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- 1. 2011Last Minute Revision L.M.R. prashantgohil@gmail.com PRASHANT CLASSES 19/01/11
- 2. About Mr Prashant Gohil • Mr Prashant Gohil is a Mathematics Examiner for IB Mathematics since Jan 2007. • He corrects IB Diploma Mathematics Answer Scripts of a number of International Schools. • He is working as the IB Diploma Coordinator for a prestigious School in South Mumbai. He is also the Head of Mathematics Department at this School. • He has attended a number of Workshops conducted by the IBO. He has attended Workshops at Seoul (South Korea), Ching Mai (Thailand) and Hongkong. • He conducts Graphic Display Calculator Workshops for Cranes Software (Authorized distributors for Texas Instruments). He has conducted a GDC workshop at Navrachna School, Baroda and Dhirubhai Ambani International School, Mumbai. • He has also completed a training workshop for IGCSE Mathematics (Cambridge). • His earlier assignments include: o IB Mathematics Teacher at BD Somani International School, o ISC Physics and Calculus AP Teacher at Cathedral and John Connon School o ICSE Mathematics Teacher at Bombay International School o ICSE Mathematics and Physics teacher at Palm Beach School • He has been tutoring students, since 1990, at various University, Pre-university and High School Level. He has trained students for o Mathematics and Statistics module at University Level (London School of Economics, Nottingham University, University of Illinois etc.) o IB Mathematics Higher Level and Standard Level ( Dhirubhai Ambani International School, Ecole Mondiale, B.D Somani, Jamnabai Narsee, Fazlani, D.Y. Patil etc) o HSC Mathematics(Std 11 and 12), o ICSE Mathematics and Physics (Std 9 and 10) • He has also tutored students for a number of entrance tests such as o SAT o SAT Subject Tests- Mathematics and Physics o GMAT • He was a Merit List holder and received a National Scholarship for his performance at B.Sc. Examinations at University of Mumbai. • Presently, he is pursuing M.Ed from IGNOU.
- 3. PRASHANT CLASSES --TUITIONS FOR IB, IGCSE- MATHS & PHYSICS. Experienced IB teacher and IB examiner. PRASHAANT CLASSES Name:_________________ for IB, IGCSE, ICSE, 11th , 12th ,- MATHS, PHYSICS. Call 2380 00 92.Last Minute Revision 2011 1. The list price of an article is Rs.4,750. A rebate of 6. On what sum of money will the difference between 5% is given on it. After the rebate sales tax at the the simple interest and the compound interest for 2 rate of 6% is charged on it. Find the total cost of years at 5% p.a will be Rs 75? the article to be paid by the buyer. 7. A part of Rs 5110 was invested in 8% Rs 100 x + 2y − z y + 2z − x z + 2x − y shares quoted at Rs 98 and the rest in 9 % shares 2. If = = quoted at Rs 105. If the total dividend received 3a − b 3b − c 3c − a x+y+z from both is Rs 430, find the sum invested in 8% show that each fraction = . shares. a +b +c 3. In the figure [not drawn to scale,] LM is parallel 8. Mr Soni invested Rs 9000 in 15% (Rs 10) shares to BC. BA=12 cm, AL=4 cm and AC=18 cm. selling at Rs.45 After a year he sold these shares Calculate : (i) the length of CM. (ii)the value at Rs 40 each and invested the proceeds in 10% (Rs20) shares selling at Rs25. Calculate: - of ratio and then (i) the number of shares purchased, (ii) the income from the first investment, (iii) the income from the second investment; (iv) percentage return on his original investment in the second investment. 9. Car A travels x km for every litre of petrol, While car B travels (x+5) km for every litre of petrol. (i) Write down the number of litres of petrol used by car A and car Bin covering a distance of 400 km. (ii)iIf car A uses 4 litres of petrol more than car B in covering the 400 km, write down an equation in x and solve it to determine the number of litres of petrol used by car B for the journey. 10. A certain sum of money amounts to Rs 6600 in 1 4. In the given figure AC is the diameter of the semi year and to Rs 7986 in 3 years, at compound circle. BM is perpendicular to AC. If AM = 16cm interest. Find the sum and the rate of interest. and the diameter of the circle is 25 cm, calculate 1 BM 2 Area of the shaded part. use =3.142. 11. Given P = { x : 5 < 2x − 1 ≤ 11, x ∈ R} Q ={ x : −1 ≤ 3 + 4x < 23, x ∈ I} where R = {real numbers}, I = { integers} Represent P and Q on number lines. Write down 5. Solve the following inequation and represent the the elements of P ∩ Q. solution set on a number line. 30 − 4(2x−1) > −8 and x ∈ { positive integers} 12. P is a point on the line joining A(4,3) and B(−2,6) such that 5AP=2BP.Find the co−ordinates of P.Shop No. 12, Mahavir Apartments, Opp Swati Snacks, Tardeo Road, Mumbai 7. 1 prashantgohil@gmail.com
- 4. PRASHANT CLASSES --TUITIONS FOR IB, IGCSE- MATHS & PHYSICS. Experienced IB teacher and IB examiner. PRASHAANT CLASSES Name:_________________ for IB, IGCSE, ICSE, 11th , 12th .- MATHS, PHYSICS. Call 2380 00 92.13. At what rate per cent per annum C.I. will Rs 16. A trader bought a number of articles for Rs 1200. 2,000 amount to Rs 2,315.25 in 3 years? Ten were damaged and he sold each of the rest at Rs 2 more than what he paid for it, thus getting a14. The scale of a map is 1: 210000. A plot of land of profit of Rs 60 on the whole transaction . Taking area 83.79 km2 is to be represented on the map. the number of articles he bought a x, form an Find : equation in x and solve it. (i) The number of kilometres on the ground which is represented by 1 centimetre on the map. 17. Solve the inequation: . (ii) The area in km2 that can be represented by 1 Represent your solution on a number line. cm2. (iii) The area on the map that represents the plot of 18. Find the ratio in which the line joining A(−2,7) land. and B(6,1) is divided by the line y=2. Hence find the co−ordinate of the point where line AB cuts the15. Calculate the annual income of five hundred, 12% line y=2. shares bought at Rs.150 at a premium of 25%. When the market value of these shares rose to a 19. Use graph paper for this question. Plot the points premium of 50%, he sold some shares, just enough A (8,2) and B(6, 4). These two points are the to raise Rs.18,000. Calculate the number of shares vertices of a figure which is symmetrical about x = remaining. 6 and y−2=0. Complete the figure o the graph . Write down the geometrical name of the figure.20. The weights of 60 boys are given in the following distribution table, find the median, lower quartile,upper quartile, interquartile range. Weight in kg 37 39 38 41 40 No. of boys 6 10 14 12 1821. Furniturewalla buys wood for Rs.17,325 including 23. A person invested 20%, 30% and 25% of his 5 % VAT. He sells the chair made from that wood savings in buying shares of three different for Rs 24,640 including 12 % VAT. companies A, B and C which declared dividends a) What is the tax paid by him on purchase? of 10%, 12% and 15% respectively. If his total b) What is the tax to be collected by him? income on account of dividends be Rs 4675, find c) What VAT will he have to pay to the his saving and the amount which he invested government? buying shares of each company. 24. Find the values of a and b so that the polynomial22. Points (3, –4 ) and (9 , –4) are invariants points x3 −4x2 + ax +b is exactly divisible by x2 + x under reflection in the line L1. Points (–6 ,5) and − 2. (–6, –8) are invariant points on reflection in line 25. If (x+2) and (x-3) are the factors of x3 + ax + b, L2 . find the values of a and b. With these values of a (i)Name or write equations for the lines L1 and L2. and b, factorise the given expression. (ii)Write down the images of points P (3 ,4 ) on 26. The product of the digits of a two digit number is reflection in L 1. Name the images as P′. (iii)Write 24. If its units digit exceeds twice its tens digit by down the images of Q(-5,-2) on reflection in L2. 2; Find the number. Name the images as Q′. Shop No. 12, Mahavir Apartments, Opp Swati Snacks, Tardeo Road, Mumbai 7. 2 prashantgohil@gmail.com
