Class 8 Mathematics - CBSE Questionnaire

Chapter 1: Rational Numbers

1. Define a rational number. Give an example.
2. Simplify the expression: 34+58\frac{3}{4} + \frac{5}{8}43​+85​.
3. Find the multiplicative inverse of −57\frac{-5}{7}7−5​.
4. Arrange the following rational numbers in ascending order: 23,56,12\frac{2}{3}, \frac{5}{6}, \frac{1}{2}32​,65​,21​.
5. Is zero a rational number? Explain why.

Chapter 2: Linear Equations in One Variable

1. Solve the equation: $5x-7=3x+9$.
2. A number decreased by 5 is 7. What is the number?
3. If $2x+3=5x-9$, find the value of $x$.
4. A sum of money is divided between A and B in such a way that A gets twice as much as B. If the total is ₹450, how much does each get?

Chapter 3: Understanding Quadrilaterals

1. Define a parallelogram. List its properties.
2. How many diagonals does a hexagon have?
3. Find the sum of the interior angles of a polygon with 12 sides.
4. What is the difference between a rhombus and a square?
5. In a parallelogram, if one angle is 60°, what are the measures of the other three angles?

Chapter 4: Practical Geometry

1. How do you construct a triangle given the lengths of all three sides?
2. Construct a square with a side length of 5 cm. Write the steps involved.
3. What is the criteria for constructing a quadrilateral when all sides are given?
4. How would you construct a parallelogram with the given base and height?

Chapter 5: Data Handling

1. Define mean, median, and mode with an example.
2. Draw a bar graph for the following data:
   • Number of students in different classes: Class 6: 45, Class 7: 50, Class 8: 55, Class 9: 60.
3. Calculate the probability of getting a head when a coin is tossed.
4. What is the range of the following data set: 12, 15, 8, 10, 20, 25?
5. What is the use of pie charts in data handling?

Chapter 6: Squares and Square Roots

1. Find the square of 23.
2. Without using a calculator, find the square root of 144.
3. Find two consecutive numbers whose squares differ by 45.
4. What is the square root of 196?
5. A square garden has an area of 400 m². Find the length of one side.

Chapter 7: Cubes and Cube Roots

1. Find the cube of 4.
2. What is the cube root of 512?
3. If the volume of a cube is 125 cm³, find the side of the cube.
4. Determine if 729 is a perfect cube. If yes, find its cube root.
5. Find the smallest number by which 135 should be multiplied to make it a perfect cube.

Chapter 8: Comparing Quantities

1. A shirt costs ₹600. If it is sold at a 20% discount, what is the selling price?
2. A car is bought for ₹80,000 and sold for ₹90,000. Find the percentage profit.
3. Convert 0.75 into a percentage.
4. If the interest rate is 5% per annum and the principal is ₹10,000, find the simple interest for 2 years.
5. A man buys a house for ₹1,20,000 and spends ₹30,000 on its renovation. He later sells it for ₹1,50,000. Find his percentage loss or gain.

Chapter 9: Algebraic Expressions and Identities

1. Simplify: $(3x+5)+(2x-4)$.
2. Find the product: $(a+2)(a+3)$.
3. Expand: (x+5)2(x + 5)^2(x+5)2.
4. If $x=2$, evaluate 3x2−5x+73x^2 - 5x + 73x2−5x+7.
5. Factorize the expression: x2−16x^2 - 16x2−16.

Chapter 10: Visualizing Solid Shapes

1. What is a polyhedron? Give two examples.
2. How many faces, edges, and vertices does a cube have?
3. Differentiate between a pyramid and a prism.
4. Draw the top, front, and side views of a cuboid.
5. How many edges does a triangular prism have?

Chapter 11: Mensuration

1. Find the area of a triangle with a base of 6 cm and height of 8 cm.
2. Calculate the surface area of a cube with a side length of 4 cm.
3. What is the volume of a cylinder with a radius of 7 cm and height of 10 cm?
4. Find the perimeter of a rectangle with length 15 cm and breadth 10 cm.
5. A circular garden has a radius of 14 m. Find its area.

Chapter 12: Exponents and Powers

1. Express $81$ as a power of $3$.
2. Simplify: (23×24)(2^3 \times 2^4)(23×24).
3. Evaluate: 5−35^{-3}5−3.
4. Write the number $256$ in scientific notation.
5. Simplify: (329)3\left( \frac{3^2}{9} \right)^3(932​)3.

Chapter 13: Direct and Inverse Proportions

1. If $x$ is directly proportional to $y$ and $x=10$ when $y=5$, find $x$ when $y=8$.
2. A car travels 60 km in 2 hours. How far will it travel in 5 hours at the same speed?
3. If $a$ and $b$ are inversely proportional and $a=4$ when $b=6$, find $b$ when $a=8$.
4. Explain direct proportion with a real-life example.
5. In inverse proportion, if the speed of a car increases, what happens to the time taken to cover a fixed distance?

Chapter 14: Factorization

1. Factorize: x2+5x+6x^2 + 5x + 6x2+5x+6.
2. Factorize the expression: 4x2−94x^2 - 94x2−9.
3. Simplify: x2−4x+2\frac{x^2 - 4}{x + 2}x+2x2−4​.
4. Find the factors of 2x2+3x2x^2 + 3x2x2+3x.
5. Factorize the quadratic expression: x2−2x−35x^2 - 2x - 35x2−2x−35.

Chapter 15: Introduction to Graphs

1. Draw the graph of the equation $y=2x+3$.
2. What are the coordinates of the origin in a Cartesian plane?
3. Explain how to plot the point $(3,-2)$ on a graph.
4. What is a linear graph? Give an example.
5. How can you use a graph to solve the equation $y=5x-1$?

Chapter 16: Playing with Numbers

1. What is the divisibility rule for 11?
2. Express 12345 as the sum of its digits multiplied by appropriate powers of 10.
3. If the product of two numbers is 90 and their HCF is 3, find their LCM.
4. Check whether 321 is divisible by 3.
5. Write the number 753 in expanded form.

This questionnaire covers the entire Class 8 CBSE Mathematics syllabus and includes a balance of direct, conceptual, and application-based questions