Topics
Compound Interest
- Compound Interest as a Repeated Simple Interest Computation with a Growing Principal
- Use of Compound Interest in Computing Amount Over a Period of 2 Or 3-years
- Use of Formula
- Finding CI from the Relation CI = A – P
Commercial Mathematics
Goods and Services Tax (G.S.T.)
Banking
Algebra
Geometry
Shares and Dividends
Symmetry
Mensuration
Linear Inequations
Quadratic Equations
- Quadratic Equations
- Method of Solving a Quadratic Equation
- Factorisation Method
- Quadratic Formula (Shreedharacharya's Rule)
- Nature of Roots of a Quadratic Equation
- Equations Reducible to Quadratic Equations
Trigonometry
Statistics
Problems on Quadratic Equations
- Method for Solving a Quadratic Word Problem
- Problems Based on Numbers
- Problems on Ages
- Problems Based on Time and Work
- Problems Based on Distance, Speed and Time
- Problems Based on Geometrical Figures
- Problems on Mensuration
- Problems on C.P. and S.P.
- Miscellaneous Problems
Ratio and Proportion
Probability
Remainder Theorem and Factor Theorem
- Function and Polynomial
- Division Algorithm for Polynomials
- Remainder Theorem
- Factor Theorem
- Applications of Factor Theorem
Matrices
Arithmetic Progression
Geometric Progression
Reflection
- Co-ordinate Geometry
- Advanced Concept of Reflection in Mathematics
- Invariant Points
- Combination of Reflections
- Using Graph Paper for Reflection
Section and Mid-Point Formulae
Equation of a Line
Similarity
Loci
- Locus
- Points Equidistant from Two Given Points
- Points Equidistant from Two Intersecting Lines
- Summary of Important Results on Locus
- Important Points on Concurrency in a Triangle
Angle and Cyclic Properties of a Circle
Tangent Properties of Circles
Constructions
Volume and Surface Area of Solids (Cylinder, Cone and Sphere)
- Mensuration of Cylinder
- Hollow Cylinder
- Mensuration of Cones
- Mensuration of a Sphere
- Hemisphere
- Conversion of Solids
- Solid Figures
- Problems on Mensuration
Trigonometrical Identities
Heights and Distances
- Angles of Elevation and Depression
- Problems based on Elevation and Depression
Graphical Representation of Statistical Data
Measures of Central Tendency (Mean, Median, Quartiles and Mode)
Probability
Definition: Quartile
The observations which divide the whole set of observations into four equal parts are known as quartiles.
Before finding quartiles, the given data must always be arranged in ascending order of magnitude.
Definition: Range
The difference between the largest and smallest values in a data set is called the range.
Range = Largest value − Smallest value
Formula: Quartiles
Case I: When n is ODD
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Lower Quartile, Q₁ = (n + 1) / 4 th term
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Upper Quartile, Q₃ = 3(n + 1) / 4 th term
Case II: When n is EVEN
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Lower Quartile, Q₁ = n / 4 th term
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Upper Quartile, Q₃ = 3n / 4 th term
Formula: Range
Inter-quartile range:
The difference between the upper quartile (Q₃) and the lower quartile (Q₁) is called the inter-quartile range.
Inter-quartile range = Q₃ − Q₁
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It is always positive, since Q₃ > Q₁.
Semi-interquartile range:
Half of the inter-quartile range is called the semi-interquartile range.
Semi-interquartile range = `1/2` (Q₃ − Q₁)
Key Points: Quartiles and Range in Statistics
Types of Quartiles
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Lower Quartile (Q₁)
The observation lies midway between the lowest value and the median. -
Middle Quartile (Q₂)
The median of the data. -
Upper Quartile (Q₃)
The observation lies midway between the median and the highest value.
