Preparation Mathematics 10 for

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1 Preparation Mathematics 0 for You have four choices for each objective type question as A, B, C and D. The choice which you think is correct; fill that circle in front of that question number. Use marker or pen to fill the circles. Cutting or filling more than two circles will result in zero mark in that question. Standard form of Quadratic Equation is a) bx + c = 0, b 0 ax 2 + bx + c = 0, a 0 c) ax 2 = bx, a 0 d) ax 2 = 0, a 0 2 The number of terms in standard quadratic equation ax 2 + bx + c = 0 is a) 2 c) 3 d) 4 3 The number of methods to solve quadratic equation is a) 3 c) 4 d) 5 4 The Quadratic Formula is a) x = b± b 2 4ac 2a x = b± b 2 4ac 2a c) x = b± b 2 +4ac 2a d) x = b± b 2 +4ac 2a 5 Two linear factors of x 2 5x + 56 are a) (x 7) and (x + 8) (x + 7) and (x 8) c) (x 7) and (x 8) d) (x + 7) and (x + 8) 6 An equation, which remains unchanged when x replaced by is x is called a) Exponential equation Reciprocal equation c) Radical equation d) None of these 7 An equation of the type 3x x + 6 = 0 is a/an a) Exponential equation Radical equation c) Reciprocal equation d) None of these 8 The solution set of equation 4x 2 6 = 0 is a) {± 4} {4} c) {+ 2} d) An equation of the form 2x 4 3x 3 + 7x 2 3x + 2 = 0 is called a/an a) Reciprocal equation Radical equation c) Exponential equation d) None of these 0 If α, β are the rots of 3x 2 + 5x 2 = 0, then α + β is a) 5/3 3/5 c) 5/3 d) 2/5 If α, β are the rots of 7x 2 x + 4 = 0, then αβ is

2 a) /7 4/7 c) 7/4 d) 4/7 2 Roots of the equation x 2 x + 4 = 0 are a) Irrational imaginary c) Rational d) None of these 3 Cube roots of are a), ω, ω 2, ω, ω 2 c), ω, ω 2 d), ω, ω 2 4 Sum of Cube roots of unity is a) 0 c) d) 3 5 Product of Cube roots of unity is a) 0 c) d) 3 6 If b 2 4ac < 0, then the roots of ax 2 + bx + c = 0 are a) Irrational Rational c) Imaginary d) None of these 7 If b 2 4ac > 0, then the roots of ax 2 + bx + c = 0 are a) Irrational Rational c) Imaginary d) None of these 8 α + β is equal to a) α α β c) α β αβ d) α+β αβ 9 α 2 + β 2 is equal to a) α 2 β 2 + c) (α + β) 2 2αβ d) α + β α 2 β 2 20 Two square roots of unity are a),, ω c), ω d) ω, ω 2 2 Roots of the equation 4x 2 4x + = 0 are a) real, equal real, unequal c) imaginary d) irrational 22 If α, β are the rots of x 2 x = 0, then the product of the roots 2α and 2β is a) 2 2 c) 4 d) 4 23 The nature of roots of equation ax 2 + bx + c = 0 is determined by a) sum of the roots Product of the roots c) Synthetic division d) discriminant 24 The Discriminant of ax 2 + bx + c = 0 is

3 a) b 2 4ac b 2 + 4ac c) b 2 + 4ac d) b 2 4ac 25 In a ratio a: b, a is called a) relation antecedent c) consequent d) none of these 26 In the ratio x: y, y is called a) relation antecedent c) consequent d) none of these 27 In a proportion a: b: : c: d, a and d are called a) means extremes c) fourth proportional d) none of these 28 In a proportion a: b: : c: d, b and c are called a) means extremes c) fourth proportional d) none of these 29 In continued proportion a: b = b: c, ac = b 2, b is said to be ---- proportional between a and c a) third fourth c) means d) none of these 30 In continued proportion a: b = b: c, c, b is said to be ---- proportional to a and b a) third fourth c) means d) none of these 3 Find x in proportion 4: x: : 5: 5 a) 75/4 4/3 c) 3/4 d) 2 32 If u v 2, then a) u = v 2 u = kv 2 c) uv 2 = k d) uv 2 = 33 If y 2 then x3 a) y 2 = k x 3 y2 = x 3 c) y 2 = x 2 d) y 2 = kx 3 34 If u = v = k, then v w a) u = wk 2 u = vk 2 c) u = w 2 k d) u = v 2 k 35 The third proportional of x 2 and y 2 is a) y 2 x 2 x 2 y 2 c) y 4 x 2 d) y 2 x 4 36 The fourth proportional w of x: y: : v: w is a) xy v vy x c) xyv d) x vy 37 If a: b = x: y then alternando property is

