Sunday, 9 February 2025

CLASS 8 MATHS WORKSHEETS

Class 8 

Mathematics - Comprehensive Worksheet (Set 1)

Chapter-Wise Questions

1. Rational Numbers

  1. Find the reciprocal of −37\frac{-3}{7}.
  2. Express −94-\frac{9}{4}as a decimal.
  3. Find the value of (25×103)÷415\left(\frac{2}{5} \times \frac{10}{3} \right) \div \frac{4}{15}.
  4. Write all rational numbers between 2 and 3.
  5. If a=23a = \frac{2}{3} and b=−34b = -\frac{3}{4}, find a×ba \times b

2. Linear Equations in One Variable

  1. Solve: 3(x−2)=2x+53(x - 2) = 2x + 5.
  2. The sum of a number and its double is 24. Find the number.
  3. If 4x−5=2x+94x - 5 = 2x + 9, find xx.
  4. Solve for yy: 7(y−3)=5(y+2)7(y - 3) = 5(y + 2).
  5. The length of a rectangle is three times its width. If the perimeter is 48 cm, find its dimensions.

3. Understanding Quadrilaterals

  1. Find the sum of the interior angles of a hexagon.
  2. A quadrilateral has three angles as 60°, 80°, and 110°. Find the fourth angle.
  3. Find the number of diagonals in an octagon.
  4. Name the quadrilateral that has all sides equal but angles are not 90°.
  5. Find the measure of each exterior angle of a regular pentagon.

4. Data Handling

  1. The mean of five numbers is 30. If four numbers are 25, 35, 40, and 20, find the fifth number.
  2. Find the median of 12, 18, 25, 30, 42.
  3. Represent the following data in a bar graph: Number of books sold in a week – Mon: 30, Tue: 45, Wed: 50, Thu: 40, Fri: 55.
  4. Find the probability of getting a head when a coin is tossed.
  5. The marks of five students in a math test are 55, 60, 65, 70, and 75. Find the mean.

5. Squares and Square Roots

  1. Find the square of 16.
  2. Find the square root of 1024.
  3. Find the smallest number that must be divided by 392 to make it a perfect square.
  4. Without actual division, check if 1156 is a perfect square.
  5. Find the square root of 2025 using the prime factorization method.

6. Cubes and Cube Roots

  1. Find the cube of 12.
  2. Find the cube root of 2197.
  3. What is the smallest number that must be multiplied with 729 to make it a perfect cube?
  4. The cube root of a number is 6. Find the number.
  5. Find the cube root of 2744 using the division method.

7. Comparing Quantities (Percentage, Profit & Loss, Interest, etc.)

  1. Convert 72% into a fraction and a decimal.
  2. A shopkeeper sells a table for ₹540 after giving a discount of 10%. Find the marked price.
  3. Find the compound interest on ₹6000 at 12% per annum for 2 years.
  4. A bag is marked at ₹1500 but sold at a discount of 20%. Find the selling price.
  5. The price of a laptop increases by 8% per year. If the current price is ₹50,000, find its price after 2 years.

8. Algebraic Expressions and Identities

  1. Expand: (x−7)2(x - 7)^2.
  2. Factorize: x2−11x+24x^2 - 11x + 24.
  3. Simplify: (3x−2)2−(x+1)(x−1)(3x - 2)^2 - (x + 1)(x - 1).
  4. If a=4a = 4 and b=−3b = -3, find the value of a3+b3a^3 + b^3.
  5. Verify the identity: (a−b)2=a2−2ab+b2(a - b)^2 = a^2 - 2ab + b^2.

9. Mensuration

  1. Find the area of a semicircle with diameter 14 cm.
  2. Find the surface area of a cuboid with dimensions 4 cm × 5 cm × 6 cm.
  3. Find the volume of a sphere with radius 7 cm.
  4. A cone has a base radius of 5 cm and height 12 cm. Find its curved surface area.
  5. The area of a triangle is 84 cm² and its base is 14 cm. Find its height.

10. Exponents and Powers

  1. Simplify: 34×333^4 \times 3^3.
  2. Write 0.0000450.000045 in standard form.
  3. Solve: (25)2÷24(2^5)^2 \div 2^4.
  4. Find the value of (15)−3\left(\frac{1}{5}\right)^{-3}.
  5. Express 1024 in exponential form using base 2.