- 5. PRASHANT CLASSES --TUITIONS FOR IB, IGCSE- MATHS & PHYSICS. Experienced IB teacher and IB examiner. PRASHAANT CLASSES Name:_________________ for IB, IGCSE, ICSE, 11th , 12th .- MATHS, PHYSICS. Call 2380 00 92.27. Given that a,b are the roots of x2−5x + 6 = 0, a> 35. A publisher buys paper for Rs. 28,090 including b, frame the equation whose roots are 2a and 6% VAT. He makes 1000 notebooks and sells them at Rs.50 each. He has to charge VAT at 10% 3b. on the finished goods. What VAT is he liable to28. Rs125 is divided equally among a certain number pay to the government? of children; if there were 25 children more, each 36. A man borrowed Rs 2048 at 6.25% p.a compound would have received 25 paise less. Find the interest. At the end of the first year he repays Rs. number of children. 176 and at the end of the second year he repays29. List the solution set of 30 − 4 [ 2x − 1] < 30, Rs253. How much should he pay (i) at the given that x is a positive integer. beginning of the 3rd year; (ii) at the end of the third year to settle the loan.30. Find the equation of the perpendicular dropped from the point (−1,2) onto the line joining the 37. The line y = 3x − 2 bisects the join of (a,3) and (2, points (1,4) and (2,3). −5), find the value of a.31. Find the values of x which satisfy the inequation: 38. Solve the given inequation and graph the solution on the number line. 2y − 5 < y + 2 ≤ 8y + 9 ; y ∈ R. Graph the solution set on the real number line. 39. If A = . Find : i At.A ii A.At, where32. In the figure alongside,find: (i)Co−ordinates of A,B and E. , (ii)Slope of CD(// to AE) , At is the transpose of matrix A. (iii)Equation of CD , (iv)Co−ordinates of C , D , (v)The ratio CB : BD. 40. Miss Mina purchased the following items for her mother and her neighbour: Mother : 5 eggs 4 pies Neighbour: 4 eggs 3 pies If eggs are 80 p. each, pies 60p. write the above information as a matrix product, hence find the total cost of the bill for her mother and neighbour. 41. A person invests Rs 4368 and buys some hundred-rupee shares at 91. Shares worth Rs 240033. Find the third proportional to face value are sold at Rs 95 and the remainder when they have fallen to 85. Find his gain or loss on the total transaction.34. Two circles touch externally. The sum of their 42. From a solid cylinder whose height is 8 cm and areas is 130 cm2 and the distance between their radius 6 cm, a conical cavity of height 8 cm and centres is 14 cm. Find the radii of the circles. of base radius 6 cm is hollowed out. Find the volume and the total surface area of the remaining solid. Shop No. 12, Mahavir Apartments, Opp Swati Snacks, Tardeo Road, Mumbai 7. 3 prashantgohil@gmail.com
- 6. PRASHANT CLASSES --TUITIONS FOR IB, IGCSE- MATHS & PHYSICS. Experienced IB teacher and IB examiner. PRASHAANT CLASSES Name:_________________ for IB, IGCSE, ICSE, 11th , 12th .- MATHS, PHYSICS. Call 2380 00 92.43. Framing quadratic equations from the given roots 50. Without solving, comment upon the nature of 3+ ,3− roots of each of the following equations: 6x 2 − 13x + 4 =044. Solve 51. The mean lengths of 25 pencils in a box is 20 cm. It was later discovered that 5 pencils were not a part of that box and were removed. The lengths of45. The catalogue price of a data projector is the pencils that were removed was 12cm, 10 cm, Rs.69,000 The shopkeeper gives a discount of 9% 8cm, 11cm and 9 cm respectively. Calculate the on the listed price. He gives a further off-season average length of the remaining pencils. discount of 15% on the balance. However, sales tax at 13% is charged on the remaining amount. 52. The line 4x−3y+12=0 meets x−axis at point A. Find: (i) The amount of sales tax a customer has Find the co−ordinates of A. Further, find the to pay. equation of the line through point A and (ii) The final price he has to pay for the perpendicular to 4x−3y+12=0. data projector. (Give all your answers to the nearest rupee) 53.46. Find the equation of the line AB, through (3,2) and perpendicular to the line 2y=3x+5. Thus line AB 54. Find the equation of the line which passes through meets the x−axis at point P and y−axis at point Q. the point (−2, 3) and is perpendicular to the line 2x Find the co−ordinates of points P and Q. Also, + 3y + 4 = 0. find the area of triangle OPQ, where O is the 55. Five year’s ago, a woman’s age was the square of origin. her son’s age. Ten years hence her age will be47. The side AB of an equilateral triangle ABC is twice that of her son’s age. Find: parallel to x-axis. Find the slopes of all its sides. (i) the age of the son five years ago (ii) the present age of the woman.48. The compound interest on a certain sum of money for 2 years is Rs 1890 and the simple interest for 2 56. The roots of x2 − 6px + 45= 0 are p and 5p. Find years at the same rate is Rs 1800. Calculate the the values of p. sum and the rate of interest. 57. If x: y be the sub duplicate ratio of x−a : :y−a ,49. A solid right circular cone of height 20 cm and base radius 15 cm is melted and casted into prove that smaller cones of equal sizes with height 5 cm and base radius 1.5 cm. Find how many cones are 58. (1,5) and (−3,−1) are the co−ordinates of vertices made. A and C respectively of rhombus ABCD. Find the equations of the diagonals AC and BD.59. Draw an ogive for the following distribution: Income in Rs 120−140 140−160 160−180 180−200 200−220 220−240 No of 30 72 90 80 70 28 employees Use the ogive i the median income, iithe number of employees whose income exceeds Rs190. Shop No. 12, Mahavir Apartments, Opp Swati Snacks, Tardeo Road, Mumbai 7. 4 prashantgohil@gmail.com
- 7. PRASHANT CLASSES --TUITIONS FOR IB, IGCSE- MATHS & PHYSICS. Experienced IB teacher and IB examiner. PRASHAANT CLASSES Name:_________________ for IB, IGCSE, ICSE, 11th , 12th .- MATHS, PHYSICS. Call 2380 00 92.60. P is the solution set of 7x − 2 > 4x + 1 and Q is 63. Spherical marbles of diameter 1.4 cm are dropped the solution set of 9x − 45 5 (x − 5); where x into cylindrical beaker containing some water and R. Represent: (i) , (ii) P − Q , (iii) are fully submerged. The diameter of the beaker is on different number lines. 7 cm. Find how many marbles have been dropped in it if the water rises by 5.6 cm.61. where Mt is transpose of M. 64. The compound interest on a certain sum of money for the fourth year is Rs.1452 and for the fifth62. The figure alongside year is Rs. 1597.20. Find: a) the rate of interest, b) the compound interest for the sixth year, c) the compound interest for the third year. 65. Without solving, comment upon the nature of roots of each of the following equations: 7x 2 − 9x + 2 =0 given represents the lines y=x+1 and y= x−1. Write down the angles that the lines make with the positive direction of the x−axis. Hence determine66. The following table gives the height of the plants in centimeter. if the mean height of the plants is 60.95 cm, find the value of ‘f’. Height [cm] 50 55 58 60 65 70 71 No. of plants 2 4 10 f 5 4 367. If x3 + ax2 +bx + 6 has x − 3 as a factor and 69. A company declares 12% dividend to the leaves a remainder 8 when divided by x +1. shareholders. If a man receives Rs. 5400 as his Find a and b. dividend, find the nominal value of his shares.68. A man sells 60, Rs 15 shares of a company paying 70. If A= ; find the matrix X 12 % dividend, at Rs.21 each and invests the proceeds in Rs 6 shares of another company at Rs such that 2AX=B. 9 each. Find his change in income, if the second company pays a dividend of 8 %. Shop No. 12, Mahavir Apartments, Opp Swati Snacks, Tardeo Road, Mumbai 7. 5 prashantgohil@gmail.com
