2021-2022 StudyChaCha

#1
January 26th, 2014, 10:26 AM
 Super Moderator Join Date: Jun 2011

Will you please priode me the KVS TGT Maths Paper????

Yes sure, here I am uploading a pdf file that contains the KVS TGT Maths Paper. There are objective types of the questions available in English. I have taken following questions from the attachment:

1. State the fundamental theorem of Arithmetic.

2. Express 2658 as a product of its prime factors.

3. Show that the square of an odd positive integers is of the form 8m + 1 for some whole number m.

4. Find the LCM and HCF of 17, 23 and 29.

Remaining questions are in the attachment, please click on it
 KVS TGT Maths Paper 1.pdf (1.38 MB, 195 views) KVS TGT Maths Paper 2.pdf (1.49 MB, 228 views)

Last edited by Aakashd; June 6th, 2019 at 09:48 AM.
 Other Discussions related to this topic Thread

#2
February 19th, 2015, 12:20 PM
 Unregistered Guest
Re: KVS TGT Maths Paper

Can you please tell me that KVS TGT Maths exam question Paper is based on which topics?
#3
February 19th, 2015, 12:29 PM
 Super Moderator Join Date: Nov 2011
Re: KVS TGT Maths Paper

Okey as you want to know the topics and syllabus on which the KVS TGT Maths exam question Paper is based so here it is as follows

Number Systems
Real Numbers
Review of representation of natural numbers, integers, rational numbers on the number line. Representation
of terminating / non-terminating recurring decimals, on the number line through successive magnification.
Rational numbers as recurring/terminating decimals.
Examples of nonrecurring / non terminating decimals. Existence of non-rational numbers (irrational numbers) such as √2, √3 and their representation on the number line. Explaining that
every real number is represented by a unique point on the number line and conversely, every point on the
number line represents a unique real number.
Existence of √x for a given positive real number x (visual proof to be emphasized).
Definition of nth root of a real number.
Recall of laws of exponents with integral powers. Rational exponents with positive real bases (to be done by
particular cases, allowing learner to arrive at the general laws.)
Rationalization (with precise meaning) of real numbers of the type (& their combinations)
Euclid's division lemma, Fundamental Theorem of Arithmetic - statements after reviewing work done earlier
and after illustrating and motivating through examples, Proofs of results - irrationality of √2, √3, √5, decimal
expansions of rational numbers in terms of terminating/non-terminating recurring decimals.

. Polynomials
Definition of a polynomial in one variable, its coefficients, with examples and counter examples, its terms,
zero polynomial. Degree of a polynomial. Constant, linear, quadratic, cubic polynomials; monomials, binomials,
trinomials. Factors and multiples. Zeros/roots of a polynomial / equation. State and motivate the Remainder
Theorem with examples and analogy to integers. Statement and proof of the Factor Theorem. Factorization
of ax2 + bx + c, a ≠0 where a, b, c are real numbers, and of cubic polynomials using the Factor Theorem.
Recall of algebraic expressions and identities. Further identities of the type (x + y + z)2 = x2 + y2 + z2 + 2xy
+ 2yz + 2zx, (x y)3 = x3 y3 3xy (x y).
x3 + y3 + z3 — 3xyz = (x + y + z) (x2 + y2 + z2 — xy — yz — zx) and their use in factorization of
polymonials. Simple expressions reducible to these polynomials.
2. LINEAR EQUATIONS IN TWO VARIABLES
Recall of linear equations in one variable. Introduction to the equation in two variables. Prove that a linear
equation in two variables has infinitely many solutions and justify their being written as ordered pairs of real
numbers, plotting them and showing that they seem to lie on a line. Examples, problems from real life,
including problems on Ratio and Proportion and with algebraic and graphical solutions being done
simultaneously.
POLYNOMIALS
Zeros of a polynomial. Relationship between zeros and coefficients of a polynomial with particular reference
to quadratic polynomials. Statement and simple problems on division algorithm for polynomials with real
coefficients.
2. PAIR OF LINEAR EQUATIONS IN TWO VARIABLES
Pair of linear equations in two variables. Geometric representation of different possibilities of solutions/
inconsistency.
Algebraic conditions for number of solutions. Solution of pair of linear equations in two variables algebraically
- by substitution, by elimination and by cross multiplication. Simple situational problems must be included.
Simple problems on equations reducible to linear equations may be included.

