2007 Sqa Advanced Higher Maths

Fully expanding a binomial involving rational expressions. Instructional exercise consisting of question 1 from the Using the Euclidean algorithm to find a solution to a Diophantine equation. Instructional exercise consisting of question 7 from the ... Deriving the Maclaurin series for cos(x) and transformations of cos(x). Instructional exercise consisting of question 6 from the Multiplication of two 3x3 matrices. Finding the determinants of 3x3 matrices. Method for simplifying the evaluation of a 3x3 matrix. Differentiating functions of function (chain rule). Differentiation using logarithmic differentiation. Instructional exercise consisting of ... Proving a complex number is a root of a cubic equation. Technique for quickly establishing the irreducible quadratic factor.

Finding the general solution to a second order differential equation. Brief explanation of the derivation of the auxiliary equation. Resolving a rational expression into partial fractions. Evaluating the integral of a rational expression. Instructional exercise ... Finding the equation of a tangent to a curve defined by parametric equations. Finding the second derivative and using this to ... Solving a separable first order differential equation. In particular, finding the constant of integration immediately against letting it ... Finding the asymptotes of the graph of inverse tangent. Finding an area using integration by parts. Sketching the graph of the ... Evaluate a definite integral using a given substitution. Evaluate the volume of a solid of revolution about the x-axis. Instructional ...

Using the summation formulae to find the sum of a series. Instructional exercise consisting of question 9 from the Finding an indefinite integral by using integration by parts twice. Instructional exercise consisting of question 7 from the 2008