CLASS 9 MATHS IMPORTANT QUESTION

                                                         SCORE CBSE 

 

Chapter 1: Number Systems

  • Important Topics:
    • Real numbers
    • Irrational numbers
    • Rational numbers
    • Laws of exponents
  • Important Questions:
    1. Express 5.272727... as a rational number.
    2. Prove that √2 is irrational.
    3. Simplify (2x^3 y^4)^2 and give the result in standard form.
    4. Show that the sum of a rational number and an irrational number is irrational.

Chapter 2: Polynomials

  • Important Topics:
    • Definition of polynomials
    • Types of polynomials (linear, quadratic, cubic)
    • Zeros of a polynomial
  • Important Questions:
    1. Find the zeros of the polynomial x² - 5x + 6.
    2. If x + 1 is a factor of the polynomial x² + x - 6, find the other factor.
    3. Verify that (x - 2) is a factor of x² - 4x + 4.
    4. Factorize the polynomial x² + 7x + 12.

Chapter 3: Coordinate Geometry

  • Important Topics:
    • Cartesian plane
    • Distance formula
    • Section formula
  • Important Questions:
    1. Find the distance between the points (3, 4) and (7, 9).
    2. Find the midpoint of the line joining the points (1, 2) and (5, 6).
    3. If A(3, 4) and B(5, 7) are two points, find the coordinates of the point dividing the line segment AB in the ratio 1:2.
    4. Show that the points (1, 2), (3, 4), and (5, 6) are collinear.

Chapter 4: Linear Equations in Two Variables

  • Important Topics:
    • Linear equations in two variables
    • Graphical representation of equations
    • Solutions of a linear equation
  • Important Questions:
    1. Solve the system of equations:
      x + y = 5
      2x - y = 1
    2. Find the solution of the system of equations by substitution method: 3x - y = 7
      2x + y = 8
    3. Represent the linear equation x + y = 10 graphically.
    4. Find whether the point (3, 4) satisfies the equation 2x + 3y = 18.

Chapter 5: Introduction to Euclid's Geometry

  • Important Topics:
    • Euclid's axioms and postulates
    • Definitions (point, line, ray, segment, etc.)
    • Angles, circles, and triangles
  • Important Questions:
    1. State Euclid’s fifth postulate.
    2. Prove that a straight line segment can be drawn joining any two points.
    3. What are Euclid’s axioms?
    4. Explain the difference between postulates and theorems with examples.

Chapter 6: Lines and Angles

  • Important Topics:
    • Types of angles (alternate, corresponding, vertically opposite)
    • Properties of angles
    • Parallel lines and transversals
  • Important Questions:
    1. Prove that if two lines are cut by a transversal and the alternate interior angles are equal, then the lines are parallel.
    2. If two lines are parallel, prove that the sum of the interior angles on the same side of the transversal is 180°.
    3. Find the value of x if 4x + 20 = 180°.
    4. In the figure, find the value of ∠x and ∠y if two parallel lines are cut by a transversal.

Chapter 7: Triangles

  • Important Topics:
    • Types of triangles (scalene, isosceles, equilateral)
    • Pythagoras theorem
    • Congruence of triangles (SSS, SAS, ASA, RHS)
  • Important Questions:
    1. Prove that the sum of the angles of a triangle is 180°.
    2. Prove the Pythagoras theorem.
    3. In △ABC, if AB = AC, then prove that ∠B = ∠C.
    4. If two triangles are congruent, prove that their corresponding parts are equal.

Chapter 8: Quadrilaterals

  • Important Topics:
    • Properties of different quadrilaterals (parallelogram, rectangle, square, rhombus, trapezium)
    • Area of quadrilaterals
  • Important Questions:
    1. Prove that the opposite sides of a parallelogram are equal.
    2. Find the area of a rhombus with diagonals 8 cm and 6 cm.
    3. In a parallelogram ABCD, if ∠A = 70°, find ∠C.
    4. Prove that diagonals of a rectangle are equal.

Chapter 9: Areas of Parallelograms and Triangles

  • Important Topics:
    • Area of parallelograms and triangles
    • Derivation of area formulas
  • Important Questions:
    1. Find the area of a triangle with base 10 cm and height 5 cm.
    2. Derive the formula for the area of a parallelogram.
    3. The base of a triangle is 15 cm, and its height is 8 cm. Find its area.
    4. Find the area of a rhombus with diagonals 12 cm and 16 cm.

Chapter 10: Circles

  • Important Topics:
    • Properties of circles (chords, tangents, secants)
    • Central angle and inscribed angle
  • Important Questions:
    1. Prove that the angle subtended by a chord at the center of a circle is twice the angle subtended on the circumference.
    2. If two tangents are drawn from a point outside the circle, prove that the tangents are equal in length.
    3. Find the length of the tangent drawn from a point 13 cm away from the center of the circle with radius 5 cm.
    4. Show that the lengths of tangents drawn from an external point to a circle are equal.

Chapter 11: Constructions

  • Important Topics:
    • Constructing bisectors of angles
    • Constructing a triangle given its sides
  • Important Questions:
    1. Construct a triangle with sides 5 cm, 6 cm, and 7 cm.
    2. Construct a perpendicular bisector of a line segment.
    3. Construct an angle of 60°.
    4. Construct a pair of tangents to a circle from an external point.

Chapter 12: Heron’s Formula

  • Important Topics:
    • Area of a triangle using Heron’s formula
  • Important Questions:
    1. Find the area of a triangle with sides 7 cm, 8 cm, and 9 cm.
    2. A triangle has sides 13 cm, 14 cm, and 15 cm. Find its area using Heron’s formula.
    3. Find the area of a right-angled triangle with base 12 cm and height 5 cm using Heron’s formula.

Chapter 13: Surface Area and Volume

  • Important Topics:
    • Surface area and volume of cuboids, cylinders, spheres
  • Important Questions:
    1. Find the surface area of a cylinder with radius 7 cm and height 10 cm.
    2. Find the volume of a cone with radius 5 cm and height 12 cm.
    3. Find the surface area of a sphere with radius 6 cm.
    4. A cube has a volume of 64 cm³. Find the length of its edge.

Chapter 14: Statistics

  • Important Topics:
    • Mean, median, mode
    • Data representation (bar graphs, histograms)
  • Important Questions:
    1. Find the mean of the following data: 2, 3, 7, 5, 8, 9.
    2. Calculate the median of the data set: 1, 2, 3, 4, 5, 6.
    3. Represent the following data in a bar graph:
      2010 - 20, 2011 - 25, 2012 - 30, 2013 - 15
    4. Calculate the mode of the following data: 12, 14, 15, 15, 18, 15, 20.

Chapter 15: Probability

  • Important Topics:
    • Probability of events
    • Basic probability concepts
  • Important Questions:
    1. A die is rolled once. What is the probability of getting a number greater than 4?
    2. A card is drawn from a well-shuffled deck. What is the probability of drawing a red card?
    3. What is the probability of getting an even number when a die is rolled?

These questions and topics should help you prepare for your Class 9 Maths exam. Make sure to practice solving these problems to strengthen your understanding of the concepts.

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