Free Practice Questions for USAC Ingeniería Específica

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Key Facts: USAC Ingeniería Específica Exam

2 tests

Matemática para Ingeniería and Computación must both be passed for admission to FIUSAC

USAC portal, Pruebas Específicas por unidad académica

20 items

The Computación test has 20 objective multiple-choice questions

FIUSAC guía temática de computación

20 min

Maximum duration published for the Computación test

FIUSAC guía temática de computación

7 temas

Published mathematics syllabus, from real numbers through trigonometry

FIUSAC temas de estudio, prueba específica de matemática

Q0.00

Charging for a Prueba Específica is prohibited by regulation

Reglamento del SUN, artículo 55

2 years

Validity of a Prueba Específica result from its publication date

Reglamento del SUN, artículo 43

Testing opportunities programmed per annual admissions cycle

FIUSAC / Escuela de Mecánica Industrial, Aspirantes

2 PCB

Prerequisite basic tests: Satisfactorio in Lenguaje and Física

FIUSAC Aspirantes and Reglamento del SUN

The USAC Ingeniería Prueba Específica is not one test but two: Matemática para Ingeniería and Computación, both of which must be passed after a Satisfactorio result on the SUN basic tests in Lenguaje and Física. FIUSAC publishes 20 multiple-choice items in a maximum of 20 minutes for Computación and a seven-tema syllabus for Matemática without an item count or time limit; results are reported as Satisfactorio or Insatisfactorio, the tests are free under artículo 55 del Reglamento del SUN, and a result stays valid for two years. The official tests are sat in Spanish; this 100-question bank is an English-language MCQ study adaptation, not an official translation or a simulation of either test's format.

Sample USAC Ingeniería Específica Practice Questions

Try these sample questions to review concepts for the USAC Ingeniería Específica exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1Which of the following numbers belongs to the set of irrational numbers (I)?

A.The fraction 22/7

B.The repeating decimal 0.333...

C.The square root of 7 (√7)

D.The integer -15

Explanation: An irrational number cannot be expressed as a quotient of two integers (a/b with b ≠ 0) and has an infinite, non-repeating decimal expansion. The square root of any non-perfect square, such as √7, is irrational. In contrast, 22/7 is a ratio of two integers, 0.333... is equal to 1/3, and -15 is an integer, all of which are rational numbers.

2What is the exact result of the arithmetic expression: (3/4 - 1/2)^2 + (3/8 ÷ 1/2)?

A.13/16

B.17/16

C.1/4

D.7/8

Explanation: First, evaluate the subtraction inside parentheses: 3/4 - 1/2 = 3/4 - 2/4 = 1/4. Next, square this value: (1/4)^2 = 1/16. Then, perform the division: 3/8 ÷ 1/2 = 3/8 × 2/1 = 6/8 = 3/4. Finally, sum the two terms by finding a common denominator of 16: 1/16 + 3/4 = 1/16 + 12/16 = 13/16.

3What is the greatest common divisor (MCD / GCD) of the three numbers 72, 108, and 180?

A.12

B.540

C.18

D.36

Explanation: Perform prime factorizations: 72 = 2^3 × 3^2; 108 = 2^2 × 3^3; 180 = 2^2 × 3^2 × 5. To find the greatest common divisor (MCD), take the common prime factors raised to their lowest exponents: 2^2 × 3^2 = 4 × 9 = 36.

4A construction crew of 6 workers can pave a section of roadway in 10 days working at a constant rate. If the project manager increases the crew size to 15 workers working at the same rate, how many days will they take to complete the identical section?

A.25 days

B.4 days

C.2.5 days

D.1 day

Explanation: The number of workers and the days required have an inverse proportional relationship: Workers × Days = Constant total work. Here, 6 workers × 10 days = 60 worker-days. With 15 workers, the time required is 60 worker-days ÷ 15 workers = 4 days.

5A structural engineering laboratory prepares a concrete sample with a design target volume. Due to aggregate expansion, the final volume is 2.30 cubic meters, which represents a 15% increase over the original design volume. What was the original design volume?

A.1.84 cubic meters

B.2.00 cubic meters

C.1.955 cubic meters

D.2.15 cubic meters

Explanation: Let V be the original design volume. A 15% increase means the final volume is V × (1 + 0.15) = 1.15 V. Setting 1.15 V = 2.30 m³ gives V = 2.30 / 1.15 = 2.00 m³.