Standard form of a quadratic equation ax2 + bx + c = 0, (a ≠0). Solution of the quadratic equations
(only real roots) by factorization and by completing the square, i.e. by using quadratic formula. Relationship
between discriminant and nature of roots.
Problems related to day to day activities to be incorporated.
4. ARITHMETIC PROGRESSIONS
Motivation for studying AP. Derivation of standard results of finding the nth term and sum of first n terms.

Geometry
1. INTRODUCTION TO EUCLID'S GEOMETRY
History - Euclid and geometry in India. Euclid's method of formalizing observed phenomenon into rigorous
Mathematics with definitions, common/obvious notions, axioms/postulates and theorems. The five postulates
of Euclid. Equivalent versions of the fifth postulate. Showing the relationship between axiom and theorem.
1. Given two distinct points, there exists one and only one line through them.
2. (Prove) two distinct lines cannot have more than one point in common.

2. LINES AND ANGLES
1. (Motivate) If a ray stands on a line, then the sum of the two adjacent angles so formed is 180o and the
converse.
2. (Prove) If two lines intersect, the vertically opposite angles are equal.
3. (Motivate) Results on corresponding angles, alternate angles, interior angles when a transversal intersects
two parallel lines.
4. (Motivate) Lines, which are parallel to a given line, are parallel.
5. (Prove) The sum of the angles of a triangle is 180o.
6. (Motivate) If a side of a triangle is produced, the exterior angle so formed is equal to the sum of the two
interiors opposite angles.

3. TRIANGLES
1. (Motivate) Two triangles are congruent if any two sides and the included angle of one triangle is equal
to any two sides and the included angle of the other triangle (SAS Congruence).
2. (Prove) Two triangles are congruent if any two angles and the included side of one triangle is equal to
any two angles and the included side of the other triangle (ASA Congruence).
3. (Motivate) Two triangles are congruent if the three sides of one triangle are equal to three sides of the
other triangle (SSS Congruence).
4. (Motivate) Two right triangles are congruent if the hypotenuse and a side of one triangle are equal
(respectively) to the hypotenuse and a side of the other triangle.
5. (Prove) The angles opposite to equal sides of a triangle are equal.
6. (Motivate) The sides opposite to equal angles of a triangle are equal.
7. (Motivate) Triangle inequalities and relation between 'angle and facing side' inequalities in triangles.
58

1. (Prove) The diagonal divides a parallelogram into two congruent triangles.
2. (Motivate) In a parallelogram opposite sides are equal, and conversely.
3. (Motivate) In a parallelogram opposite angles are equal, and conversely.
4. (Motivate) A quadrilateral is a parallelogram if a pair of its opposite sides is parallel and equal.
5. (Motivate) In a parallelogram, the diagonals bisect each other and conversely.
6. (Motivate) In a triangle, the line segment joining the mid points of any two sides is parallel to the third
side and (motivate) its converse.
5. AREA
Review concept of area, recall area of a rectangle.
1. (Prove) Parallelograms on the same base and between the same parallels have the same area.
2. (Motivate) Triangles on the same base and between the same parallels are equal in area and its converse.
6. CIRCLES
Through examples, arrive at definitions of circle related concepts, radius, circumference, diameter, chord,
arc, subtended angle.
1. (Prove) Equal chords of a circle subtend equal angles at the center and (motivate) its converse.
2. (Motivate) The perpendicular from the center of a circle to a chord bisects the chord and conversely,
the line drawn through the center of a circle to bisect a chord is perpendicular to the chord.
3. (Motivate) There is one and only one circle passing through three given non-collinear points.
4. (Motivate) Equal chords of a circle (or of congruent circles) are equidistant from the center(s) and
conversely.
5. (Prove) The angle subtended by an arc at the center is double the angle subtended by it at any point on
the remaining part of the circle.
6. (Motivate) Angles in the same segment of a circle are equal.
7. (Motivate) If a line segment joining two points subtends equal angle at two other points lying on the
same side of the line containing the segment, the four points lie on a circle.
8. (Motivate) The sum of the either pair of the opposite angles of a cyclic quadrilateral is 180o and its
converse

