The following Topics and Sub-Topics are covered in this chapter and are available on MSVgo:
Algebra is a branch of mathematics that involves studying numbers, equations, geometry, and mathematical analysis.
For better understanding, algebra is divided into five branches:
A linear inequality is a mathematical statement with both sides not equal to each other. For example: y + 5 > 10. The solution set of linear inequalities is a subset of a universal set with solutions that satisfy the inequality.
Following are properties of linear inequalities:
The factorisation is the act of factoring a number or a polynomial into various numbers of factors. When these factors are multiplied, they give the original number or polynomial. The factorisation is generally considered opposite to the properties of expansion.
Two theorems of factorisation of polynomials:
Quadratic equations are equations that can be written in the general form of ax^2 + b× + c. The maximum power of the quadratic equations is 2. For any quadratic equation, there are two roots, α and β, whose sum is equal to –b/a and multiplication is equal to c/a where the coefficient of x^2, b is the coefficient of x. The “c” is the constant term in the polynomial.
Discriminant (D) of the polynomial is calculated as b^2 – 4ac. The following are the properties of discriminant:
For any two numbers a and b, a/b is the ratio of a and b. When two or more ratios are multiplied by each other term-wise, then the ratio so obtained is known as the compound ratio.
Proportion is a term used for four numbers such that the ratio of the first and second number is equal to the ratio of the third and fourth number. It is represented as a/b = c/d, where a and d terms are known as extreme terms while b and c terms are known as middle terms.
A rectangular arrangement of numbers in the form of columns and rows is known as the matrix. The matrix order is depicted in rows × columns like a matrix with three columns and four rows with the order 4×3.
Two matrices are equal if the order is the same for both the matrices and the matrices’ elements are also the same.
A pair of points located on the plane are known as coordinates, and the geometrical formulas used on these coordinates are known as coordinate geometry.
Distance between two coordinates (a, b) and (c, d) is calculated using the following formula:
Distance = √[c – a)^2 +(d – b)^2]
Arithmetic progression (AP) is a sequence of numbers where the difference between two consecutive numbers is the same, represented by d.
A general form of AP is a, a+d, a+2d…
The nth term of the AP can be calculated using the formula a+(n–1)d.
The chapter ‘Algebra’ is not only an important topic for class 10th mathematics, but it is also an essential concept for advanced mathematics. This chapter’s thorough knowledge will smoothen your journey through the upcoming mathematics chapter, like geometry, equations, number system, etc.