# Category Archives: School Learning

Question 10. For the following parts of matrices verify that (AB)-1 = B-1A-1. (i) A = and B =  Solution: To prove (AB)-1= B-1A-1 We take LHSâ€¦ Read More
Question 25. Show that the matrix A =  satisfies the equation A3 – A2 – 3A – I3 = 0. Hence, find A-1. Solution: Here, Aâ€¦ Read More
Quadrilaterals are encountered everywhere in life, every square rectangle, any shape with four sides is a quadrilateral. We know, three non-collinear points make a triangle.â€¦ Read More
Triangle is the simplest form of a Polygon. The word “Tri” means three and therefore a figure with 3 angles is a triangle, and Itâ€¦ Read More
A Linear equation is defined as an equation with the maximum degree of one only, for example, ax = b can be referred to asâ€¦ Read More
Any Algebraic expression with constants and variables is known as a Polynomial. Polynomial is a combination of two words, “Poly” and “nominal” where poly meansâ€¦ Read More
An algebraic identity is an equality that holds for any value of its variables. They are generally used in the factorization of polynomials or simplificationâ€¦ Read More
Differential Equations are used to describe a lot of physical phenomenons. They help us to observe something happening in real life and put it inâ€¦ Read More
Question 11. Read the following bar graph and answer the following questions: (i) What information is given by the bar graph?(ii) What was the production ofâ€¦ Read More
A system of linear equations is just a pair of two lines that may or may not intersect. Graph of a linear equation is aâ€¦ Read More
Polynomials are of different types out of which degree two polynomials are in the form ax2 + bx + c, a â‰  0. When weâ€¦ Read More
Nowadays, managing and representing data systematically has become very important especially when the data provided is large and complex, This is when Data Handling comesâ€¦ Read More
Question 1. Two opposite angles of a parallelogram are (3x – 2)Â° and (50 – x)Â°. Find the measure of each angle of the parallelogram.â€¦ Read More
Evaluate the following integrals. Question 11. âˆ«ex(sin4x-4)/(2sin22x)dx Solution:  We have,  âˆ«ex(sin4x-4)/(2sin22x)dx =âˆ«ex(2sin2xcos2x-4)/(2sin22x)dx =âˆ«ex(((2sin2xcos2x)/(2sin22x))-4/(2sin22x))dx =âˆ«ex(cot2x-2cosec22x)dx =âˆ«excot2xdx-2âˆ«excosec22xdx Integrating by parts, excot2x-2âˆ«exd(cot2x)/dx-2âˆ«excosec22xdx  = excot2x+2âˆ«excosec22xdx-2âˆ«excosec22xdx = excot2x+C Question 12. âˆ«ex(2-x)/(1-x)2dxâ€¦ Read More
Question 23. At every point on a curve, the slope is the sum of the abscissa and the product of the ordinate and the abscissa,â€¦ Read More