Algebra Quiz PDF

6. Which is true regarding the signs of the natural functions for angles between 90⁰ and 180⁰? NAME :...

6. Which is true regarding the signs of the natural functions for angles between 90⁰ and 180⁰? NAME : a) the tangent is positive b) the cotangent is positive CLASS : Algebra c) the cosine is negative d) the sine is negative DATE : 262 Questions 7. What is the inverse natural function of the cosecant? 1. For a given function that f(t) = f(-t). What type of symmetry does f(t) have? a) secant b) sine a) odd symmetry b) even symmetry c) cosine d) cotangent c) rotational symmetry d) quarter-wave symmetry 8. The graphical representation of a cumulative frequency distributionis a set of statistical data is called_______. 2. Which number has four signi cant gure? a) histogram b) kurtosis a) 0.0014 b) 0.01414 c) lepticurtic d) ogive c) 0.141 d) 1.4140 9. A statement of truth of which follows with little or no proof 3. Naperian logarithm have a base closest to which number? from a theorem. a) 2.17 b) 2.72 a) Axiom b) Hypothesis c) 3.14 d) 10 c) corollary d) Conclusion 4. If the second derivative of the equation of a curve is equal 10. It is a sequence of numbers such that the successive terms to the negative of the equation of that same curve, the di er by a constant. curve is a) Arithmetic progression b) In nite progression a) an exponential b) a sinusoid c) Geometric progression d) Harmonic progression c) a tangent d) a parabola 11. A frequency curve which is composed of series of 5. To nd the angle of a triangle, given only the lengths of the rectangles constructed with the steps as the base and the sides, one would use frequency as the height. a) the law of cosines b) the law of sines a) Histogram b) Ogive c) the law of tangents d) the inverse-square law c) Frequency distribution d) Bar graph 12. If the roots of an equation are zero, then they are classi ed 18. The ratio of product of two expressions in direct or inverse as relation with each other is called a) hyperbolic solution b) zeros of function a) ratio and proportion b) means c) extraneous roots d) trivial solution c) extremes d) constant of variation 13. Convergence sequence is a sequence of decreasing 19. Is a sequence of terms whose reciprocal from the number or when succeeding term is ________the preceding arithmetic progression? term. a) Geometric progression b) Harmonic progression a) greater than b) equal to c) Algebraic progression d) Ratio and proportion c) lesser than d) none of the above 20. An array of m x n quantities is a system of notation for 14. If a=b then b=a. This illustrates what axiom in algebra? reaal number that composed of elements in rows and columns is known as a) Symetric axiom b) Re exive axiom a) Transposed matrix b) Cofactor of a matrix c) Transitive axiom d) Replacement axiom c) Matrix d) Determinant 15. A and B are independent events. The probability that event A will occur is Pa and the probability that A and B will occur 21. Binary number system is a system of notation for real is Pab. From these two statements, what is the probability number that uses the place value method with 2 as base, that event B will occur? What is another name of the binary number system? a) Pa - Pab b) Pb - Pab a) Binary digits b) Binumber system c) Pa x Pb d) Pab / Pa c) Dyadic number system d) Bits 16. Two or more equations are equal if and only if they have 22. The number 0.123123123... Is a/an the same a) irrational number b) surd a) solution set b) degree c) rational number d) trancedental c) order d) variable set 23. MCMXCIV is the Roman numeral equivalent to 17. In any square matrix,, when the elements of any two rows a) 1974 b) 1984 are exactly the same, the determinant is c) 1994 d) 2994 a) zero b) positive integer c) negative integer d) unity 24. A sequence of numbers where the succeeding term is 31. The part of theorem which assumed to be true. greater than the preceding term is called a) Corollary b) Hypothesis a) dissonant series b) convergent series c) Postulate d) Conclusion c) divergent series d) isometric series 32. A statement of truth which follows with little or no proof 25. Terms that di ers only in numeric coe cient are known as from the theorem. a) unlike terms b) unequal terms a) Corollary b) Axiom c) like terms d) similar questions c) Postulate d) Conclusion 26. In complex algebra, we use the diagram to represent 33. Refers to the construction of drawing of lines and gures complex plane commonly called the possiblity of which is admitted without proof. a) Argand diagram b) Venn diagram a) Corollary b) Theorem c) Maxwell diagram d) Cartesian diagram c) Postulate d) Hypothesis 27. 