VCE Specialist Mathematics Pocket Study Guide Contents Introduction 1 Vectors in two and three dimensions 2 Complex numbers 3 Coordinate geometry and sketch graphs 4 Circular functions 5 Antidifferentiation 6 Integration 7 Differential equations 8 Kinematics 9 Vector calculus 10 Dynamics iv 1 12 26 40 53 62 70 79 86 92 Introduction What do you really need to know for Specialist Mathematics? We’ve answered that question in this Pocket Study Guide. This handy guide gives you a summary of
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meanings in mathematics. The modern and advanced meaning refers to the geometry of analytic varieties. This article focuses on the classical and elementary meaning. In classical mathematics‚ analytic geometry‚ also known as coordinate geometry‚ or Cartesian geometry‚ is the study of geometry using a coordinate system and the principles of algebra and analysis. This contrasts with the synthetic approach of Euclidean geometry‚ which treats certain geometric notions as primitive‚ and uses deductive reasoning
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The Amazing Planes of World War II Planes played a very important role in World War II. Most attacks in World War II were from planes in air attacks. “Air superiority is a condition for all operations‚ at sea‚ in land‚ and in the air‚” said Air Marshal Arthur Tedder (“World War 2 Quotes”). After World War II‚ planes became more common and popular. Today‚ many people use planes for travel. The planes in World War II had a huge impact on history and all of the countries that used planes. First‚ World
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Linear Programming D.V. – Decision Variables O.F. – Objective Funtion S.T. or CONST - Constraints Constrained Mathematical Model – a model with an objective and one or more constraints EXAMPLE: 50D + 30C + 6M is the total profit for a production run($50 profit for Desk‚ $30 profit for Chair and $6 per pound for steel) Functional Constraints - ≤ ≥ or = --Restrictions that involve expressions with 1 or more variables EXAMPLE: 7d+3c+1.5M <= 2000 (constraint on raw steel) Variable Constraints
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of his argument‚ i.e. demonstrate that the mind and the body are separate substances) is that it is logically impossible for the mind and body to be the same substance; but‚ as he fails to do this‚ I must reject his conceivability argument‚ and Cartesian dualism in general as the right account of mind and body. A further criticism of substance dualism asks how one can conceptually reconcile the interaction between the physical (the body) and the non-physical (the mind). This can be demonstrated
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heard that accidents occur more often because of pilot errors and less so because of mechanical problems. But why? Why do pilots make errors? What kind of errors do they make? According to Malcolm Gladwell’s book‚ The Outliers‚ a large number of plane crashes happen because of miscommunication and language issues. There are two places where miscommunication occurs: among pilots in the cockpit and between air traffic controllers and pilots. And‚ there are two major reasons for miscommunication
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with exactly two terms. 8. A pair of numbers in which the order is specified. 9. A comparison between two quantities. 10. The horizontal number line in a Cartesian coordinate plane. 11. The abscissa of the point of intersection of a line and the x-axis. 12. The vertical number line in a Cartesian coordinate plane. 13. The ordinate of the point of intersection of a line and the y-axis. 14. An angle with a measure greater than 90 but less than 180. 15. A space figure
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hill‚ and decorated war hero‚ gives the order to shoot down a private plane. This has been the third violation over the Capitol within a month "This has got to stop! I’ve had it with these crazies making a circus of this place... Well here’s the price of the ticket. Shoot the damn thing down... an example has got to be made” To his horror and regret‚ it is piloted by his precocious grandson. A child of 12‚ who has taken the plane up‚ with intent of surprising his grandfather at lunch. The grandfather
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Path planning 2D plotting machine for efficient automated PCB drilling. S.C Alwis‚ A.S Premarathna‚ Y.P Fonseka‚ S.M Samarasinghe J. Wijayakulasooriya ABSTRACT 2D vector plotters are designed to take a pointer to any given coordinate in the xy plane. An application of this plotting device is in PCB drilling. In PCB drilling the location of the drill holes are fed into the system which will drill the PCB at the specified coordinates. The main objective of this project is to be able to take a pointer
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visualizing algebraic formulas”. He developed the coordinate system as a “device to locate points on a plane”. The coordinate system includes two perpendicular lines. These lines are called axes. The vertical axis is designated as y-axis while the horizontal axis is designated as the x-axis. The intersection point of the two axes is called the origin or point zero. The position of any point on the plane can be located by locating how far perpendicularly from each axis the point lays. The position of the
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