UNSA ETF Math Entrance Exam study plan

Compute the exact values of sine, cosine and tangent at the standard angles without consulting a table

Derive and apply the sine rule and cosine rule to solve triangles, including the ambiguous case

Classify numbers as prime, composite, rational or irrational and prove simple divisibility claims

Apply the Euclidean algorithm to compute greatest common divisors and solve linear Diophantine equations

Prove and use the Pythagorean, double-angle and sum-to-product identities in simplification problems

Solve quadratic equations by factoring, completing the square and the discriminant test

Solve systems of two and three linear equations and interpret inconsistent or dependent cases

Simplify rational expressions and solve inequalities with sign charts

Factor and solve polynomial equations of degree three and four using the factor and remainder theorems

State the domain, range and asymptotes of rational functions and sketch them

Apply the laws of logarithms and exponents to solve equations and model growth

Transform basic graphs by shifting, scaling and reflecting, then write the resulting equation

Solve trigonometric equations and identify all solutions in a given interval

Compute dot and cross products and use them to find angles, projections and areas

Determine equations of lines and planes in vector and Cartesian form

Find distances between points, lines and planes using vector methods

Identify arithmetic and geometric sequences and compute general terms and partial sums

Evaluate limits of rational and radical expressions by factoring and rationalising

Apply the sum of an infinite geometric series and test convergence informally

Use mathematical induction to prove summation formulas

Count arrangements and selections using permutations, combinations and the multiplication principle

Apply the binomial theorem to expand powers and find specific terms

Compute probabilities using conditional probability and independence

Solve inclusion-exclusion and complementary counting problems

Convert complex numbers between rectangular, polar and exponential forms and plot them

Apply De Moivre's theorem to compute powers and roots

Solve quadratic equations with complex roots and interpret conjugates geometrically

Use vectors and complex numbers together to solve rotation and locus problems

Complete two full-length timed mock exams under exam conditions

Diagnose weak areas from mock results and re-teach the three weakest topics

Memorise and rehearse the formula sheet until it can be reproduced in five minutes

Practise pacing by allocating time per question according to domain weighting