Common Mistakes & How to avoid them Class X - Math. Unit: Algebra. Types of Question Common Mistakes Points to be emphasised. points.

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1 Common Mistakes & How to avoid them Class X - Math Unit: Algera Chapter: Pair of Linear Equations in Two Variales Types of Question Common Mistakes Points to e emphasised Solving the system of (i) Error in equations graphially plotting (i) (ii) points Error in marking axes (iii) Not mentioning the point of intersetion as the solution (iv) Not mentioning the equation of the line along with the line in the graph v) Not using the penil and sale to draw the graph Always take three points on eah line and as far as possile hoose points as whole numers or terminating deimal. Avoid 1/3,2/3 1/7 et. Taulate the x and y values for eah line. (ii) Point of intersetion of two lines is the solution. Write x ----and y. As the solution of the system of equations. (iii) Pratie the questions ased on this topi using the graph sheet and try answering the questions in the same way as you will do in atual examination. i.e pratie must e real time

2 Questions ased on Consisteny Conditions i.e to find the value of unknown onstant for whih the system of equations has (i) unique solution (ii) No solution (iii) Infinite solution (i) Error in finding the value of onstant. For example in the system of equations kx+3y-(k-3) 0 12x+ky-k 0 Gives k 0,6,-6 and students stop at this step (ii) Error in interpreting the answer. In ase of unique solution when the answer is k 6 Students write value of unknown k 6 (iii) In ase of onsistent system only unique solution is onsidered y students Always put ak the value of onstant in the III equations and eliminate those values of onstant whih do not satisfy the equations. For example The value of k 0 does not satisfy (i) and (ii) and -6 does not satisfy equation (ii) and only 6 satisfies all the three equations hene the answer is k6. (ii) Always write the interpretation of k 6 as system of equations has unique solution for all values of k exept 6. elimination and sustitution method Cross Multipliation Method (i) In elimination method while sutrating the II equation from the I equation not hanging the signs. (ii) Not writing final answers Error in applying the formula. Always hange the signs of the II equation. It is always etter to verify the answer y sustituting the values of variales in the system of equations Rememer for the system of equations of the form a x + y a x + y Solution is given y x 1 1

3 y 1 a a a a While for a x + y a x + y 2 Solution is Reduile Equations Word Prolems (i) Often students write answer in terms of sustituted variales Students often Misinterpret the prolem and are unale to form the equation. x 1 1 y 1 a a a a To avoid onfusion it is etter to adopt one of the formula and always onvert the system of equations to that form In the questions ased on equations reduile to linear form like (1) (2) Let 1 A and 1 B Solving 2A+3B 2 And 4A -9B -1 Gives A ½ and B 1/3 ut Solutions will e omplete when the value of variales x and y is alulated. Keep this point in mind Pratie a lot of situation ased prolems and formation of equations generally the quantities to e determined are taken

4 Chapter: Polynomials Zeroes of a polynomial Error in interpretation students interpret that numer 0is a zero of every as unknowns x and y (i) If age of Ram and his father is asked take the ages as x and y and then apply the ondition (ii) In ase of a two digit numer take units plae and tens plae digit as x and y the numer will e 10y+x and then apply the onditions of prolem. Also, keep in mind that when the digits of this two-digit numer are reversed, then the new numer eomes 10x+y and not x+10y (iii) In questions that involve the movement of a oat upstream and downstream, rememer that the speed in the 2 ases is: Upstream Speed of oat speed of river Downstream Speed of oat + speed of river. Zero of the polynomial is the real numer at whih polynomial eomes zero it may or may not e

5 Chapter: Quadrati Equations Quadrati formula polynomial. Graph of polynomial intersets the axes at the zero Error in the use of radials numer 0. For example x+1 vanishes at x -1 and not at 0 Graph of the polynomial P(X) intersets or touh x axis at its zeroes and not y axis While applying the quadrati formula e areful in applying the rules of radials for example a + a + k k ompleting the square Not ale to identify the term to e added and sutrated. Before ompleting the square of any quadrati equation make sure to make the oeffiient of square term x 2 or y 2 unity y dividing the whole equation appropriate real numer. One this is done add and sutrat the square of half the oeffiient of x or y.

Lesson 23: The Defining Equation of a Line

Lesson 23: The Defining Equation of a Line Student Outomes Students know that two equations in the form of ax + y = and a x + y = graph as the same line when a = = and at least one of a or is nonzero. a Students know that the graph of a linear