Trigonometric Formulae, Equations and Inequalities

You will find the period of a trigonometric function; derive and use the addition, double-angle, half-angle and product–sum formulae; solve equations of the forms sin(x + a) = k, sin nx = k and a sin x + b cos x = c, and trigonometric inequalities; and apply them to simple harmonic motion and the refraction of light.

2

Sequences

You will define sequences by a general term or by a recurrence relation, decide whether they are monotone and bounded, work with arithmetic, geometric and harmonic sequences (terms, means and the sum of the first n terms), decide whether a sequence converges or diverges, and use sequences to model savings, depreciation, growth and other real-life problems.

3

Logarithmic and Exponential Equations

You will study exponential and logarithmic functions of any base, their graphs and the laws of logarithms; solve exponential and logarithmic equations and inequalities, checking domains; and use them to model compound interest and mortgages, population growth, radioactive decay and carbon dating, and the magnitude and risk of earthquakes.

4

Points, Straight Lines and Shapes in 2D

You will use coordinates for distances, midpoints and division points; write the vector, parametric and Cartesian equations of a line and pass from one to another; decide whether two lines meet, are parallel or are perpendicular, and find the angle between them; find the distance from a point to a line and which side of a line a point lies on; and work with the equation of a circle and the relative position of a circle and a line.

5

Trigonometric and Inverse Trigonometric Functions

You will study the domain, range and parity of the six trigonometric functions and of the inverse functions arcsin, arccos and arctan; find limits involving them, starting from the limit of sin x over x; differentiate trigonometric and inverse trigonometric functions and find successive derivatives; and apply these tools to refraction in a prism, simple harmonic motion and optimisation problems.

6

Matrices and Determinants of Order 3

You will add, multiply and transpose 3 × 3 matrices, write the matrix of a linear transformation of space, evaluate determinants of order 3 and use their properties, find an inverse with the adjugate, and solve systems of three linear equations by the inverse matrix and by Cramer's rule.

7

Vector Space ℝ³ of Real Numbers

You will add and scale vectors in three dimensions, decide whether vectors are linearly independent, find the coordinates of a vector in a basis, use the scalar product for lengths, angles, projections, direction cosines and work, and use the vector and mixed products for areas, volumes and coplanarity.

8

Points, Straight Lines and Shapes in 3D

You will find distances, midpoints, dividing points and centroids in space, write the equations of lines and planes, decide how lines and planes lie relative to each other and find the angles between them, compute distances from a point to a line or plane and between skew lines, and work with the equation of a sphere.

9

Bivariate Statistics

You will draw and read scatter diagrams, describe the type and strength of a correlation, organise paired data in a double-entry frequency table, compute the covariance and Pearson's coefficient of correlation, and use the regression lines of y on x and of x on y to make and judge predictions.

10

Elementary and Conditional Probability

You will describe experiments by their sample spaces, use counting and the rules of probability, apply the addition rule to mutually exclusive and inclusive events and the multiplication rule to independent ones, draw tree diagrams, compute conditional probabilities and their properties, and use the law of total probability and Bayes' theorem to update a probability with new evidence.

Units