4 a) a x = b y a b = x y c) a+b b = x+y y d) a b x = x y y 38 If a: b = x: y then invertendo property is a) a x = b y a a b = x x y c) a+b b = x+y y d) b a = y x 39 If a b = c d then Componendo property is a) a a+b = c c+d a a b = c c d c) ad bc d) a b b = c d d 40 The identity (5x + 4) 2 = 25x x + 6 is true for a) One value of x two values of x c) all values of x d) none of these 4 A function of the form f(x) = N(x), with D 0, where N(x) and D(x) are polynomials in x is called D(x) a) an identity an equation c) a fraction d) none of these 42 A fraction in which the degree of the numerator is greater or equal to the degree of denominator is called a) a proper fraction an improper fraction c) an equation d) algebraic relation 43 A fraction in which the degree of the numerator is less than degree of denominator is called a) an equation an improper fraction c) an identity d) a proper fraction 44 2x+ (x+)(x ) is a) an improper fraction an equation c) a proper fraction d) none of these 45 (x + 3) 2 = x 2 + 6x + 9 is a) a linear equation an equation c) an identity d) none of these 46 x 3 + (x )(x+2) is a) a proper fraction an improper fraction c) an identity d) a constant term 47 x 2 Partial fraction of are of the form (x )(x+2) a) A + B x x+2 Ax + B x x+2 c) A + Bx+C x x+2 d) Ax+B x + C x+2 48 Partial fraction of x 2 (x+)(x 2 +2) are of the form

5 a) A x+ + B x 2 +2 A + Bx+C x+ x 2 +2 c) Ax+B x+ + C x 2 +2 d) A + Bx x+ x Partial fractions of x 2 + (x+)(x ) are of the form a) A + B x+ x + A + Bx+C x+ x c) + A x+ + B x d) Ax+B x+ + C x 5 A collection of well-defined object is called a) subset power set c) set d) none of these 52 A set Q = { a a, b Z b 0} is called a set of b a)whole numbers Natural Numbers c) Irrational Numbers d) Rational Numbers 53 The different number of ways to describe a set are a) 2 c) 3 d) 4 54 A set with no elements is called a) subset empty set c) singleton set d) super set 55 The set {x x W x 0} is a) Infinite Set Subset c) Null Set d) Finite Set 50 The set having only one element is called a) Null set Power set c) Singleton set d) Subset 56 The power set of an empty set is a) {a} c) {, {a}} d) { } 57 The number of elements in power set {, 2, 3} is a) 4 6 c) 8 d) 9 58 If A B, then AUB is equal to a) A B c) d) none of these 59 If A B, then A B is equal to a) A B c) d) none of these 60 If A B, then A B is equal to a) A B c) d) B A 6 (A B) C is equal to

