10th Class Mathematics Quiz

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Questions and Answers

What type of number is the square root of 2 classified as?

  • Irrational Number (correct)
  • Rational Number
  • Real Number (correct)
  • Integer

Which method is NOT used to solve a pair of linear equations?

  • Substitution Method
  • Graphical Method
  • Elimination Method
  • Rational Root Theorem (correct)

In the context of quadratic equations, what does a discriminant of zero indicate?

  • Exactly one real root (correct)
  • Complex roots with no real part
  • No real roots
  • Two distinct real roots

How is the sum of the first n terms of an arithmetic progression calculated?

<p>$S_n = \frac{n}{2}(a + l)$ (B), $S_n = \frac{n}{2}(2a + (n - 1)d)$ (C)</p> Signup and view all the answers

What is the correct formula for calculating the distance between two points (x1, y1) and (x2, y2) in the Cartesian plane?

<p>$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$ (D)</p> Signup and view all the answers

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Study Notes

Number Systems

  • Rational and Irrational Numbers
  • Real Numbers and their Properties
  • Decimal Expansions

Polynomials

  • Definition and Types (Linear, Quadratic, etc.)
  • Zeroes of a Polynomial
  • Factorization and Remainder Theorem

Pair of Linear Equations

  • Graphical Method of Solution
  • Algebraic Methods (Substitution, Elimination)
  • Application in Real-World Problems

Quadratic Equations

  • Standard Form: ax² + bx + c = 0
  • Methods of Solutions (Factoring, Quadratic Formula)
  • Nature of Roots (Discriminant)

Arithmetic Progressions

  • Definition and General Term
  • Sum of n Terms
  • Applications in Problem Solving

Triangles

  • Basic Properties and Theorems (Pythagoras, Congruence, Similarity)
  • Area and Perimeter Calculations
  • Coordinate Geometry Related to Triangles

Statistics

  • Collection and Representation of Data (Graphs, Charts)
  • Mean, Median, Mode
  • Measures of Dispersion (Range, Variance, Standard Deviation)

Probability

  • Basic Concepts (Experiment, Sample Space, Event)
  • Probability of Events (Addition and Multiplication Rules)
  • Real-life Applications

Mensuration

  • Area and Volume of Various Shapes (Circle, Triangle, Cylinder, Sphere)
  • Surface Area Calculations
  • Application of Formulas in Word Problems

Coordinate Geometry

  • Cartesian Plane Basics
  • Distance Formula
  • Section Formula and Midpoint Formula

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