Page 1 : Dakshina Kannada Zilla Panchayat, Department of Public Instruction, Office of Deputy Director of Public Instruction, (Administration), Mangalore, and, , District Institute of Education and Training, Kodialbail, Mangalore, Dakshina Kannada, , Sopana, For Achievement in Mathematics…, , Mathematics Question Bank, (Resource material prepared during the S.S.L.C. Exam, Preparation Programme 2021-22)

Page 2 : Foreword, The global pandemic Covid-19 has had an adverse effect on the, Educational System. At this juncture, I sincerely thank the resource persons who, have prepared the Question Bank in Mathematics even during these testing, times. I also thank the Staff of the DDPI Office Mangalore and the Lecturers of, the DIET Mangalore who have extended their co-operation and guidance during, the preparation of the Question Bank., The 10 standard classes for the year 2021-22 have officially begun, on September-2021 and as per the guidance of the Government 20% of the, portion from the syllabus has been reduced and the teachers have completed the, teaching of the portion from the reduced syllabus, on time. The Question Bank, has been well prepared in order to benefit the students. This Question Bank is, useful for the students, and hence every teacher should procure the copy of this, book and reach it to every student and help them score their best marks., Wishing that everyone works in this regard and join hands in making Dakshina, Stand First in the State., Smt K RAJALAKSHMI, Principal and DDPI (Development), DIET Mangalore DK, , Department of Public Instruction, Mangalore, Dakshina Kannada District

Page 6 : Content, S.No., , Unit, , 1., , Arithmetic Progressions, , 2., , Triangles, , 3., , Pair of Linear Equations in two variables, , 4., , Circles, , 5., , Area related to circles, , 6., , Constructions, , 7., , Coordinate Geometry, , 8., , Quadratic Equations, , 9., , Introduction to Trigonometry, , 10., , Some applications of Trigonometry, , 11., , Statistics, , 12., , Surface Areas and Volumes, , Department of Public Instruction, Mangalore, Dakshina Kannada District

Page 7 : 1. Arithmetic Progression, Multiple choice questions :, 1) In an arithmetic progression, if an=2n+1 ,then the common difference of the given, progression is _________, a) 0, , b) 1 c) 2 d) 3, , 2) If the common difference of an A.P. is 5 then the value of, a18-a13 is _________, a) 5, , b) 20, , c) 25, , d) 30, , 3) The 10th term of an A.P. 5,9,13….. is _________, a) 36, , b) 31 c) 41 d) 21, , th, , 4) If the n term of an A.P. is 4n2-1 then the 8th term is _________, a) 32, , b) 31 c) 256 d) 255, , 5) In an A.P. if s1=5 and s2=12 then value of d is _________, a) -2, , b) 1, , c) 2 d) 3, , 6) If the nth term of an A.P. is an = 24-3n then its 2nd term is _________, a) 18, , b) 15 c) 0 d) 2, , th, , 7) If the n term of an A.P. is 5n+3, then the 3rd term is _________, a) 11 b) 18 c) 12 d) 13, 8) In an A.P. nth term of an A.P. is an=2n-1 then 5th term is _________, a) 16, , b) 9, , c) 14, , d) -14, , 9) If the first term of an A.P. is 3, common difference is 2 then its 20th term is, _________, a) 39, , b) 41, , c) 42 d) 43, , 10) If an=2n+3 then the value of S3 is _________, a) 15, , b) 17, , c) 21, , d) 24, , 11) The sum of first n natural number is _________, a) Sn = n2, , b) Sn=, , c) Sn = n(n+1) d) Sn =, , 12) Number of 2-digit numbers divisible by 3 is _________, a), , 30, , b) 33, , c), , 29, , d) 99, , 13) If 3,8,13 are in A.P. then the common difference is _________, a) 19, , b) 15, , c) 11 d) 7, , 14) If (x+2),x and (2x+3) are in A.P. then the value of x is_________, Department of Public Instruction, Mangalore, Dakshina Kannada District

Page 8 : a) 6 b) -5, , c) 5, , d) 3, , 15) The sum of n odd natural numbers is _________, a) Sn=n2 b) Sn=n3, , c) Sn=n(n-1) d) Sn = n(n+1), , 16) The sum of n even natural number is _________, a) Sn=n(n+1) b)Sn=n3 c) Sn=n(n-1) d) Sn = n2, 17) Value of ∑5 is _________, a) 20 b) 15 c) 5 d) 25, , 1 mark questions :, 1) Write the general form of an A.P., 2) Write the nth term of an A.P., 3) If the first term of an A.P. is x and common difference is y then write the nth term of, A.P., 4) Find the 10th term of an A.P. 2,8,14………, 5) If the first term of an A.P. is a and last term is l then write the formula to find sum of, nth terms., 6) Find the first term and common difference of the given A.P. 3,1,-1,-3…., 7) Write the formula to find the sum of n terms of an A.P., 8) What is the sum of first n positive integers?, 9) Find the sum of first 10 positive integers., 10) What is the common difference of an A.P. where an =3n-2?, 11) Find the 9th term of an A.P. whose nth term is given an=2n-5, 12) Find the 10th term of an A.P. whose nth term is given an=2n-5, 13) In an A.P. if an=n2+4 then find a2., 14) In an A.P.an=n2+3 then find a3, 15) Find the 2nd term of sequence where nth term is, , 2 marks, , 1) Find the sum of even numbers between 1 and 100, 2) x,13,y and 3 are in A.P. Find the value of x and y, 3) How many two-digit numbers are divisible by 3?, Department of Public Instruction, Mangalore, Dakshina Kannada District

