Mathematics – Secondary Grade 1

Course highlights

• Use the imaginary unit and its powers, write complex numbers in the form a + bi, and add, subtract, multiply and divide them (conjugates) and solve equations with complex roots
• Determine the nature of the roots of a quadratic equation by the discriminant, use the sum and product of roots, and form an equation from given roots
• Study the sign of linear and quadratic functions and solve quadratic inequalities in one unknown
• Prove and use the similarity of polygons and triangles and the relation between the areas (and perimeters) of similar polygons
• Apply similarity in the circle: intersecting chords, secants and tangents from an external point (power of a point)
• Apply the theorems of parallel lines and proportional segments (Thales) and of internal and external angle bisectors
• Use directed angles in standard position, convert between degree and radian measure, find arc lengths, and define the trigonometric functions and their signs
• Use related angles to evaluate trigonometric functions, sketch sine and cosine graphs, and find an angle from one of its trigonometric ratios
• Organise data in matrices; add, subtract and multiply matrices and multiply by a scalar; evaluate 2 × 2 and 3 × 3 determinants; find the inverse of a 2 × 2 matrix; solve linear systems with determinants and with the inverse (t2, 2023/24 structure)
• Graph linear inequalities and systems of linear inequalities; model a situation with constraints and find the optimal value of an objective function at the vertices
• Distinguish scalar and vector quantities; write vectors in component, unit-vector and polar form; add, subtract and scale vectors; test parallel and perpendicular vectors; apply vectors to geometry and forces
• Divide a segment in a given ratio; write the equation of a straight line in several forms; find the angle between two lines and the perpendicular distance from a point to a line
• Prove trigonometric identities and solve trigonometric equations in a given interval
• Solve a right-angled triangle and problems on angles of elevation and depression
• Find the area and perimeter of a circular sector, the area of a circular segment, and areas of triangles and regular polygons with ½ ab sin C

Course content

• 11units
• 40sessions
• 16quizzes

The lecturer