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Questions and Answers
What is the definition of a rational number?
What is the definition of a rational number?
A rational number is a number that can be expressed as p/q, where p and q are integers and q ≠0.
What is the difference between a linear equation and a quadratic equation?
What is the difference between a linear equation and a quadratic equation?
A linear equation has a degree of 1, whereas a quadratic equation has a degree of 2.
What is the purpose of factorization in algebra?
What is the purpose of factorization in algebra?
To express an algebraic expression as a product of simpler expressions.
What is the coordinate geometry used for?
What is the coordinate geometry used for?
What is the formula for the circumference of a circle?
What is the formula for the circumference of a circle?
What is the definition of mean in statistics?
What is the definition of mean in statistics?
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Study Notes
Numbers Systems
- Real Numbers: A combination of rational and irrational numbers.
- Rational Numbers: Can be expressed as p/q, where p and q are integers and q ≠0. Examples: 3/4, 22/7.
- Irrational Numbers: Cannot be expressed as a finite decimal or fraction. Examples: π, e, sqrt(2).
Algebra
- Linear Equations: Equations of the form ax + by + c = 0, where a, b, and c are constants.
- Quadratic Equations: Equations of the form ax^2 + bx + c = 0, where a, b, and c are constants.
- Factorization: Expressing an algebraic expression as a product of simpler expressions.
Geometry
- Coordinate Geometry: Study of geometric shapes using coordinates (x, y) on a graph.
- Properties of Lines: Slope, intercept, and midpoint formulae.
- Properties of Triangles: Angle sum property, exterior angle theorem, and inequalities in triangles.
Mensuration
- Perimeter and Area of Triangles: Formulae for perimeter and area of triangles.
- Circles: Properties of circles, including circumference, area, and sector area.
- Surface Areas and Volumes of Solids: Formulae for surface areas and volumes of cubes, cuboids, and cylinders.
Statistics and Probability
- Measures of Central Tendency: Mean, median, and mode.
- Range and Interquartile Range: Measures of dispersion.
- Basic Concepts of Probability: Experimental probability, theoretical probability, and events.
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