7 + 0i is 34. A mathematical statement which has neither been proved a) an irrational number b) real number nor denied by counterexamples. c) imaginary number d) a variable a) Fallacy b) Conjecture c) Theorem d) Paradox 28. The number of successful outcomes divided by the number of possible outcomes is 35. A proved proposition which is useful mainly as a a) odd b) combination preliminary to the proof of a theorem. c) permutation d) probability a) Lemma b) Hypothesis c) Postulate d) Corollary 29. If the two digit number has x for its unit digit and y for its tens digit, yhe number is represented as 36. Axioms are propositions of a general logical nature (about a) x + y b) y - x equal or unequal) while ______ are the propositions concerning objects and constructions. c) 10y + x d) 10x - y a) theorems b) corollaries c) conclusions d) postulates 30. A statement of truth which is admitted without proof. a) Axiom b) Theorem c) Postulate d) Corollary 37. A ______ is an ancillary theorem whose result is not target 43. The axiom which relates addition and multiplication is the for proof. ________ law. a) postulate b) lemma a) commutative b) associative c) hypothesis d) conclusion c) Distributive d) none of the above 38. Statements that are accepted without discussion or proof 44. Any combination of symbols and numbers related by the are called axioms. The word "axiom" comes from the Greek fundamental operation of algebra is called a/an "axioma"which means a) equation b) algebraic expression a) worth b) correct c) term d) algebraic sum c) true d) perfect 45. The algebraic expression consisting a sum of any number 39. In the mathematical and other elds of logical reasoning, of terms is called a axioms are used as basis for the formulation of statements a) multinomial b) summation called c) binomial d) monomia a) lemma b) hypothesis c) postulate d) theorem An equation which is sati ed by all values of the variable for 46. which the members of the equation de ned is known as 40. "The product of two or more number is the same in a) Linear equation b) Rational equation whatever order they are multiplied." This refers to c) Conditional equation d) Irrational equation a) Associative law of addition b) Associative law of multiplication c) Commutative law of multiplication d) Distributive law of multiplication 47. An equation in which some or all of the known quantities are represented by letters is called 41. If a=b, then b can replace a in any equation. This illustrates a) Redundant equation b) Literal equation what identity? c) Linear equation d) Defective equation a) Re exive law b) Law of symmetry c) Transitive law d) Substitution law 48. An equation which the variable appear under the radical symbol 42. If a=b, and b=c, then a=c. This illustrates a) Irradical equation b) Irrational equation a) Re exive law b) Law of symmetry c) Quadratic equation d) Linear equation c) Transitive law d) Substitution law 49. An equation which, because of some mathematical process, 55. The numbers which are represented with letters has required an extra root is sometimes called as a) Variables b) Unknowns a) Redundant equation b) Literal equation c) Literal numbers d) Terms c) Linear equation d) Defective equation 56. Equations whose members are equal only for certain or 50. An equation which, because of some mathematical process, possibly no value of the unknown. has fewer roots than its original is sometimes called as a) Conditional equations b) Inequalities a) Redundant equation b) Literal equation c) Unconditional equations d) Temporary equations c) Linear equation d) Defective equation 57. An algebraic expression consisting of one term 51. An algebraic expression which can be represented as a a) monomial b) binomial qoutient of two polynomials. c) linear d) monomode a) Irrational algebraic expression b) Reduced algebraic expression c) Rational algebraic expression d) Complex algebraic expression 58. In algebra,this consist of products and quotients of ordinary numbers and letters which represent numbers. 52. A statement containing one or more variables and having a) Expression b) Term the property that it becomes either true or false when the variables are given speci c values from their domains. c) Equation d) Coe cient a) Solution b) Problem c) Open sentence d) Worded problem 59. The degree of a polynomial or equation is the a) maximum exponent b) maximum sum of exponents 53. Any algebraic term is a/an ______ term in certain c) exponent of the rst variable d) maximum exponent of x representing numbers if if it consist of the product of possible integral powers of these numbers and a factor not containing them. 60. What is the degree of the polynomial 3x4y + 2x3z3 - 4yz2 ? a) integral b) rational a) 6th b) 5th c) irrational d) integral rational c) 4th d) 3rd 54. An equation in x and y which is not easily solved for y in 61. Any fraction which contains one or more fractions in either terms of x is called numerator or denominator, or both is called a) explicit b) implicit function a) compound fraction b) composite fraction c) discontinuity d) quadratic c) complex fraction d) all of the above 62. A common fraction with unity for the numerator and a 68. A concept of spread of a random variable or a set of positive integer as denominator (i.e. 1/n). observations. a) ordinary fraction b) unit fraction a) variance b) standard deviation c) common fraction d) improper fraction c) dispersion d) range 63. If the absolute value of the numerator of a fraction is 69. A number containing non-terminating but repeating smaller than the denominator, it is called decimal is a/an a) proper fraction b) improper fraction a) Integer b) Rational