Mathematics
What you must know
Algebra is the backbone: linear and quadratic equations, systems, inequalities, exponents and logarithms, and factoring. Geometry covers triangles (Pythagoras, similarity, angle sums), circles, areas and volumes, and coordinate geometry (slope, distance, midpoint). Sequences, basic combinatorics, probability, and percentages round out the syllabus. Trigonometry usually stays at right-triangle level: sine, cosine, tangent ratios and the unit-circle signs.
Traps that appear
- Inequalities: multiplying or dividing by a negative flips the sign.
- Quadratics: forgetting the negative root, or misreading the discriminant. If (b^2-4ac<0), there are no real solutions.
- Units and scaling: doubling a side of a similar figure quadruples its area, not its perimeter.
- Percent change: a 20% rise then a 20% fall does not return to the start.
- Domain restrictions: logarithms need positive arguments; denominators cannot be zero.
Worked example
Solve (x^2-5x+6=0). Factor as ((x-2)(x-3)=0), so (x=2) or (x=3). Check with the discriminant: (25-24=1), a perfect square, confirming two rational roots.
Rule of thumb
Substitute your answer back into the original equation. For word problems, translate one sentence at a time into symbols before solving, and sanity-check that the result is physically plausible.