- 8. PRASHANT CLASSES --TUITIONS FOR IB, IGCSE- MATHS & PHYSICS. Experienced IB teacher and IB examiner. PRASHAANT CLASSES Name:_________________ for IB, IGCSE, ICSE, 11th , 12th .- MATHS, PHYSICS. Call 2380 00 92.71. Describe and draw the following loci 73. Find the 2×2 matrix X which satisfies the equation i ) A and B are two fixed points, the locus of a point P such that angle APB = 90. ii) AB is a chord of a circle, the locus of a point in 74. At what rate will a sum of money become 1.96 the circle so that it is equidistant from A and times of itself in 2 years at compound interest? B. 75. Points (5 , 1) and (−2, 1) are invariants points iii) The locus of a point, which is equidistant from under reflection in the line L1. Points (2, −6) and two fixed points. (2 ,3) are invariant points on reflection in line L2. iv) The locus of a point, intersecting straight in Give the equation of line L1 and L2.Write down the which is equidistant from two intersecting images of P(2,4) and Q (-3,8) on reflection in L2. lines. Name the images as P′′ and Q′′respectively. v ) The locus of the mid-points of all equal chords 76. Do not use a graph paper. Points A (2, −1) and B in a circle. (2 , 4) are invariant when reflected in line L1. vi) The locus of mid-points of all parallel chords Points C (−3 , 5) and D (4, 5) are invariant when in a circle reflected in line L2 . (i) Find the equation of line L1 and L2; (ii) Reflect point A in line L2 (iii) Reflect vii) The locus of a point equidistant from two point C in line L1. concentric circles. viii) The locus of the centre of a given circle of 77. If the speed of a car is increased by 10 km per hr, it takes 9 minutes less to cover a distance of 18 which rolls around the outside of a second km. Find the speed of the car. circle and is always touching it. ix) The locus of the centres of all circles that are 78. A shopkeeper buys a certain number of books for Rs.720. If the cost per book was Rs.5 less, the tangent to both sides of a given angle. number of books that could be bought for Rs.720 x) The locus of the centres of all circles passing would be 2 more. Taking the original cost of each through two fixed points. book to be Rs. x, write an equation in x and solve xi) The locus of points equidistant from three it. given non-collinear points. 79. Framing quadratic equations from the given roots xii) The locus of vertices of all isosceles triangles having a common base. xiii) The locus of the vertices of all triangles with a given base and a given altitude. 80. In an auditorium, the number of rows was to the xiv) The locus of a point P so that AB2 = AP2 + number of seats in each row. When the number of BP 2 where A and B are two fixed points. rows was doubled and the number of seats in each row was reduced by 10, the total number of seats xv) The locus of a point P so that ∆ ABP is increased by 300. How many rows were there? constant, where A and B are two fixed points. xvi) The locus of a point in rhombus ABCD so 81. Three consecutive natural numbers are such that the square of the middle number exceeds the that it is equidistant from difference of the squares of the other two by 32.72. Solve, 2 significant figures: x2 + 9x + 5 = 0 Assume the middle number to be x and form a quadratic equation satisfying the above statement. Hence; find the three numbers. Shop No. 12, Mahavir Apartments, Opp Swati Snacks, Tardeo Road, Mumbai 7. 6 prashantgohil@gmail.com
- 9. PRASHANT CLASSES --TUITIONS FOR IB, IGCSE- MATHS & PHYSICS. Experienced IB teacher and IB examiner. PRASHAANT CLASSES Name:_________________ for IB, IGCSE, ICSE, 11th , 12th .- MATHS, PHYSICS. Call 2380 00 92.82. Mr. Mistry has 120 shares of nominal value of Rs 83. The hypotenuse of a right−angled triangle is 17 100 and he decides to sell them when they are at a cm and the sum of other two sides is 23 cm. Find premium of 60% . He invests the proceeds in the lengths of its sides. shares of nominal value of Rs. 50, quoted at 4% discount, paying 15% dividend annually. Calculate : (i) the sale proceeds; (ii) the number of shares he buys; and (iii) the annual dividend from these shares.84. Find the equation of the mirror line in each of the cases. Sr. No Point Image Equation of the mirror line 1 (2 ,4) (2 , 8) 2 (-6 , 8) (4 , 2) 3 (3 , -2) (3 , 0) 4 (2 , 3) (6 , 3) 5 (-3 , 7) (-4 , 0) 6 (2 , 5) (- 1 , 8)85. Which is a better investment : 12 % at Rs 120 or 91. If A and B are square matrices, is ( A+ B)2 = A2 + 8% at Rs 90 ? 2 AB + B2? Explain.86. Calculate the amount and compound interest on 92. The equation of a line is x − y = 4. Find its slope Rs.14500 at 6 % p.a. for 12 months compounded and y−intercept. Also, find its inclination. half yearly. 93. In what ratio is the join of (4,3 and (2,−6 divide by87. If q is the mean proportional between p are r, x−axis. also find the co−ordinates of the point of intersection. prove that:p2−q2 + r2 = q4 94. A sum of money is lent out at compound interest for 2 years at 20 % p.a., compound interest being88. The mean age of a class of 40 students is 13 reckoned yearly. If the same sum of money was years. The mean age of 25 boys in the class is 13 lent out at compound interest at the same rate per years 3 months, what is the mean age of the girls cent per annum, compound interest being reckoned in the class. half-yearly, it would have fetched Rs 482 more by89. The roots of x 2−4kx + 12 = 0 are k and 3k. Find way of interest. Calculate the sum lent out. the value of k. 95. The abscissa of a point is four times its ordinate.90. An article is sold for Rs 810. It was sold after a Find the co−ordinates of the points if its distance discount of 10% on the list price and then adding from (6,2) is units. sales tax at a rate of 20%. Calculate the list price 96. Lines 2x−by+5=0 and ax+3y=2 are parallel to of the article. each other. find the relation connecting a and b. Shop No. 12, Mahavir Apartments, Opp Swati Snacks, Tardeo Road, Mumbai 7. 7 prashantgohil@gmail.com