6What is the completely rationalized and simplified form of the fraction 6 / (√5 - √2)?

A.6(√5 + √2)

B.2(√5 - √2)

C.√5 + √2

D.2(√5 + √2)

Explanation: To rationalize the denominator, multiply both numerator and denominator by the conjugate of (√5 - √2), which is (√5 + √2): [6(√5 + √2)] / [(√5 - √2)(√5 + √2)]. The denominator simplifies by difference of squares to (√5)^2 - (√2)^2 = 5 - 2 = 3. Dividing 6 by 3 gives 2(√5 + √2) or 2√5 + 2√2.

7Simplify the algebraic expression containing negative and rational exponents: (8 · a^(-3) · b^6)^(2/3).

A.4 · b^4 / a^2

B.4 · a^2 · b^4

C.2 · b^4 / a^2

D.16 · b^9 / a^2

Explanation: Apply the power of a product rule (x · y · z)^k = x^k · y^k · z^k. First, 8^(2/3) = (∛8)^2 = 2^2 = 4. Next, (a^(-3))^(2/3) = a^((-3) × (2/3)) = a^(-2) = 1/a^2. Finally, (b^6)^(2/3) = b^(6 × 2/3) = b^4. Combining these gives 4 · b^4 / a^2.

8What is the complete solution set for the absolute value equation |2x - 5| = 9?

A.x = -7 and x = 2

B.x = 14 and x = -4

C.x = 7 and x = -2

D.x = 7 and x = 2

Explanation: By definition of absolute value, |u| = a (with a > 0) means u = a or u = -a. Case 1: 2x - 5 = 9 → 2x = 14 → x = 7. Case 2: 2x - 5 = -9 → 2x = -4 → x = -2. Thus, the solution set contains x = 7 and x = -2.

9Subtract the polynomial (4x^3 - 5x^2 + 7x - 2) from (7x^3 + 2x^2 - 3x + 8). What is the simplified difference?

A.-3x^3 - 7x^2 + 10x - 10

B.11x^3 - 3x^2 + 4x + 6

C.3x^3 - 3x^2 + 4x + 6

D.3x^3 + 7x^2 - 10x + 10

Explanation: Subtracting (4x^3 - 5x^2 + 7x - 2) from (7x^3 + 2x^2 - 3x + 8) means calculating: (7x^3 + 2x^2 - 3x + 8) - (4x^3 - 5x^2 + 7x - 2) = (7 - 4)x^3 + (2 - (-5))x^2 + (-3 - 7)x + (8 - (-2)) = 3x^3 + 7x^2 - 10x + 10.

10What is the product of the binomials (3x - 4) and (2x + 5)?

A.6x^2 - 7x - 20

B.5x^2 + 7x - 20

C.6x^2 + 7x - 20

D.6x^2 + 23x - 20

Explanation: Using the distributive property (FOIL): First: (3x)(2x) = 6x^2; Outside: (3x)(5) = 15x; Inside: (-4)(2x) = -8x; Last: (-4)(5) = -20. Combining like terms: 15x - 8x = 7x. The resulting polynomial is 6x^2 + 7x - 20.

About the USAC Ingeniería Específica Exam

The Pruebas Específicas of the Facultad de Ingeniería at the Universidad de San Carlos de Guatemala (USAC) are the faculty admission tests required for entry to every engineering degree programme (Civil, Ciencias y Sistemas, Mecánica, Mecánica Industrial, Industrial, Química, Eléctrica and Electrónica). There are two of them - Matemática para Ingeniería and Computación - and a candidate must obtain a Satisfactorio result on both.

Exam sponsor: Facultad de Ingeniería, Universidad de San Carlos de Guatemala (FIUSAC). The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

Two faculty tests that must both be passed: Prueba Específica de Matemática para Ingeniería, covering the seven published temas (real numbers; fundamentals of algebra; equations and inequalities; functions and graphs; analytic geometry; geometry; trigonometry), and Prueba Específica de Computación, covering the four published areas (Internet, Windows 10, Word and Excel) in 20 objective multiple-choice items. Both are assigned separately on the FIUSAC aspirantes portal and, in the current cycle, sat online through Safe Exam Browser.