11. Direct and Inverse Proportions

  1. If 6 men can complete a work in 10 days, how many men are needed to finish it in 4 days?
  2. If a car travels 150 km in 5 hours, how far will it travel in 7 hours at the same speed?
  3. If the cost of 9 pens is ₹81, find the cost of 12 pens.
  4. If xx and yy are inversely proportional, and x=5x = 5 when y=20y = 20, find yy when x=8x = 8.
  5. If 25 machines can complete a work in 18 days, how many days will 40 machines take?

12. Probability

  1. A bag contains 6 red balls, 4 blue balls, and 5 green balls. Find the probability of picking a blue ball.
  2. What is the probability of getting an even number when a die is rolled?
  3. A deck of 52 cards is shuffled. Find the probability of drawing a queen.
  4. Find the probability of picking a consonant from the word "EDUCATION".
  5. If a coin is tossed 200 times and heads appear 120 times, find the probability of getting tails.
Answers

1. Rational Numbers

  1. Reciprocal of −37\frac{-3}{7} = −73\frac{-7}{3}.
  2. −94-\frac{9}{4}as a decimal = -2.25.
  3. (25×103)÷415=2\left(\frac{2}{5} \times \frac{10}{3} \right) \div \frac{4}{15} = 2.
  4. Some rational numbers between 2 and 3: 2.1, 2.2, 2.3, 2.4, 2.5, ...
  5. a×b=23×(−34)=−612=−12a \times b = \frac{2}{3} \times \left(-\frac{3}{4}\right) = -\frac{6}{12} = -\frac{1}{2}.

2. Linear Equations in One Variable

  1. 3(x−2)=2x+53(x - 2) = 2x + 5
    3x−6=2x+53x - 6 = 2x + 5
    3x−2x=5+63x - 2x = 5 + 6
    x=11x = 11.
  2. Let the number be xx, then x+2x=24⇒3x=24⇒x=8x + 2x = 24 \Rightarrow 3x = 24 \Rightarrow x = 8.
  3. 4x−5=2x+9⇒4x−2x=9+5⇒x=74x - 5 = 2x + 9 \Rightarrow 4x - 2x = 9 + 5 \Rightarrow x = 7.
  4. 7(y−3)=5(y+2)⇒7y−21=5y+10⇒2y=31⇒y=15.57(y - 3) = 5(y + 2) \Rightarrow 7y - 21 = 5y + 10 \Rightarrow 2y = 31 \Rightarrow y = 15.5.
  5. Length = 18 cm, Width = 6 cm.

3. Understanding Quadrilaterals

  1. Sum of interior angles of hexagon = (6−2)×180=720∘(6-2) \times 180 = 720^\circ.
  2. Fourth angle = 360∘−(60∘+80∘+110∘)=110∘360^\circ - (60^\circ + 80^\circ + 110^\circ) = 110^\circ
  3. Number of diagonals in an octagon = 8(8−3)2=20\frac{8(8-3)}{2} = 20
  4. Rhombus has all equal sides but angles are not 90°.
  5. Each exterior angle of a pentagon = 3605=72∘\frac{360}{5} = 72^\circ.

4. Data Handling

  1. Fifth number = (5×30)−(25+35+40+20)=50(5 \times 30) - (25 + 35 + 40 + 20) = 50
  2. Median of 12, 18, 25, 30, 42 = 25.
  3. Draw a bar graph based on given data.
  4. Probability of getting a head when a coin is tossed = 12\frac{1}{2}.
  5. Mean marks = 55+60+65+70+755=65\frac{55+60+65+70+75}{5} = 65

5. Squares and Square Roots

  1. 162=25616^2 = 256
  2. 1024=32\sqrt{1024} = 32.
  3. Smallest number to divide 392 = 2.
  4. 1156 is a perfect square as 342=115634^2 = 1156.
  5. 2025=45

6. Cubes and Cube Roots

  1. 123=172812^3 = 1728
  2. 21973=13\sqrt[3]{2197} = 13.
  3. Smallest number to multiply with 729 to make it a perfect cube = 9.
  4. Number = 63=2166^3 = 216.
  5. 27443=14\sqrt[3]{2744} = 14.

7. Comparing Quantities (Percentage, Profit & Loss, Interest, etc.)

  1. 72% = 72100=1825\frac{72}{100} = \frac{18}{25}, Decimal = 0.72.
  2. Marked price = 5400.9=600
  3. C.I. = ₹ 1,512.
  4. Selling price = ₹ 1200 - (1200 × 0.2) = 960.
  5. Future price = ₹ 50,000 × (1.08)^2 = ₹58,320.