number c) decimal fraction d) mixed number c) Natural number d) Integer 64. A number that consist of an integer part (which may be 70. A positive integer which has no perfect-square factor zero) and a decimal part less than the unity that follows the greater than 1. decimal marker, which may be a point or comma. a) Radical expression b) Square integer a) Proper fraction b) Improper fraction c) Square integer d) Square-free integer c) Decimal fraction d) Mixed number 71. Numbers are used to describe a 65. Considered as the "counting numbers". a) magnitude b) position a) Integers b) Rational numbers c) magnitude and position d) none of the above c) Irrational numbers d) Natural numbers 72. Are symbols or combinations of symbols which describe a 66. A number represented by non- terminating, non-repeating number. decimal. a) Numerals b) Digits a) Irrational numbers b) Rational numbers c) Terms d) Notations c) Natural numbers d) Integers 73. Which of the following is not classi ed as an integer? 67. The completeness axiom proved that the real number a) Negative numbers b) Positive numbers system has numbers other than c) Zero d) Imaginary numbers a) Integers b) Rational numbers c) Natural numbers d) Irrational numbers 74. When an imaginary number is raised to an even exponent, it a) becomes in nite b) becomes negative imaginary number c) becomes relatively small number d) become real number 75. The complex number is in the form of a + bi. If a=0, what do A composite number has a least _______ divisors. 82. you call the resulting number? a) 1 a) absolute value of the complex number b) pure imaginary number b) 2 c) 3 c) argument d) irrational number d) 4 76. For a complex number a+bi, the real number √a²+b² is 83. Two natural numbers a and b are _______. If their greatest ______ of the complex number. common divisor is 1. a) absolute value b) magnitude a) relative prime b) relative composite c) modulus d) all of the these c) equal d) reciprocal 77. The _______ of the complex number is found by multiplying 84. Numbers used to count the objects or ideas in a given each term of the one by every term of the other. collection. a) sum b) di erence a) Cardinal numbers b) Irrational numbers c) product d) qoutient c) Ordinal numbers d) Numerals 78. A number which can be expressed as a qoutient of two 85. Numbers which is used to state the position of individual integers (division of zero excluded) is called objects in a sequence. a) Irrational number b) Rational number a) Cardinal numbers b) Irrational numbers c) Imaginary number d) Real number c) Ordinal numbers d) Numerals 79. The prime number has exactlt how many divisors? 86. An integer number that is equal to the sum of all its a) 1 b) 2 possible divisors except the number itself is called c) 3 d) 4 a) amicable number b) perfect number c) defective number d) redundant number 80. The prime number is an integer greater than 1 which has a) 1 as its only positive divisor b) Itself as its only positive divisor 87. An integer the sum of all its possible divisors except the c) 1 and itself as its only positive divisors d) 1 and its additive inverse as its only number itself is greater than the integer is called positive divisor a) abundant number b) perfect number c) defective number d) amicable number 81. An integer which is the product of two integers, both di erent from 1 and -1 is called a) Prime number b) Composite number c) Rational number d) Compound number 88. An integer the sum of all its possible divisors except the 95. "Every even integer greater than 2 can be written as sum of number itself is less than the integer is called two primes". This known as a) abundant number b) amicable number a) Fermat's last theorem b) Goldbach conjecture c) friendly number d) defective number c) Prime number theorem d) Mersenne's theorem 89. What is the smallest perfect number possible? 96. "Every positive integer greater than 1 is a prime or can be a) 1 b) 6 expresses as a unique product of primes and powers". This is known as c) 12 d) 8 a) Fundamental theorem of arithmetic b) Pseudo prime theorem c) Prime number theorem d) Mersenne's theorem 90. All perfect numbers are a) even numbers b) odd numbers 97. "Every su ciently large o number can be expresses as c) odd numbers d) composite numbers sum of three prime numbers". This is known as a) Goldbach conjecture b) Vinogradov's theorem c) Pascal's law d) Mersenne's theorem 91. Two integer numbers are said to be _____ if each is the sum of all possible divisors of the other. a) perfect number b) defective number 98. The term "ratio"comes from Latin verb meaning "ratus" c) amicable number d) Fermat's number meaning a) to divide b) to estimate c) to get the mean d) to make a proportion 92. What is another name for amicable numbers? a) Compatible numbers b) Friendly numbers c) Fermat's numbers d) Inconsistent numbers 99. In the proportion of four quantities, the rst and fourth terms are referred to as the a) means b) extremes 93. What is the smallest pair of friendly numbers? c) denominators d) numerators a) 180 and 190 b) 200 and 120 c) 220 and 284 d) 220 and 264 100. The rst term of a ratio is called a) antecedent b) consequent 