Page 9 : 4) How many two digit numbers are divisible by 7 ?, 5) Find the sum of first 30 terms of the A.P. 1+5+9+13+……, 6) Find the 50th term of the A.P. 5,10,15…………., 7) Find the sum of 5+8+11+……. to 10 terms using the formula, 8) What is the sum of the first 40 positive integers divisible by 6?, 9) Find the sum of the first 15 multiples of 8, 10) Find the sum of the odd numbers between 0 and 50, 11) Find the sum of the even numbers between 0 and 50, 12) The first term of an A.P. is 5, the last term is 45 and the sum is 400. Find the number, of terms and the common difference., 13) Find the sum of first 22 terms of an A.P. in which d=7 and 22nd term is 149., 14) How many terms of the A.P. 24,21,18….. must be taken so that their sum is 78?, 15) Find the sum of first 15 terms, whose nth term is given by an=3+2n, 16) Find the sum of first 15 terms of an A.P. 4,7,10……., 17) Find how many terms are there in an A.P.100,96,92…… 12, 18) Find the 30th term of an A.P. 10,7,4……., 19) Find 15th term of an A.P. 2,7,12….., 20) Which term of the A.P. 3,8,13…… is 78?, 21) Find the sum of the first 22 terms of an A.P. 8,3,-2……, 22) In an A.P. if a=7, d=3 n=8 then find an, 23) In an A.P. if a=-18, n=10 an=0 find d, 24) Find the sum of first 100 natural numbers, 25) In an A.P. a12=37, d=3 find a and S12., 26) How many three-digit numbers are divisible by 7?, , 3 marks /4 marks, 1) Determine the A.P. whose third term is 16 and the 7th term exceeds the 5th term by 12., 2) The sum of 4th and 8th terms of an A.P. is 24 and the sum of 6th and 10th term is 44 Find, the first three terms of the A.P., 3) Find the 31st term of an A.P. whose 11th term is 38 and 16th term is 73. Also find the, sum of 10 terms of the A.P., , Department of Public Instruction, Mangalore, Dakshina Kannada District

Page 10 : 4) The seventh term of an A.P. is 4 times the 2nd term and twelfth term is 2 more than, three times the 4th term. Find the Arithmetic Progression., 5) A line segment is divided into four parts forming an A.P. The sum of the lengths of 3rd, and 4th parts is 3 times the sum of the lengths of first 2 parts. If the length of fourth part, is 14cm.Find the total length of the line segment., 6) The first term of two A.P.s are equal and the ratios of their common differences is 1:2., If the 7th term of first A.P. and 21st term of 2nd A.P. are 23 and 125 respectively. Find, two A.P.s., 7) In an A.P. 3rd term is 7 and the 7th term is 2 more than three times the third term. Find, the sum of first 20 terms of the A.P., 8) Tenth term of an A.P. is 21 and the sum of the first 10 terms is 120. Find the 20th term, of the A.P., 9) The sum of first 6 terms of an A.P. is 42 The 10th term and 30th term are in the ratio 1:2, Find the 13th term of the A.P., 10) In an A.P. the sum of four terms is 20 and the sum of their squares is 120. Find the four, terms., 11) The number of mobile telephones manufactured by a new company increases every, month by a constant number. If the company manufactures 600 mobiles in 3rd month, and 1600 mobiles in the 7th month. Find the total product in the first year., 12) In an AP. if the 2nd and 3rd terms are 14 and 18 respectively. Find the sum of first 51, terms, 13) If 12th and 22nd terms of an A.P. are 42 and 62 respectively. Find the 25th term., 14) Three angles of a triangle are in an A.P. If the largest angle is 75 find the remaining, angles., 15) In an AP. the 3rd and 7th terms are 14 and -2 respectively which term of the A.P. is -14, 16) The fourth term of an A.P. is 10 If 11th term is one more than three times the fourth, term. Find the sum of its 25th term., 17) The sum of 2nd and 5th terms of an A.P. is 23. The difference of 3rd term and 10th term is, 21 Find to terms of the A.P., 18) The third term of an A.P. is 8 if 9th term is two more than the three times of 3rd term, find the sum of its 19 term, 19) The sum of first 9 terms of an A.P. is 81 and the sum of first 15 terms is 225. Find the, sum of first 20 terms, , Department of Public Instruction, Mangalore, Dakshina Kannada District

Page 11 : 20) The thirteenth term of an A.P. is two times its 10th term and the third term is 6 more, than two times its sixth term. Find the first three terms., 21) 3rd term of an A.P. exceeds the first term by 12. If the last term is 205 and the 5th term is, 25 .Find the number of terms of the A.P., 22) An A.P. having four terms whose sum equal to 68 and the product of its middle two, terms is 280. Find these four terms., 23) Subba Rao started work in 2015 at an annual salary of Rs.50,000 and received an, increment of Rs.2000 each year. In which year did his income reach Rs.70,000?, 24) There are 5 terms in an A.P. the sum of these terms is 55 and the 4th term is fife more, than the sum of the first two terms .Find the terms of A.P., 25) Find three consecutive terms which are in A.P. whose sum is 27 and product is 648., , 5 marks, 1) In an A.P. mth term is n and nth term is m then find the sum of (m+n)th term., 2) The ratio of the sums of m and n terms of an A.P. is m2:n2 . Show that the ratio of the, mth and nth terms is (2m-1):(2n-1), 3) In an A.P. 6th term is one more than twice the third term. The sum of 4th and 5th terms is, 5 times the 2nd term. Find the 10th term of the A.P. and sum of 10 terms of A.P., 4) The sum of first 3 terms of an A.P is 24 and the sum of their square is 224 Find the first, 3 terms of A.P., 5) The sum of four consecutive terms which are in an A.P. is 32 and the ratio of the, product of the first and the last term to the product of two middle terms is 7:15.Find the, number., , Department of Public Instruction, Mangalore, Dakshina Kannada District

