In this article, we shall study the use of the bisection method to solve an equation. Intermediate Value Theorem : If a function f is continuous on closed interval [a, b] and f (a). f (b) < 0, i.e. ƒ (a) and ƒ (b) are opposite signs, then there exists at least one c ∈ […]
A circle is defined as the locus of all the points in a plane, which are at a fixed distance from a fixed point. The fixed point is called the centre of the circle and the fixed distance is called the radius of the circle. The radius of a circle is denoted by the letter […]
Science > Mathematics > Pair of Straight Lines > Condition That Line is Represented by Homogeneous Equation In this article, we shall study problems to find the condition when one of the lines represented by a homogeneous equation is given. ALGORITHM : Write the auxiliary equation of joint equation. Find the slope of given line […]
Science > Mathematics > Algebra > Logarithms > Concept of Logarithm In this article, we shall study the concept of logarithms and interconversion between exponential form and logarithmic form. Laws of Indices: am × an = am + n am ÷ an = am – n (a ≠ 0) (am)n = amn […]
Science > Mathematics > Pair of Straight Lines > Use of Auxiliary Equation of Pair of Lines In this article, we shall study the use of the auxiliary equation of par of lines to find the required condition. Algorithm: Write the auxiliary equation of the joint equation. Find the slope of given line m. Substitute […]
Science > Mathematics > Pair of Straight Lines > Joint Equation of Pair of Lines Perpendicular To Another Pair of Lines In this article, we shall study to find a joint equation of lines perpendicular to another pair of lines. Note: If m1 and m2 are the slopes of the two lines represented by joint […]
The word Logic is derived from the Greek word ‘Logos’ which means reason. Logic deals with the methods of reasoning. Logic is a process by which we arrive at a conclusion from known statements or assertions with the help of valid assumptions. The valid assumptions are known as laws of logic. The Greek philosopher and […]
Science > Mathematics > Pair of Straight Lines > Nature of Lines Represented by Joint Equation In this article, we shall study to predict the nature of lines using the joint equations of lines. Notes: If ax2 + 2hxy + by2= 0 is a joint equation of lines then the lines represented by joint equation […]
Science > Mathematics > Pair of Straight Lines > Separate Equations of Lines (Auxillary Equation Method) In this article, we shall study to find separate equations of lines from a combined or joint equation of pair of lines by auxiliary equation method. Algorithm: Check if lines exist. use the same method used in the case […]
Science > Mathematics > Pair of Straight Lines > Separate Equations of Lines (Factorization Method) In this article, we shall study to obtain separate equations of lines from a combined or joint equation of pair of lines by factorization method. Algorithm: Check if lines exist. use the same method used in the case to find […]