94. Prime numbers that appear in pair and di er by 2 (eg. 3 c) mean d) extreme and 5, 11 and 13 etc.) are called a) Mersenne primes b) Prime number theorem c) Twin primes d) Pseudo primes 101. The second term of a ratio is called a) antecedent b) mean c) consequent d) extreme 102. The ______ is the square root of the product of the 108. An inequality is preserved if the both sides are multiplied extremes. by a) antecedent b) consequent a) zero b) -1 c) mean proportional d) mean c) a positive number d) a negative number 103. If the means of a proportion are equal, their common value 109. An inequality is reversed if both sides are multiplied by is called a) zero b) -1 a) mean b) extreme c) a positive number d) a negative number c) mean proportional d) extreme proportional 110. Division of a population or same into two groups based 104. The theorem that in every arithmetic progression a, a+b, either on measurable variables (e.g. age under 18, age over a=2d,...., where a and d are relatively prime. 180) or on attributes (e.g. male, female). a) Fibonacci theorem b) Gauss theorem a) decomposition b) denomination c) Lejeune Theorem d) Dirichlet Theorem c) deviance d) dichotomy 105. A statement that one mathematical expression is greater 111. A 3 x 2 matrix can be multiplied to a than or less than another is called a) 3 x 2 matrix b) 3 x 3 matrix a) absolute condition b) non-absolute condition c) 2 x 5 matrix d) row matrix c) Inequality d) conditional expression If there as many equations as unknowns, the matrix of the 112. 106. If an equality is true for all the values of the variable, it is coe cient is a a/an a) Row matrix b) Column matrix a) conditional equality b) equivalent equality c) Square matrix d) Rectangular matrix c) absolute inequality d) non-conditional equality 113. A method of solving linear equation with several unknowns 107. If the same number is added to both sides of an inequality, simultaneously using determinants. the inequality a) Simpsom's rule b) Cramer's rule a) becomes negative b) becomes positive c) Trapeziodal rule d) Chain rule c) is reversed d) is preserved 114. Using Cramer's rule, the determinant of the coe cient is always is always the a) numerator of a qoutient b) denominator of the qoutient c) the qoutient itself d) none of these 115. In any square matrix, when the elements of any two rows 121. Which of the following cannot be an operation of matrices? are exactly the same (i.e. row 1 = row 2 or row 1 = row 3, or a) addition b) subtraction row 2 = row 3...), the determinant is c) multiplication d) division a) zero b) positive integer c) negative integer d) unity 122. An irrational number which is a root of a positive integer of fraction is called 116. When the corresponding elements of two rows of a a) radical b) radix determinant are proportional,. then the value of the determinant is c) surd d) radicant a) one b) indeterminate c) in nite d) zero A symbol n√b means the principal nth. "n" is called the 123. a) radicand 117. An array of mxn quantities which represent a single b) radical c) radix number and is composed of elements in rows and columns d) index is known as a) transpose of a matrix b) determinant c) co-factor of a matrix d) matrix 124. A symbol n√b means the principal nth. "b" is called the a) radicand b) radical c) radix d) index 118. When two rows are interchanged in position, the value of the determinant will a) remain unchanged b) be multiplied by -1 125. A symbol n√b means the principal nth. The symbol √ is c) become zero d) become in nite value called a) radical b) radical symbol c) index d) Radical or radical symbol 119. If every elements of a row (or column) are multiplied by a constant, k, then the value of the determinant is a) multiplied by - k b) zero 126. The rules of combining radicals follows the rule for c) one d) multiplied by k a) signed numbers b) logarithms c) fractional exponents d) factoring 120. If two rows a determinant are interchange, the determinant a) changes sign b) changes sign and value 127. When a number has both a positive and negative nth root, c) remain unchanged d) becomes the inverse of the former the principal nth root is a) The positive root b) The negative root c) Both the negative and positive root d) None of the above 128. Every positive number has ______ nth root. 135. A surd that contains no rational number, that is, all its a) zero b) two factors or terms are surds, example: ?3 or ?3+?2 c) four d) three a) Mixed surd b) Pure surd c) Binomial surd d) Conjugate surd 129. The principal nth root of a negative number is the negative root if n is 136. The process of removing surd from a denominator is to a) even b) odd a) Rationalize the denominator b) Invert the divisor and proceed to c) positive d) negative multiplication c) Get its multiplicative inverse d) Multiply it why its additive inverse 130. To eliminate a surd, multiply it by its a) square b) cube 137. A quadratic equation of the form ax² +bx + c = 0, without the coe cient of the rst degree term is a/an c) reciprocal d) conjugate a) General quadratic equation b) Pure quadratic equation c) Quadratic polynomial d) Incomplete quadratic equation 131. To