8. Algebraic Expressions and Identities

  1. (x−7)2=x2−14x+49(x - 7)^2 = x^2 - 14x + 49
  2. x2−11x+24=(x−8)(x−3)x^2 - 11x + 24 = (x - 8)(x - 3)
  3. (3x−2)2−(x2−1)=9x2−12x+4−x2+1=8x2−12x+5(3x - 2)^2 - (x^2 - 1) = 9x^2 - 12x + 4 - x^2 + 1 = 8x^2 - 12x + 5
  4. 43+(−3)3=64−27=374^3 + (-3)^3 = 64 - 27 = 37.
  5. Identity verified: (a−b)2=a2−2ab+b2(a - b)^2 = a^2 - 2ab + b^2.

9. Mensuration

  1. Area of semicircle = 12πr2=12×3.14×49=76.93\frac{1}{2} \pi r^2 = \frac{1}{2} \times 3.14 \times 49 = 76.93cm².
  2. Surface area = 2(4×5+5×6+6×4)=1482(4×5 + 5×6 + 6×4) = 148 cm².
  3. Volume of sphere = 43πr3=1436.76\frac{4}{3} \pi r^3 = 1436.76 cm³.
  4. Curved Surface Area = πrl=3.14×5×13=204.1\pi r l = 3.14 \times 5 \times 13 = 204.1 cm².
  5. Height of triangle = 12 cm.

10. Exponents and Powers

  1. 34×33=34+3=373^4 \times 3^3 = 3^{4+3} = 3^7.
  2. Standard form of 0.000045 = 4.5×10−54.5 \times 10^{-5}.
  3. (25)2÷24=210÷24=26=64(2^5)^2 \div 2^4 = 2^{10} \div 2^4 = 2^6 = 64.
  4. (15)−3=53=125\left(\frac{1}{5}\right)^{-3} = 5^3 = 125.
  5. 1024 in exponential form = 2102^{10}.

11. Direct and Inverse Proportions

  1. Men required = 15.
  2. Distance = 210 km.
  3. Cost of 12 pens = ₹108.
  4. When x=8x = 8, y=12.5y = 12.5.
  5. Days needed = 11.25 days.

12. Probability

  1. 415\frac{4}{15}.
  2. Probability of even number = 36=12\frac{3}{6} = \frac{1}{2}.
  3. Probability of drawing a queen = 452=113\frac{4}{52} = \frac{1}{13}.
  4. Probability of consonant in "EDUCATION" = 59\frac{5}{9}.
  5. Probability of getting tails = 80200=0.4\frac{80}{200} = 0.4.

Class 8

Mathematics - Complete Worksheet (Set 2) for Board Exam Preparation

Chapter-wise Questions

1. Rational Numbers

  • Simplify: 34+58\frac{3}{4} + \frac{5}{8}
  • Find the multiplicative inverse of −25-\frac{2}{5}
  • Solve: 23÷56\frac{2}{3} \div \frac{5}{6}

2. Linear Equations in One Variable

  • Solve: 5x−7=3x+95x - 7 = 3x + 9
  • If x3+4=10\frac{x}{3} + 4 = 10, find xx.
  • The sum of two numbers is 45. One number is twice the other. Find them.

3. Understanding Quadrilaterals

  • Classify the following quadrilaterals: Parallelogram, Rhombus, Square, Trapezium.
  • Find the sum of interior angles of a quadrilateral.
  • The measure of three angles of a quadrilateral are 110∘,90∘,70∘110^\circ, 90^\circ, 70^\circ. Find the fourth angle.

4. Data Handling

  • The marks obtained by 10 students are: 45, 50, 55, 60, 40, 45, 50, 55, 60, 50. Find the mode and median.
  • Draw a bar graph for the following data:
    • Apples: 40
    • Bananas: 35
    • Grapes: 50
    • Oranges: 45

5. Square and Square Roots

  • Find the square of 15.
  • Find the square root of 144.
  • Estimate 50\sqrt{50} to the nearest decimal.

6. Cube and Cube Roots

  • Find the cube of 4.
  • Find the cube root of 125.
  • Identify whether 729 is a perfect cube.

7. Comparing Quantities

  • A shirt costs ₹800 and is sold at 10% discount. Find the selling price.
  • If ₹5000 is deposited in a bank at 5% per annum simple interest for 3 years, find the interest earned.