- 10. PRASHANT CLASSES --TUITIONS FOR IB, IGCSE- MATHS & PHYSICS. Experienced IB teacher and IB examiner. PRASHAANT CLASSES Name:_________________ for IB, IGCSE, ICSE, 11th , 12th .- MATHS, PHYSICS. Call 2380 00 92. 97. The daily expenditure of 50 students is given below: Expenditure [Rs.] 10−20 20−30 30−40 40−50 50−60 60−70 No. of students 5 14 a b 11 8 The mean daily expenditure per student is Rs.40.20 p. Find the values of a and b. 98. The points (K, 3), (2, −4) and (−K + 1, −2) are 103. Two solid spheres have surface areas of 5 cm 2 and collinear, Find K. 45 cm 2 respectively and the mass of the smaller sphere is 3 kg. Find the mass of the larger sphere. 99. A merchant buys an article for Rs. 44,000/- and sells it to a customer for Rs.68,000/-. If the VAT 104. Given A(x+2,−2) and B (11,6). Find x if AB=17. rate is 11%; find the VAT paid by the merchant. 105. The centre of a circle of radius 13 units is the point (3,6). P (7,9) is a point inside the circle.100. In , given A (2 , 4), B (−4, −6) and C (0 , APB is a chord of the circle such that AP=PB. 8). Find :(1) equation of median AM (2) altitude Calculate the length of AB. BN (3) perpendicular bisector of AB. 106. Attempt this on a graph paper. (i)Plot A (2 ,2), B (101. Find the equation of the line passing through (5, 0 , − 2) and C (4 , − 2). Locate M, the midpoint of −3) and parallel to x−3y = 4. AC. (ii)Complete the figure ABDC, so that it is symmetrical about the line BC. Write the102. Find the positive integers p and q such that coordinates of D. write the geometrical name of È ˘ Í ˙ È ˘Í p ˙ ˙ Í ˙ = [25] the figure ABDC. (iii)Is the figure ABDC Í p q ˙Í ˙ Í ˙Í ˙ Í Í Î ˙Í ˙ ˚Í ˙ Í ˙ Í ˙ symmetrical about AD ? Locate , the image of Íq˙ Í ˙ M on reflection in BC. Write the coordinates of Î ˚ . 107. Find the equation of the line passing through (−5,7) and parallel to (i)x − axis (ii)y − axis.108. The diagram represents two inequations A and B on real number lines. (i) Write down A and B in set builder notation. (ii) Represent A ∩ B, A ∩ B′ on two different number lines.109. Salman purchased a pair of shoes for Rs.7920, 111. The centre of a circle is (2k −1, 3k +1) and it which included sales tax. If the rate of sales tax is passes through the point (−3,−1). Find the value or 10%, find the list price of shoes. values of k, if the diameter of the circle is of length 20 units.110. Factorise: x3 − 37x − 84. Shop No. 12, Mahavir Apartments, Opp Swati Snacks, Tardeo Road, Mumbai 7. 8 prashantgohil@gmail.com
- 11. PRASHANT CLASSES --TUITIONS FOR IB, IGCSE- MATHS & PHYSICS. Experienced IB teacher and IB examiner. PRASHAANT CLASSES Name:_________________ for IB, IGCSE, ICSE, 11th , 12th .- MATHS, PHYSICS. Call 2380 00 92.112. An article is bought at a certain price and a VAT 114. Draw two intersecting lines to include an angle of at a rate of 10% was paid. It was sold for 30°. Use ruler and compasses only to locate Rs.1,600 more for which he has to charge 11 % points which are equidistant from these lines and VAT. If he deposits Rs. 816 as VAT with the also 2 cm away from their point of intersection. government, find the cost price of the article. How many such points exist? a + 3b + a − 3b 115. Use ruler and compasses only for this question. 2113. If x = , prove that 3bx - Draw a circle of radius 4 cm and mark two chords a + 3b − a − 3b AB and AC of the circle of length 6 cm and 5 cm 2ax + 3b = 0. respectively. (i) Construct the locus of points, inside the circle, that are equidistant from A and C. Prove your construction. (ii)Construct the locus of points, inside the circle, that are equidistant from AB and AC.116. Draw a histogram for the frequency distribution and use it to find the mode. Also, calculate the Arithmetic mean. Marks 31−40 41−50 51−60 61−70 71−80 81−90 91−100 frequenc 5 9 12 18 15 6 3 y117. Points A and B have co-ordinates (–1, –5 ) and 119. Ms. Bachan goes to a shop to buy a walkman, (–1 , –1) respectively. Find: costing Rs.3638. The rate of sales tax is 7%. She (i)The equation of the mirror line so that A is tells the shopkeeper to reduce the price of the radio image of B. to such an extent that she has to pay Rs 3638 (ii) the equation of the line in which both the inclusive of sales tax. Find the reduction needed in points are invariant. the price of the radio.118. Find two numbers such that the mean proportional 120. between them is 12 and the third proportional to them is 96.121. Draw a cumulative frequency table, plot an ogive for the data given below and form the cumulative frequency curve, find : (i) the median marks, (ii) the lower quartile, (iii) the upper quartile , (iv)Find passing marks if 80% of students passed, (v)If students scoring more than 75% mark are awarded scholarship, how many get? Mar 1−10 11−20 21−30 31−40 41−5 51−60 61−7 71−80 81− 91− ks 0 0 90 100 No.o 4 6 7 16 25 21 12 5 3 1 f pupil s Shop No. 12, Mahavir Apartments, Opp Swati Snacks, Tardeo Road, Mumbai 7. 9 prashantgohil@gmail.com
- 12. PRASHANT CLASSES --TUITIONS FOR IB, IGCSE- MATHS & PHYSICS. Experienced IB teacher and IB examiner. PRASHAANT CLASSES Name:_________________ for IB, IGCSE, ICSE, 11th , 12th .- MATHS, PHYSICS. Call 2380 00 92.122. Solve 129. Find the equation of the perpendicular bisector of the line segment obtained on joining the points123. Points (−2,−1) and (1,8) lie on the line y = mx + c. (6,−3) and (0,3). Find the numerical values of m and c. 130. A triangle whose area is 12 cm 2 is transformed124. A map of a country is drawn to the scale 1 : under enlargement about a point in space. If the 400000. Calculate: (i) the distance on the map area of its image is 108 cm2, find the scale factor which will represent an actual country side of the enlargement. distance of 40 km. (ii)the area in cm2 on the map which would represent an actual area of 64 km2. 131. A person invested Rs 16,000 and Rs 20,000 in buying shares of two companies which later on125. What point on x−axis is equidistant from points declared dividends of 12% and 8% respectively. (7, 6) and (−3,4). He collects the divided and sells out all his shares at a loss of 2% and 3% respectively on his126. Solve : investment. Find his total earning from the above transaction.127. Two numbers are in the ratio 2:5 and if 3 be added 132. Solve for matrix X if to each, they are in the ratio 5:11. Find the numbers.128. Match the equations A, B, C, D with the lines L1 , L2 , L3, L4 , whose graphs are roughly drawn in 133. If (p − 1) x + 2y = 4 is perpendicular to x + y = 3 the adjoining diagram. find p. Hence, find the point of intersection of B and C. Shop No. 12, Mahavir Apartments, Opp Swati Snacks, Tardeo Road, Mumbai 7. 10 prashantgohil@gmail.com
- 13. PRASHANT CLASSES --TUITIONS FOR IB, IGCSE- MATHS & PHYSICS. Experienced IB teacher and IB examiner. PRASHAANT CLASSES Name:_________________ for IB, IGCSE, ICSE, 11th , 12th .- MATHS, PHYSICS. Call 2380 00 92.134. Calculate the mean, median and mode: X 0 2 4 6 8 10 F 2 3 5 7 2 1135. Points (5 , 0) and (−2, 0) are invariants points 138. Plot the points A (2,1), B (2,8), C(5,5) and D under reflection in the line L1. Points (0, −6) and (5,−2) on graph paper. (i) Name the figure ABCD; (0 ,3) are invariant points on reflection in line L2. (ii) Write down the equation of its line of Write down the images of points P (3 ,4) and Q ( symmetry. (iii) If P, Q are the images of A and D −5 , −2) on reflection in L1. Name the images as P′ when reflected in the line CD. Write down the and Q′ respectively. co−ordinates of P and Q. Name the completed figure ABPQD.136. If 6x2 − 3y2: x2 + y2 is equal to 6:25, find the value of x:y. 139. Mukesh deposited Rs.220/- per month in a bank for 24 months under the Recurring Deposit137. If Scheme. What will be the maturity value of his deposits, if the rate of interest is 7 % per annum and interest is calculated at the end of every month? 140. By purchasing Rs 25 auto shares for Rs 40 each a man gets 4% profit on his investment. What rate per cent is company paying? What is his dividend if he buys 120 shares?141. Complete the following: Sr. No. P P′ Mirror line Line in which points are invariant 1 (2 , 0) (- 4 , 0) 2 (0 , 3) (0 , - 6) 3 (3 , 1) (9 , 1) 4 (2 , 7) (2 , -1)142. Solve, 2 significant figures: x2 − 10x + 6 = 0 Shop No. 12, Mahavir Apartments, Opp Swati Snacks, Tardeo Road, Mumbai 7. 11 prashantgohil@gmail.com
