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Math Tutoring for Grade/class 10- Find math home tutors, online math tutors, home tuitions & private home tutors


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Affordable Math Test Preperation Programs


MLK Home and Online Tutoring Service 's Math Refresher course is designed to build a strong foundation in the basic math skills essential for success on the following tests:

SAT
GMAT
GRE
CAT
MAT
IIT-JEE
AIEEE
OLYMPIADS
NDA
SSC
Bank PO/Clerk
RRB
Delhi & UP-SI Exam

Topics Covered by our Math Home Tutoring Program:


Arithmetic
Pre-Algebra
Algebra 1
Algebra 2
Geometry
Pre-Calculus
Calculus
Statistics & Probability
Trigonometry
General Math

First Term Exam Syllabus for Grade X

UNIT I : NUMBER SYSTEMS

1. REAL NUMBERS

  • 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

UNIT II : ALGEBRA

1. POLYNOMIALS

  • Zeros of a polynomial
  • Relationship between zeros and coefficients of 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 and their graphical solution
  • Geometric representation of different possibilities of solutions/inconsistency
  • Algebraic conditions for number of solutions
  • Solution of a 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

UNIT III : GEOMETRY

1. TRIANGLES

  • Definitions, examples, counter examples of similar triangles
  • (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
  • (Motivate) If a line divides two sides of a triangle in the same ratio, the line is parallel to the third side
  • (Motivate) If in two triangles, the corresponding angles are equal, their corresponding sides are proportional and the triangles are similar
  • (Motivate) If the corresponding sides of two triangles are proportional, their corresponding angles are equal and the two triangles are similar
  • (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
  • (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
  • (Prove) The ratio of the areas of two similar triangles is equal to the ratio of the squares on their corresponding sides
  • (Prove) In a right triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides
  • (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

UNIT IV : TRIGONOMETRY

1. INTRODUCTION TO TRIGONOMETRY

  • Trigonometric ratios of an acute angle of a right-angled triangle
  • Proof of their existence (well defined)
  • motivate the ratios
  • whichever are defined at 0o & 90o
  • Values (with proofs) of the trigonometric ratios of 30o, 45o & 60o. Relationships between the ratios

2. TRIGONOMETRIC IDENTITIES

  • Proof and applications of the identity sin2 A + cos2A = 1. Only simple identities to be given
  • Trigonometric ratios of complementary angles

UNIT VII : STATISTICS AND PROBABILITY

1. STATISTICS

  • Mean
  • median
  • mode of grouped data
  • Cumulative frequency graph

Second Term Exam Syllabus for Class X

UNIT II : ALGEBRA (Contd.)

3. QUADRATIC EQUATIONS

  • Standard form of a quadratic equation ax2 + bx + c = 0, (a ≠ 0)
  • Solution of the quadratic equations (only real roots) by factorization, by completing the square and 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
  • sum of first n terms
  • their application in solving daily life problems

UNIT III : GEOMETRY (Contd.)

2. CIRCLES

  • Tangents to a circle motivated by chords drawn from points coming closer and closer to the point
  • (Prove) The tangent at any point of a circle is perpendicular to the radius through the point of contact
  • (Prove) The lengths of tangents drawn from an external point to circle are equal

CONSTRUCTIONS

  • Division of a line segment in a given ratio (internally)
  • Tangent to a circle from a point outside it
  • Construction of a triangle similar to a given triangle

UNIT IV : TRIGONOMETRY

3. HEIGHTS AND DISTANCES

  • Simple and believable problems on heights and distances
  • Angles of elevation / depression should be only 30o, 45o, 60o

UNIT V : STATISTICS AND PROBABILITY

2. PROBABILITY

  • Classical definition of probability
  • Connection with probability as given in Class IX
  • Simple problems on single events, not using set notation

UNIT VI : COORDINATE GEOMETRY

1. 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

UNIT VII : MENSURATION

1. AREAS RELATED TO CIRCLES

  • the area of a circle
  • area of sectors and segments of a circle
  • Problems based on areas, perimeter, and circumference of the above said plane figures (In calculating area of segment of a circle, problems restricted to central angle of 60o, 90o & 120o only

2. SURFACE AREAS AND VOLUMES

  • 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
  • Problems involving converting one type of metallic solid into another and other mixed problems


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