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.

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 non-collinear 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

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.

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).