## HIGHER COURSE OUTLINE |

**Entrance Requirement**

National 5 Grade A or B

**Course Descriptor**

The Higher Mathematics Course enables learners to select and apply mathematical techniques in a variety of mathematical situations. Learners interpret, communicate and manage information in mathematical form.The course consists of 3 units designed to develop both mathematical knowledge and ability to reason mathematically.

**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 equat**i**on, 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