CBSE Class 8 Mathematics Practice Worksheet Set 01

PREPARE AN ATTRACTIVE SCRAP BOOK INCLUDING:

Question 1. Make a word book (Dictionary) taking mathematical terms you have studied so far.
Answer: To create a mathematical dictionary in your scrap book, collect and define at least 15 to 20 terms studied up to Class 8 in alphabetical order. For example:
1. Acute Angle: An angle whose measure is less than \(90^\circ\).
2. Binomial: An algebraic expression consisting of two terms, such as \(2x + 3y\).
3. Chord: A line segment joining any two points on a circumference of a circle.
4. Diagonal: A line segment connecting two non-consecutive vertices of a polygon.
5. Equation: A statement of equality between two mathematical expressions containing one or more variables.
In simple words: A mini math dictionary containing definitions and examples of important terms learned in class.

Exam Tip: Include clear diagrams or mathematical formulas next to each term to make your scrap book more visually appealing and informative.

Question 2. Design a T- shirt with a mathematical design/ quotation and discuss about the different sizes available.
Answer: Design concept: Draw or print a creative mathematical quote on the front of a T-shirt, such as Euler's identity \(e^{i\pi} + 1 = 0\), a geometric fractal pattern, or the quote: "Math is the only place where people buy 64 watermelons and nobody asks why."
Discussion on sizes: T-shirts are typically manufactured in standard sizes such as Small (S), Medium (M), Large (L), and Extra Large (XL). The variation in sizes involves proportional scaling of dimensions such as chest width, shoulder length, and overall height, which is a practical application of ratio and proportion.
In simple words: Create a sketch of a T-shirt featuring a fun math quote and write a short paragraph explaining standard clothing sizes using ratios.

Exam Tip: Relate the sizing differences to scale factors and ratio concepts to incorporate mathematical relevance into your discussion.

Question 3. Take 6 cubes of the same size. Measure its length, breadth & height.
i) Find the surface area of 1 cube.
Answer: Let the side length of each identical cube be \(a = 5\text{ cm}\) (measured using a ruler: length = 5 cm, breadth = 5 cm, height = 5 cm).
Total surface area of 1 cube = \(6a^2\)
Surface area = \(6 \times (5\text{ cm})^2 = 6 \times 25\text{ cm}^2 = 150\text{ cm}^2\)
In simple words: The surface area of a single cube is calculated using the formula \(6a^2\) where \(a\) is the side length.

Exam Tip: Always include proper units (square centimeters, \(\text{cm}^2\)) when calculating areas.

Question 3. ii) Paste 2 cubes together & find the surface area of cuboid so formed.
Answer: When 2 identical cubes of side \(a = 5\text{ cm}\) are pasted face-to-face, they form a cuboid with dimensions:
Length \(l = 5\text{ cm} + 5\text{ cm} = 10\text{ cm}\)
Breadth \(b = 5\text{ cm}\)
Height \(h = 5\text{ cm}\)
Surface area of the cuboid = \(2(lb + bh + hl)\)
Surface area = \(2((10 \times 5) + (5 \times 5) + (5 \times 10))\)
Surface area = \(2(50 + 25 + 50) = 2(125) = 250\text{ cm}^2\)
In simple words: Joining two cubes creates a cuboid whose length doubles while breadth and height remain the same.

Exam Tip: Notice that joining two faces together hides two square areas of \(a^2\) from the total individual surface area (\(300\text{ cm}^2 - 50\text{ cm}^2 = 250\text{ cm}^2\)).

Question 3. iii) Paste 3 cubes in 2 different ways & compare their surface areas. Present in the form of a model.
Answer: Way 1 (Linear Arrangement): 3 cubes placed in a straight line.
Dimensions of the cuboid: Length \(l = 3 \times 5 = 15\text{ cm}\), breadth \(b = 5\text{ cm}\), height \(h = 5\text{ cm}\).
Surface area = \(2(15 \times 5 + 5 \times 5 + 5 \times 15) = 2(75 + 25 + 75) = 2(175) = 350\text{ cm}^2\).

Way 2 (L-Shaped or Block Arrangement): 2 cubes placed side-by-side with the 3rd cube placed on top of one of them.
Surface area calculation: A solid block of 3 cubes in an L-shape exposes fewer outer square faces. Counting the exposed square faces (each of area \(25\text{ cm}^2\)): Top (3), Bottom (3), Front (3), Back (3), Left (2), Right (2) = Total 16 square faces.
Total surface area = \(16 \times 25\text{ cm}^2 = 400\text{ cm}^2\).
Comparison: The linear arrangement has a surface area of \(350\text{ cm}^2\), whereas the compact L-shaped arrangement has a surface area of \(400\text{ cm}^2\).
In simple words: Different ways of arranging the same number of cubes result in different total surface areas due to varying degrees of overlapping faces.

Exam Tip: Counting exposed square faces directly is often faster and less prone to arithmetic errors than using standard cuboid formulas for composite shapes.

Question 4. Watch the TV show on various mathematicians called "The Story of Maths" on discovery channel and write its description.
Answer: "The Story of Maths" is a documentary series presented by mathematician Marcus du Sautoy that explores the history of mathematics from ancient civilizations to modern breakthroughs. It highlights key mathematical developments across different cultures including ancient Egypt, Mesopotamia, Greece, India, China, and the Islamic world. The description should include notes on how mathematical concepts like zero, calculus, and geometry evolved to solve practical human problems in astronomy, architecture, and commerce.
In simple words: A summary of a documentary showing how math was discovered and used by different ancient civilizations across the world.

Exam Tip: Mention specific contributions such as the invention of zero in India or geometry in ancient Greece to make your description detailed.

Question 5. Write any 5 math puzzles by taking help from newspaper or any magazine.
Answer: Here are 5 classic math puzzles suitable for your scrap book:
1. Sudoku: Fill a \(9 \times 9\) grid so that each column, row, and \(3 \times 3\) subgrid contains digits from 1 to 9 without repetition.
2. Age Puzzle: A father is 4 times as old as his son. After 20 years, he will be twice as old as his son. Find their present ages. (Solution: Son is 10, Father is 40).
3. Number Series: Find the missing number in the sequence: 2, 6, 12, 20, 30, ?. (Solution: 42, since differences increase by 2: +4, +6, +8, +10, +12).
4. Clock Puzzle: What is the angle between the hands of a clock at 3:15? (Solution: \(7.5^\circ\)).
5. Coin Puzzle: You have 9 identical-looking coins, one of which is slightly heavier. What is the minimum number of weighings on a balance scale to find the heavy coin? (Solution: 2 weighings).
In simple words: Five interesting brain teasers and number puzzles collected from print media with their solutions.

Exam Tip: Always provide clear step-by-step solutions below each puzzle in your scrap book.

Question 6. Do the assignment given from R.S. Aggarwal (reference book)
Answer: Complete the assigned chapter exercises (such as Rational Numbers, Squares and Square Roots, or Algebraic Expressions) from your R.S. Aggarwal textbook in a separate homework notebook or designated section of your scrap book, showing all working steps clearly.
In simple words: Complete the textbook practice questions assigned by your subject teacher.

Exam Tip: Show all rough work clearly on the left-hand side or margin of your notebook.