Recall of linear equations in one variable. Introduction to the equation in two variables. Prove that a linear equation in two variables has infinitely many solutions and justify their being written as ordered pairs of real numbers, plotting them and showing that they seem to lie on a line. Examples, problems from real life, including problems on Ratio and Proportion and with algebraic and graphical solutions being done simultaneously.

1. (Prove) The diagonal divides a parallelogram into two congruent triangles.
2. (Motivate) In a parallelogram opposite sides are equal, and conversely.
3. (Motivate) In a parallelogram opposite angles are equal, and conversely.
4. (Motivate) A quadrilateral is a parallelogram if a pair of its opposite sides is parallel and equal.
5. (Motivate) In a parallelogram, the diagonals bisect each other and conversely.
6. (Motivate) In a triangle, the line segment joining the mid points of any two sides is parallel to the third side and (motivate) its converse.

1. (Prove) Parallelograms on the same base and between the same parallels have the same area.
2. (Motivate) Triangles on the same base and between the same parallels are equal in area and its converse.

Through examples, arrive at definitions of circle related concepts, radius, circumference, diameter, chord, arc, subtended angle.
1. (Prove) Equal chords of a circle subtend equal angles at the center and (motivate) its converse.
2. (Motivate) The perpendicular from the center of a circle to a chord bisects the chord and conversely, the line drawn through the center of a circle to bisect a chord is perpendicular to the chord.
3. (Motivate) There is one and only one circle passing through three given noncollinear points.
4. (Motivate) Equal chords of a circle (or of congruent circles) are equidistant from the center(s) and conversely.
5. (Prove) The angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle.
6. (Motivate) Angles in the same segment of a circle are equal.
7. (Motivate) If a line segment joining two points subtendes equal angle at two other points lying on the same side of the line containing the segment, the four points lie on a circle.
8. (Motivate) The sum of the either pair of the opposite angles of a cyclic quadrilateral is 180 and its converse

1. Construction of bisectors of line segments & angles, 60, 90, 45 degree angles etc., equilateral triangles.
2. Construction of a triangle given its base, sum/difference of the other two sides and one base angle.
3. Construction of a triangle of given perimeter and base angles.

6. Surface Areas and Volumes Quick link

Surface areas and volumes of cubes, cuboids, spheres (including hemispheres) and right circular cylinders/cones.

7. Statistics Quick link

Introduction to Statistics : Collection of data, presentation of data — tabular form, ungrouped or grouped, bar graphs, histograms (with varying base lengths), frequency polygons, qualitative analysis of data to choose the correct form of presentation for the collected data. Mean, median, mode of ungrouped data.

8. Probability Quick link

History, Repeated experiments and observed frequency approach to probability. Focus is on empirical probability. (A large amount of time to be devoted to group and to individual activities to motivate the concept; the experiments to be drawn from real  life situations, and from examples used in the chapter on statistics).

Monday, 6 October 2014
9th class Maths NCERT Solution and previous Question
Saturday, 30 August 2014
DAV and DPS Question Papers for class 9 and 10 SA1 September 2014  2015
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Tuesday, 29 July 2014
Geetha told her classmate radha that (root2  1 upon root root2 + 1) is an irrational number. Radha told Geetha that she was wrong and further claimed that if there is a number x such that x3 is irrational then x5 is also irrational. Geetha said that Radha was wrong. Radha accepted her mistake.justify both these statements.
CBSE Class IX Chapters for Mathematics

Test Paper And Study Materials

Thursday, 20 February 2014
PRACTICE QUESTIONS CLASS VIII: CHAPTER – 15_ INTRODUCTIONS TO GRAPH
QUESTIONS CLASS VIII
PRACTICE CHAPTER – 15_ INTRODUCTIONS TO
GRAPH
1. If
y – coordinate of a point is zero, then this point always lies:
(a) I quadrant (b) II quadrant (c) x – axis (d) y – axis
2. If
x – coordinate of a point is zero, then this point always lies:
(a) I quadrant (b) II quadrant (c) x – axis (d) y – axis
3. Point
(–6, 4) lies in the quadrant:
(a) I (b) II (c) III (d) IV
4. The
point (–4, –3) means:
(a) x = –4, y = –3 (b) x = –3, y = –4 (c) x = 4, y = 3 (d)
None of these
5. Point
(0, 4) lies on the:
(a) I quadrant (b) II quadrant (c) x – axis (d) y – axis
6. Point
(5, 0) lies on the:
(a) I quadrant (b) II quadrant (c) x – axis (d) y – axis
7. On
joining points (0, 0), (0, 2), (2,2) and (2, 0) we obtain a:
(a) Square (b) Rectangle (c) Rhombus (d) Parallelogram
8. Point
(–2, 3) lies in the:
(a) I quadrant (b) II quadrant (c) III quadrant (d) IV
quadrant
9. Point
(0, –2) lies:
(a) on the xaxis (b) in the II quadrant (c) on the yaxis
(d) in the IV quadrant
10. Abscissa
of the all the points on x – axis is:
(a) 0 (b) 1 (c) –1 (d) any number
11. Ordinate
of the all the points on x – axis is:
(a) 0 (b) 1 (c) –1 (d) any number
12. Abscissa
of the all the points on y – axis is:
(a) 0 (b) 1 (c) –1 (d) any number
13. Ordinate
of the all the points on y – axis is:
(a) 0 (b) 1 (c) –1 (d) any number
14. The
point whose ordinate is 4 and which lies on y – axis is:
(a) (4, 0) (b) (0, 4) (c) (1, 4) (d) (4, 2)
15. The
perpendicular distance of the point P(3,4) from the y – axis is:
(a) 3 (b) 4 (c) 5 (d) 7
2 or 3 marks
11. Draw
the graph of y = 3x. From the graph, find the value of y when (i) x = 4 and
(ii) x =5.
12. Consider
the relation between the perimeter and the side of a square, given by P = 4a.
Draw a graph to show this relation. From the graph, find the value of P when
(i) a = 4 and (ii) a =5.
13. Consider
the relation between the area and the side of a square, given by A = x^{2}. Draw a
graph to show this relation. From the graph, find the value of P when x = 4.
14. Simple
interest on a certain sum is Rs. 40 per year then S = 40x, where x is the
number of years. Draw a graph of this relation. From the graph, find the value
of S when (i) x = 5 and (ii) x =6.
15. Plot the points
(0, 2), (3, 0), (–3, 0) and (0, –2) in the graph sheet. Join these points. Name
the figure obtained and find the area of the figure so obtained.
1.(c)

2.(d)

3. (b)

4. (a)

5. (d)

6. (c)

7. (a)

8. (b)

9. (c)

15. (a)

10. (a)

11.

12. (d)

13. (a)

14. (d)

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