can anyone please tell the syllabus of std 10th 1st semester examination 2020 gujarat board
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Answer:
Explanation:
Gujarat SSC Syllabus for Mathematics
UNIT I: Number System
Euclid's Division Lemma
Fundamental Theorem of Arithmetic - statements after reviewing work done earlier and after illustrating and motivating through examples,
Proofs of results and decimal expansions of rational numbers in terms of terminating and non-terminating recurring decimals.
UNIT II: Algebra
1.Polynomials.
Zero of Polynomial
The relationship between zeros and their coefficients of quadratic polynomials.
Statement and simple problems on the 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. Also, The Geometric representation of different possibilities of solutions/inconsistency.
Algebraic conditions for the number of solutions.
The solution of the 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.
3. Quadratic Equations
Standard form of a quadratic equation ax2 + Bx + c = 0, (a ≠ 0).
The solution of the quadratic equations (only real roots) by factorization, by completing the square and by using the quadratic formula.
The relationship between discrimination and the nature of roots. Problems related to day to day activities to be practiced.
UNIT III: Trigonometry
1. Introduction
a. Trigonometric ratios of an acute angle of a right-angled triangle.
b. Proof of their existence (well defined); motivate the ratios, whichever are defined at 0o & 90o.
c. 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 will be given. Trigonometric ratios of complementary angles.
3. Heights and Distances
a. Simple and believable problems on heights and distances.
b. Problems should not involve more than two right triangles.
c. Angles of elevation and depression should be only 300, 450, 600.
UNIT IV: Coordinate Geometry
1. Lines (In two-dimensions)
a. Review the concepts of coordinate geometry done earlier including graphs of linear equations.
b. Awareness of the geometrical representation of quadratic polynomials.
c. The distance between two points and section formula.
d. Area of a triangle. Basic questions will be given.
UNIT V: Geometry
1. 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.
2. If a line divides two sides of a triangle in the same ratio, the line is parallel to the third side.
3. If in two triangles, the corresponding angles are equal, their corresponding sides are proportional and the triangles are similar.
4. If the corresponding sides of two triangles are proportional, their corresponding angles are equal and the two triangles are similar.
5. 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. 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. The ratio of the areas of two similar triangles is equal to the ratio of the squares on their corresponding sides.
8. In a right triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides.
9. In a triangle, if the square on one side is equal to the sum of the squares on the other two sides, the angles opposite to the first side is a right triangle.
2. Circles
1. The tangent at any point of a circle is perpendicular to the radius through the point of contact.
2. 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.
Unit IV: Mensuration