Math Tutoring for Grade/class 10
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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:
Topics Covered by our Math Home Tutoring Program:
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/nonterminating 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 rightangled 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 twodimensions)
 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
