# 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 LHS… Read More
Question 25. Show that the matrix A =  satisfies the equation A3 – A2 – 3A – I3 = 0. Hence, find A-1. Solution: Here, A… 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.… 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 It… 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 as… 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 means… 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 simplification… 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 in… 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 of… 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 a… Read More
Polynomials are of different types out of which degree two polynomials are in the form ax2 + bx + c, a ≠ 0. When we… 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 comes… Read More
Question 1. Two opposite angles of a parallelogram are (3x – 2)° and (50 – x)°. Find the measure of each angle of the parallelogram.… Read More
Evaluate the following integrals. Question 11. ∫ex(sin4x-4)/(2sin22x)dx Solution:  We have,  ∫ex(sin4x-4)/(2sin22x)dx =∫ex(2sin2xcos2x-4)/(2sin22x)dx =∫ex(((2sin2xcos2x)/(2sin22x))-4/(2sin22x))dx =∫ex(cot2x-2cosec22x)dx =∫excot2xdx-2∫excosec22xdx Integrating by parts, excot2x-2∫exd(cot2x)/dx-2∫excosec22xdx  = excot2x+2∫excosec22xdx-2∫excosec22xdx = excot2x+C Question 12. ∫ex(2-x)/(1-x)2dx… 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,… Read More