7. CONSTRUCTIONS
1. Construction of bisectors of line segments & angles, 60o, 90o, 45o angles etc., equilateral triangles.
2. Construction of a triangle given its base, sum/difference of the other two sides and one base angle.
3. Construction of a triangle of given perimeter and base angles.
. TRIANGLES
Definitions, examples, counter examples of similar triangles.
1. (Prove) If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct
points, the other two sides are divided in the same ratio.
2. (Motivate) If a line divides two sides of a triangle in the same ratio, the line is parallel to the third side.
62
3. (Motivate) If in two triangles, the corresponding angles are equal, their corresponding sides are
proportional and the triangles are similar.
4. (Motivate) If the corresponding sides of two triangles are proportional, their corresponding angles are
equal and the two triangles are similar.
5. (Motivate) If one angle of a triangle is equal to one angle of another triangle and the sides including
these angles are proportional, the two triangles are similar.
6. (Motivate) If a perpendicular is drawn from the vertex of the right angle of a right triangle to the
hypotenuse, the triangles on each side of the perpendicular are similar to the whole triangle and to each
other.
7. (Prove) The ratio of the areas of two similar triangles is equal to the ratio of the squares on their
corresponding sides.
8. (Prove) In a right triangle, the square on the hypotenuse is equal to the sum of the squares on the other
two sides.
9. (Prove) In a triangle, if the square on one side is equal to sum of the squares on the other two sides, the
angles opposite to the first side is a right traingle.

2. CIRCLES
Tangents to a circle motivated by chords drawn from points coming closer and closer and closer to the
point.

1. (Prove) The tangent at any point of a circle is perpendicular to the radius through the point of contact.
2. (Prove) The lengths of tangents drawn from an external point to circle are equal.

3. CONSTRUCTIONS
1. Division of a line segment in a given ratio (internally)
2. Tangent to a circle from a point outside it.
3. Construction of a triangle similar to a given triangle

COORDINATE GEOMETRY
The Cartesian plane, coordinates of a point, names and terms associated with the coordinate plane, notations,
plotting points in the plane, graph of linear equations as examples; focus on linear equations of the type
57
ax + by + c = 0 by writing it as y = mx + c and linking with the chapter on linear equations in two variables.
LINES (In two-dimensions)
Review the concepts of coordinate geometry done earlier including graphs of linear equations. Awareness of
geometrical representation of quadratic polynomials. Distance between two points and section formula
(internal). Area of a triangle.

1. AREAS
Area of a triangle using Hero's formula (without proof) and its application in finding the area of a quadrilateral.
2. SURFACE AREAS AND VOLUMES
Surface areas and volumes of cubes, cuboids, spheres (including hemispheres) and right circular cylinders/
cones.

AREAS OF PLANE FIGURES
Motivate the area of a circle; area of sectors and segments of a circle. Problems based on areas and
perimeter / circumference of the above said plane figures. (In calculating area of segment of a circle, problems
should be restricted to central angle of 60o, 90o & 120o only. Plane figures involving triangles, simple
quadrilaterals and circle should be taken.)

2. SURFACE AREAS AND VOLUMES
(i) Problems on finding surface areas and volumes of combinations of any two of the following: cubes,
cuboids, spheres, hemispheres and right circular cylinders/cones. Frustum of a cone.
(ii) Problems involving converting one type of metallic solid into another and other mixed problems. (Problems
with combination of not more than two different solids be taken.)

For complete syllabus here is the attachment
 KVS TGT Maths Syllabus.doc (119.5 KB, 73 views)
__________________
#4
April 20th, 2015, 11:01 AM
 Junior Member Join Date: Apr 2015

KVS TGT Maths Paper 1.pdf (1.38 MB) KVS TGT Maths Paper 2.pdf (1.49 MB)
.....does not downloded,appears an error.plz correct it.