eliminate a surd, multiply it by its a) square b) cube 138. In the quadratic equation ax² +bx + c = 0 , when the two c) reciprocal d) conjugate roots are multiplied, the result is a) C/A b) B/A c) -C/A d) A/C 132. A radical which is equivalent to a non-terminating and non- repeating decimal a) irrational number b) natural number 139. In the quadratic equation ax² +bx + c = 0 , when the two c) surd d) transcendental number roots are added, the result is a) C/A b) - B/A c) -C/A d) A/C 133. The radical expressing an irrational number is called a) surd b) radix c) index d) complex number 140. If the discriminant of a quadratic equation of a quadratic equation is less than zero, the equation has a) no real root b) one root only 134. A surd which contain at least one rational term c) two real roots d) none of the above a) Pure surd b) Mixed surd c) Binomial surd d) Conjugate surd 141. When can we say that the two roots of a quadratic equation 147. For a cubic equation, the discriminant found to be greater are equal? than zero. The roots are a) when the discriminant is greater than 1 b) when the discriminant is zero a) three distinct real roots b) one real root and two conjugate complex c) when the coe cient of the second degree d) none of the above roots term is equal to the coe cient of the rst c) three real roots, of which two are equal d) none of these degree term 148. A succession of numbers in which one number is 142. What is the discriminant of the quadratic equation Ax² +Bx designated as rst, another as second, another as third and +C=0? so on is called a) √(B²-4AC) b) (B²-4AC) a) series b) arrangement c) (B²+4AC) d) √(B²+4AC) c) arrangement d) seqeunce 143. What determine the nature of the roots of a quadratic 149. An indicated sum a1+ a2 + a3... Is called equation? a) series b) sequence a) Coe cient b) Discriminant c) arrangement d) partial sum c) Factors d) Factors 150. The repeating decimal 0.333... is a geometric series of a1 = 144. The real roots of a cubic equation are the 0.3 and r = a) points of in ection of the graph of the b) points of intersection of the graph of the a) 3/10 b) 1/10 equation equation with the x-axis c) 10 d) 5 c) points of intersection of the graph of the d) obtained by using the quadratic formula equation with the y-axis 151. A progression whose reciprocal forms an arithmetic progression 145. For a cubic equation, if the discriminant is equal to zero, we a) Arithmetic means b) Harmonic means produce c) Geometric means d) Harmonic means a) three equal real roots b) one real root and two conjugate complex roots c) three distinct real roots d) three real roots, of which two are equal 152. The number between two geometric terms. a) Means b) Arithmetic means 146. For a cubic equation, we produce three disticnt roots only if c) Geometric means d) Median the discriminant is a) Equal to zero b) Less than zero c) Greater than zero d) Either less than or greater than zero 153. The sum of the terms of an arithmetic progression a) Arithmetic means b) Arithmetic sum c) Arithmetic series d) All of the above 154. The harmonic mean between a and b. 161. A sequence 1, 4, 10, 20, 35, 56...is known as a) (a+b)/2 b) 2ab/(a+b) a) pyramid numbers b) cubic numbers c) (a+b)/ab d) ab/(a+b) c) tetrahedral numbers d) square numbers 155. The arithmetic mean of a and b is 162. A sequence of numbers where every term is obtained by adding all the prededing terms a square number series a) (a+b)/2 b) 2ab/(a+b) such as 1, 5, 14, 30, 55, 91... c) (a+b)/ab d) ab/(a+b) a) Pyramid numbers b) Tetrahedral numbers c) Euler's numbers d) Triangular numbers 156. The geometric mean of a and b is a) (a+b)/2 b) 2(a+b) 163. A sequence of numbers where the number is equal to the c) ab/(a+b) d) ?ab sum of the two preceding numbers such as 1, 1, 2, 3, 5, 8,13,21... a) Fermat's numbers b) Fibonacci numbers 157. A numbers which can be drawn as dots and arranged in c) Gaussian numbers d) Archimedean numbers triangular shape (i.e. 1, 3, 6, 10, 15,21...) a) Triangular number b) Square numbers c) Pentagonal numbers d) Tetrahedral numbers What is the multiplicative inverse of the integer 5? 164. a) 1 b) 5 c) -5 158. A gure numbers which can be drawn as dots and arranged d) 1/5 in square shape (i.e. 1, 4, 9, 16, 25...) a) Cubic numbers b) Square numbers c) Pyramid numbers d) Pentagon numbers 165. What is the additive identity element? a) 0 b) 1 c) -1 d) in nity 159. A sequence 1, 5, 12, 22, 35... Is known as a) Oblong numbers b) Pentagonal numbers c) Cubic numbers d) Pyramid numbers 166. What is the multiplicative identity element? a) 0 b) 1 c) -1 d) in nity 160. A sequence1, 8, 27, 64, 125, 216... is known as a) Pyramid numbers b) Cubic numbers c) Tetrahedral numbers d) Square numbers 167. A number 0 such that 0+a=a for all a is called the a) Additive inverse b) Additive identity c) Commutative law of addition d) Associative law ofo addition 168. What additive inverse of a complex number a+bi is 175. A triangular array numbers forming the coe cient of the expansion of binomial is called a) a-bi b) a+bi a) Egyptian triangle b) Golden triangle c) -a-bi d) -a+bi c) Pascal's triangle d) Bermuda triangle 169. All real