Page 12 : 2. Triangles, 1 MARKS, 1) State Basic proportionality theorem., 2) State the converse of Thales theorem., 3) State the Pythagoras theorem, 4) State the converse of Pythagoras theorem., 5) State equiangular triangles, 6) State similarity of triangles., 7) Define similar figures., 8) In Δ ABC, , B =900 AC=17 cm , AB = 8cm Find the length of BC., , 9) In the given figure, , Q = 900. Apply the Pythagoras Theorem and, , write the equation., , 10) Give an example for Pythagorean triplet., , M C Q 1 marks, 1) Sides of two similar triangles are in the ratio 4:9. Areas of these triangles are in the, ratio _________, a) 2:3, , b) 4:9, , c) 81:16, , d) 16:81, , 2) If the areas of two triangles are in the ratio 81:16 then the ratios of their, corresponding sides are _________, a) 9:4, , b) 4:9, , c) 2:3, , d) 16:81, , 3) Sides of a triangle are given below. Determine which of them is a right angled, triangle _________, a) 2,3,5, , b) 6,8,10, , c) 8,4,6, , d) 6,8,9, , 4) In the given figure Δ ABN~Δ AMC of AM and AN‘s ratio is 2:5. Find CM:BN, a) 5:2, , b) 2:5, , c) 1:2, , d) 2:3, , Department of Public Instruction, Mangalore, Dakshina Kannada District

Page 14 : 3) In trapezium ABCD AB ‖ DC, AB=2CD, Δ AOB=84sq.cm. Find the area of Δ COD., 4) In fig. if PQ ‖ RS Prove that Δ POQ ~Δ SOR., , 5) Let Δ ABC~ Δ DEF and their areas be respectively 64cm2 and 121cm2 ., If EF =11cm find BC., 6) Diagonals of a trapezium ABCD with AB ‖ DC intersect each other at the, point O. If AB = 2CD find the ratio of the areas of triangles AOB and COD., 7) ABC is an isosceles triangle right angle at C. Prove that AB2=2AC2, 8) A guy wire attached to a vertical pole of height 18m is 24m long and has a stake, attached to the other end. How far from the base of the pole should the stake be driven, so that the wire will be taut?, 9) ABC is an isosceles triangle with AC=BC If AB2 = 2AC2 prove that ABC is a right, triangle., 10) In the fig. if AE ‖ DB, CD =4cm CE=12cm and BD = 5cm find AE., , 3 marks, , 1) From airport two airplanes start at the same time. If the speed of first airplane due, North is 1000km/h and that of other due East is 1200km/h, then find the distance, between two airplanes after 2 hours., 2) In the figure ABC is a triangle and AD ꓕ AC., Prove that AB2 + CD2 = BD2 + AC2., , Department of Public Instruction, Mangalore, Dakshina Kannada District

Page 15 : 3) In Δ ABC D,E and F are the midpoints of the sides AB ,BC and AC respectively ., Find the ratio of area of Δ ABC and area of Δ DEF., 4) In fig. ∟ ACB =90‘ and CD ꓕ AB. Prove that, , =, , 5) In fig ABC and DBC are two triangles on the same, base BC. If AD intersects BC at O Show that, =, , 6) Prove that the ratio of the areas of two similar triangles is equal to the square of the, ratio of their corresponding medians ., 7) Two poles of heights 6m and 11m stand on a plane ground. If the distance between, the feet of the poles is 12m find the distance between their tops., , 4 marks, , 1) State and prove Thales theorem., 2) State and prove Pythagoras theorem., 3) Prove the ratio of the areas of two similar triangles is equal to the square of the ratio, of their corresponding sides., 4) State and prove Angle-Angle-Angle criterion for similarity of two triangles., 5) BL and CM are medians of a triangle ABC right angled at A., Prove that, , 4(BL2+CM2) = 5BC2, , 6) In an equilateral triangle ABC, D is a point on side BC such that BD= BC. Prove, that 9AD2=7AB2, , Department of Public Instruction, Mangalore, Dakshina Kannada District

Page 16 : 3. Pair of Linear Equations in Two Variables, 1 MARKS, 1) Write the general form of linear equation in one variable., 2) Write the general form of linear equation in two variables., 3) Write the value of a,b and c in the following linear equation 2x+3y=7., 4) Find whether the following pair of linear equations are consistent or inconsistent, x-2y=0, , and 3x+4y-20=0, , 5) Find whether the lines representing the following pairs of linear equations intersect at, a point, are parallel or coincident, 9x-3y+12=0 and 18x+6y+24=0, 6) The larger of two supplementary angles exceeds the smaller by 280. Represent the, situation algebraically., 7) Find the number of solutions for the following linear equations, x+y=3, , and 5x-5y=1, , 8) If the following pair of lines are parallel, find the value of k, 3x+2ky-2=0, , 2x+5y+1=0, , 9) Find the value of x and y for the following pair of linear equations, x-y=2, x+y=4, 10) If, , ≠, , of a pair of linear equations. Write the number of solutions., , 2 marks, , 1) Solve the following pair of linear equations, a) 3x+5y=4, , b) 2x+y=8, , x—5y=8, , x+y=5, , c) 2x+y=8, x+2y=7, , 2) For what values of k will the following pair of linear equations have infinitely many, solutions?, kx+3y-(k-3)=0, 12x+ky-k=0, 3) The difference between two numbers is 36 and one number is three times the other, represent the situation algebraically, , Department of Public Instruction, Mangalore, Dakshina Kannada District

Page 17 : 3 marks, , 1) If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces, to 1. It becomes ½ if we add 1 to the denominator, what is the fraction?, 2) The area of a rectangle gets reduced by 9 square unit if its length is reduced by 5 units, and breath is increased by 3 units. If we increase the length by 3 units and the breadth, by 2 units, the area increases by 67 square units. Find the dimensions of the rectangle., , 4 marks, , 1) Solve graphically, , a) x+y=8, x-y=2, , b) 3x+4y=10, 2x-2y=2, , e) 3x+4y=12, , f) 3x+5y=15, , x-y=5, , x+y=3, , c) 3x+2y=0, , d) 2x+3y=6, , x+3y=7, g) 2x+3y=6, , x+y=3, h) 2x+y=8, , 3x+4y=12, , Department of Public Instruction, Mangalore, Dakshina Kannada District, , x+4y=8

