Download Math needed for class 11 entering students

BASIC MATH NEED FOR INTER STUDENTS
( Shorter version of Foundation in Mathematics )
1
Arithmetic of Naturals, Integers, Fractions. Decimal representation.
Conversion from rational to decimal and vice-versa.
Arithmetic of decimals. Finding square roots. Exponentiation.
2
Basic Number Systems, Evolution of Irrationals, Number (Real)Line,
Properties of rationals and irrationals, Laws of Rational exponents.
3
ED, Basic Identities and factorization (including quadratic factorization).
4
Basic inequalities
5
Linear and quadratic Equations and inequations in single variable, SLE’s.
6
Cartesian Plane, Basic formulae and simple graphs, Graphical solutions
7
Trigonometric Ratios of common angles, Trigonometric Identities,
Trigonometric values of allied angles, Applications
8
Definitions of Polynomial, Logarithm, Progression ( AP, GP, AM, GM)
Factorising Polynomial, Geometric meaning of absolute value.
9
Geometry – Basic Geometrical objects, measuring angle, story of
transversal, polygon, triangle ( classification, basic side and angle
properties, special points and lines ), Pythogoras theorem, BPT,
quadrilateral, characteristic property of parallelogram, trapezium,
rhombus, rectangle, square, Circle ( basic chord, angle and tangent
properties ), AST, Cyclic quadrilateral. Simple Euclidean constructions.
10
Basic Number Theory ( Divisibility tests, divisor, GCD, LCM, Primes,
co-primes )
11
Binomial Theorem for natural index
12
Commercial Mathematics – Percentage problems, Time-work problems
13
Mensuration – Lengths, areas, volumes of simple regular entities
14
Basic Set Theory
COMPLETE MODEL QUESTIONS
1
Simplify given numerical expression. ( All arithmetic covered )
2
Convert given number to decimal form.
3
Convert given number to rational form.
4
Decide if given number is rational or irrational from decimal part.
5
Find square root of given number.
6
Relate the given basic number systems.
7
Show that there is no rational number whose square is given number.
8
Generate infinite set of irrational numbers.
9
Plot the given number on number line.
10
Divide the given polynomial by the given polynomial.
11
Factorise the given expression using identities
12
Establish the given inequality using basic inequalities.
13
Solve the given linear equation in single variable.
14
Solve the given linear inequation in single variable.
15
Solve the given quadratic equation.
16
Solve the given quadratic inequation.
17
Solve the given SLE’s.
18
Solve equations graphically.
19
Solve inequations graphically.
20
Give all trigonometric ratios of given angle.
21
Derive the given trigonometric identity.
22
Find all trigonometric ratios of given allied angle.
23
Give trigonometric expression of given compound angle.
24
Define Polynomial, Logarithm, Progression, Rational number, Zero of
Polynomial, Absolute value.
25
Factorise given polynomial.
26
Find all zeroes of given polynomial.
27
Derive the given law of logarithms.
28
Find the logarithms of given numbers
29
Find the n th term and sum to n terms of given progression.
29
Solve the given absolute value equality.
30
Solve the given absolute value inequality.
31
Define the given geometrical object.
32
State the given geometrical theorem.
33
Prove the given geometrical theorem.
34
Make the given Euclidean construction.
35
Decide if a given number is divisible by a given number.
36
Find the factors, prime factors, GCD and LCM of given numbers.
37
Give the given term of given binomial expansion.
38
Do the given percentage problem.
39
Do the given time-work problem.
40
Find the perimeter (length) of given regular geometrical object.
41
Find the surface area of given regular geometrical object.
42
Find the volume of given regular geometrical object.
43`
Give the symbols for elements, sets, belonging, existence, universality
44
Decide if given set is finite.
45
Write a given set in the asked form.
44
Define set, subset, equality, union, intersection, difference, universal
set, complement, Cartesian product.
45
Very very simple application of above definitions and facts.