CBSE X MATHS SA2 QN PAPER (BOARD)
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mercredi 4 mars 2015
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Affichage des articles dont le libellé est EDUCATION. Afficher tous les articles
Affichage des articles dont le libellé est EDUCATION. Afficher tous les articles
Mid-Point Theorem - MATHEMATICS
The midpoint of the line segment is the geometric centre of the line segment. Midpoint of line segment divides the line into two equal halves.
The line segment joining the mid-points of two sides of a triangle is parallel to the third side and equal to half the third side.
The line drawn through the mid-point of one side of a triangle and parallel to another side bisects the third side.
The line segment joining the mid-points of two sides of a triangle is parallel to the third side and equal to half the third side.
The line drawn through the mid-point of one side of a triangle and parallel to another side bisects the third side.
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dimanche 23 mars 2014
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Areas of Combinations of Plane Figures - MATHEMATICS
A collection of points that are on a plane is known as a plane figure.
We can calculate the area of the figure, which has a non-standard form
Involving basic geometric figures such as circles, squares, triangles, rectangles etc.
We can calculate the area of the figure, which has a non-standard form
Involving basic geometric figures such as circles, squares, triangles, rectangles etc.
Area of the figure= Area of the rectangle + 2
Area of semi circles
Area of semi circles
Area of the required region=
Area of the required region= 
Heron's Formula- MATHEMATICS
In general, we calculate The area of a triangle using the formula 
where b is the base and h is the height of the triangle. Heron’s formula states that ,if a, b, c are the sides of the triangle, then area of the triangle is 
,where s is thesemi perimeter and s=
where b is the base and h is the height of the triangle. Heron’s formula states that ,if a, b, c are the sides of the triangle, then area of the triangle is ,where s is thesemi perimeter and s=
s=
How to Study effectively?
Schedule in study breaks
Don't plan to study non-stop for the next five days. You'll go insane, and you'll be too fried to do well on the exams. When you write your schedule, include short study breaks to help you recharge. You'll feel so much better and will be able to concentrate so much more.
Schedule in sleep
Some people can function well on three hours of sleep a night. Most cannot. You'll do much better during exams if your mental state is good, and sleep is essential for this.
Exercise
There's no better source for stress relief. Just don't over do it to the point that you're procrastinating heavily. Go for short, stress-relieving activities, like outdoor or board games . And don't underestimate the value of a brisk walk.
Prioritize
You have limited time to study and will have to choose what to spend the most time with. Choose what chapters you want to focus on know them well.
Ask your teachers/parents/friends siblings for help
If you're confused about your notes or the readings, go to the resident expert. This works much better if you don't put off studying until the last minute. It's a good idea to read through all of your notes before you start to study, so that you can inquire early about things that confuse you.
Eat Frequent Small Meals
Avoid eating a big meal before a study session. Too much food will send your body into a 'rest' mode. On the other hand, don't starve yourself either. Frequent small meals are best.
Study When You're Sharpest
Study according to your body-clock. Are you sharpest in the morning or at the evening? Schedule your most difficult materials when you are mentally at your best, and schedule the easier ones when you are mentally less efficient.
Drink Water Often
Drink plenty of water during a study session, especially when you feel sluggish. Caffeine may help you to stay awake, but it can increase your anxiety - use it in moderation.
Don't Get Too Comfortable in Your Chair
Choose a chair that supports your back. It should be comfortable, but not too comfortable. Just like an athlete during a performance, your body should be relaxed, so that all your energy goes to where it matters - your brain.
Clear Your Desk of Everything You Don't Need
Have everything you need on the desk. Put away what you do not need for the study session.
Take Breaks Every Hour
It is important to take a break before you feel tired and lose your concentration completely. Regular breaks at least once an hour helps to sustain your concentration. If the work is not going too well and you have difficulties in concentrating, you may need a long break and go back to it later.
Stretch During Your Breaks
Know and respect your concentration span which will vary from hour to hour and from day to day. When you sit for long periods, gravity draws the blood to the lower part of your body. When you take a break, take a few deep breaths and get more oxygen to your brain: try walking around and doing some light stretching for a few minutes. It will help to release tension in your body, and help your circulation.
Study at the Same Time, Same Place
Study at the same time and at the same place, devoted to study only. This helps you to associate the time and place with studying and concentrating. You will find that you get into a habit of studying as soon as you sit down.
At LearnNext, we strive to make your studies easier & learning better. If you haven,t already tried it, try watching a demo at www.LearnNext.com. or download sample papers to revise your preparation. Meanwhile, here are some tips to help you with your Board Exams. All the best.
Tips before Exams:
Take a Xerox of your Hall ticket and keep it safely.
Keep your Compass Box, Hall Tickets and all writing materials ready a day prior to the exam.
Have a healthy snack -so that you don,t feel hungry and low on energy on the exam day.
Take care of these while writing your exam:
Use Black pen to write titles, subtitles & keywords, and underline them.
If there is any mistake don't make it look shabby by scratching it many times; just put a line over it.
Attempt the questions that you know well first and only after that try to recall the questions you are not quite thorough with.
