Buds Public School, Dubai
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1 Buds Public School, Dubai Subject: Maths Grade: 11 AB Topic: Statistics, Probability, Trigonometry, 3D, Conic Section, Straight lines and Limits and Derivatives Statistics and Probability: 1. Find the mean deviation about the mean for the following data : 2. Find the mean deviation about the median for the following data : 3. Find the mean and variance of the following frequency distribution : Calculate the mean deviation about the median Class Interval 5. Calculate mean, variance and S. D of the following distribution : 15 C. I f One card is drawn from a well shuffled deck of 52 cards. Calculate the probability that the card drawn will not be an ace. 7. Find the probability of getting the product as a perfect square (square of a natural number) when two dice are thrown together. 8. A coin is tossed twice, then find the probability of getting a) at least one head b) at most one head c) exactly one head. 9.. A bag contains 9 balls of which 4 are Red, 3 are Blue, 2 are Yellow. The balls are similar in shape and size. A ball is drawn at random from the bag. Calculate the probability that it will be a) blue b) not red c) either Red or yellow d) Neither Red nor Yellow. 10. If A and B are events such that find
2 11. The letters of the word SOCIETY are placed at random in a row. what is the probability that three vowels come together? 12. The probability that a student will pass the final examination in both English and Hindi is 0.5 and the probability of passing neither is 0.1. If the probability of passing the English examination is 0.75, what is the probability of passing Hindi Examination? Trigonometry : 1. Prove that sin 2. Sin Prove that 2 5. Prove that 6. Prove that (sin 3A +sin A)sin A + (cos 3A- cos A ) cos A = Prove that 8. prove that = tan x 9. If then find the value of 10. Solve : 11. Find the general solution of the equation 12. Find the value of 13. What is the value of a)? 14. Find the general solution of Three Dimensional Geometry : 1. Find the distance between the points (1,3,4) and (-1,6,10). 2. Find the value of p such that the distance between the points (4,5, p) and (7,1,-3) is Show that the points A(1,2,3), B(-1,-2,-1), C(2,3,2) and D(4,7,6) are the vertices of a parallelogram ABCD, but not a rectangle. 4. Find the Coordinates of the point which divides the join of P(2,-1,4) and Q(4,3,2) in the ratio 2:3 i) internally ii) externally.
3 5. Find the ratio in which the line joining the points (1,2,3) and (-3,4,-5) is divided by the xy- plane. Also find the coordinates of the point of division. 6. Three students are standing in a park with signboards SAVE ENVIRONMENT : DON T LITTER : KEEP YOUR PLACE CLEAN. Their positions are marked by the points A(0,7,10), B( -1,6,6 ) and C(-4,9,6). The three are holding GREEN coloured ribbon together. Does the ribbons form of sides of a right angled triangle? Do you feel the need to promote, what is written on signboards? 7. Show that the points (a, b, c), (b, c, a) and (c, a, b) are the points of an equilateral triangle. 8. Centroid of a triangle with vertices ( a, 1,3 ), (-2, b, -5) and (4, 7, c) is at origin. Find the values of a,b and c. 9. Find the ratio in which the join of A( 2, 1, 5) and B( 3, 4, 3) is divided by the plane 10. Show that the points (1,3,4), (-1,6,10) (-7,4,7) and (-5,1,1) are the vertices of a rhombus. Conic Sections : 1.. Find the equation of the circle passing through (0,-1), (2,0) and whose centre lies on the line 2. Find the equation of the circle passing through (2,-2), (3,4) and whose centre lies on the line 3. Find the focus, directrix and eccentricity of the parabola 4. Find the length of the axes, coordinates of foci,eccentricity of the conic section. 5. Find the coordinates of the foci, the vertices, the eccentricity, the length of the latus rectum of the following ellipse : a) b) 6. Find the coordinates of the foci, the vertices, the eccentricity, the length of the latus rectum of the following hyperbola : a) b) c) 7. Find the centre and radius of the following Circles : a) 8. Find the focus, directrix and eccentricity of the parabola 9. Find the length of the axes, coordinates of foci,eccentricity of the conic section. 10. Find the equation of the circle passing through (0,0) and making intercepts a and b on the coordinate axes. Straight Lines : 1. Find the slope of the line passing through the points 2. Calculate the slope of the line passing through the points (3,2) and (4, 1). Also find the inclination of the line with x-axis.
4 3. Find the angle between the line joining the points (3,-1) and (2,3) and the points (5,2) and (9,3) 4. Find the equation of a line which cuts the x axis at a distance of 3 units to the left of the origin and has a slope equal to Find the equation of line passing through the intersection of the lines and parallel to the line 6. In what ratio the line joining the points A(-1,1) and B(5,7) is divided by the line 7. Two lines passing through the point (2,3) intersects each other at an angle of 60 If slope of one line is 3, find the equation of the other line. 8. Find the equation of the line passing through the point (-4,-5) and which is perpendicular to the line joining the points (0,-5) and (-1,3) 9. Find the equation of perpendicular bisector of the line segment joining the points (0,3) and (-4,1) 10. without using the pythogoras theorem, show that the points (1,2), (4,5) and (6,3) represent the vertices of a right triangle. Limits and Derivatives : 1. Evaluate the following : Find the derivative of the following : Find the derivative of 8. Find the derivative of 9. Find the derivative of at x= Find the derivative of 11. Differentiate the following with respect to x : a) b) d) g) h)
5 12. For the function. Prove that 13. Find the derivative of 14. Find the derivative of and at.
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