Class 10th Board Exam Mathematics papers

[Nitin Sharma]

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UNIT I : NUMBER SYSTEMS
1. REAL NUMBERS (15) Periods
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 (7) Periods
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 (15) Periods
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 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.
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UNIT III : GEOMETRY
1. TRIANGLES (15) Periods
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.
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.

UNIT IV : TRIGONOMETRY
1. INTRODUCTION TO TRIGONOMETRY (10) Periods
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 (15) Periods
Proof and applications of the identity sin2
A + cos2
A = 1. Only simple identities to be given. Trigonometric
ratios of complementary angles.

UNIT VII : STATISTICS AND PROBABILITY
1. STATISTICS (18) Periods
Mean, median and mode of grouped data (bimodal situation to be avoided). Cumulative frequency graph.