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: Arithmetic Mean
The arithmetic mean (or, simply, mean) of a set of numbers is obtained by dividing the sum of the numbers in the set by the number of numbers.
\[\mathbf{Mean}=\frac{\left(x_1+x_2+x_3+\ldots+x_n\right)}{n}=\frac{\Sigma x_i}{n}\]
Example
Two vessels contain 20 liters and 60 liters of milk respectively. What is the amount that each vessel would have if both share the milk equally?
The average or the arithmetic mean would be
= `"Total quantity of milk"/"Number of vessels"`
= `(20 + 60)/2` litres
= 40 litres.
Thus, each vessel would have 40 liters of milk.
Example
Find range of following data: 1, 0, 2, 3, 2, 6, 8, 10, 12, 12, 13.
Arrange the following data in ascending order:
0, 1, 2, 2, 3, 6, 8, 10, 12, 12, 13.
Maximum number = 13 and Minimum number = 0
Range = Maximum number - Minimum number
Range = 13 - 0
Range = 13.
Example
Ashish studies for 4 hours, 5 hours, and 3 hours respectively on three consecutive days. How many hours does he study daily on average?
The average study time of Ashish would be
`"Total number of study hours"/"Number of days for which he studied" = (4 + 5 + 3)/3` hours = 4 hours per day
Thus, we can say that Ashish studies for 4 hours daily on an average.
Example
The ages in years of 10 teachers of a school are:
32, 41, 28, 54, 35, 26, 23, 33, 38, 40
(i) What is the age of the oldest teacher and that of the youngest teacher?(ii) What is the range of the ages of the teachers?
(i) Arranging the ages in ascending order, we get:
23, 26, 28, 32, 33, 35, 38, 40, 41, 54.
We find that the age of the oldest teacher is 54 years and the age of the youngest teacher is 23 years.
(ii) Range of the ages of the teachers = (54 – 23) years = 31 years
Example
A batsman scored the following number of runs in six innings: 36, 35, 50, 46, 60, 55. Calculate the mean runs scored by him in an inning.
Total runs = 36 + 35 + 50 + 46 + 60 + 55 = 282.
To find the mean, we find the sum of all the observations and divide it by the number of observations.
Therefore, in this case, mean = `282/6` = 47.
Thus, the mean runs scored in an inning is 47.
