Learn about Quadratic equations and prepare your test.
1. A quadratic equation in x can be written in form………………
2. Another name for quadratic equation in x is ……………… in x.
3. The solutions of an equation are also called its ………………
4. Quadratic formula is given by………………
5. Equation in which variable occurs in exponent are called ………………
6. An equation which remains unchanged when x (variable) replaced by
(reciprocal of variable) 1/x, is called a ………………
7. Equations involving ……………… of the variable are called radical equation.
8. The extra solutions of an equation are called ………………
9. w and w2 are called ……………… cube roots of unity.
10. Each complex cube root of unity is ……………… of other.
11. Sum of all three cube roots of unity is ………………
12. 1+w +w2 = ………………
13. The product of all three cube roots of unity is ………………
14. w-12 = ………………
15. w27 = ………………
16. w11 = ………………
17. Four fourth roots of unity are ………………
18. Sum of all four fourth roots of unity is ………………
19. The real fourth roots of unity are ……………… of each other
20. Both complex fourth roots of unity are ……………… of each other.
21. Product of all fourth roots of unity is ………………
22. The highest power of x in polynomial of x is called ……………… of
polynomial.
23. Degree of x3 + 2x2 + 4 is ………………
24. Dividend = (divisor)( ………………) + remainder
25. Remainder obtained when f(x) is divided by……………… is same as value of
polynomial f(x) at x = a.
26. (x - a) is a factor of f (x) if ………………
27. Sum of roots of quadratic equation = ………………
28. Product of roots of quadratic equation = ………………
29. The nature of roots of an equation depends on value of ………………
30. Value of Discriminate is ………………
31. If b2 - 4ac = 0 , roots are ……………… and ………………
32. If b2 - 4ac ¹ 0 , roots are ……………..
33. If b2 - 4ac > 0 , roots will be ……………… and unequal.
34. If b2 - 4ac < 0 , roots will be ……………… and unequal.
35. If b2 - 4ac is perfect square, the roots are ………………
36. If b2 - 4ac is not perfect square, the roots are ………………
37. Two quadratic equations in which xy term is missing and co-efficient x2 and
y2 are equal give a linear equation by………………
You can learn about Sets, Functions & Groups in detail and prepare your Mathematics.
Sets, Functions & Groups
1) A set is defines as a well defined collection of……………. 2) The objects in a set are called its …………… or ……………. 3) …………… are used as names of sets. 4) Small letters are used as …………… of sets. 5) The method by which a set may be specified by which a set described in words is called …………… method. 6) The method by which a set may be specified by listing its elements with in brackets is called …………… method. 7) …………… is more convenient in specifying sets. 8) …………… is done by using letter or symbol for an arbitrary member of set and stating the property common to all members. 9) A symbol used for …………… of a set is Î . 10) aÎA means, a is a …………… of A. 11) In algebra, we usually deal with set of……………. 12) N is symbol of set of…………… numbers. 13) W is symbol of set of…………… numbers. 14) Z is symbol of set of…………… numbers. 15) Z¢ is symbol of set of…………… numbers. 16) O is symbol of set of…………… numbers. 17) E is symbol of set of…………… numbers. 18) Q is the symbol of set of…………… numbers. 19) Q¢ is the symbol of set of…………… numbers. 20) R is symbol of set of…………… numbers. 21) Two sets are equal if they have same ……………. 22) While describing a set in…………… form, its elements can be written in any order. 23) If the elements of two sets are paired in such a way that each element of one set is paired with only one element of one element of other set, then the pairing is called a ……………. 24) Two sets are said to be …………… if one to one correspondence can be established. 25) Two equivalent sets are not always ……………. 26) The symbol…………… is used for equivalent set. 27) A set having only one element is called a ……………. 28) A set having no element is called an…………… or …………… set. 29) The empty set is denoted by……………. 30) The set of odd integers between 2 and 4 is a …………… set. 31) The set of even integers between 2 and 4 is a …………… set. 32) The solution of equation x2 +1= 0 in set of real numbers is ……………. 33) Set {0} is not …………… set. 34) If a set is equivalent to {1, 2, 3, ……, n} for fixed natural number n, it is called a …………… set. 35) Sets of N, Z and Z¢ are …………… sets. 36) If every element of a set is a member of other set, the set is called …………… of other set. 37) Subset is denoted by symbol……………. 38) If A is subset of B, then B is …………… of A. 39) If A is subset of B and B contains at least one element which is not in A, then A is said to be …………… of B. 40) If A is subset of B and A = B, A is said to be …………… of B. 41) …………… set is a subset of every set. 42) A power set of a set is a set containing all possible …………… of that set. 43) The power set of empty set is …………… . 44) A bigger set, all the sets are whose subsets, is called a …………… set or ……………. 45) In arithmetic, we deal with…………… numbers only. 46) When we deal with negative numbers and fractions, the set of…………… numbers can be treated as universal set. 47) The operation of union and intersections are performed on……………. 