Secondary 2 Mathematics

Secondary 2 finishes the general Mathematics syllabus before it splits — quadratics, and right-angled triangle trigonometry with Pythagoras' theorem, are the two big additions.

Building on Secondary 1

Ratio extended to map scales, and to direct and inverse proportion.
Simultaneous linear equations, and inequalities.
Congruent and similar figures, including scale factors.
Volume and surface area of pyramids, cones and spheres.

Quadratics and factorising

This is the first time students multiply out two brackets and then have to reverse the process — factorising a quadratic expression back into two brackets. It's a skill built on pattern recognition as much as calculation, and it's worth as much practice as any other single topic this year, since every level after this one assumes it's solid.

Qn 1

Factorise x² + 5x + 6.

Find two numbers that multiply to 6 and add to 5: 2 and 3

x² + 5x + 6 = (x + 2)(x + 3)

Factorised form: (x + 2)(x + 3) ✓

Right-angled triangles: Pythagoras and trigonometry

Pythagoras' theorem and the three trigonometric ratios (sine, cosine, tangent) both apply only to right-angled triangles, and the two get combined constantly — using Pythagoras to find a side, then trigonometry to find an angle, or the reverse. Sorting out which one a question is actually asking for is the real skill here.

Qn 2

A right-angled triangle has two shorter sides of 9 cm and 12 cm. Find the length of the hypotenuse.

c² = 9² + 12² = 81 + 144

c² = 225

c = 15 cm ✓

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