# ICSE Mathematics Class 10 Semester-1 Syllabus 2022

Semester 1 is of 40 marks. The syllabus consists of three units: Commercial Mathematics, Algebra, Geometry.

### 1. Commercial Mathematics

(i) Goods and Services Tax (GST)

Computation of tax including problems involving discounts, list-price, profit, loss, basic/cost price including inverse cases. Candidates are also expected to find price paid by the consumer after paying State Goods and Service Tax (SGST) and Central Goods and Service Tax (CGST) - the different rates as in vogue on different types of items will be provided. Problems based on corresponding inverse cases are also included.

(ii) Banking

Recurring Deposit Accounts: computation of interest and maturity value.

### 2. Algebra

(i) Linear Inequations

Linear Inequations in one unknown for x ε N, W, Z, R. Solving

• Algebraically and writing the solution in set notation form.
• Representation of solution on the number line.

(ii) Quadratic Equations in one variable

(a) Nature of roots

• Two distinct real roots if b2 - 4ac > 0
• Two equal real roots if b2 - 4ac = 0
• No real roots if b2 - 4ac < 0

• Factorisation
• Using Formula

(c) Solving simple quadratic equation problems

(iii) Ratio and Proportion

(a) Proportion, Continued proportion, mean proportion

(b) Componendo, dividendo, alternendo, invertendo properties and their combinations

(iv) Factorisation of polynomials

(a) Factor Theorem.

(b) Remainder Theorem.

(c) Factorising a polynomial completely after obtaining one factor by factor theorem.

Note: f(x) not to exceed degree 3.

(v) Matrices

(a) Order of a matrix. Row and column matrices.

(b) Compatibility for addition and multiplication.

(c) Null and Identity matrices.

(d) Addition and subtraction of 2 x 2 matrices.

(e) Multiplication of a 2 x 2 matrix by

• a non-zero rational number
• a matrix

(vi) Arithmetic Progression

• Finding General term
• Finding Sum of first n terms

### 3. Geometry

(a) Similarity

Similarity, conditions of similar triangles.

(i) Comparison with congruency, keyword being proportionality.

(ii) Three conditions: SSS, SAS, AA. Simple applications (proof not included).