Page 18 : 4. Circles, Multiple Choice Questions, , 1. In the adjoining figure TP and TQ are the tangents to the, circle with centre O the measurement of, , PTQ is, , _______________, a) 900, , b) 1100, , c) 700, , d)400, , 2. In the figure if PA and PB are tangents and AP=AB then APB, is ___________, a) 900, , 3. In, , the, , b) 600, , PTQ, , =, , c) 1800, , 800, , d)700, , Type equation here.POT, , then, , is, , ___________, a) 1000, , b) 400, , c) 800, , d)500, , 4. The distance between two parallel tangents of a circle of radius 4 cm is _____________, a) 2 cm, , b) 4 cm, , c) 6 cm, , d) 8 cm, , 5. A tangent is drawn from a point at a distance of 17 cms of circle C of radius 8 cm. It‘s, length is _______, a) 5 cm, , b) 9 cm, , c) 15cm, , d) 23 cm, , One Mark Questions, 1. In the given figure, O is the centre of a circle AB is a chord and ST, is the tangent at A. It |AOB = 1000 then calculate |BAT, , Department of Public Instruction, Mangalore, Dakshina Kannada District

Page 19 : 2. How many tangents can be drawn from an external point to the circle?, 3. How many parallel tangents can be drawn to a circle at the most?, 4. If the perimeter and the area of a circle are numerically equal, then find the radius of the, circle., 5. Write the angle between the radius and the tangent drawn at the end point of the radius., Two marks Questions, 1. Prove that the tangents drawn at the ends of a diameter of a circle are parallel., 2. Two concentric circles are of radius 5 cm and 3 cm. Find the length of the chord of the, larger circle which touches the smallest circle., Three Marks Questions, 1. Prove that ―The length of tangents drawn from an external point to a circle are equal‖, 2. Prove that ―The tangents at any point of the circle is perpendicular to the radius through, the point of contact.‖, , Department of Public Instruction, Mangalore, Dakshina Kannada District

Page 20 : 5. Areas Related to Circles, One Mark Questions, 1) What is the formula to find the circumference of a circle?, 2) What is the formula to find the Area of a circle?, 3) What is a sector?, 4) What is a segment?, 5) What is the area of the sector with angle, , and radius ‘r‘?, , 6) What is the formula to find the length of the arc of a sector with angle, , and radius, , ‘r‘?, 7) If the circumference and area of a circle are numerically equal then what is the radius, of that circle?, 8) What is formula to find the area of a square?, 9) What is the formula to find the area of an equilateral triangle?, 10) What is formula to find the area of a rectangle?, 11) What is the formula to find the area of a triangle?, One Mark Questions (Multiple Choice Questions), 1) If the area of a sector of a circle is, , times the area of the circle, then the angle of the, , sector _____________, A) 1000, , B) 2000, , C) 500, , D) 1500, , 2) If the ratio of the radii of two circles is 3 : 2 then the ratio of their areas is _________, A) 3 : 4, , B) 4 : 9, , C) 9 : 4, , D) 27 : 8, , 3) If the area of a circle is 154 cm2 then the length of its radius is _____________, A) 14cm, , B)21cm, , C) 28cm, , D) 7cm, , 4) The area of the biggest square that can be circumscribed inside a circle with radius 6cm, ____________, A) 72 cm2, , B) 74 cm2, , C) 36 cm2, , D) 120 cm2, , 5) A circle is circumscribed inside a square as shown in the figure. If the, length of the side of the square is 14 cm, then the area of the shaded, region is ___________, A) 21 cm2, , B) 42 cm2, , C) 48 cm2, , D) 196 cm2, , Department of Public Instruction, Mangalore, Dakshina Kannada District

Page 21 : 6) The circumference of a circle and the perimeter of a square are equal. If the area of the, square is 484 cm2 then the diameter of the circle is ______________, A) 14cm, , B)21cm, , C) 28cm, , D) 7cm, , Two marks Questions, 1) Find the area of the sector whose radius is 4 cm and the angle subtended at the centre, is 300, 2) Find the area of the sector whose diameter is 6 cm and the angle subtended by the arc, at the centre of the circle is 600, , 3) Find the area of the shaded region in the given figure, if radii of two, concentric circles with centre O are 7 cm and 14 cm respectively and, = 400 ., , 4) If ABCD is a square with sides equal to 14 cm then find the area of, the shaded region in the given figure., , 5) ABCD is square with sides 14 cm. If APD and BPC are semicircles as, shown in the figure, then find the area of the shaded region., , 6) Find the area of the shaded region in the given figure., , Department of Public Instruction, Mangalore, Dakshina Kannada District

Page 22 : 7) In the given figure, ABCD is a square of side 14 cm. With centres, A, B, C and D, four circles are drawn such that each circle touch, externally two of the remaining three circles. Find the area of the, shaded region., , 8) AB and CD are respectively the arcs of two concentric circles of radii 21, cm and 7 cm and centre O . If  AOB = 30°, find the area of the shaded, region.‗O‘, , Three marks Questions, 1) In a circle of radius 21 cm, an arc subtends an angle of 600 at the centre. Find the, length of the arc and the area of the sector formed by the arc., 2) ‗O‘ is the centre of the circle whose radius is 6cm. What is the area, of the sector AOB?, , 3) A sheet of paper ABCD is in the shape of a rectangle., AB= 20cm, BC= 14cm, A semicircle is cut out from it, with BC as the diameter. Find the area of the remaining, part., , 4) What is the area of the remaining portion of a square shaped sheet, of paper whose sides are of length 24cm, when four congruent, quadrants are cut out from its four vertices as shown in the figure?, , Department of Public Instruction, Mangalore, Dakshina Kannada District

