MADRAS MATHEMATICS

HIGHER COURSE OUTLINE

EXPRESSIONS & FUNCTIONS
Algebraic skills —laws of logarithms and exponents; solving logarithmic and exponential equations, identifying and sketching related algebraic functions; determining composite and inverse functions,
Trigonometric skills - application of the addition or double angle formulae; application of trigonometric identities; wave function; identifying and sketching related trigonometric functions
Geometric skills —vector pathways in three dimensions; working with collinearity; determining the coordinates of an internal division point of a line; evaluating a scalar product given suitable information and determining the angle between two vectors

RELATIONSHIPS & CALCULUS

Algebraic skills — factorising a cubic polynomial expression with unitary x 3 coefficient;
solving cubic polynomial equations with unitary x 3 coefficient; given the nature of the
roots of an equation, use the discriminant to find an unknown
Trigonometric skills — solve trigonometric equations in degrees, including those
involving trigonometric formulae or identities, in a given interval
Calculus skills — differentiating an algebraic function which is, or can be simplified to,
an expression in powers of x; differentiating ksinx, kcosx ; determining the equation
of a tangent to a curve at a given point by differentiation; integrating an algebraic
function which is, or can be, simplified to an expression of powers of x; integrating
functions of the form f(x)= (x+q)n , n ≠ −1; integrating functions of the form
f(x) = p cosx and f(x)=  p sin(x)  ; calculating definite integrals of polynomial functions
with integer limits.

APPLICATIONS

Algebraic skills — finding the equation of a line parallel to and a line perpendicular to
a given line; using m = tanθ to calculate a gradient or angle; determining and using
the equation of a circle; using properties of tangency in the solution of a problem;
determining a recurrence relation from given information and using it to calculate a
required term; finding and interpreting the limit of a sequence, where it exists
Calculus skills — determining the optimal solution for a given problem; finding the
area between a curve and the x-axis; finding the area between two curves or a straight
line and a curve
The course is appropriate to anyone with a good pass at National 5 maths, wishing to develop their knowledge and understanding of mathematics. The external exam includes a calculator and a non-calculator paper.
The Work of the Course
In class pupils discover, develop and practice ideas and examples from the course topics through various resources such as jotters, posters, show-me boards, group work, textbooks, IT.
At home there will be daily revision, practice of work covered in class and formal homework at fortnightly intervals (at least).
Assessment
Final Grade: Course Work 0%                   External Exam 100%

Possible Progression to Advanced Higher Maths or Advanced Higher Applied Maths