar methods?
a) 6.7 b) 6.9 c) 7.0 d) 7.5
Competency : Understanding the Concepts
Understanding Perfect Squares
Riya has a small collection of square tiles. Each tile is a perfect square with a specific area. She is organising them by their side lengths to form different patterns.
1.If one of her tiles has an area of 225 cm², what is the side length of that tile?
(a) 13 cm (b) 14 cm (c) 15 cm (d) 16 cm
2. If she arranges her square tiles to form a larger square with an area of 400 cm², what will be the side length of this larger square?
(a) 18 cm (b) 19 cm (c) 20 cm (d) 21 cm
3.Which of the following areas can Riya achieve by combining two square tiles with side lengths of 12 cm each?
(a) 144 cm² (b) 288 cm² (c) 172 cm² (d) 192 cm²
4.Riya finds a tile with an area of 196 cm². Which of the following statements is correct about this tile?
(a) It has an odd side length. (b) It has a side length of 13 cm.
(c) Its side length is 14 cm. (d) It is not a perfect square.
5. If she wants to form a pattern with tiles that have areas of 1 cm², 4 cm², 9 cm², and 16 cm², which of the following characteristics do these tile areas share?
(a) They are all odd numbers. (b) They are consecutive squares of natural numbers.
(c) They form an arithmetic sequence. (d) They are all multiples of 5.
Competency : Ability to Compute
Solar Panel Installation
A company installs solar panels on a square rooftop with an area of 900 m². Each solar panel covers an area of 25 m².
1.What is the side length of the rooftop?
(a) 20 m (b) 30 m (c) 40 m (d) 50 m
2. How many solar panels are needed to cover the entire rooftop?
(a) 36 panels (b) 40 panels (c) 45 panels (d) 50 panels
3. If each solar panel costs ₹5000, what is the total cost to install solar panels on the rooftop?
(a) ₹150,000 (b) ₹180,000 (c) ₹200,000 (d) ₹250,000
4.If the area covered by each panel is increased to 36 m², how many panels would be needed to cover the entire rooftop?
(a) 20 panels (b) 25 panels (c) 30 panels (d) 35 panels
5. If the cost per panel is reduced to ₹4500, what will be the total cost to install 36 panels?
(a) ₹150,000 (b) ₹162,000 (c) ₹170,000 (d) ₹180,000
Competency : Problem Solving
Painting a Square Wall
An artist is asked to paint a square wall with an area of 2025 m². She plans to cover the wall with square tiles, each having an area of 25 m².
1. What is the side length of the wall?
(a) 35 m (b) 40 m (c) 45 m (d) 50 m
2.What is the side length of each tile?
(a) 4 m (b) 5 m (c) 6 m (d) 7 m
3.How many tiles are needed to cover the entire wall?
(a) 80 (b) 120 (c) 140 (d) 160
4. If the artist decides to leave a 1-metre-wide border unpainted on each side, what would be the area of the unpainted border?
(a) 121 m² (b) 125 m² (c) 145 m² (d) 165 m²
5. If each tile costs ₹50, what will be the total cost for the tiles needed to cover the entire wall?
(a) ₹4000 (b) ₹6000 (c) ₹7500 (d) ₹8000
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