Linear Equations in Two Variables
Introduction to Euclid’S Geometry
Lines and Angles
- Concept of Quadrilaterals - Sides, Adjacent Sides, Opposite Sides, Angle, Adjacent Angles and Opposite Angles
- Angle Sum Property of a Quadrilateral
- Types of Quadrilaterals
- Another Condition for a Quadrilateral to Be a Parallelogram
- Theorem of Midpoints of Two Sides of a Triangle
- Property: The Opposite Sides of a Parallelogram Are of Equal Length.
- Theorem: A Diagonal of a Parallelogram Divides It into Two Congruent Triangles.
- Theorem : If Each Pair of Opposite Sides of a Quadrilateral is Equal, Then It is a Parallelogram.
- Property: The Opposite Angles of a Parallelogram Are of Equal Measure.
- Theorem: If in a Quadrilateral, Each Pair of Opposite Angles is Equal, Then It is a Parallelogram.
- Property: The diagonals of a parallelogram bisect each other. (at the point of their intersection)
- Theorem : If the Diagonals of a Quadrilateral Bisect Each Other, Then It is a Parallelogram
- Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles
- Angle Subtended by a Chord at a Point
- Perpendicular from the Centre to a Chord
- Circles Passing Through One, Two, Three Points
- Equal Chords and Their Distances from the Centre
- Angle Subtended by an Arc of a Circle
- Cyclic Quadrilateral
Areas - Heron’S Formula
Surface Areas and Volumes
Statistics and Probability
- Mean , Median , Mode
- Quartile , Inter quartile
The three measures of central tendency for ungrouped data are :
The mean (or average) of a number of observations is the sum of the values of all the observations divided by the total number of observations.
So, `bar x =
(sum_(i=1)^n x_i)/ n`.
For an ungrouped frequency distribution, it is `bar x = (sum_(i=1)^n f_ix_i)/(sum_(i=1)^n f_i)`
The median is that value of the given number of observations, which divides it into exactly two parts.
If n is an odd number, the median = value of the `((n + 1)/2)^(th)` observation.
If n is an even number, median = Mean of the values of the `(n/2)^(th)` and `(n/2 + 1)^(th)` observation.
The mode is that value of the observation which occurs most frequently, i.e., an observation with the maximum frequency is called the mode.
Shaalaa.com | Measures of Central Tendency
Durations of sunshine (in hours) in Amritsar for first 10 days of August 1997 as reported by
the Meteorological Department are given below: 9.6, 5.2, 3.5, 1.5, 1.6, 2.4, 2.6, 8.4, 10.3, 10.9
(i) Find the mean 𝑋 ̅
(ii) Verify that = `sum _ ( i = 1)^10`(xi - x ) = 0
Candidates of four schools appear in a mathematics test. The data were as follows:
|Schools||No. of candidates||
If the average score of the candidates of all the four schools is 66, find the number of
candidates that appeared from school 3.
Explain, by taking a suitable example, how the arithmetic mean alters by
(i) adding a constant k to each term
(ii) subtracting a constant k from each them
(iii) multiplying each term by a constant k and
(iv) dividing each term by a non-zero constant k.