numbers have additive inverse, commonly called 176. The coe cient of the second term of the expansion of a) reciprocals b) opposites (x+y)n is always equal to c) addends d) equivalent a) n b) n-1 c) n+1 d) n/2 170. All real numbers except zero have multiplicative inverse, commonly called 177. How is a number in Pascal's triangle obtained? a) equivalents b) factors a) By getting the product of the two numbers b) By getting the sum of the two numbers c) opposites d) reciprocals directly above it. directly above it. c) By getting the di erence of the two d) By getting the mean of the two numbers numbers directly above it. directly above it. 171. The number zero has no a) Multiplicative inverse b) Additive inverse c) Multiplicative identity d) Additive identity 178. If the sign between the terms of the binomial is negative, its expansion will have signs which are a) all positive b) all negative 172. What is the additive inverse of a+bi? c) alternating starting with positive d) alternating starting with negative a) bi b) -a-bi c) 1/(a+bi) d) a-bi 179. In the absence of the Pascal's triangle, the coe cient of any term of the binomial expansion can be obtained by dividing the product of coe cient of preceding term and exponent 173. What is the multiplicative inverse of a+bi? of x of preceding term by _______ of the preceding term. a) 0 b) 1 a) the exponent of y b) the exponent of y+1 c) -a-bi d) (a/(a2+b2)-bi(a2+b2) c) the exponent of y-1 d) the square root of y 174. Whichof the following is NOT a property of a binomial 180. The fundamental principle of counting states that in one expansion of (x+y)n? thing can be done in "m"di erent ways and another thing a) power of x is decreasing b) power of y is increasing can be done in "n"di erent ways, then the two things can c) sum of exponents in each term=n d) number of terms = n-1 be done in _______ di erent ways. a) m + n b) m x n c) m! + n! d) mn 181. Is the arrangement of the objects in speci c order. 187. If two events A and B are mutually exclusive events and the probability that A will happen is Pa and the probability that a) permutation b) combination B will happen is Pb, then the probability tahat A nd B c) probability d) any two of the above happen is a) Pa + Pb b) Pa x Pb c) Pa/Pb d) Pb/Pa 182. Is the arrangement of the objects regardless of the order they are arrange. a) permutation b) combination 188. A and B are two independent events. The probability that A c) probability d) any two of the above can occur is p and that for A and B to occur is q. The probability that event B can occur is a) p + q b) p - q 183. The shifting of the entire order sequence of elements one c) p/q d) q/p or more steps forwards to backward - the rst element taking the position of the last, or vice versa without changing the order of the elements in the sequence is called 189. If the probability of occurrence of a is Pa, what is the probability that will not occur? a) inversion b) cyclic permutation a) 1/Pa b) 1-Pa c) transposition d) identical elements c) 1 + Pa d) √Pa 184. The number of elements in the collection being permuted is the _______ of the permutation. 190. In statistics, a pictorial description of the probability concepts of independent and dependent events is called a) degree b) sum a) venn diagram b) histogram c) index d) all of the above c) frequency polygon d) ogive 185. The ratio of successful outcomes over the total possible outcomes is called 191. The di erence between the highest score and the lowest score in the distribution. a) combination b) permutation a) deviation b) range c) probability d) speculation c) median d) mode 186. The value of probability of any outcome will never be equal to nor exceed 192. The second power of the standard deviation is called a) 0.1 b) 0.5 a) mode b) central tendency c) 0.75 d) 1 c) variance d) dispersion 193. The graph of cumulative frequency distribution plotted at 199. If the absolute error does not exceed a half unit in the last class marks and connected by straight lines. digit, this digit is usually re ered to as the a) histogram b) venn diagram a) Signi cant digit b) Leading digit c) ogive d) scattergram c) Reliable digit d) Relative digit 194. A point in the distribution of scores at which 50 percent of 200. The most signi cant digit of the number 0.2015 is the scores fall below and 50 percent of the scores fall a) 0 b) 1 above. c) 2 d) 5 a) mode b) mean c) median d) range 201. The ________ is stated in the magnitude of the absolute or relative error of the approximated value. 