11 and 12 Grade Math

11 and 12 grade math practice the topics are divided into three parts. Part one deals with elementary Algebra, part two provides a basic course in trigonometry and part three considers elements of two dimensional Co-ordinate Geometry including solid geometry and mensuration.

Each topic that are covered in 11 and 12 grade math, concepts is enlightened with a summarization which includes important theorems, results and formula are discussed in each topic with numerous types of solved examples. Sufficient number of problems have been inserted in grade 11 and 12 practice math task worksheets beginning with easier followed gradually by harder ones.

It is expected that students should be acquainted with the basic 11 and 12 grade math concepts relating to each topic and should be able to apply those to simple elementary problems, preferably numerical.



Algebra:

In 11 and 12 grade math these are the topics which are covered in Algebra.

● Variation: Direct, inverse and joint variation, theorem of joint variation. Application to simple examples of time and worktime and distance, mensuration, physical laws, economics.

● Arithmetical Progression:

Definition of A. P., common difference, term, summation of terms. Sum of n natural numbers. Sum of the and cubes of first natural numbers, A. M. 

● Geometric Progression: Definition of G. P., Common ratio, general term, summation of n terms, G. M.

● SurdsRational numbers. To show that √2 is not rational. Idea of irrational numbers, surds, quadratic surds, mixed surds, conjugate surds, properties of surds, if a + √b = 0 then a = 0, b = 0 ; if a + √b = c + √d , then a = c, b = d. Rationalization of surds. Square root of quadratic surds. 


● Laws of Indices: Proofs for fundamental laws of indices for positive integers, statement for fractional, zero and negative indices : simple applications.

Logarithms: Definition, base, index, general properties of logarithms, common logarithm, characteristic and mantissa, antilogarithm, use of logarithmic tables.

Complex Numbers: Complex numbers, significance of the imaginary unit i, addition, multiplication and division, properties of complex numbers ; if a + ib = 0, then a= 0, b= 0 ; if a + ib = c + id, then a = c, b = d. Argand diagram. Modulus. Argument, complex conjugate. Square root of complex numbers, cube roots of unity and their properties.

● Theory of Quadratic Equations: Quadratic equations with real roots. Statement of fundamental theorem of algebra. Roots (two and only two roots), relation between roots and coefficients of a quadratic equation. Nature of roots, common roots. Nature of the quadratic expression ax\(^{2}\) + bx + c — its sign and magnitude.

● Permutations: Definition. Theorem on permutations of n different things taken r at a time, things not all different, permutation with repetitions (circular permutation excluded).

● Combinations: Definition : Theorem on combination of n different things taken r at a time, things not all different. Basic identities. Division into two groups (circular combination excluded).

● Binomial Theorem for Positive Integral Index: Statement of the theorem, proof by method of induction. General term, number of terms, middle term, equidistant terms. Simple properties of binomial coefficients.

● Infinite Series: The power series Σxn. Binomial series (1 + x)n (n ≠ positive integer), exponential and logarithmic series with ranges of validity (statement only). Simple applications.


Trigonometry:

In 11 and 12 grade math these are the topics which are covered in Trigonometry.

Revision exercises of the topics covered in the syllabus of Secondary Mathematics.

The relation s = rθ.

● The Negative and Associated angles: - θ, 90° ± θ, 180° ± θ, 270° ± θ, 360° ± θ.

● Trigonometrical Ratios of Compound Angles: Geometrical methods (for Sine and Cosine only). Product formulae, sum & difference formulae.

● Multiple and Sub-multiple Angles: Simple problems.

Identities (conditional) of Trigonometrical Ratios (Sum of angles π or π/2)

General Solutions of Trigonometrical Equations.

Trigonometrical Inverses (specific mention of principal branch).

● Graphs of Trigonometrical Functions: y = sin mx, y = cos mx and y = tan mx, where m is an integer with stated values.

● Properties of Triangles: Basic relations between sides, angles, circus-radius and in-radius. Area of triangles in different forms. Simple and direct applications.


Plane Analytical Geometry, Mensuration & Solid Geometry:

In 11 and 12 grade math these are the topics which are covered in Plane Analytical Geometry, Mensuration & Solid Geometry.

Rectangular Cartesian Co-ordinates: Directed line and directed line segment, co-ordinate system on a directed line and rectangular Cartesian co-ordinate system in a plane.

Polar Co-ordinates: Notion of directed angles and polar co-ordinate system. (Radius vector o be taken as positive.)

Transformation from Cartesian to Polar Co-ordinates and vice-versa.

Distance between Two Points: Division of a line segment in a given ratio. Area of a triangle (all in terms of rectangular Cartesian co-ordinates). Application to geometrical properties. Verification of Apollonius’ Theorem.

Locus: Concept of locus by simple illustration. Equation of locus in term of rectangular Cartesian co-ordinates.

Equations of Straight Lines (in rectangular Cartesian co-ordinates only): Notion of inclination and slope of a line. Slope in terms of co-ordinates of two points on it. Equations of co-ordinate axes, equations of lines parallel to co-ordinate axes, slope-intercept form, point-slope form, equation of the line through two given points, intercept form, symmetric form, normal form. Every first degree equation represents a straight line.

