475 - Additional Mathematics

Pure Mathematics

a) Indices, logarithms and surds. Arithmetic and geometric progressions. Factor and Remainder theorems.

Including the sum of finite number terms.

b) Use of the Binomial theorem for an integral index, and its use for simple approximations. Elementary permutations and combinations.

Questions on the greatest term and on sums and properties of the coefficients will not be asked.

c) Elementary properties of quadratic expressions and equations.

Range of values of the function ax2 + bx + c by graphical and other methods.

d) Gradient of a straight line.

Relationship between gradients of perpendicular and parallel lines.

e) Representation of a curve by means of a pair of parametric equations.

Single parameter only.

f) Equations of tangent and normal lines. Elementary locus problems. Equations of a circle.

Including eliminations of parameter.

g) Easy simultaneous equations in two unknowns.

At least one linear.

h) Complex numbers.

Geometrical representation. Modulus and argument. Addition and multiplication.

i) Circular measure, arc length, area of a sector of a circle, trigonometical ratios of angles of any magnitude.

To be used in graphs of simple trigonometrical functions.

j) Use of formulae for sin(A+-B), cos(A+-B), tan(A+-B).

Applications to multiple angles and simple identities.

k) Sine and cosine formulae and the formulae (1/2bc)sin A. Simple trigonometrical problems in three dimensions.

To be used in solving triangles and determination of area of triangles. Proofs of these formulae will not be required.

l) Derivative of kxn where n is a positive integral index.

Application to small increments, rates of change, velocity and acceleration, maxima and minima (any method of discrimination will be acceptable).

m) Derivatives of simple algebraic, trigonometrical functions including sums, products, quotients, composite functions.

Implicit functions and inverse trigonometric functions are excluded.

n) Integration as the inverse of differentiation. Definite integral. Integration of simple functions: applications to plane areas and volumes of solids and to kinematics.

Excluding integration by parts and by change variable.

Vectors and Matrices

a) Displacement and position vectors (2-dimensions).

Addition subtraction and multiplication by scalars. Application of the scalar product to test perpendicularity in a plane.

b) Matrices and their applications.

• The use of determinant of a 2 x 2 matrix to solve a pair of linear simultaneous equations. Geometrical interpretation of the value of the determinant.
• Matrices applied to probability, e.g. routes through network.

Mechanics

a) Forces, velocities, and acceleration as vectors, composition and resolution of velocities, relative velocity.

b) Kinematics of particle moving in a straight line.

Include its graphical treatment.

c) Motion with uniform acceleration.

Discussion of Newton's Laws of Motion. Application to connected bodies. Ideas of mass, force, energy, work and power.

d) Composition and resolution of forces, moments.

An experimental basis is sufficient, proofs of the fundamental theorems of statics will not be required.

e) Simple cases of friction.

The laws of friction between solids in contact.

f) The conservation of momentum in rectilinear motion. conservation of energy. Equilibrium of a particle and centre of gravity of a rigid body under coplanar forces.

Statistics

a) Scope and limitations of statistics.

b) The tabulation and appropriate representation of numerical data, choice of class intervals.

Frequency distributions, histograms, cumulative frequency.

c) Measure of central tendency. Measure of dispersion.

Mean, median and mode. Interquartile range and standard deviation.

d) Moving averages. Index numbers.

e) Addition and multiplication laws of probability.

f) Discrete variable. Expectation: expected values. Simple probability and frequency distributions.

General ideas of correlation. Calculation of a rank correlation coefficient and its interpretation. General ideas of sampling and surveys. Knowledge of normal distributions. Estimation of the limits of a mean of a population from a large sample. Calculated for discrete and mathematically defined continuous distributions. Particularly the Binomial distribution and its mean and standard deviation. Include scatter graphs.

Kendall's or Spearman's method of calculation