Page 23 : 5) A square OABC is inscribed in a quadrant OPQ. If OA = 14 cm,, find the area of the shaded region., , 6) In the figure, if ‗O‘ is the centre of the circle and BC= BD= 8cm, AC= AD= 15cm then what is the area of the shaded region?, , 7) In figure, ABC is a quadrant of a circle of radius 14 cm and a, semicircle is drawn with BC as diameter. Find the area of the, shaded region., , Department of Public Instruction, Mangalore, Dakshina Kannada District

Page 24 : 6.Constructions, Two marks Questions, 1. Draw a line segment of length 10 cms and divide it in the ratio 3:2. Measure the two, parts, 2. Draw a circle of radius 3.5 cms. From a point 8cm away from its centre, construct the, pair of tangents to the circle and measure their length., 3. Draw a circle of radius 4cms and construct a pair of tangents to the circle from a point, 5cms away from the circle., 4. Draw a pair of tangents to a circle of radius 5cm which are inclined to each other at, angle of 600., 5. Draw a circle of radius 4cm. Construct a pair of tangents to the circle such that angle, between the radii 700., 6. Construct a tangent to a circle of radius 4cm at any point P on its circumference., 7. Draw a pair of tangents to a circle of radius 4cm which are inclined to each other at an, angle of 700 and write the measure of its length., 8. Draw a line segment of AB=8cm and divide it in the ratio 5:3 by geometrical, construction., Three Marks Questions, , 1., , Construct a triangle with sides 5cms, 6cms and 7cms and then draw a similar triangle, whose sides are in the ratio, , 2., , of the corresponding sides of the first triangle., , Construct a triangle of sides 4cms, 5cms and 6cms and then a triangle similar to it whose, sides are of the corresponding sides of the first triangle., , 3., , Construct a triangle ABC of its sides BC=4cm, AB=6cm and AC=4.5cm then construct a, triangle similar to it, whose sides are of the corresponding sides of the triangle ABC., , 4., , Construct a triangle ABC of its sides BC=4cm, AB=6cm and AC=5cm then construct a, triangle similar to it, whose sides are of the corresponding sides of the triangle ABC., , 5., , Construct a right-angled triangle with sides other than the hypotenuse 5cms and 6 cms, each and then construct triangle similar to it whose sides are of its corresponding sides., , Department of Public Instruction, Mangalore, Dakshina Kannada District

Page 25 : 7.Coordinate Geometry, 1 MARKS, , 1. Write the formula to find the distance of the point P(x,y) from the origin., 2. Write the formula to find the distance between any two points P(x1,y1) and Q(x2,y2), 3. Write the Mid-point formula., 4. Write the section formula., 5. Write the formula to find the area of a triangle whose vertices are (x1,y1),(x2,y2)and, (x3,y3), 6. What is the distance of point (3,4) from the origin?, 7. Find the distance of point (-6,8) from the origin ?, 8. Find the distance between the points (2,3) and (6,6,) ?, 9. Find the distance between the points (2,3) and (-3,-7) ?, 10. Find the mid - point of the line segment joining the points (5,3) and (1,-1) ?, 11. Find the mid-point of the line segment joining the points (4,7) and (2,-3) ?, 12. What is the area of triangle whose vertices are collinear?, 13. If area of triangle is zero then the vertices of triangle are____., , 2 marks, , 1) Find the coordinates of the point which divides line segment joining the points (4,-3), and (8,5)in the ratio 3:1 internally?, 2) Find the value of ‗y‘ for which distance between the points P(2,-3) and Q(10,y) is 10, units ?, 3) In what ratio does the points (-4,6) divide the line segment joining the points A(-6,10), and B(3,-8), 4) If the points A(6,1), B(8,2),C(9,4)and D(p,3) are the vertices of a parallelogram taken, in order. Find the value of p, 5) Do the points (3,2), (-2,-3)and (2,3) form a triangle? If so, name the type of the, triangle formed., , Department of Public Instruction, Mangalore, Dakshina Kannada District

Page 26 : 3 marks, , 1. Find the area of a triangle whose vertices are (1,-1).(-4,6) and (-3,-5), 2. Find the value of k if the points A (2,3), B (4,k) and C(6,-3) are collinear, 3. Find the area of triangle formed by the points A(5,2), B(4,7) and C(7,-4), 4. If A (-5,7), B (-4, -5) and C (-1,-6) and D(4,5) are the vertices of a quadrilateral. Find, the area of quadrilateral., 5. Find the area of a triangle whose vertices are P (2,3), Q (4,0), , and R (6,-3), , 6. Check whether A (8,-4), B(9,5)and C(0,4) are the vertices of an isosceles triangle ?, 7. In the given fig. the vertices of a ΔABC are A (0,6), B (8,0) and C (5,8). CD ꓕ AB ., Find the height CD of ΔABC, , 8. The vertices of a triangle ABC are A(-3,2), B(-1,-4) and C(-5,2) If the M and N are, the mid-point of AB and AC respectively show that 2MN=BC, 9. The vertices of ΔABC are A(-5, -1)B(3,-5),C(5,2) show that the area of the ΔABC is, four times the area of the triangle founded by the joining the mid-points of the sides of, the triangle ABC., , Department of Public Instruction, Mangalore, Dakshina Kannada District