6 a) A (B C) (A B) C c) A (B C) d) A (B C) 62 A (B C) is equal to a) (A B) (A C) A (B C) c) (A B) (A C) d) A (B C) 63 If A and B are disjoint sets, then A B is equal to a) A B c) d) B A 64 If number of elements in a set A is 3 and in set B is 4, then number of elements in A B is a) 3 4 c) 2 d) 7 65 If number of elements in a set A is 3 and in set B is 2, then number of binary relations in A B is a) c) 2 8 d) The domain of R = {(0, 2), (2, 3), (3, 3), (3, 4)} is a) {0, 3, 4} {0, 2, 3} c) {0, 2, 4} d) {2, 3, 4} 67 The range of R = {(, 3), (2, 2), (3, ), (4, 4)} is a) {, 2, 4} {3, 2, 4} c) {, 2, 3, 4} d) {, 3, 4} 68 Point (, 4) lies in the quadrant a) I II c) III d) IV 69 The relation {(, 2), (2, 3), (3, 3), (3, 4)} is a) onto function into function c) not a function d) one-one function 65 The group frequency distribution is also called a) data frequency distribution c) frequency polygon d) none of these 70 A histogram is a set of adjacent a) squares rectangles c) circles d) triangles 7 A frequency polygon is a many sided a) close figure rectangle c) square d) triangle 72 A cumulative frequency distribution is also called a)frequency distribution data c)less than frequency distribution d) none of these 73 A cumulative frequency polygon frequencies are plotted against

7 a) mid points upper class boundaries c) class limits d) none of these 74 Arithmetic mean is a measure that determines a value of the variable under study by dividing the sum of all values of the variable by their a) number group c) denominator d) none of these 75 A Deviation is defined as a difference of any value of the variable from a a) constant histogram c) sum d) none of these 76 A data in the form of frequency distribution is called a) grouped data ungrouped data c) histogram d) none of these 77 Mean of a variable with similar observations say constant k is a) negative k itself c) zero d) none of these 78 Mean is affected by change in a) value ratio c) origin d) none of these 79 Mean is affected by change in a) place scale c) rate d) none of these 80 Sum of the deviations of the variable X from its mean is always a) zero one c) same d) none of these 8 The n th positive root of product of the x, x 2, x 3,, x n observations is called a) mode mean c) geometric mean d) none of these 83 The value obtained by reciprocating the mean of the reciprocal of x, x 2, x 3,, x n observations is called a) geometric mean median c) harmonic mean d) none of these 84 The most frequent occurring observation in a data set is called a) mode median c) harmonic mean d) none of these 85 The measure which determine the middlemost observation in a data is called a) average dispersion c) central tendency d) none of these 86 The observation that divide data into four equal parts are called a) Deciles quartiles c) percentiles d) none of these 87 The spread or scatterness of observation in a data set is called

8 a) average dispersion c) central tendency d) none of these 88 The measures that are used to determine the degree or extent of variation in a data set are called measures of a) dispersion central tendency c) average d) none of these 89 The extent of variation between two extreme observations of data is measured by a) average range c) quartile d) none of these 90 The mean of squared deviations of x i (i =, 2, 3,, n) observation from their arithmetic mean is called a) variance standard deviation c) range d) none of these 9 The positive square root of mean of squared deviation of x i (i =, 2, 3,, n) observation from their arithmetic mean is called a) harmonic mean range c) standard deviation d) none of these 92 The union of two non collinear rays, which have common end point is called a) an angle a degree c) a minute d) a radian 93 The system of measurement in which the angle is measured in radians is called a) CGS system Sexagecimal system c) MKS system d) circular system o = a) c) 200 d) π 4 radians= a) 5 o 35 o c) 50 o d) 30 o 96 If tanθ = 3, then θ is equal to a) 90 o 45 o c) 60 o d) 30 o 97 sec 2 θ = a) sin 2 θ + tan 2 θ c) + cos 2 θ d) tan 2 θ 98 + sinθ + sinθ a) 2sec 2 θ 2cos 2 θ c) sec 2 θ d) cosθ 99 cosec 45o 2

9 a) c) 2 d) secθ cotθ = a) sin θ cosθ c) sinθ d) sinθ cosθ 0 cosec 2 θ cot 2 θ = a) c) 0 d) tanθ