- 14. PRASHANT CLASSES --TUITIONS FOR IB, IGCSE- MATHS & PHYSICS. Experienced IB teacher and IB examiner. PRASHAANT CLASSES Name:_________________ for IB, IGCSE, ICSE, 11th , 12th .- MATHS, PHYSICS. Call 2380 00 92.143. Mr. Pascal invested Rs 8000 in 8% Rs 100 shares 146. In the figure given alongside AB and CD are the selling at Rs80. After a year he sold these shares lines 2x−y+6=0 and x−2y=4 respectively.(i) Write at Rs 75 each and invested the proceeds in Rs 90 down the co−ordinates of A,B,C and D; (ii) Prove shares selling at Rs 100 with a dividend of 12%. that triangles OAB and ODC are similar; (iii) Is Calculate : (i.)his income from the first the figure ABCD cyclic? Give reasons for your investment; (ii) his income from the second answer. investment, (iii) the increased percentage return on his original investment.144. Without solving, comment upon the nature of roots of each of the following equations: 25 x2 −10x + 1 = 0145. A owns 560 shares of a company. The face value of each share is Rs 25. The company declares a dividend of 9%. Calculate : (i) the dividend A would receive; (ii) the rate of interest on his investment considering that A bought these shares at Rs 30 per share in the market. 147. Prove that : If two triangles are similar the ratio of their areas equals ratio of the square of their corresponding sides. 148. A spherical ball of lead has been melted and made into identical small balls each with radius equal to half the radius of the original one. How many such balls can be made? 149. If b is the mean proportional between a and c. Prove: Shop No. 12, Mahavir Apartments, Opp Swati Snacks, Tardeo Road, Mumbai 7. 12 prashantgohil@gmail.com
- 15. PRASHANT CLASSES --TUITIONS FOR IB, IGCSE- MATHS & PHYSICS. Experienced IB teacher and IB examiner. PRASHAANT CLASSES Name:_________________ for IB, IGCSE, ICSE, 11th , 12th .- MATHS, PHYSICS. Call 2380 00 92.150. Fill in the blanks: Sr.no. point Reflect in Image 1 (2 , 6) x-axis 2 (3 , −4) y-axis 3 (−2 , 4) y= 0 4 (6 , −2) x=0 5 (−2 , −4) origin 6 (−3 , 2) (−3, −2) 7 (−3 , 7) (3 , 7) 8 (3 , 4) x = −1 9 (−2 , 3) y= 5 10 (−2 , 8) (−2 , 4) 11 (4 ,−3) (4 , 5)151. A girl goes to her friends house, which is at a 154. Use ruler and compasses only for the following distance of 12 km. she covers half the distance at a question. Construct triangle BCP where CB = 5 speed of x km/hr. and the remaining at a speed of cm , BP = 4 cm and ∠ PBC = 45°,Complete the x+2 km/hr. If she takes 2 hrs. 30 minutes to cover rectangle ABCD such that: the whole distance, find ‘x’. (i) P is equidistant from AB and BC; and (ii) P is equidistant from C and D.152. Draw a triangle ABC in which AB = 6 cm, BC = Measure and write down the length of AB. 4.5 cm and AC = 5 cm. (i) Draw and label the locus of the centres of all circles which touch AB and AC, (ii)the locus of the centres of all the circles of radius 2 cm which touch AB. Hence, construct the circle of radius 2 cm which touches AB and AC. È Í ˘ ˙ Í Í0 4 ˙ Í Í Í 6 ˙ ˙ ˙ ˙ and153. A = Í Í ˙ ˙ Í Í 3 0 −1 ˙ ˙ Í Î ˙ ˚ È Í ˘ ˙ Í sin00 Í tan450 ˙ ˙ Í Í ˙ ˙ Í Í ˙ ˙ Í Í 0 ˙ ˙ Í B = Í −cot 45 0 ˙ cos e c 30 ˙ , Í Í ˙ ˙ Í Í ˙ ˙ Í −5 Í 0 ˙ Í Í −2cot 30 ˙ 2 ˙ ˙ Í Î ˙ ˚ find if possible (i)AB , (ii) BA , (iii)A 2 . Shop No. 12, Mahavir Apartments, Opp Swati Snacks, Tardeo Road, Mumbai 7. 13 prashantgohil@gmail.com
- 16. PRASHANT CLASSES --TUITIONS FOR IB, IGCSE- MATHS & PHYSICS. Experienced IB teacher and IB examiner. PRASHAANT CLASSES Name:_________________ for IB, IGCSE, ICSE, 11th , 12th .- MATHS, PHYSICS. Call 2380 00 92.155. A is represented on number line as given below. 159. In the figure given alongside BC parallel to DE. Area of triangle ABC = 150 cm 2, area of trapezium BCED = 66 cm2, DE = 42 cm. B is also represented on a number line given below . a)Write A in the set builder form. b) Write B in the set builder form. c) On the given number line show A ∩ B. d) On the given number line show A ∪ B Calculate the length of BC. 160. The value of a machinery in 2007 is Rs.29160. If . the rate of depression is 10 % p.a., find the value e) On the given number line show A ∩ B. of the computer in 2004. 161. A certain sum of money is invested for three years at 10% p.a., if the compound interest for the f) On the given number line show A∩ B. second year is Rs 880, calculate the amount at the end of three years. 162. The line passing through (−4, −2) and (2, −3) is perpendicular to the line passing through (a, 5)156. Parul holds 1350; Rs 100 shares of a company and (2, −1). Find a. that pays 15% dividend annually Calculate her 163. Two isosceles triangles have equal vertical angles annual dividend. If she had bought these shares at and their areas are in the ratio 16 : 25. Find the 40% premium, what percentage return does she ratio of their corresponding heights. get on her investment? Give your answer to the nearest integer. 164. A foot path of uniform width runs round the inside of a rectangular field 16m long and 14 m wide. If the path occupies 56 m2, Find the width of the157. Points (5 , 0) and (−2, 0) are invariants points path. under reflection in the line L1. Points (0, −6) and (0 ,3) are invariant points on reflection in line L2. 165. If A, B and C are 2X2 matrices, is A. (B.C ) = Name or write equations for the lines L1 and L 2. (A.B) C? Why?158. A man invests Rs 2,400 for two years at 166. The compound interest on a certain sum of money compound interest. After one year this money at a certain rate is Rs 300 for the first year and the amounts to Rs 2,550. Find the interest for the compound interest for 2 years is Rs 612. Find the second year correct to the nearest paise. sum and the rate of interest. 167. Calculate the co−ordinates of the centre of the circle which passes through the points (4,2), (2,−2) and (7,−7). Find the value of its radius. Also, calculate the centroid of ∆ formed by joining the three points. Shop No. 12, Mahavir Apartments, Opp Swati Snacks, Tardeo Road, Mumbai 7. 14 prashantgohil@gmail.com
- 17. PRASHANT CLASSES --TUITIONS FOR IB, IGCSE- MATHS & PHYSICS. Experienced IB teacher and IB examiner. PRASHAANT CLASSES Name:_________________ for IB, IGCSE, ICSE, 11th , 12th .- MATHS, PHYSICS. Call 2380 00 92.168. If A and B are square matrices and if A.B = 0, 178. Lines mx+3y+7=0 and 5x−ny−3=0 are then A = 0 or B = 0? Why? perpendicular to each other. find the relation connecting m and n.169. For what values of a and b, the expression 2x3 + ax2 + b x + 3 is divisible by 179. A motor boat whose speed is 15 km/hr in still 2x 2 + x −1. water goes 30 km downstream and comes back in a total of 4 hour 30 minutes. Determine the speed170. The mean of 1,7,5,3,4 and 4 is m.The numbers of the stream. 3,2,4,2,3,3 and p have mean m−1 and median q. Find p and q. 180. In what time will Rs 1500 yield Rs 496.50 as compound interest at 20% per compounded171. If A= , B= and (A+B)2= A2 + semi-annually? B2, find the value of x. 181. Using the information in the given histogram, calculate the mean.172. Find the co−ordinates of the points of trisection of the line joining the points (−3,0) and (6,6).173. A man invests Rs 46,875 at 4% per annum compound interest for 3 years. Calculate : (i) The interest for the 1st year; ( ii) The amount standing to his credit at the end of the second year; (iii) The interest for the 3rd year.174. If x =175. By investing Rs 7500 in a company paying 10% 182. A model of a missile is made to a scale of 1:600. dividend an income of Rs.500 is received. What (i) The length of the model is 6 m; calculate the price is paid for each Rs 100 share? length of the missile. (ii) The area of the surface of the missile is176. Find the ratio compounded of the reciprocal ratio 7,200,000 m2; find the surface area of the model. of 15:28 , the sub−duplicate ratio of 36:49 and (iii) The volume of the model is 200 litre; triplicate ratio of 5 :4. calculate the volume of the missile is m3.177. Solve : 183. Prove that the points A(−5,4),B(−1,−2) and C(5,2) are vertices of an isosceles right angled triangle. Find the co−ordinates of D so that ABCD is a square. Shop No. 12, Mahavir Apartments, Opp Swati Snacks, Tardeo Road, Mumbai 7. 15 prashantgohil@gmail.com