195. The number that occurs most frequent in a group of a) precision b) accuracy numbers c) mistakes d) error a) median b) mode c) means d) standard deviation 202. The rst non-zero digit from the left of the number. a) Whole number b) Leading digit 196. The di erence between an aprroximate value of a quantity c) Tens digit d) Units digit and its exact value or true value. a) Relative error b) Absolute error c) Mistake d) Relative error 203. It is anyone of the digit from 1 to 9 inclusive, and 0 except when it is used to place a decimal. a) Leading digit b) Signi cant gure 197. Is the qoutient of the absolute error divided by the true c) Decimal number d) Numerals value. a) Relative error b) Relative change c) Absolute error d) Mistake 204. In algebra, the operation of the root extraction is called a) evolution b) involution c) revolution d) indexing 198. Refers to a value which is not exact but might be accurate enought for some speci c considerations. a) Approximate value b) Absolute value 205. The operation of raising to the integral power known as c) Relative value d) Accurate value a) evolution b) involution c) revolution d) indexing 206. Each of two or more numbers which is multi ied together 212. The sum of any point number and its reciprocal is to form a product are called a) always less than 2 b) always equal to 2 a) terms b) expression c) always greater than 2 d) always equal to the number's additive c) divedends d) factors inverse 207. When the factors of a product are equal, the product is 213. What is the absolute value of a number less than one but called a _________ of the factor. greater than negative one raised to exponent in nity? a) coe cient b) identity a) in nity b) zero c) power d) algebraic sum c) one d) indeterminate 208. A relationship in which every ordered pair (x,y) has one and 214. If a is an odd number and b is an even number, which of only one value of y that corresponds to the value of x is the following expression must be even? called a) a + b b) a - b a) Terms b) Coordinates c) ab d) a/b c) Function d) Domain 215. In the equation n x m = q, n is called the If the probability of occurrence of a is Pa, what is the 209. a) multiplier b) minuend probability that will not occur? c) multiplicand d) product a) The objects in a set are called its elements. b) Even number is either rational or irrational c) The additive inverse of number "a" is 1/a. d) The negative of zero is zero 216. Any one of the individual constant of an expressed sum of constant is called 210. A symbol holding a place for sn unspeci ed constant is a) addend b) multiple called c) factor d) summation a) arbitrary constant b) parameter c) variable d) all of the these 217. In the equation 5 + 2 = 7, 5 is known as a) augend b) minuend 211. Which of the following is NOT true about signi cant gures? c) divedend d) addned a) All non-zero digits are signi cant. b) Any zero between non-zero digits are signi cant. c) Any zero not needed for placing a decimal d) Zeros used for the purpose of placing a point is not signi cant. decimal point arte signi cant. 218. A number of the form a + bi with a and b real constant and i is the square root of -1. a) Imaginary number b) Complex number c) Radical d) Compound number 219. The absolute value of non-zero number is 226. For any two rational number a/b and c/d, which of the a) always 0 b) always negative following realtionship is true? c) always positive d) sometimes zero and sometimes positive a) a/b + c/d = ab/cd b) a/b + cd = (ab+cd) / ad c) a/b + c/d = (ad+bc) / bd d) ab + cd = ac/bd 220. A polynomial which is exactly divisible by two or more polynomials is called Two rational numbers a/b and c/d are said to be equal if 227. a) least common denominator b) common multiple a) ad = bc c) factors d) binomial b) ac = bd c) ab = cd d) a + b = c + d 221. A polynomial with real coe cient can be factored into real linear factors and irreducible ________ factors. 228. Any number divided by in nity equals a) linear b) quadratic a) 0 b) 1 c) cubic d) repeated c) in nity d) indeterminate 222. If the degree of the numerator is one more than the degree 229. The study of the properties of positive integers is known as of the denominator, the quotient is a _________ polynomial. a) Number of Theory b) Theory of equation a) linear b) quadratic c) Set Theory d) Arithmetic c) cubic d) quartic 230. Indicate the FALSE statement. 223. Which of the following statement is NOT true? a) A quotient of two polynomials is called as b) a³ - b³ = ( a + b )( a²- ab + b² ) a) The sum of even number is even. b) The di erence of even number is even. rational algebraic expression. c) The product of even number is even. d) The quotient of even number is even c) The equation ax + b = 0 has exactly one d) The equation 3x² + 2y² - 3x + 2y = 10 root. 224. For every law of addition and subtraction, there is a parallel law for multiplication and division, except divison by 231. A numbers is said to be in ______ when it is written as the a) negative values b) zero product of a number having the decimal point just after the c) one d) positive values leading digit, and a power of 10. a) scienti c notation b) exponential c) irrational d) logarithm 225. Indicate the FALSE statement: a) The multiplicative identity is 1. b) The product of a positive number and a negative number is negative. c) ab = ba is associative law for multiplication. d) x² - y² = (x + y)(x - y) 232. A number which cannot be a root of an integral rational 239. The conjecture that every even number (except 2) equals equation is called the sum of two prime numbers. a) trancendental number b) euler's number a) Goldbach conjecture b) Fibonacci series c) irrational number d) natural number c) Number conjecture d) Fermat's last theorem 233. Refers to the numbers which are not the roots of any 240. The unending sequence of integers formed according to algebraic equation. the rule that each integer is the sum of the preceeding two. a) Irrational numbers b) Transcendental numbers a) Fermat's last theorem b) Fibonacci numbers c) Imaginary numbers d) Composite c) Goldbach conjecture d) Triangular numbers 234. Any number multiplied by _______ equals unity. 