# ICSE Mathematics Class 9 Syllabuses.

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-à-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.