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|1||Metrices and Determinants|
|2||Real and Complex Numbers|
|4||Algebraic Expressions and Algebraic Formulas|
|7||Linear Equations and Inequalities|
|8||Linear Graphes and Their Application|
|9||Introduction to Coordinate Geometry|
|11||Parallelograms and Triangles|
|12||Line Bisectors and Angle Bisectors|
|13||Sides and Angles of a Triangle|
|14||Ratio and Proportion|
|16||Theorems Related with Area|
|17||Practical Geometry - Triangles|
After studying this unit you will be able to define
After studying this unit you will be able to recall the set of real numbers as a union of sets of rational and irrational numbers, depict real numbers on the number line, demonstrate a number with terminating and non-terminating recurring decimals on the number line. To carryout basic operations, apply the laws of exponents to simplify expressions with real exponents.
After studying this unit you will be able to express a number in standard form of scientfic notation and vice versa, define logarithm of a number y to the base a as the power to which a must be raised to give the number.
After studying this unit you will be able to know that a rational expression behaves like a rational number, define a rational expression as the quotient of two polynomials p(x) and q(x) where q(x) is not the zero polynomial, examine whether a given rational algebraic expression is in lowest from or not.
After studying this unit you will be able to state and prove Remainder theorem and explain through examples, define zeros of polynomial, state and prove factor theorem, use Factor theorem to factorize a cubic polynomial.
After studying this unit you will be able to find highest common Factor and Least common Multiple of algebraic expressions, use factor or division method to determine highest common factor and Least common multiple, know the relationship between H.C.F and L.C.F. You will also be able to solve real life problems related to H.C.F and L.C.M.
After studying this unit you will be able to recall linear equation in one variable, solve linear equation with rational coefficients, reduce equations, involving radicals, to simple linear form and find their solutions.
After studying this unit you will be able to indentify pair of real numbers as an ordered pair, recognize an ordered pair through different examples, describe rectangular or Cartesian plane consisting of two number lines interesting at right angles at the point O, draw different geometrical shapes by joining a set of given points, solve appropriate real life problems, interpret conversion graph as a linear graph relating to two quantities which are in direct proportion.
After sudying this unit you will be able to define coordinate geometry, derive distance formula to calculate distance between two points given in Cartesian plane, use distance formula to find distance between two given points.
After studying this unit you will be able to prove that in any correspondence of two triangles, if one side and any two angles of one triangle are congruent to the corresponding side and angles of the other, then triangles are congruent. You will also learn to prove that if in the correspondence of two right-angled triangles, the hypotenuse and one side of one are congruent to the hypotenuse and the corresponding side of the other, then the triangles are congruent.
After studying this chapter you will be able to prove that if two opposite sides of a quadrilateral are congruent and parallel, it is a parallelogram. You will also learn to prove that if three or more parallel lines make congruent segments on a transversal, they also intercept congruent segments on any other line that cuts them.
After studying this unit you will be able to prove that any point on the right bisector of a line segment is equidistant from its end points, prove that any point equidistant from the end points of a line segment is on the right bisector of it.
After studying this unit you will be able to prove that if two sides of a triangle are unequal in length, the longer side has an angle of greater measure opposite to it, prove that if two angles of a triangle are unequal in measure, the side opposite to the greater angle is longer than the side opposite to the smaller angle.
After studying this unit you will be able to prove that a line parallel to one side of a triangle, intersecting the other two sides, divides them proportionally, prove that if a line segment intersects the two sides of a triangle in the same ratio, then its is parallel to the third side. You will also learn to prove that if two triangles are similar, the measures of their corresponding sides are proportional.
After studying this chapter you will be able to prove that in a right-angled triangle, the square of the length of hypotenuse is equal to the sum of the squares of the lengths of the other two sides(Pythagoras Theorem). You will also be to able to prove that if the square of one side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right angled triangle(converse to Pythagoras Theorem).
After studying this unit you will be able to prove that parallelograms on the same base and lying between the same parallel lines (or of the same altitude) are equal in area, prove that parallelograms on equal bases and having the same altitude are equal in area, prove that triangles on the same base and of the same altitude are equal in area.
After studying this unit you will be able to construct a triangle having given: two sides and the included angle, one side and two of the angles, two of its sides and the angle opposite to one of them (with all three responsibilities). You will also learn to construct a triangle equal in area to a given quadrilateral.
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