Do not waste long period of time on a single question. If you find it difficult, leave some space and move ahead to come back later after solving the other questions.
Do rough calculation in the rough column drawn on the right hand side of the answer sheet. Do all your calculations neatly.
Do not use short cuts like -etc., & i.e. while answering questions, especially in English.
Do not leave any question. Try to answer it by whatever knowledge you have.
Do not write anything on the question paper.
Revise the answer paper after you have finished writing.
Make no-breaks a rule.
Make diagrams wherever possible, and neatly wit scale and pencil.
Tangents to a Circle - MATHEMATICS
A straight line intersects a circle at one or two point. The tangent to a circle is a line that touches the circle at one point. Secant intersects the circle at two points. The point at which the straight line touches the circle is called the point of contact or point of tangency.
Some properties of tangents to a circle are Infinite number of tangents can be drawn to a circle but only one tangent can be drawn at any given point on a circle. From an external point we can draw two tangents of equal length. The radius of the circle isperpendicular to the tangent at its point of contact and the tangents drawn at the extremities of the diameter of a circle are parallel.
Some properties of tangents to a circle are Infinite number of tangents can be drawn to a circle but only one tangent can be drawn at any given point on a circle. From an external point we can draw two tangents of equal length. The radius of the circle isperpendicular to the tangent at its point of contact and the tangents drawn at the extremities of the diameter of a circle are parallel.
The tangent at any point on a circle is perpendicular to the radius drawn to the point of contact.
Given: A tangent AB with point of contact P.
To prove: OP ⊥ AB
Proof:
Consider point C on AB other than P.
C must lie outside the circle. (∵ A tangent can have only one point of contact with the circle)
OC > OP (∵ C lies outside the circle)
This is true for all positions of C on AB.
Thus, OP is the shortest distance between point P and line segment AB.
Hence, OP ⊥ AB.
From an external point we can draw only two tangents to a circle.
Theorem: Tangents drawn to a circle from an external point are equal in length.
Given: Two tangents AB and AC from an external point A to points B and C on a circle.
To prove: AB = AC
Construction: Join OA, OB and OC.
Proof:
In triangles OAB and OAC,
∠OBA = 90o (Radius OB ⊥ Tangent AB at B)
∠OCA = 90o (Radius OC ⊥ Tangent AC at C)
In triangles OBA and OCA,
∠OBA = ∠OCA = 90o
OB = OC (Radii of the same circle)
OA = OA (Common side)
Thus, ΔOBA 
ΔOCA (RHS congruence rule)
ΔOCA (RHS congruence rule)Hence, AB = AC (Corresponding sides of congruent triangles)
The tangents drawn at the extremities of the diameter of a circle are parallel.
COORDINATE GEOMETRY Area of Triangle - MATHEMATICS
Area of triangle is half the product of its base and corresponding altitude if the base and altitude are given.
If a, b and c are sides of a triangle then its area is given by herons formula 
.
.we can calculate the area of a triangle even if its three vertices are given. If (x1, y1), (x2, y2) and (x3, y3) are the vertices of a triangle
then its area is given by 
square units.
If the area of triangle is zero then the points are called collinear points or vice-versa.
square units.If the area of triangle is zero then the points are called collinear points or vice-versa.
Area of triangle =
square units.If area of triangle is zero then the points are collinear.
Quadratic Equations - MATHEMATICS
An equation of the form ax2 +bx +c =0 is called a 
in one variable, where a, b, c are real numbers and a ≠0. It’s a 
. There are various 
, they are (i) 
(ii) 
(iii) 
(iv) 
.
In factorization method the quadratic equation is solved by splitting them into factors.
In
the quadratic equation is converted into either 
or 
The quadratic formula to find the
are 
where 
is called the discriminant of the quadratic equation denoted by D or D. The sum of the roots of the quadratic equation is 
or 
and the product of the roots of the quadratic equation is 
or 
.
If D=0 roots are real and equal , D>0 roots are real and unequal, D<0 roots are imaginary.
The graph of a quadratic equation is a parabola. It depends on the value of ‘a’, if a>0 the parabola opens upwards, a<0parabola opens downwards.
If D>0 parabola intersects x-axis at two distinct points, D<0 parabola does not intersect the parabola and D=0 parabola touches x-axis at only one point.
in one variable, where a, b, c are real numbers and a ≠0. It’s a . There are various , they are (i) (ii) (iii) (iv) .In factorization method the quadratic equation is solved by splitting them into factors.
In
the quadratic equation is converted into either or The quadratic formula to find the
are where is called the discriminant of the quadratic equation denoted by D or D. The sum of the roots of the quadratic equation is or and the product of the roots of the quadratic equation is or .If D=0 roots are real and equal , D>0 roots are real and unequal, D<0 roots are imaginary.
The graph of a quadratic equation is a parabola. It depends on the value of ‘a’, if a>0 the parabola opens upwards, a<0parabola opens downwards.
If D>0 parabola intersects x-axis at two distinct points, D<0 parabola does not intersect the parabola and D=0 parabola touches x-axis at only one point.
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