10 Preparation Mathematics 0 for Section-I Q.No. Answers to the following Questions. Solve x 2 + 2x 2 = 0 2 Solve by factorization 5x 2 = 5x 3 Write in standard form + = 3 x+4 x 4 4 Write the names of the methods for solving a quadratic equation. 5 Solve (2x 2 )2 = Solve 3x + 8 = x 7 Define quadratic equation. 8 Define reciprocal equation. 9 Define exponential equation. 0 Define radical equation. Q.No.2 Answers to the following Questions. Discuss the nature of the roots of the equation x 2 + 3x + 5 = 0 2 Discuss the nature of the roots of the equation x 2 + 6x = 0 3 Discuss the nature of the roots of the equation 2x 2 7x + 3 = 0 4 Discuss the nature of the roots of the equation 6x 2 8x + = 0 5 Find ω 2, if ω = Prove that the sum of the all cube roots of unity is zero. 7 Find the product of complex cube roots of unity. 8 Show that x 3 + y 3 = (x + y) (x + wy) (x + w2y) 9 Evaluate w 37 + w Evaluate ( w + w 2 ) 6 If w is cube root of unity, form an equation whose roots are 3w and 3w 2. 2 Using synthetic division, find the remainder and quotient when (x 3 + 3x 2 + 2) (x 2) 3 Using synthetic division, show that x 2 is the factor of x 3 + x 2 7x Find the sum and product of the roots of the equation 2px 2 + 3qx 4r = 0. 5 Find α 2 + β 2 of the roots of the equation x2 4x + 3 = 0 6 If a, b are the roots of 4x 2 3x + 6 = 0, find a 2 + b 2 7 If a, b are the roots of 4x 2 3x + 6 = 0, find α + β β α 8 If a, b are the roots of 4x 2 3x + 6 = 0, find a b 9 If a, b are the roots of x 2 5x + 7 = 0, find an equation whose roots are a, b 20 If a, b are the roots of x 2 5x + 7 = 0, find an equation whose roots are 2a, 2b. Q.No.3 Answers to the following Questions.

11 Define ratio and give one example. 2 Define proportion. 3 Define direct variation. 4 Define inverse variation. 5 State theorem of componendo-dividendo. 6 Find x, if 6 x : If x and y 2 varies directly, and x = 27 when y = 4. Find the value of y when x = 3. 8 If u and v varies inversely, and u = 8, when v = 3. Find v when u = 2. 9 Find the fourth proportional to 8, 7, 6. 0 Find a mean proportional to 6 and 49. Find a third proportional to 28 and 4. 2 If y x2 and y = 28 when x = 7, z = 2, then find y z 3 If z xy and z = 36 when x = 2, y = 3, then find z. 4 If w v2 and w = 2 when v = 3, then find w Q.No.4 Answers to the following Questions. Define a rational fraction. 2 What is a proper fraction? 3 What is an improper fraction? 4 What are partial fractions? 5 How can we make partial fractions of 6 Resolve into partial fraction 7 Find partial fractions of x 2 3 (x+)(x ) x 8 Resolve into partial fraction (x 3) 2 9 How we can make the partial fractions of x 2 (x+2)(x+3) (x+a)(x a) 0 Whether (x + 3) 2 = x 2 + 6x + 9 is an identity? x Q.No.5 Answers to the following Questions. Define a subset and give one example. 2 Write all the subsets of the set {a, b} 3 Show by Venn diagram A (B C). 4 Define intersection of two sets. 5 Define a function. 6 Define one-one function. 7 Define an onto function. 8 Define a bijective function. 9 Write De Morgan s laws. 0 Show A B by Venn diagram. When A B

12 Q.No.6 Answers to the following Questions. Define class limits 2 Define class mark 3 What is cumulative frequency? 4 Define a frequency distribution 5 What is histogram? 6 Name two measures of central tendency 7 Define Arithmetic mean. 8 Write three properties of Arithmetic mean. 9 Define Median. 0 Define Mode? What do you mean by Harmonic mean? 2 Define Geometric mean. 3 What is Range? 4 Define Standard deviation. Q.No.7 Answers to the following Questions. Define an angle. 2 What is the sexagesimal system of measurement of angles? 3 How many minutes are in two right angles? 4 Define radian measure of an angle. 5 Convert π radian to degree measure. 4 6 Convert 5 o to radians. 7 What is radian measure of the central angle of an arc 50m long on the circle of radius 25m? 8 Find r when l = 56 cm and θ = 45 o 9 Find tanθ when cosθ = 9 and terminal side of the angle q is in fourth quadrant 4 0 prove that ( sin 2 θ)( + cos 2 θ)