241. It was conjecture that the number in the form, Fp = 2p+1 will a) negative of the number b) one always result to a prime number, however proved wrong. What do you call the numbers obtain using the said c) conjugate d) its reciprocal formula? a) Mersene numbers b) Fermats number c) Euler number d) Pseudo prime 235. The number denoted as "e" and equals to 2.718... Is called the a) Einstein number b) Euler's number 242. A theorem which states that if n > 2, the equation xn + yn = c) Fibonacci number d) Fermat's number zn cannot be solved in positive integers x, y, and z. a) Pythagorean theorem b) Mersenne theorem 236. The notation that represent the product of all positive c) Goldbach conjecture d) Fermat s theorem integers from 1 to a number, n, inclusive a) factorial b) exponent c) summation d) all of the above 243. The number π = 3.141592563.. If only four decimals are required, it becomes 3.1415 This process is called a) rounding o b) truncation 237. Simplify n!/( n - 1 ) ! c) rounding up d) union a) n + 1 b) n - 1 c) ( n + 1 )! d) n 244. A set of all subset of a given set, containing the empty set and the original set. a) Empty b) Null 238. The factorial symbol (!) was introduced in 1808 by c) Power set d) Union a) Christian Goldbach b) Christian Kramp c) Christian Leatner d) Robert Hooke 245. A set containing the elements that is common to the 252. QED is often written at the end of a proof to indicate that its original sets. conclusion has been reached. This means a) Union b) Intersection a) quod erat daciendum b) duod erat demonstratum c) Normal set d) Subset c) quod erat decientrandum d) none of the above 246. If an in nite series has a nite sum, it is referred to as a 253. A sequence of numbers where the succeeding term is greater than the preceding term. a) Convergent series b) Divergent series a) Isometric series b) Divergent series c) Geometric series d) None of the above c) Dissonant series d) Convergent series 247. If an in nite series no sum, it is referred to as a 254. The process of reasoning wherein a nal conclusion is a) Convergent series b) Divergent series obtained by experimental method. c) Geometric series d) None of the above a) Mathemathical deduction b) Mathemathical opposition c) Mathemathical conversion d) Mathemathical induction 248. The sum of the factorial in nite 1 + 1/1! + 1/2! + 1/3! + 1/4! +... is 255. A set of all subset of a given set, containing the empty set a) π b) e and the original set. c) √2 d) √3 a) Intersection b) Power set c) Proper set d) Improper set 249. Refers exclusively to equations with integers solutions. a) Determinate equations b) Intermediate equations 256. A sequence having a de ned rst and last terms is called c) Diophantine equations d) L Hospital equations a) In nite sequence b) Convergent sequence c) Divergent sequence d) Finite sequence 250. "My Dear Aunt Sally" is the basic rule used I operation of algebra. Which is used in determining the signs of trigonometric functions in all quadrants? 257. A series is said to be _______ if it converges when the terms are replaced by their absolute value. a) All chemist thick solution. b) All students can think. a) absolute convergent b) conditional convergent c) All students take chemistry d) All teachers can sing. c) in nite convergent d) nite convergent 251. The investigation of numbers, space and many generalizations of these concepts created by the intellectual 258. A covergent series is said to be _______ if it diverges when genius of man. terms are replaces by their absolute values. a) Science b) Arts a) absolute convergent b) conditional convergent c) Mathematics d) Astronomy c) in nite convergent d) nite convergent 259. Refers to the product of the several prime numbers Answer Key occuring in the denominations, each taken with greater 1. b 48. b 95. b 142. b multiplicity. 2. b 49. a 96. a 143. b 3. b 50. d 97. b 144. b a) Least common denominator b) Least common multiple 4. b 51. c 98. b 145. d c) Least square d) none of these 5. a 52. c 99. b 146. b 6. c 53. d 100. a 147. b 7. b 54. b 101. c 148. d 8. d 55. c 102. c 149. a 260. The sum of the exponents of the several variables of the 9. c 56. a 103. c 150. b term is re ered to as the _______ of the term. 10. a 57. a 104. d 151. d a) power b) degree 11. a 58. b 105. c 152. c c) partial product d) absolute power 12. d 59. b 106. c 153. c 13. c 60. a 107. d 154. b 14. a 61. c 108. c 155. a 15. d 62. b 109. c 156. d 261. Venn diagram is a pictorial representation which helps us 16. a 63. a 110. d 157. a visualize the relations and operations with sets. This was 17. a 64. c 111. c 158. b intruduced by 18. d 65. d 112. c 159. b a) John Venn b) Jan Michael Venn 19. b 66. a 113. b 160. b 20. c 67. b 114. b 161. c c) James Venn d) Stephen Venn 21. c 68. c 115. a 162. a