48) The …………… of a set is the set of all elements of the given sets. 49) The …………… of a set is the set of all elements common in given sets. 50) If the intersection of two sets is an empty set, sets are called …………… sets. 51) If the intersection of two sets is not empty but neither is a subset of other, sets are called …………… sets. 52) The set of all elements of universal set which do not belong to a given set is called …………… of that set. 53) The difference of two sets A and B contain all elements which…………… to A but …………… to B. 54) Venn diagrams were first used by English Mathematician……………. 55) In Venn diagrams, …………… represents universal set. 56) The sets whose elements are not specified are called …………… sets. 57) (AÈ B)¢= A¢Ç B¢ and (AÇ B)¢= A¢È B¢ are called ……………. law. 58) The way of drawing conclusion from opinions on the basis of few contacts is called ……………. 59) The way of reasoning drawing conclusion from premises believed to be true is called ……………. 60) Basic principle for deductive logic was laid down by Greek philosopher ……………. 61) A declarative statement which may be true or false but not both is called a ……………. 62) Deductive logic in which every statement is regarded as true or false and there is no other possibility is called ……………. 63) The logic in which there is a scope of 3rd or 4th possibility is called ……………. 64) If p is any proposition, its negation is ……………. 65) Conjunctions of two statements p and q are denoted by……………. 66) A conjunction is considered to be true if…………… of its components are true. 67) Disjunction of two statements is considered to be true if…………… of the components is true. 68) A compound statement of the form if p then q also written as p implies q is called a …………… or an……………. 69) In an implication of statement if p then q , p is called …………… and q is called ……………. 70) A conditional is regarded as false if antecedent is …………… and consequent is ……………. 71) q® p is called …………… of p®q . 72) ~ p®~ q is called …………… of p®q . 73) ~ q®~ p is called …………… of p®q . 74) The converse and inverse are …………… to each other. 75) The statement which is true for all possible values of variables involved in it is called ……………. 76) A statement which is already false is called an……………. 77) A statement which may be true or false depending upon the truth values of variables involved is called……………. 78) The words or symbols which convey idea of quantity or number are called ……………. 79) The words of symbols which convey idea of quantity or number are called ……………. 80) Truth set of tautology and absurdity in universal set is …………… set. 81) …………… is a set of ordered pairs. 82) For two non empty sets A and B, Cartesian product A´ B is called ……………. 83) The set of first elements of ordered pairs forming a relation is called ……………. 84) The set of second elements of ordered pairs forming a relation is called ……………. 85) If A is a non-empty set, any subset of A´ A is called ……………. 86) If in a function A®B , the range = B, the function is called …………… function. 87) Onto function is also called …………… function. 88) The function {(x, y)| y = mx + c} is called a …………… function. 89) A function {(x, y) | y = ax2 + bx + c} is called a …………… function. 90) Inverse of a line is a ……………. 91) The function {(x, y) | y = x} is an…………… function. 92) An operation which when performed on a single number yields another number of a same or different system is called a ……………. 93) A…………… is a non-empty set on which a binary operation * is defined. 94) A non-empty set is a semi group if it is …………… w.r.t operation * and the * is associative. 95) Semi-group having an identity is called ……………. 96) A monoid having inverse of each of its elements under an operation is called …………… under operation. 97) A group satisfies the commutative law is called …………… group.
Keys
1- Set 2 - Member, elements 3 - Capital letters 4- Members
5- Description 6- Tabular 7- Set builder method 8- Set builder method
9- Membership 10- Member 11- Numbers 12- Natural 13- Whole
14- Integer 15- Negative integer 16- Odd 17- Even 18- Rational
19- Irrational 20- Real 21- Elements 22- Tabular
23- One to one correspondence 24- Equivalent 25- Equal 26- ~
27- Singleton set 28- empty, null set 29- {} or j 30- Singleton
31- Empty 32- Empty 33- Empty 34- finite 35- infinite 36- Subset
37- Í 38- Superset 39- Proper subset 40- Improper subset
41- Empty set 42- Subsets 43- Not empty
44- Universal set, Universe of discourse 45- Whole 46- Rational
47- Sets 48- Union 49- Intersection 50- Disjoint 51- Overlapping
52- Compliment 53- Belong, does not belong 54- John Venn
55- Rectangular region 56- Abstract 57- Demorgan’s 58- Induction
59- Deduction 60- Aristotle 61- Proposition 62- Aristotelians logic
63- Non aristoltian logic 64- ~ p 65- p Ù q 66- Both 67- At least one
68- Conditional, Implication 69- Antecedent, Consequent 70- True, False
71- Converse 72- Inverse 73- Contrapositive 74- Equivalent 75- Tautology
76- Absurdity 77- Contingency 78- Quantifiers 79- Quantifiers
80- Empty 81- Relation 82- Binary relation 83- Domain 84- Range
85- Relation in A 86- Onto 87- Surjective 88- Linear 89- Quadratic
90- Line 91- Identity 92- Unary operation 93- Groupoid 94- Closed
95- Monoid 96- Group 97- Abelian