13 Fill in the blanks Chapter No: The standard form of the quadratic equation is. The number of methods to solve a quadratic equation are. The name of the method to derive a quadratic formula is. The solution of the equation ax 2 + bx + c = 0, a 0 is. The solution set of 25x 2 = 0 is. An equation of the form 2 2x 3 2x + 5 = 0 is called a/an equation. The solution set of the equation x 2 9 = 0 is. An equation of the typex 4 + x 3 + x 2 + x + = 0 called a/an equation. A root of an equation, which do not satisfy the equation is called root. An equation involving impression of the variable under is called radical equation. Fill in the blanks Chapter No: 2 The discriminant of ax 2 + bx + c = 0 is. If b 2-4ac = 0, then roots of ax 2 + bx + c = 0 are. If b 2-4ac > 0, then the roots of ax 2 + bx + c = 0 are. If b 2-4ac < 0, then the root of ax 2 + bx + c = 0 are. If b 2-4ac > 0 and perfect square, then the roots of ax 2 + bx + c = 0 are. If b 2-4ac > 0 and not a perfect square, then roots of ax 2 + bx + c = 0 are. If a, b are the roots of ax 2 + bx + c = 0, then sum of the roots is. If a, b are the roots of ax 2 + bx + c = 0, then product of the roots is. If a, b are the roots of 7x 2-5x + 3 = 0, then the sum of the roots is. If a, b are the roots of 5x 2 + 3x - 9 = 0, then product of the roots is. For a quadratic equation ax 2 + bx + c = 0, αβ is equal to. Cube roots of unity are. Under usual notation sum of the cube roots of unity is. If, w, w 2 are the cube roots of unity, then w -7 is equal to. If a, b are the roots of the quadratic equation, then the quadratic equation is written as. If 2 w and 2 w 2 are the roots of an equation, then equation is. Fill in the blanks Chapter No: 3 The simplest form of the ratio In a ratio x y; x is called. In a ratio a b; b is called. In a proportion a b : x y; a and y are called. In a proportion p q : m n; q and m are called. In proportion 7 4 : p 8, p =.

14 If 6 m : 9 2, then m =. If x and y varies directly, then x =. If v varies directly as u 3, then u 3 =. If w varies inversely as p 2, then k =. A third proportional of 2 and 4, is. A third proportional of 2 and 4, is. The mean proportional of 4m 2 n 4 and p 6 is. Fill in the blanks Chapter No: 5 If A B, then A B =. If A B = φ then A and B are. If A B and B A then. A (B C) =. A (B C) =. The complement of U is. The complement of φ is. A Ac =. A Ac =. The set {x x A and x B} =. The point ( 5, 7) lies in quadrant. The point (4, 6) lies in quadrant. The y co-ordinate of every point is on-x axis. The x co-ordinate of every point is on-y axis. The domain of {(a,, (b, c), (c, d)} is. The range of {(a, a), (b,, (c, c)} is. Venn-diagram was first used by. A subset of A A is called the in A. If f : A B and range of f = B, then f is an function. The relation {(a,, (b, c), (a, d)} is a function.

15 Fill in the blanks Chapter No: 7 π radians = degree. The terminal side of angle 235 o lies in quadrant. Terminal side of the angle -30 o lies in quadrant. Area of a circular sector is. If r = 2 cm and q = 3 radian, then area of the circular sector is. The general form of the angle 480 o is If sinθ =, then θ =. 2 If θ = 300 o, then sec( 300) o = + cot 2 θ =. Secθ tanθ =

1 Chapter 2 Perform arithmetic operations with polynomial expressions containing rational coefficients 2-2, 2-3, 2-4

1 Chapter 2 Perform arithmetic operations with polynomial expressions containing rational coefficients 2-2, 2-3, 2-4 NYS Performance Indicators Chapter Learning Objectives Text Sections Days A.N. Perform arithmetic operations with polynomial expressions containing rational coefficients. -, -5 A.A. Solve absolute value