- 18. PRASHANT CLASSES --TUITIONS FOR IB, IGCSE- MATHS & PHYSICS. Experienced IB teacher and IB examiner. PRASHAANT CLASSES Name:_________________ for IB, IGCSE, ICSE, 11th , 12th .- MATHS, PHYSICS. Call 2380 00 92.184. The results of an examination are tabulated below: Marks less than 10 20 30 40 50 60 70 80 90 100 No. of candidates 0 25 42 65 95 120 128 135 148 150 Draw an ogive for the above data and find :(i) the number of candidates who got less than 45; (ii) the number of candidates who got more than 75.185. If [2x−1] : [5x+15] be in the duplicate ratio of 3 : 187. The marks obtained by 19 boys are given : 5, find x. 27,36,22,31,25,26,33,24,37,32,29,28,36,35,27,26 ,32,35,28, find the (i) median, (ii) lower quartile,186. A can do a piece of work in ‘x’ days and B can do (iii) upper quartile and (iv) Interquartile range. the same work in x+8 days . If both working together can do it in days; Calculate ‘x’. 188. The machinery of a particular factory is valued at Rs 18400 at the end of 1990. If it is supposed to depreciate each year at 8% of the value at the beginning of the year, calculate the value of the machinery at the end of 1989 and 1991.189. Calculate the mean from the following ogive. Shop No. 12, Mahavir Apartments, Opp Swati Snacks, Tardeo Road, Mumbai 7. 16 prashantgohil@gmail.com
- 19. PRASHANT CLASSES --TUITIONS FOR IB, IGCSE- MATHS & PHYSICS. Experienced IB teacher and IB examiner. PRASHAANT CLASSES Name:_________________ for IB, IGCSE, ICSE, 11th , 12th .- MATHS, PHYSICS. Call 2380 00 92.190. In the given ∆ PQR, LM is parallel to QR and 191. If x + a is a common factor of expressions PM:MR = 3:4.Calculate the value of ratio:(i) f(x) = x2 + px + q and g(x)=x2 +mx + n; show that and then . (ii) . (iii) . , (iv ) . 192. If . 193. John deposited Rs.260/- per month in a bank for 9 months under the Recurring Deposit Scheme. If the maturity value of his deposits is Rs.2437.5, what is the rate of interest given that the interest is calculated at the end of every month? 194. If195. The following data gives the frequency distribution for the no. of apples in the farm: Weight.in grams 60−64 65−69 70−74 75−79 80−84 No. of apples 7 11 22 16 4 Calculate: (a) the mean weight of the apples in grams,(b) If the weight of each apple is increased by 5 gm, what will be the new mean weight be? (c) the total weight of all the apples in the above table. (d) if the number of apples in each category is doubled, what is the new mean weight (e)the medial class of the above data. (f) the modal class of the above data.196. A page from the pass book of Mr. Shah is given below. Find the interest for the period January to December 1998 at 4.5% per annum. Date Particulars Debit (Rs.) Credit (Rs.) Balance (Rs.) Jan. 1 Balance B/F 7,500 = 00 March 7 By Cheque 1,875 = 00 March 10 To Cash 625 = 00 July 17 To Self 3,250 = 00 Oct. 5 By Cheque 2,160 = 00 Dec. 19 To Cheque 1,340 = 00 Shop No. 12, Mahavir Apartments, Opp Swati Snacks, Tardeo Road, Mumbai 7. 17 prashantgohil@gmail.com
- 20. PRASHANT CLASSES --TUITIONS FOR IB, IGCSE- MATHS & PHYSICS. Experienced IB teacher and IB examiner. PRASHAANT CLASSES Name:_________________ for IB, IGCSE, ICSE, 11th , 12th .- MATHS, PHYSICS. Call 2380 00 92.197. By selling at Rs 77, some 2 ¼ % shares of face 205. Evaluate x and y if ; value Rs 100 and investing the proceeds in 6% shares of face value Rs 100 selling at Rs 110 a person increased his income by Rs 117 a year. Find : (i) How many shares did he sell? (ii) How 206. A circus tent is cylindrical to a height of 4 m and many shares did he buy? (iii)What was his original conical above it. If it is diameter is 105 m and its income? slant height is 80 m, calculate the area of canvas required. Also find the total cost of canvas used at198. Framing quadratic equations from the given roots Rs.15 per metre if the width is 1.5 m. a, −b 207. Find the order of matrix M and hence, find matrix199. Framing quadratic equations from the given roots M in each of the following −1 ± 2 M×200. Factorise the following, using Factor theorem: x3 − 4x2 + x +6.201. Solve : x2 = 25 208. The compound interest, calculated yearly, on a certain sum of money for the second year is Rs202. Find the equations of the lines passing through 630 and for the third year is Rs 661.50. Calculate point (−2,0) and equally inclined to the the rate of interest and the sum. co−ordinate axes. 209. Solve :x2 − 5x = 0203. Given . Find x 210. A sector of radius 35 cm is cut out of a thin cardboard with angle 1440. It is folded into a cone and y. of maximum size. Find the curve surface and the204. One pipe can fill a cistern in 3 hours less than the volume of the cone. Take = 22/7. other. The two pipes together can fill the cistern in 211. Find the ratio in which the line joining (3,4) and 6 hours 40 minutes. Find the time that each pipe (−2,8) is divided by the line x-=1. will take to fill the cistern.212. Mr. Ashok has an account in the Central Bank of India. The following entries are from his pass book: Date Particulars Withdrawals Deposits Balance 01.01.05 B/F 1200.00 07.01.05 By cash 500.00 1700.00 17.01.05 To cheque 400.00 1300.00 10.02.05 By cash 800.00 2100.00 25.02.05 To cheque 500.00 1600.00 20.09.05 By cash 700.00 2300.00 21.11.05 To cheque 600.00 1700.00 05.12.05 By cash 300.00 2000.00 If Mr.Ashok gets Rs.167.50 as interest at the end of the year where the interest is compounded annually, calculate the rate of interest paid by the bank in his Savings Bank Account on 31st December, 2005. Shop No. 12, Mahavir Apartments, Opp Swati Snacks, Tardeo Road, Mumbai 7. 18 prashantgohil@gmail.com
- 21. PRASHANT CLASSES --TUITIONS FOR IB, IGCSE- MATHS & PHYSICS. Experienced IB teacher and IB examiner. PRASHANT CLASSES Name:_________________ for IB, IGCSE, ICSE, 11th, 12th - MATHS, PHYSICS. Call 2380 00 92.2011 LMR contd213. A card is drawn from a well-shuffled pack of 52 221. Given that two circles intersect at T and S. BA cards. Find the probability that the card drawn is: and CD are produced to meet at P. (i)a spade (ii)a red card (iii)a face card (iv)5 of i Prove that PATD is a cyclic quadrilateral. heart or diamond (v)Jack or Queen (vi) ace and iiProve PA PB = PC PD. king (vii)a red and a king (viii)a red or a king iiiIf PA = 3 cm, AB = 7 cm, PD = 4 cm, Find PC. Read carefully and answer fully showing all steps of working214. An aeroplane flying horizontally 1 km above the ground is observed at an elevation of 600. After 10 seconds, its elevation is observed to be 300; find the uniform speed of the aeroplane in km per hour. 222. Evaluate: sin 150 cos 750 + cos 150 sin 750215. Quad OABC is a parallelogram. Calculate 223. The height of a tree is times, the length of its ∠OAB. shadow. Find the angle of elevation of the sun. 224. In the given figure ∠XYZ = 52° and ∠YZX = 70°. Calculate ∠ABC, ∠BAC, ∠ACB.216. Prove : sin (90−A)cos (90−A)=tanA cos2A217. The length of the direct common tangent to two circles of radii 12 cm and 4 cm is 15 cm. 225. Prove : Calculate the distance between their centres.218. A person standing on the bank of a river observes 226. In a circle with centre O. Chords BA and DC are that the angle of elevation of the top of a tree produced to meet at a point P. If PA=2 cm, standing on the opposite bank is 600. He moves 40 AB=7cm and PC=3 cm. Find CD. m away from the bank, he finds the angle of 227. The given diagram represents the area swept by elevation to be 300, find : i the height of the tree; the wiper of a car with the dimensions given in the iithe width of the river. diagram, calculate the shaded area swept by the219. A copper wire when bent in the form of a square wiper. Take encloses an area of 121 cm2. If the same wire is bent into the form of a circle, find the area of the circle.220. The area of a circle, inscribed in an equilateral triangle, is 154 cm2. Find perimeter of the triangle. Take = 1.73. Give answer correct to one decimal place. Calculate the area of circumcircle to the above triangle.Shop No. 12, Mahavir Apartments, Opp Swati Snacks, Tardeo Road, Mumbai 7. 19 prashantgohil@gmail.com