Angle between Two Lines: Conditions of perpendicularity and parallelism of two lines. Equation of a line parallel to a given line. Equation of a line perpendicular to a given line, conditions that two lines may be identical.

Distance of a Point from a Given Line: Notion of a signed distance of a point from a line, position of a point with respect to a line, sides of a line. Equations of bisectors of angles between two lines, equation of bisector of an angle that contains the origin.

● Equations of Circles: Standard equation. Equation of a circle given center and radius. General equation of the form x2 + y2 + 2gx + 2fy + c = 0 represents a circle. Reduction to standard form (parallel. transformation assumed). Equation of a circle if end points of a diameter be given (all in terms of rectangular Cartesian co-ordinates). Parametric equation of a circle. Outside and inside points of a circle. Intersection of a line with a circle. Equation of a chord with respect to the middle point.

● Conic Section: Idea of conic sections as sections of cone. Focus— Directrix definitions of a conic section, eccentricity, classification according to the value of eccentricity.

● Parabola: Standard equation. Reduction of a parabola of the form x = ay2 + by + c or y = ax2 + bx + c to the standard form y2 = 4ax or x2 = 4ay respectively, elementary properties. Parametric equation.


● Ellipse and Hyperbola: Standard equations only. Conjugate hyperbola. Elementary properties. Parametric equation.

To investigate whether a point is inside, on or outside a conic. Intersection of a straight line with a conic, equation of chord of a conic with respect to the middle point.

● Diameters of Conic: Definition, equation of a diameter. Equation of a conjugate diameter: elementary properties of conjugate diameter (statement only).

Solid Geometry: Incidence relations between points and planes, lines and planes, coplanarity, skew lines, parallel planes. Intersecting planes—Two intersecting planes cut one another in a straight line and in no point outside it, perpendicular to a plane, projection of a line segment on a line and on a plane. Dihedral angle.

Corollary: Three straight lines intersecting pair wise or two parallel lines and its transversal lie in the same plane.

Theorems: Theorem 1: If a straight line is perpendicular to each of two intersecting straight lines at their point of intersection, it is also perpendicular to the plane in which they lie. (Apollonius’ Theorem may be used.)
Theorem 2: All straight lines drawn perpendicular to a given straight line at a given point are co-planar.

Theorem 3: If two straight lines are parallel and if one of them is perpendicular to a plane, then the other is also perpendicular to the same plane and its converse.

Theorem 3: Theorem of Three Perpendiculars

Mensuration:

Surface areas and volumes of prism and pyramid


Formula


Mathematical Induction


Variation


Surds


Complex Numbers


Arithmetic Progression


 Geometric Progression


Theory of Quadratic Equation


Logarithm



Trigonometry


Measurement of Angles


Trigonometric Functions


Compound Angle


Converting Product into Sum/Difference and Vice Versa


Multiple Angles


Submultiple Angles


Conditional Trigonometric Identities


Graphs of Trigonometrical Functions



Trigonometric Equations


Inverse Trigonometric Functions


Properties of Triangles


Trigonometrical Table


Co-ordinate Geometry


Locus


The Straight Line


The Circle


The Parabola


The Ellipse


The Hyperbola


Solid Geometry


Mensuration




From 11 and 12 Grade Math to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.

Share this page: What’s this?

Recent Articles

  1. Comparison of Numbers | Compare Numbers Rules | Examples of Comparison

    May 18, 24 02:59 PM

    Rules for Comparison of Numbers
    Rule I: We know that a number with more digits is always greater than the number with less number of digits. Rule II: When the two numbers have the same number of digits, we start comparing the digits…

    Read More

  2. Numbers | Notation | Numeration | Numeral | Estimation | Examples

    May 12, 24 06:28 PM

    Numbers are used for calculating and counting. These counting numbers 1, 2, 3, 4, 5, .......... are called natural numbers. In order to describe the number of elements in a collection with no objects

    Read More

  3. Face Value and Place Value|Difference Between Place Value & Face Value

    May 12, 24 06:23 PM

    Face Value and Place Value
    What is the difference between face value and place value of digits? Before we proceed to face value and place value let us recall the expanded form of a number. The face value of a digit is the digit…

    Read More

  4. Patterns in Numbers | Patterns in Maths |Math Patterns|Series Patterns

    May 12, 24 06:09 PM

    Complete the Series Patterns
    We see so many patterns around us in our daily life. We know that a pattern is an arrangement of objects, colors, or numbers placed in a certain order. Some patterns neither grow nor reduce but only r…

    Read More

  5. Worksheet on Bar Graphs | Bar Graphs or Column Graphs | Graphing Bar

    May 12, 24 04:59 PM

    Bar Graph Worksheet
    In math worksheet on bar graphs students can practice the questions on how to make and read bar graphs or column graphs. Test your knowledge by practicing this graphing worksheet where we will

    Read More