My Math skills,

#1

ANyone willing to hand a hand in overlooking what i know and what i should really know? SO far I earned a grade C in Pure Mtath at an intermediate level, but since i’m studying solo for the time being and recently became instredted in the games development side of animation i was wondering idf any one could lookover what i know, i will post a list of topics which i know in the next post…

#2

Pure MAthe INtermediate level: (MATRIC board of studies Malta)
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[left]Topics
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[left]Notes
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[left]1.
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[left]Positive and negative rational indices. Laws of indices. Laws of logarithms
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[left]Solution of simple equations involving indices and logarithms of the form [font=‘Times New Roman’] only. Problems involving change of base will not be set.[/font]
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[left]Use and manipulation of surds.
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[left]2.
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[left]Polynomials, rational functions, factor and remainder theorems.
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[left]Simple partial fractions.
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[left]Problems on partial fractions could include denominators such as
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[left][font=‘Times New Roman’]and [/font]
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[left]3.
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[left]The quadratic equation in one variable.
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[left]Solution of the quadratic equation by completing the square or the use of the formula.
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[left]Nature of roots.
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[left]Knowledge of the relation between the roots and the coefficients of a quadratic equation. Forming new equations with roots related to the original. Calculation of expressions such as:
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[left]4.
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[left]Arithmetic series, finite and infinite geometric series. Pascal’s triangle. The binomial expansion for positive integral indices.
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[left]The general term and the summation of an arithmetic and geometric progression are included. Knowledge of the notation .
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[left]5.
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[left]Simple counting problems involving permutations and combinations. Applications to simple problems in probability
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[left]The knowledge of probability expected will be limited to the calculation of probabilities arising from simple problems of enumeration of equally likely possibilities, including simple problems involving the probability of the complement of an event and of the union and intersection of two events.
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[left]Knowledge of the rules:
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[left]is expected
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[left]Questions on conditional probability will not be set.
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[left]Tree and Venn diagrams may be used.
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[left]6.
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[left]Plane Cartesian coordinates. Distance between two points and the perpendicular distance from a point to a line. Elementary treatment of lines.
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[left]Intersection of a straight line with a curve.
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[left]Reduction of a relation to linear form, and graphical determination of the constants
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[left]Relations will be limited only to equations of the form:
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[left]and
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[left]The concept of a function as a[font=‘Times New Roman’] mapping: domain and range. [/font]
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[left]Use of function notations,[font=‘Times New Roman’][/font]
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[left][font=‘Times New Roman’]e.g. [/font]
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[left]The exponential and logarithmic functions and their graphs.
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[left][font=‘Times New Roman’]The six trigonometric functions[/font]
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[left][font=Arial]Graphs of functions of the type [/font] [font=‘Times New Roman’] where is a positive integer. Graphs of [/font] [font=‘Times New Roman’]and are not required.[/font]
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[left]Solution of simple trigonometric equations. [font=‘Times New Roman’][/font]
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[left]Trigonometric equations of the[font=‘Times New Roman’] type and where n is a positive integer only. [/font]
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[left]Quadratic trigonometric equations may be included.
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[left]General solutions are not required.
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[left] [font=‘Times New Roman’][/font]
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[left][font=‘Times New Roman’]The identity and simple corollaries. [/font]
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[left][font=‘Times New Roman’]Other trigonometric identities, and the addition theorems are not required.[/font]
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[left]8.
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[left]Simple curve sketching.[font=‘Times New Roman’][/font]
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[left]Curve sketching of polynomials not higher than the third degree.
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[left]Transformations.
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[left]Knowledge of the effect of the simple[font=‘Times New Roman’] transformations [/font]
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[left][font=Arial] and [/font].
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[left]Transformations of exponential, logarithmic, trigonometric and polynomial functions.
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[left]Combinations of transformations will not be required.
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[left]Simple inequalities in one variable.
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[left]Graphical or algebraic solution of inequalities such as the following :
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[left]9.
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[left]Radian measure.
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[left]Knowledge of the values of cosine, sine, and tangent of , in surd or rational form. Use of the formulae:
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[left]10.
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[left]The derivative as a limit.
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[left]Differentiation of sums, products, quotients and composition of functions.
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[left]Differentiation of algebraic, trigonometric, exponential and logarithmic functions. Applications of differentiation to gradients, tangents, maxima and minima, points of inflexion and curve sketching.
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[left]A rigorous treatment of limits is not expected.
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[left]Inverse trigonometric functions are excluded.
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[left]Differentiation of implicit and parametric functions is not required.
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[left]Second order derivatives are not required.[font=‘Times New Roman’][/font]
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[left]Simple problems on rates of change.
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[left]Problems involving the chain rule of [font=‘Times New Roman’]the type may be set.[/font]
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[left]11.
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[left]Integration as the limit of a sum and as the inverse of differentiation.
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[left]A rigorous treatment is not required.
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[left][font=‘Times New Roman’]The evaluation of integrals by means of standard forms and by partial fractions. [/font]
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[left][font=Arial] Integrals of the functions [/font]
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[left][font=Arial]and are required.[/font]
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[left][font=‘Times New Roman’]Use of the result .[/font]
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[left]Definite integrals. Application of integration to the calculation of areas.
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[left]12.
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[left]First order differential equations with separable variables.
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[left]Problems requiring the formation of a differential equation will not be set.[font=‘Times New Roman’][/font]
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[left]13.
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[left]The algebra of matrices.
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[left]Addition and multiplication.
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[left]Distributivity of multiplication over addition. Associativity. The zero matrix and the identity matrix. Non-commutativity of multiplication. The inverse of a matrix.
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[left]Students will only be expected to be able to find inverses of 2 X 2 matrices but they should be able to verify that, say, two given 3 X 3 matrices are inverses of each other.
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[left]Applications will be limited to linear transformations in the plane.
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[left]Students are expected to find the matrices of the following transformations:
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[left]a) enlargement,
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[left]b) rotation through multiples of ,
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[left][font=Arial]c) [/font]reflections in the lines [font=‘Times New Roman’] and . [/font]
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#3

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