- 22. PRASHANT CLASSES --TUITIONS FOR IB, IGCSE- MATHS & PHYSICS. Experienced IB teacher and IB examiner. PRASHANT CLASSES Name:_________________ for IB, IGCSE, ICSE, 11th, 12th - MATHS, PHYSICS. Call 2380 00 92.228. The angles of elevation of the top of a tower from 234. In the diagram I is the incentre of triangle XYZ, two points on the ground at distances a and b XI produced meets the circum circle of triangle metres from the base of the tower and in the same XYZ at W. ∠YXZ = 50°, ∠XYZ=70°. Calculate : straight line with it are complementary. Prove that i∠WYZ; the height of the tower is metre. ii∠IYZ; iii∠YIW.229. In a circle with centre O, diameter AB is produced to point T. TC is tangent to the circle, if∠CAB = 24°, Calculate ∠CTB. 235. A chord AB subtends an angle of 1210 at the centre O of the circle. If the length of the chord is 20 cm; calculate the radius of the circle.230. In the adjoining diagram chords AB and CD of the circle are produced to meet at O. Prove that 236. At a point on level ground, the angle of vertical triangle ODB and OAC are similar. Given that tower is found to be such that its tangent is 5/12. CD = 2 cm, DO = 6 cm and BO = 3 cm, Calculate On walking 192 metres towards the tower, the AB. tangent of the angle is found to be 3/4. find the height of the tower. 237. Calculate the circumference of a circle whose area is equal to the sum of areas of the circles with diameters 24 cm, 32 cm and 96 cm. 238. Prove :231. An equilateral triangle of side 8 cm is inscribed in a circle. Find the radius of the circle. 239. The upper part of tree, broken over by the wind, makes on angle of 450 with ground ; and distance232. In the given figure, AB is a side of a regular five from the root to the point where the top of the tree sided polygon and AC is a side of a six sided touches the ground, is 15m. What was the height polygon inscribed in the circle, centre S. Calculate of the tree before it was broken? the sizes of i∠ASB; ii∠ACB; iii∠ABC. 240. Prove : 241. In the figure PT is a tangent to the circle. PA = 2 cm and AB = 16 cm. Prove that PT2 =PA. PB. Hence, find PT.233. Evaluate: sin420sin480−cos420cos480 Shop No. 12, Mahavir Apartments, Opp Swati Snacks, Tardeo Road, Mumbai 7. 20 prashantgohil@gmail.com
- 23. PRASHANT CLASSES --TUITIONS FOR IB, IGCSE- MATHS & PHYSICS. Experienced IB teacher and IB examiner. PRASHANT CLASSES Name:_________________ for IB, IGCSE, ICSE, 11th, 12th - MATHS, PHYSICS. Call 2380 00 92.242. From the top of a light house, it is observed that a 249. O is the centre of the circle, PQR is an isosceles ship is sailing directly towards it and the angle of triangle inscribed in a circle PQ = PR = 25 cm and depression of the ship changes from 300 to 450 in QR = 14 cm. Calculate the radius of the circle. 10 minutes. Assuming that ship is traveling at uniform speed, calculate how long will it take to reach the light house.243. A chord of length 24 cm is at a distance of 5 cm from the centre of the circle. Find the length of the chord of the same circle which is at a distance of 12 cm from the centre.244. AB and CD are two chords in a circle that intersect at P. If AP = 2 cm ,DP= 3 cm and CP= 5 cm. Find BP. 250. ABCD are the vertices of a rectangle in the given figure, on the circumference of a circle. If the245. Evaluate: tan 100 tan 150 tan750 tan 800 length of the rectangle is 24 cm and the width is 7 cm. Find the area of the shaded region. Take π =246. Draw a line AP = 7.5 cm. Mark a point Q on AP 3.14 such that PQ = 4 cm. Using a ruler and compasses only, construct: (1) a circle of radius 2.5 cm to pass through A and Q. (2) a tangent to the above circle from P. Measure its length.247. Calculate the length of the radius of the circumcircle and the incircle of a right angled triangle of side 5 cm and 12 cm, that contain the 251. In the adjoining diagram AB and CD are two right angle. . chords intersecting at P. If CD = 9 cm, find CP and PD.248. In the diagram, if the length of the chord is 30 cm and CE:AB=5:6, find the radius of the circle. 252. If 00 < A < 900 , solve the following eqns: (i)sin 3A = cos 2A ,(ii) tan 5A = cot A , (iii) sin (3A−4) = cos (5A+6) ,(iv) sin 2 300 + cos2 (2A + 20)=1 253. A piece of card board is in the shape of quarter of a circle of a radius 7 cm, bounded by perpendicular radii OX and OY, points A and B lie on OX and OY respectively such that OA = 3 cm and OB = 4 cm. The triangular part is removed. Calculate the area and the perimeter of the remaining piece. Shop No. 12, Mahavir Apartments, Opp Swati Snacks, Tardeo Road, Mumbai 7. 21 prashantgohil@gmail.com
- 24. PRASHANT CLASSES --TUITIONS FOR IB, IGCSE- MATHS & PHYSICS. Experienced IB teacher and IB examiner. PRASHANT CLASSES Name:_________________ for IB, IGCSE, ICSE, 11th, 12th - MATHS, PHYSICS. Call 2380 00 92.254. Construct a regular pentagon of side 4cm. 261. AC, BQ and BP are the tangents to the circle. Construct all the lines of symmetry for this Prove that BQ= semi−perimeter of ∆ABC. pentagon.255. Two circles of radii 25 cm and 9 cm touch each other externally. Find the length of the direct common tangent.256. If tan A + sin A = m and tan A – sin A = n ; prove that ; m 2 – n2 = 4257. A vertical tower is 20m high. A man at some distance from the tower knows that the cosine of the angle of elevation of the top of the tower is 0.53. How far is he standing from the foot of the tower.258. From the top of a cliff, 60 metres high the angle of 262. In the figure alongside, PR is a diameter of the depression of the top and bottom of a tower are circle, PQ = 7 cm, QR = 6 cm and RS = 2cm. observed to be 300 and 600. Find the height of the Calculate the perimeter of the cyclic quadrilateral. tower.259. The figure given below shows a circle with centre O in which diameter CD bisects the chord AB at point E. If AE = EB = 8 cm and ED = 4 cm, find the radius of the circle. 263. Two parallel chords are drawn in a circle of diameter 30 cm. The length of one chord is 24 cm and the distance between the two chords is 21 cm; find the length of another chord. 264. Prove : sec 700 sin 200 + cosec 700cos200 =2. 265. Prove : 266. A boy of height 1.7 m is standing 20m away from260. Construct triangle ABC, ∠B=60°, ∠A = 45° and a flag staff on the same level ground. He observes the circumradius = 4 cm. Hence, complete cyclic that the angle of elevation of the top of the quadrilateral ABCD such that D is equidistant flagstaff is 240. Calculate the height of the from A and C. flagstaff. 267. In the area enclosed between the concentric circles, is 770 cm 2. Given that the radius of the outer circle is 21 cm. Calculate the radius of the inner circle. ( ) Shop No. 12, Mahavir Apartments, Opp Swati Snacks, Tardeo Road, Mumbai 7. 22 prashantgohil@gmail.com
