solve converse of a theorem

Question: Solve graphically x - 2y = 1 and x + y = 4. Use 2cm = 1 unit on both axes and plot only 3 points per line. Answer: x - 2y = 1 2y = x - 1 x + y = 4 y = 4 - x ..

When p(x) is divided by x-a, R = p(a) (by remainder theorem) p(x) = (x-a).q(x)+p(a) (Dividend = Divisor x quotient + Remainder Division Algorithm) But p(a) = 0 is given. Hence p(x) = (x-a).q(x) Conversely if x-a is a factor of p(x) then p(a)=0. p(x) = (x-a).q(x) + R If (x-a) ..

Definitions, postulates, reasoning, theorems Euclidean/non-Euclidean geometries Coordinate, transformational, axiomatic systems Conditional statements Properties of geometric figures Inductive/deductive reasoning Tessellations Pythagorean Theorem Coordinate systems M..

Question: Solve the following equation: Answer: 2x-(1-2x) = 5-3(1+x) 2x-1+2x = 5-3-3x 4x+3x = 5-3+1 7x=3 ..

Question: Solve the following equation: Answer: 5(3x+5) = 2(2x-1) (by cross-multiplication) 15x-4x = -2-25 11x = -27 ..

Question: Solve graphically x = 4 and 3x - 2y = 10. Answer: A) x = 4 B) 3x - 2y = 10 2y = 3x - 10 Ans : x = 4; y = 1..

Limits- operations on functions Continuity of a function Intermediate value, extreme value theorem Derivatives, differentiability Derivatives of functions Chain rule Rolle's theorem, mean value theorem, and L'Hopital's rule Maxima, minima, inflection points, interv..

Question: Prove the converse of mid-point theorem using Basic Proportionality Theorem. That is, prove that the line drawn from the mid-point of one side of a triangle, parallel to the second side, bisects the third side. [2 Mark] Answer: Given: ABC is ..

ABC is a right-angled triangle. (By converse of Pythagoras theorem..

Absolute value to solve equations/inequalities Systems of linear equations/inequalities Operations on polynomials Factoring polynomials/trinomials Operations on complex numbers Operations on rational expressions Graphing quadratic equations Quadratic equations in complex number s..