UNSA ETF Math Entrance Exam study guide
UNSA ETF Math Entrance Exam · Work through your exam, one topic at a time.
The UNSA ETF Mathematics Entrance Examination is the subject-specific admission assessment used by the Faculty of Electrical Engineering (Escuela Técnica / Facultad de Ingeniería Eléctrica) at the Universidad Nacional de San Agustín de Arequipa for applicants seeking a place in its engineering programmes. It is intended for secondary-school graduates and transfer candidates who need to demonstrate mathematical readiness before beginning university-level coursework in circuits, signals, control and computing. The UNSA ETF Math Entrance Exam study guide has 8 sections and about 2,350 words.
01Arithmetic and Number Theory
Arithmetic questions test fluency with fractions, decimals, percentages, ratios, and powers, plus the number-theoretic tools that let you avoid brute computation: divisibility rules, prime factorisation, greatest common divisor (GCD) and least common multiple (LCM), remainders and modular thinking, and the distinction between rational and irrational numbers. Know that every integer factors uniquely into primes, that GCD x LCM = product of the two numbers, and that a fraction is in lowest terms exactly when numerator and denominator share no prime factor.
300 words, about 2 min02Algebra
Algebra rewards structural thinking: manipulating expressions, factoring, solving linear and quadratic equations and inequalities, working with exponents and radicals, and handling systems of equations. You should be able to complete the square, apply the quadratic formula, use the discriminant to count real roots, and recognise when substitution or elimination is faster than direct solving.
286 words, about 1 min03Functions and Graphs
Function questions test domain and range, composition, inverses, transformations, and the shapes of standard graphs: linear, quadratic, polynomial, exponential, logarithmic, rational, and absolute value. You should be able to shift, stretch, and reflect a graph from its equation, read intercepts and asymptotes, and determine whether a relation is a function (vertical line test) or invertible (horizontal line test).
283 words, about 1 min04Geometry and Trigonometry
This domain covers angle relationships, triangle congruence and similarity, the Pythagorean theorem, circle theorems, area and volume formulas, coordinate geometry basics, and right-triangle and unit-circle trigonometry. You must know the sine, cosine, and tangent ratios, the exact values at 30, 45, and 60 degrees, the Pythagorean identity, the law of sines, and the law of cosines.
292 words, about 1 min05Sequences, Series and Limits
You must handle arithmetic and geometric sequences, their nth terms and partial sums, infinite geometric series, and the idea of a limit. Know that an arithmetic sequence has constant difference d with a n = a 1 + (n-1)d and S n = n(a 1 + a n)/2, while a geometric sequence has constant ratio r with a n = a 1 r^(n-1) and S n = a 1(1 - r^n)/(1 - r).
327 words, about 2 min06Combinatorics and Probability
Counting and probability questions test the multiplication principle, permutations versus combinations, factorials, arrangements with restrictions, and basic probability rules. Know that P(A or B) = P(A) + P(B) - P(A and B), that P(A and B) = P(A)P(B) for independent events, and that conditional probability is P(A B) = P(A and B)/P(B).
255 words, about 1 min07Complex Numbers
Complex numbers extend the reals with i, where i² = -1. You must be able to add, subtract, multiply, and divide complex numbers, find the modulus a + bi = sqrt(a² + b²), use the conjugate a - bi to rationalise denominators, and represent numbers on the complex plane.
306 words, about 2 min08Analytic Geometry and Vectors
This domain blends coordinate geometry with vectors. You should know the distance and midpoint formulas, slope conditions for parallel and perpendicular lines, equations of lines in several forms, and the equations of circles and parabolas.
301 words, about 2 min