Page 27 : 8.Quadratic Equation, One Mark Questions, 1. Write the general form of quadratic equations., 2. Write the discriminant of the quadratic equation, 3. If b2-4ac = 0 find the nature of the root, 4. If b2-4ac > 0 write the nature of the root, 5. If b2-4ac < 0 find the nature of the root, 6. Write the formula to find the roots of the quadratic equation, 7. Write the discriminant of the quadratic equation ax2+c=0, 8. If the root of the equation (x+4)(x+3) =0 is -4 then find the other root of the equation, 9. Write the quadratic equation having roots 2 and -2., 10. Write the quadratic equation having roots 2 and -3, 11. If the product of two consecutive positive odd numbers is 35 then the quadratic, equation of this statement is _____________, 12. If (x-2)2=25 then find the value of ‗x‘, 13. Write given equation in the standard form x+ =5, 14. If the roots of the quadratic equation are real and distinct what is the value of the, discriminant?, 15. Which of the following is a quadratic equation?, a) x(x+1)(x+2), , b) x+ =5, , c)2x+3=4, , d)x2+y=5, , 16. If the quadratic equation x2+kx+64=0 has equal roots then the value of ‗k‘ is_______, a) 4, , b) 8, , c) 12, , d)16, , 17. Write the discriminant of the quadratic equation px2+qx+r=0, Two marks questions, 1. Find the roots of the quadratic equation using formula, a) x2+5x+6=0, b) 2x2 = x-5, c) 5x2 – 3 = 0, , e) x- = 3, , h) 4y2 + 4√ x + 4 = 0, , f) 2p2+7p+3=0, , i) 2p2 -6q +3 = 0, , g) 2m2-m- 4 = 0, , j), , -, , =3, , 2, , d) 2x – x =3, Department of Public Instruction, Mangalore, Dakshina Kannada District

Page 28 : 2. Write the nature of the roots for the following quadratic equation, a) x2-x+12=0, , c) x2-5x+1=0, , e) x2-6x=-4, , b) x2-4x+4=0, , d) 2x2=8x-6, , f) (x-3)2 = 4, , 3. Find the value of ‗k‘ for each of the following quadratic equation so that they have, two equal roots, a) 4x2-2(k+1)x+(k+1)=0, b) x2-(k+1)x +9 =0, c) x2-6x+(k-2)=0, d) kx2-10x+1=0, 4. The product of two consecutive positive integers is 240. Find those numbers, 5. If the sum of the number and its reciprocal is, , . Find the numbers, , 6. If the two sides of the right angled triangle are (x+3) and (x+1) and its hypotenuse is, 100 Find the value of ‗x‘, 7. The height of the right-angled triangle is 7 cm less than its base and its hypotenuse is, 13 cm. Find its base, 8. If the two sides of the rectangle are (x+3) and (x+2) its area is 30 cms2. Find those, sides, 9. In a triangle the length of the base and the height are (x+1) and (x+5) respectively. Its, area is 30 cm2. Find the value of ‗x‘, 10. The sum of the squares of two consecutive integers is 41. Find the numbers., 11. Find the side of the square whose area is 144cm2, 12. Find the area of an equilateral triangle is 4√ cm2. Find the height., 13. Solve using the formula: q2x2+(q2-p2)x-p2=0, Three marks questions, 1. A train travels 360 km at a uniform speed. If the speed had been 5 km/hr. more, it, would have taken 1 hour less for the same journey. Find the speed of the train., 2. Mohan‘s mother is 26 years older than him. The product of their ages (in years) is 3, years from now will be 360. What is Mohan‘s present age., , Department of Public Instruction, Mangalore, Dakshina Kannada District

Page 29 : 3. A train travels a distance of 480 km at a uniform speed. If the speed had been 8km/hr., less then it would have taken 3 hours more to cover the same distance. Find the speed, of the train., 4. Solve -, , =3, , 5. If the roots of the equation (a2+b2)x2 + 2(bc-ad)x+c2+d2=0 are real and equal. Show, that ac+bd=0 ., 6. If twice the area of a smaller square is subtracted from the area of a larger square is, equal to 14cm2. However, if twice the area of the larger square is added to 3 times the, area of the smaller square the result is 203 cm2. Determine the side of the two squares., 7. The radius of the circle is 3x+4 its area is 54 cm2. Find the value of ‗x‘ and hence the, radius of the circle., 8. The numerator of a fraction is 3 less than its denominator. If 2 is added to both the, numeration and the denominator, then the sum of the new fraction and original, fraction is, , Find the original fraction., , 9. The speed of the boat in still water is 15km/hr it goes 3km/hr. upstream and returns, downstream to the original point in 4 hours 30 minutes. Find the speed of the stream., 10. Students of a school arranged a picnic. Total cost of the food Rs. 2250. If 5 students, were less, the food contribution for each will be Rs. 5 less. Find the total number of, students who participated in the picnic., , Department of Public Instruction, Mangalore, Dakshina Kannada District

Page 30 : 9.Introduction to Trigonometry, I., , Choose the correct answers, , 1. sinA=, a), 2. If tanA=, a), , then cosecA = _______, b), , c), , d) None of the above, , then secA = _______, b), , c), , d), , 3. The value of cos 450 _______, a) 1, , b), , √, , 4. The value of, a) 1, , b) 0, , c), , d), , √, , √, , _______, c) 2, , d) None of the above, , 5. The value of Cosec310 – sec 590 is _______, a) 1, , b) 2, , 6. If 2cos =1 and, , c) 0, , d) None of the above, , is an acute angle then the value of, , _______, , a) 00 b) 300 c)450 d)600, 7. sinA.cosA.tanA + cosA.sinA.cotA is equivalent to _______, a) sin2A-cos2A, , b) tan2A+cot2A, , c) sin2A+cos2A, , d) sin2A+tan2A, , 8. If 13sin = 5 then the value of tan is _______, a), II., , b), , c), , d), , One Mark Questions, , 1. Find the value of sin300+tan450, 2. Find the value of cos, , x sec, , 3. If √ cot =1 then find the value of acute angle, 4. Find the value of, , Department of Public Instruction, Mangalore, Dakshina Kannada District