- 25. PRASHANT CLASSES --TUITIONS FOR IB, IGCSE- MATHS & PHYSICS. Experienced IB teacher and IB examiner. PRASHANT CLASSES Name:_________________ for IB, IGCSE, ICSE, 11th, 12th - MATHS, PHYSICS. Call 2380 00 92.268. From a boat, 300 m away from a vertical cliff, the 276. PA = 10 cm, find AB. If PT is a tangent as shown, angles of elevation of the top and the foot of a find its length. vertical concrete pillar at the edge of the cliff are 55 040′ and 54020′ respectively. find the height of the pillar correct to the nearest metre.269. A kite is flying at a height of 175 metres from the level ground, attached to a string inclined at 600 to the horizontal. Find the length of the string to the 277. Prove : cos4 A – sin4 A = 2 cos2 A – 1 nearest metre. 278. Given that O is the centre of a circle. Chord QP is270. Prove : produced to any point R such that ∠TRQ= 26°. Also given that ∠OQP = 48°. Calculate ∠PTQ271. In a circle with centre O, given that AB is parallel and ∠TPQ. to diameter CD. If ∠ABC = 25°. Calculate ∠AEB. 279. MN is a diameter of a semicircle with centre O. P, Q, and R are points on the circumference such that PM = PQ. If ∠QRN = 136°. Calculate ∠MPQ and ∠PNQ. Prove that OP is parallel to QN.272. The angle of elevation of a stationary cloud from a point 25m above a lake is 150 and the angle of depression of its reflection in the lake is 450. What is the height of the cloud above the lake−level?273. The length of common chord of two intersecting circles is 30 cm. If the diameters of two circles be 50 cm and 34 cm, calculate the distance between their centres. 280. In the given diagram chord AB and CD of a circle intersect at E. (i)Prove that triangle ADE and274. The radii of two concentric circles are 17 cm and CBE are similar. ( ii)Given DC = 12 cm, DE = 4 10 cm ; a line PQRS cuts the larger circle at P and cm and AE = 16 cm, Calculate the length of BE. S and the smaller circle at Q and R. If QR = 12 cm. Calculate PQ.275. In the figure the tangent PT = 8 cm. PA = 5 cm, find the length of the chord AB. Shop No. 12, Mahavir Apartments, Opp Swati Snacks, Tardeo Road, Mumbai 7. 23 prashantgohil@gmail.com
- 26. PRASHANT CLASSES --TUITIONS FOR IB, IGCSE- MATHS & PHYSICS. Experienced IB teacher and IB examiner. PRASHANT CLASSES Name:_________________ for IB, IGCSE, ICSE, 11th, 12th - MATHS, PHYSICS. Call 2380 00 92.281. Given two circles that intersect at points B and E. 289. O is the centre of the circle. TP bisects ∠OPQ. HEC and AEG are straight lines. i Prove TO // PQ Prove ∠AHE + ∠EGC = 180°. ii if ∠POQ = 64°, calculate ∠TQR.282. The perimeter of a semi−circle is 90 cm. Calculate 290. Prove :sec2 A cosec2 A = tan2 A + cot2 A + 2 its area. 291. A box contains 150 bulbs out of which 15 are283. Draw a circle of radius 3 cm. Mark P, any point defective. It is not possible to just look at a bulb on the circle. Construct a tangent to the circle at and tell whether or not it is defective. One bulb is point P. Mark point A on the tangent such that AP taken out at random from this box. Calculate the = 4.5 cm, construct another tangent to the circle probability that the bulb taken out is : from point A. (i)a good one (ii)a defective one284. The angle of elevation of a cloud from a point 20m above lake level is xo, where tan xo= and 292. In the given figure, if the angle of depression of its reflection in the lake ∠ACE = 430 and ∠CAF = 620 find the values of a, b and c. water is yo where tan yo= . Calculate the height of the cloud above the lake level, correct to the nearest m.285. Two parallel chords of lengths 16 cm and 12 cm are drawn in a circle of diameter 20 cm. Find the distance between the chords, if both the chords are ion the same side of the centre, (ii) on the opposite sides of the centre.286. In the figure AB is a diameter of the circle, centre O ,CD // AB. If angle CAB = x , find the value of i ∠COB ii∠DOC ,iii∠DAC ,iv∠ADC. 293. Find the values of x which satisfy the inequation: Graph the solution set on the real number line.287. Prove : 294. Prove that :sin2 A + cos 2 A = 1 295. The mid point of the line segment joining (2a , 4)288. Three spheres of diameters x, 8 cm and 10 cm are and (-2 , 2b) is (1 , 2a + 1). Find the values of a melted and recasted into a single sphere of and b. diameter 12 cm. Calculate the value of x. Shop No. 12, Mahavir Apartments, Opp Swati Snacks, Tardeo Road, Mumbai 7. 24 prashantgohil@gmail.com
- 27. PRASHANT CLASSES --TUITIONS FOR IB, IGCSE- MATHS & PHYSICS. Experienced IB teacher and IB examiner. PRASHANT CLASSES Name:_________________ for IB, IGCSE, ICSE, 11th, 12th - MATHS, PHYSICS. Call 2380 00 92.296. An article is bought at a certain price. It is marked 303. In a single throw of a die, find the probability of up by 30% on the purchased price. A discount of getting : 10% is given on the marked price. A sales tax of (i)5 (ii)8 (iii)a number less than 8 , (iv) a prime 10% is marked on the discounted price and the number. article is sold for Rs 3861.Find: 304. If P(E) = 0.39; find P (not E). a) the cost price of the article; b) the marked price on the article. 305. A bag contains 3 white, 5 black and 2 red balls, all of the same shape and size. A ball is drawn from297. Let a, b, c and d be integers such that a < b, the bag without looking into it, find the probability b < c and c = d. that the ball drawn is: The mode of these four numbers is 11. (i)a black ball , The range of these four numbers is 8. (ii)a red ball , The mean of these four numbers is 8. (iii) awhite ball, Calculate the value of each of the integers a, (iv)not a red ball, b, c, d. (v)not a black ball298. An inverted cone of height 10 cm and base radius 306. In a single throw of two dice, find the probability 6.4cm contains water to a depth of 5 cm, of : measured from the vertex. Calculate the volume of (i)a doublet water in the cone. (ii)a number less than 3 on each die (iii)an odd number as a sum299. An archery target has three concentric regions. (iv)a total of at most 10 The diameters of the regions are in the ratio 1:2:3. (v)an odd number on one die and a number less than or equal to 4 on the other die. 307. An inverted cone of height 15cm and base radius 4 cm contains water to a depth of 10 cm. Calculate the volume of water in the cone. 308. Draw a circle of radius 4 cm. Draw two tangents Find the ratio of their areas. to this circle so that the angle between the tangents is 45°. Measure distance of centre from exterior300. (i)If A and B are two complementary events then point. what is the relation between P(A) and P(B)? (ii)If the probability of happening of an event A is 309. A card is drawn from a pack of 100 cards 0.46. What will be the probability of not numbered 1 to 100. Find the probability of happening of the event A? drawing a number which is a square.301. Using a ruler, construct a triangle ABC with BC = 310. Two dice are thrown simultaneously. Find the 6.4 cm, CA = 5.8 cm and ∠ABC = 600 . Draw its probability that : incircle. Measure and record the radius of the (i)both the dice show the same number, incircle. (ii)the first die shows 6, (iii)the total (sum) of the numbers on the dice is 9,302. Two dice are rolled together. Find the probability (iv)the product of the numbers on the dice is 8, of getting: (v)the total of the numbers on the dice is greater (i)a total of at least 10 than 9. (ii)a multiple of 2 on one die and an odd number on hte other die Shop No. 12, Mahavir Apartments, Opp Swati Snacks, Tardeo Road, Mumbai 7. 25 prashantgohil@gmail.com

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