Semester 2 is of 40 marks. The syllabus consists of six units: Algebra, Geometry, Mensuration, Trigonometry, Statistics, Probability.

**(vii) Co-ordinate Geometry**

(a) Reflection

- Reflection of a point in a line: x = 0, y = 0, x = a, y = a, the origin.
- Reflection of a point in the origin.
- Invariant points

(b) Co-ordinates expressed as (x,y), Section formula, Midpoint formula, Concept of slope, equation of a line, Various forms of straight lines.

(i) Section and Mid-point formula (Internal section only, co-ordinates of the centroid of a triangle included).

(ii) Equation of a line:

Slope-intercept form y = mx + c

Two- point form (y - y_{1}) = m(x - x_{1})

Geometric understanding of m as slope/ gradient/ tanθ where θ is the angle the line makes with the positive direction of the x axis.

Geometric understanding of c as the y-intercept/the ordinate of the point where the line intercepts the y axis/ the point on the line where x=0.

Conditions for two lines to be parallel or perpendicular.

Simple applications of all the above.

**(b) Circles**

(i) Angle Properties

- The angle that an arc of a circle subtends at the centre is double that which it subtends at any point on the remaining part of the circle.
- Angles in the same segment of a circle are equal (without proof).
- Angle in a semi-circle is a right angle.

(ii) Cyclic Properties

- Opposite angles of a cyclic quadrilateral are supplementary.
- The exterior angle of a cyclic quadrilateral is equal to the opposite interior angle (without proof).

(iii) Tangent and Secant Properties

- The tangent at any point of a circle and the radius through the point are perpendicular to each other.
- If two circles touch, the point of contact lies on the straight line joining their centres.
- From any point outside a circle, two tangents can be drawn, and they are equal in length.
- If two chords intersect internally or externally then the product of the lengths of the segments are equal.
- If a chord and a tangent intersect externally, then the product of the lengths of segments of the chord is equal to the square of the length of the tangent from the point of contact to the point of intersection.
- If a line touches a circle and from the point of contact, a chord is drawn, the angles between the tangent and the chord are respectively equal to the angles in the corresponding alternate segments.

Note:

- Proofs of all Theorems EXCLUDED.
- Only application of all Circle Theorems in solving numerical problems are included.

Area and volume of solids - Cylinder and Cone.

Three-dimensional solids - right circular cylinder and right circular cone: Area (total surface and curved surface) and Volume. Direct application problems including cost, Inner and Outer volume and melting and recasting method to find the volume or surface area of a new solid. Combination of solids included.

Note: Problems on Frustum are not included.

(a) Using Identities to solve/prove simple algebraic trigonometric expressions

- sin
^{2}A + cos^{2}A = 1 - 1 + tan
^{2}A = sec^{2}A - 1+co
^{t2}A = cosec^{2}A; 0 ≤ A ≤ 90°

(b) Heights and distances: Solving 2-D problems involving angles of elevation and depression using trigonometric tables.

Note: Cases involving more than two right angled triangles excluded.

Statistics - basic concepts, Mean, Median, Mode. Histograms and Ogive.

(a) Computation of:

- Measures of Central Tendency: Mean*, median class and modal class for continuous grouped data.
- *Mean by any method: Direct, Short-cut, Step-deviation.

(b) Graphical Representation. Histograms and Less than Ogive.

- Finding the mode from the histogram, the upper quartile, lower Quartile and median etc. from the ogive.
- Calculation of inter Quartile range.

Random experiments, Sample space, Events, definition of probability, Simple problems on single events.