Page 31 : 5. Find the value of cot230.tan670, 6. Find the value of, III., , Two marks Questions, , 1. If tan2A = cot (A - 180) where 2A is an acute angle, find the value of A, 2. If tanA = cotB prove that A+B = 900, 3. Evaluate, 4. Prove that (tanA x sinA) + cosA = secA, 5. If cos, , = 0.6 then prove that 5sin, , (Hint : 0.6 =, , ), , 6. Show that cos380. Cos520- sin380sin520 = 0, 7. If A=600 B=300 then prove that tan(A-B) =, 8. Prove that 2cos2 -1=cos2, 9. Prove that, 10.If, IV., , sin2, , = cosec + cot, , =, , then find the value of (sinA + cosA) secA, , Prove the following (3 marks questions), , 1. secA(1- sinA)(secA + tanA) = 1, 2. (1+cot, 3. If, , tan(A+B), , =, , √, , and, , tan(A-B), , =, , √, , ;, , 00<(A+B) 900, , A>B find A and B, , 4., , +, , 5. √, , = secA + tanA, , 6., , =, , 7., , +, , 8., , = 2 sec, , = 2cosec, +, , = 7 + tan2A + cot2A, , Department of Public Instruction, Mangalore, Dakshina Kannada District, , ;

Page 33 : 10. Some Applications of Trigonometry, I., , Choose the correct Answers, 1. If the length of the shadow of a tree is decreasing then the angle of elevation is, _______, a) Increasing b) Decreasing c) Remains the same d) None of the above, 2. The angle formed by the line of sight with the horizontal when the point is below, the horizontal level is called ___________, a) Angle of elevation, , b) Angle of depression, , c) No such angle is formed, , d), , None f the above, 3. The line drawn from the eye of an observer is said to be __________, a) Angle of elevation b) Angle of depression c) Line of sight d) None of the, above, II., , Answer the following (2 marks), 1. The angle of elevation of the top of a building from a point on the ground which is, 15m away from the foot of the building is 600. Find the height of the building, 2. The height of the tower is 12m. What is the length of its shadow when the sun‘s, altitude is 450?, 3. A ladder leaning against a wall, makes an angle of 600 with the horizontal. If the, foot of the ladder is 2.5m away from the wall, find the length of the ladder., 4. The angles of elevation of the top of a tower from two points at a distance of 4m, and 9m from the base of the tower and in the same straight line with it are, complementary. Find the height of the tower., , III., , Solve the following (3 marks), 1. The angle of elevation of the top of a building from the foot of the tower is 30 0, and the angle of elevation of the top of the tower from the foot of the building is, 600. If the tower is 50m high, find the height of the building., 2. The angle of elevation of the top of a tower at a distance of 120m from a point A, on the ground is 450. If the angle of elevation of the top of a flag staff fixed at the, top of the tower at A is 600, then find the height of the flagstaff., 3. As observed from the top of a 50m high lighthouse from the sea level the angles, of depression of two ships are 300 and 600. If one ship is exactly behind the other, on the same side of the lighthouse, find the distance between the two ships., , Department of Public Instruction, Mangalore, Dakshina Kannada District

Page 34 : IV., , Solve the following (4 marks), 1. The angle of elevation of an aeroplane from a point A on the ground is 60 0. After, a flight of 15 seconds its angle of elevation changes to 300. If the aeroplane is, flying at a constant height of 1500√ m, find the speed of the plane in km/hr., 2. The angle of elevation of the top of a hill from the foot of a tower is 600 and the, angle of depression from the top of the tower of the hill is 300. If the tower is 50m,, high find the height of the hill., , Department of Public Instruction, Mangalore, Dakshina Kannada District

Page 35 : 11.Statistics, Multiple Choice Questions, 1. The mode and mean is given by 7 and 8 respectively then the median is, a), , b), , c), , d) 33, , 2. The correct relationship between mean, median and mode is ______, a) 3median = Mode + 2Mean, b) 2Median = 2Mode + Mean, c) Median = 2Mode + 2 Mean, d) 3Median = 2 Mode + Mean, 3. Cumulative frequency curve is also called ________, a) Histogram, , b) Ogive, , c) Bar Graph, , d) Median, , 4. Construction of a cumulative frequency table is useful in determining the ________, a) Mean, , b) Median, , C) Mode, , d) All the above, , Three Marks Questions, 1. Find the mean of the given data, C.I, , 0-10, , 10-20, , 20-30, , 30-40, , 40-50, , f, , 3, , 5, , 9, , 5, , 3, , 2. Calculate the median for the following data, C.I, , 0-20, , 20-40, , 40-60, , 60-80, , 80-100, , 100-120, , 120-140, , f, , 6, , 8, , 10, , 12, , 6, , 5, , 3, , 3. Calculate the mode for the following frequency distribution table, C.I, , 5-15, , 15-25, , 25-35, , 35-45, , 45-55, , 55-65, , f, , 6, , 11, , 21, , 23, , 14, , 5, , Department of Public Instruction, Mangalore, Dakshina Kannada District

Page 36 : 4. Calculate the ‗mean‘ for the frequency distribution table given below, by direct, method., Class Interval, 5 - 15, 15 - 25, 25 - 35, 35 - 45, 45 - 55, , Frequency, 4, 3, 6, 5, 2, , 5. Find the ‗mode‘ of the frequency distribution table given below., Class Interval, 0 - 10, 10 - 20, 20 - 30, 30 - 40, 40 - 50, , Frequency, 7, 9, 15, 11, 8, , 6. Find the median of the following data., Class Interval, 1-5, 5-9, 9-13, 13-17, 17-21, , Frequency, 4, 3, 5, 7, 1, , 7. Draw a less than Ogive for the given distribution table, Height (in Kg), , No. of Students, , Less than 38, , 0, , Less than 40, , 3, , Less than 42, , 5, , Less than 44, , 9, , Less than 46, , 14, , Less than 48, , 28, , Less than 50, , 32, , Less than 52, , 35, , Department of Public Instruction, Mangalore, Dakshina Kannada District

