SPM(U) 2006 : http://mathsmozac.blogspot.com Section A [52 marks] Answer all questions in this section. 1 The Venn diagram in the answer space shows sets P‚ Q and R such that the universal set‚ ξ = P ∪ Q ∪ R . On the diagram in the answer space‚ shade (a) the set P ∪ R ‚ (b) the set (P ∩ R ) ∪ Q ’ . [3 marks] Answer: (a) P Q R (b) P R Q 2 Diagram 1 shows a solid cuboid. A cone is removed from this solid. 12 cm 10 cm 15 cm DIAGRAM 1 The diameter of the base of the cone is 7 cm
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the average and rms values of the periodic voltage or current waveforms‚ are computed? Some examples are also described there. In this lesson‚ the representation of sinusoidal (ac) voltage/current signals by a phasor is first explained. The polar/Cartesian (rectangular) form of phasor‚ as complex quantity‚ is described. Lastly‚ the algebra‚ involving the phasors (voltage/current)‚ is presented. Different mathematical operations – addition/subtraction and multiplication/division‚ on two or more phasors
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step used. 2. Bisect the original line segment from problem one. 3. Draw an angle and copy it to the right of the original angle. Explain your steps and justify each step used. 4. Bisect the original angle from problem three. 05.04 Coordinate Geometry Warning: There is
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with equation 2y = 11x + 3. (3) 7. (a) Factorise completely x3 - 4x. (3) (b) Sketch the curve with equation y = x3 - 4x‚ showing the coordinates of the points where the curve crosses the x-axis. (3) (c) On a separate diagram‚ sketch the curve with equation y = (x - 1)3 - 4(x - 1)‚ showing the coordinates of the points where the curve crosses the x-axis. (3) 8. The straight line l1 has equation y = 3x - 6. The straight line l2 is perpendicular to l1
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the acceleration due to gravity‚ g is always vertically downwards and hence has no effect on the horizontal motion of the projectile.Thus projectile motion is two-dimensional motion.We can consider the plane of plane of motion as the x- coordinate and y- coordinate with the x-axis horizontal and the y-axis vertically upward. In another words‚ projectile motion can be resolved into two perpendicular component: a horizontal component with constant velocity (zero acceleration)and a vertical
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bending of two unsymmetrical section cantilevers: 1. An equal angle with one axis of symmetry. 2. A Z section completely unsymmetrical. Apparatus: Vertical cantilever system‚ dial gauges‚ standard weight‚ hanger‚ cantilever beams of L and Z section. Procedure: 1. Mount up a beam section on the vertical cantilever system and measure the cross sectional dimensions. 2. Set the position of a geometrical axis of the beam section at zero degree. 3. Start the bending test on the cantilever
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5/3/2011 Lecture 1 LECTURE 1 TOPICS I. Product of Inertia for An Area Definition Parallel Axis Theorem on Product of Inertia Moments of Inertia About an Inclined Axes Principal Moments of Inertia Mohr’s Circle for Second Moment of Areas II. Unsymmetrical Bending II Unsymmetrical Bending Unsymmetrical Bending about the Horizontal and Vertical Axes of the Cross Section Unsymmetrical Bending about the Principal Axes 1 5/3/2011 Lecture 1‚ Part 1 Product of Inertia for an Area
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the screen make sure that you don’t draw outside the screen. This can be very fast‚ but increases the complexity of the triangle-filler (and it’s not as easy as 3D-clipping can be). This clipping method works directly with two-dimensional screen-coordinates. In 3D clipping you do everything in 3D space. (In my examples it’s done in camera-space. If you don’t know about this don’t worry about it.) If we want to clip in 3D space we need to have a description of the stuff the camera of our rendering-engine
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They fought for their weakness‚ fought for the temptation and fought for the evil things which blocked their paths to destinations. The similarity between Tayo and Laguna reminds me of the phrase “timeful world” (CP 23)‚ which seems to be a coordinate system‚ the x-axis represents behavior and the y-axis represents time‚ there exists a helix goes up
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Chapter 2: Linear Functions Chapter one was a window that gave us a peek into the entire course. Our goal was to understand the basic structure of functions and function notation‚ the toolkit functions‚ domain and range‚ how to recognize and understand composition and transformations of functions and how to understand and utilize inverse functions. With these basic components in hand we will further research the specific details and intricacies of each type of function in our toolkit and use
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