8. Algebraic Expressions and Identities

  • Expand: (a+b)2(a + b)^2
  • Factorize: x2−9x^2 - 9
  • Simplify: 3x(2x+5)−4(x2−2)3x(2x + 5) - 4(x^2 - 2)

9. Mensuration

  • Find the area and perimeter of a rectangle with length 10 cm and breadth 5 cm.
  • Find the volume of a cube with side 6 cm.
  • Find the surface area of a cylinder with radius 7 cm and height 10 cm.

10. Exponents and Powers

  • Simplify: (23×24)÷22(2^3 \times 2^4) \div 2^2
  • Express 0.00045 in standard form.
  • Find the value of (32)3


ANSWERS

Here are the answers to the Class 8 CBSE Math worksheet:

1. Rational Numbers

  • 34+58=68+58=118\frac{3}{4} + \frac{5}{8} = \frac{6}{8} + \frac{5}{8} = \frac{11}{8}
  • Multiplicative inverse of −25-\frac{2}{5} is −52-\frac{5}{2}
  • 23÷56=23×65=1215=45\frac{2}{3} \div \frac{5}{6} = \frac{2}{3} \times \frac{6}{5} = \frac{12}{15} = \frac{4}{5}

2. Linear Equations in One Variable

  • 5x−7=3x+95x - 7 = 3x + 9
    → 5x−3x=9+75x - 3x = 9 + 7
    → 2x=162x = 16
    → x=8x = 8
  • x3+4=10\frac{x}{3} + 4 = 10
    → x3=6\frac{x}{3} = 6
    → x=18x = 18
  • Let the numbers be xx and 2x2x. Given x+2x=45x + 2x = 45,
    → 3x=453x = 45
    → x=15x = 15, so the numbers are 15 and 30.

3. Understanding Quadrilaterals

  • The sum of interior angles of a quadrilateral is 360°.
  • Fourth angle = 360°−(110°+90°+70°)=90°360° - (110° + 90° + 70°) = 90°

4. Data Handling

  • Mode = Most frequent value = 50
  • Median = Middle value (sorted order: 40, 45, 45, 50, 50, 50, 55, 55, 60, 60)
    → 50+502=50\frac{50 + 50}{2} = 50.

5. Square and Square Roots

  • Square of 15 = 225
  • Square root of 144 = 12
  • 50≈7.07\sqrt{50} \approx 7.07

6. Cube and Cube Roots

  • Cube of 4 = 43=644^3 = 64
  • Cube root of 125 = 1253=5\sqrt[3]{125} = 5
  • 729 is a perfect cube because 93=7299^3 = 729.

7. Comparing Quantities

  • Discount = 10%10\% of 800 = 10100×800=80\frac{10}{100} \times 800 = 80
    → Selling price = 800−80=720800 - 80 = 720
  • Simple interest = P×R×T100=5000×5×3100=750\frac{P \times R \times T}{100} = \frac{5000 \times 5 \times 3}{100} = 750

8. Algebraic Expressions and Identities

  • (a+b)2=a2+2ab+b2(a + b)^2 = a^2 + 2ab + b^2
  • x2−9=(x−3)(x+3)x^2 - 9 = (x - 3)(x + 3)
  • 3x(2x+5)−4(x2−2)=6x2+15x−4x2+8=2x2+15x+83x(2x + 5) - 4(x^2 - 2) = 6x^2 + 15x - 4x^2 + 8 = 2x^2 + 15x + 8

9. Mensuration

  • Perimeter of rectangle = 2(l+b)=2(10+5)=302(l + b) = 2(10 + 5) = 30
    → Area = 10×5=5010 \times 5 = 50cm²
  • Volume of cube = a3=63=216a^3 = 6^3 = 216cm³
  • Surface area of cylinder = 2πr(h+r)=2×3.14×7(10+7)=748.642\pi r(h + r) = 2 \times 3.14 \times 7(10 + 7) = 748.64

10. Exponents and Powers

  • (23×24)÷22=2(3+4−2)=25=32(2^3 \times 2^4) \div 2^2 = 2^{(3+4-2)} = 2^5 = 32
  • 0.00045=4.5×10−40.00045 = 4.5 \times 10^{-4}
  • (32)3=32×3=36=729(3^2)^3 = 3^{2 \times 3} = 3^6 = 729

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