Page 37 : 8. Draw a more than type Ogive for the following data, , Production, , 50-55, , 55-60, , 60-65, , 65-70, , 70-75, , 75-80, , Number of, , 2, , 8, , 12, , 24, , 38, , 16, , farms, , 9. The following table gives the production yield per hectare of wheat of 100 farms of a, , village. Draw a ‗more than type ogive‘ for the given data., Production yield in kg/hectare, , Cumulative Frequency, , More than or equal to 50, , 100, , More than or equal to 55, , 98, , More than or equal to 60, , 90, , More than or equal to 65, , 78, , More than or equal to 70, , 54, , More than or equal to 75, , 1, , 10. Draw a ―less than type ogive‖ for the data given in the following table, Class Interval, , Frequency, , 0 - 10, , 2, , 10 - 20, , 12, , 20 - 30, , 2, , 30 – 40, , 4, , 40 - 50, , 3, , Department of Public Instruction, Mangalore, Dakshina Kannada District

Page 38 : 12.Surface Areas and Volumes, One Mark Questions, 1. Write the formula to find the Lateral Surface Area of a Cuboid, 2. Write the formula to find the Total Surface Area of a Cuboid, 3. Write the formula to find the Volume of a Cuboid, 4. Write the formula to find the Lateral Surface Area of a Cube, 5. Write the formula to find the Total Surface Area of a Cube, 6. Write the formula to find the Volume of a Cube, 7. Write the formula to find the Curved Surface Area of a Cylinder, 8. Write the formula to find the Total Surface Area of a Cylinder, 9. Write the formula to find the Volume of a Cylinder, 10. Write the formula to find the Curved Surface Area of a Cone, 11. Write the formula to find the Total Surface Area of a Cone, 12. Write the formula to find the Volume of a Cone, 13. Write the formula to find the Curved Surface Area of a Hemisphere, 14. Write the formula to find the Total Surface Area of a Hemisphere, 15. Write the formula to find the Volume of a Hemisphere, 16. Write the formula to find the Surface Area of a sphere, 17. Write the formula to find the Volume of a sphere, 18. Write the formula to find the Curved Surface Area of a Frustum, 19. Write the formula to find the Total Surface Area of a Frustum, 20. Write the formula to find the Volume of a Frustum, 21. If the radius of a cylinder is 3 cm and height 5 cm then find its volume., 22. If the curved surface area of a cone is 440cm2 and slant height is 7cm then find the, radius of its base., 23. If the radius of a hemisphere is 3.5cm then find its lateral surface area, 24. If the height of a cylinder whose lateral surface area is 132 cm2 is 7cm then find its, radius, 25. If the surface area of a sphere is 616cm2. Find its radius., , Department of Public Instruction, Mangalore, Dakshina Kannada District

Page 39 : Two Marks Questions, 1. A solid is made by joining the faces of two cubes of sides 5cm each. Find the surface, area of this solid., 2. A copper rod of diameter 1cm and length 8cm is drawn into a wire of length 18 m of, uniform thickness. Find the thickness of the wire., 3. A drinking glass is in the shape of a frustum of a cone of height 14cm. The diameters of, its two circular ends are 4 cm and 2 cm. Find the capacity of glass., 4. A sphere of radius 9 cm is melted and reshaped into a cylinder of radius 6cm. Find the, height of the cylinder., 5., , A dustbin which is the shape of a frustum had its radius of both circular ends as 15cm, and 8 cm. If its depth is 63cm then find its volume., , 6. A cone of height 24cm and radius of base 6cm is made up of modeling clay. A child, reshapes it in the form of a sphere. Find the radius of the sphere., Three Marks Questions, 1. A toy is in the form of a cone of radius 3.5cm mounted on a hemisphere of same radius., The total height of the toy is 15.5cm. Find the total surface area of the toy., 2. A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of, its ends. The length of the entire capsule is 14mm, and the diameter of the capsule is 5, mm. Find its surface area., 3. A hemispherical tank full of water is emptied by a pipe at the rate of 3 litres per second., How much time will it take to empty half the tank, if it is 3m in diameter? (Take, , =, , ), , 4. Mayank made a birdbath for his garden in the shape of a cylinder with a hemispherical, depression at one end. The height of the cylinder is 1.45m and its radius is 30cm. Find, the total surface area of the bird-bath. (Take, , =, , ), , 5. A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The, diameter of the hemisphere is 14cm and the total height of the vessel is 13cm. Find the, inner surface area of the vessel., 6. A gulab jamun, contains sugar syrup up to about 30% of its volume. Find approximately, how much syrup would be found in 45 gulab jamuns, each shaped like a cylinder with, two hemispherical ends with length 5cm and diameter 2.8cm., , Department of Public Instruction, Mangalore, Dakshina Kannada District

Page 40 : 7. A well of diameter 3m is dug 14m deep. The earth taken out of it has been spread evenly, all around it in the shape of a circular ring of width 4 m to form an embankment. Find, the height of the embankment., , Four Marks Questions, , 1. Rasheed got a playing top (lattu) as his birthday present, which surprisingly had no colour, on it. He wanted to colour it with his crayons. The top is shaped like a cone surmounted, by a hemisphere. The entire top is 5cm in height and the diameter of the top is 3.5cm., Find the area he has to colour. (Take, , =, , ), , 2. The radii of the ends of a frustum of a cone 45 cm high are 28cm and 7cm. Find its, volume, the curved surface area and the total surface area (Take, , =, , ), , 3. Water in a canal, 6m wide and 1.5m deep, is flowing with a speed of 10km/h. How much, area will it irrigate in 30 minutes, if 8cm of standing water is needed?, , 4. A wooden toy rocket is in the shape of a cone mounted on a cylinder. The height of the, entire rocket is 26 cm, while the height of the conical part is 6cm. The base of the conical, portion has a diameter of 5 cm, while the base diameter of the cylindrical portion is 3 cm., If the conical portion is to be painted orange and the cylindrical portion yellow, find the, area of the rocket painted with each of these colours., , Department of Public Instruction, Mangalore, Dakshina Kannada District