There will be one paper of two and a half hours duration
carrying 80 marks and Internal Assessment of 20 marks. The paper will be
divided into two sections, Section I (40 marks), Section II (40 marks). Section
I: will consist of compulsory short answer questions. Section II: Candidates
will be required to answer four out of seven questions. The solution of a
question may require the knowledge of more than one branch of the syllabus.

**1.**

**Pure Arithmetic**

Rational and Irrational Numbers

Rational, irrational numbers as real numbers,
their place in the number system. Surds and rationalization of surds.
Simplifying an expression by
rationalizing the denominator.

**2.**

**Commercial Mathematics**

Compound Interest

(a) Compound interest as a repeated
Simple Interest computation with a growing Principal. Use of this in computing
Amount over a period of 2 or 3 years.

(b) Use of formula = (1 + ) n . Finding
CI Using the formula to find one
quantity§ Interest compounded half-yearly
included. §from the relation CI = A – P.
Given different combinations of A, P, r, n, CI and SI;
differenccombinations of A, P, r, n, CI and SI; difference between CI and SI
type included.Rate of growth and depreciation.n Note: Paying back in equal
installments, being given rate of interest and installment amount, not
included.

**3. Algebra**

(i) Expansions Recall of
concepts learned in earlier classes

. (a ± b)

^{2}
(a ± b)

^{3}
(x ± a)(x ± b) (a ± b ± c)

^{3}**(ii) Factorisation**

a 2 – b 2

a 3 ± b 3

ax2 + bx + c, by splitting the middle term.

(iii) Simultaneous Linear
Equations in two Solving algebraically
by:§variables. (With numerical
coefficients only) - Elimination -
Substitution and - Cross Multiplication method
Solving simple problems by framing§ appropriate equations.

(

**iv) Indices/ Exponents**
Handling positive,
fractional, negative and “zero” indices.

Simplification of expressions involving
various exponents ¸
= ´ -
+a a a ,a a a ,(a ) a etc.

**Use of laws of exponents.**
(v) Logarithms (a)
Logarithmic form vis-Ã -vis exponential form: interchanging. (b) Laws of
Logarithms and their uses. Expansion of expression with the help of laws of
logarithms eg. y = 3 4 2 c b´a log y = 4 log
a + 2 log b – 3 log c etc. .

4. Geometry

(i) Triangles

(a) Congruency: four cases: SSS, SAS, AAS, and RHS. Illustration through
cutouts. Simple applications.

Angles opposite equal sides are equaln(b) Problems based
on: If two sides of a triangle are
unequal,nand
converse. then the greater angle is
opposite the Sum of any two sides of a
triangle isngreater
side and converse. Of all straight
lines that can be drawnngreater
than the third side. to a given line
from a point outside it, the perpendicular is the shortest.

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