Time Limit

Computación: 20 minutes maximum (FIUSAC guía temática). Matemática: not published by FIUSAC. The two tests are sat as separate sessions.

Passing Score

Published as Satisfactorio or Insatisfactorio, with no numeric pass mark published for either specific test. The 61/100 minimum in artículo 35 del Reglamento del SUN governs the Pruebas de Conocimientos Básicos and the 61-point minimum in artículo 50 governs PAP promotion; neither applies to the Pruebas Específicas.

Exam / Certification Fees

Q0.00. Artículo 55 del Reglamento del SUN prohibits any charge for the Pruebas Específicas; only the USAC-wide Orientación Vocacional test (Q70.00) is paid.

Exam sponsor website

Fees, eligibility, and exam policies can change. Confirm them with the exam sponsor before applying or paying.

Official sources

Our practice resources: topics covered

We aim to reflect publicly available exam outlines and topic information in our study resources. Coverage, format, and difficulty may differ from the actual exam, and we cannot guarantee that every detail is accurate or current. Confirm exam requirements, fees, and policies with the official exam sponsor.

Practice-bank coverage: 55 of 100 questions. FIUSAC publishes no per-tema weighting and no item count for this test.

Matemática para Ingeniería (Engineering Mathematics)

Official guide topics are grouped in seven temas: real numbers (classification, operations, roots and rational exponents, rationalisation, order of operations, GCD and LCM, absolute value, numerical patterns, ratio and proportion, percentages); fundamentals of algebra (like terms, operations, non-integer powers, special products including the binomial squared and the binomial theorem, factoring, the remainder and factor theorems, algebraic fractions); equations and inequalities (first-degree equations, quadratics with real roots, equations reducible to quadratics, applied problems, first-degree inequalities); functions and graphs (Cartesian plane, definition, domain and range, linear and quadratic functions, symmetry, combination and composition); analytic geometry (distance, midpoint, slope, forms of the equation of a line, parallel and perpendicular conditions, the circle, the parabola in standard form); geometry (points, lines and angles between parallels, triangles, the Pythagorean theorem, similar triangles, arcs and angles in a circle, areas and perimeters of plane figures, volumes of solids); and trigonometry (angles, degree-radian conversion, trigonometric functions of an acute angle in a right triangle, trigonometric functions on the unit circle, and right-triangle problem solving).

Practice-bank coverage: 45 of 100 questions. The official test is 20 objective multiple-choice items in at most 20 minutes; FIUSAC publishes no per-area weighting.

Computación (Computing)

Official guide topics are grouped in four areas: Internet (what the Internet is, connection types and Wi-Fi, home networks and file/printer sharing, browsers and their toolbars, favourites, history, pop-ups and private browsing, search engines and advanced search technique, e-mail and attachments, and security - viruses, malware, spam, firewalls, Windows Defender, phishing and social engineering); Windows 10 (windows and the desktop, Start menu and taskbar, File Explorer with files, folders, drives and extensions, search, the Recycle Bin, mouse and touchpad settings, installing and removing programs and Windows Update, adding hardware and drivers via Device Manager, and Windows help); Microsoft Word (ribbon and Backstage, basic editing, find and replace, lists, save/open/print and page setup, tables, illustrations and text wrapping, headers and footers, themes, watermarks, page borders, margins, orientation, columns and breaks, review tools and views); and Microsoft Excel (worksheet navigation, data types and errors, workbook operations, selecting/copying/moving cells, formulas and functions including AutoSum, date, text and lookup functions, cell formatting, number formats, conditional formatting, structural changes, inserting and deleting elements, page setup, sorting and filtering, review tools and views).

Preparing for the USAC Ingeniería Específica Exam

What You Need to Know

Passing score: Published as Satisfactorio or Insatisfactorio, with no numeric pass mark published for either specific test. The 61/100 minimum in artículo 35 del Reglamento del SUN governs the Pruebas de Conocimientos Básicos and the 61-point minimum in artículo 50 governs PAP promotion; neither applies to the Pruebas Específicas.
Assessment: Two faculty tests that must both be passed: Prueba Específica de Matemática para Ingeniería, covering the seven published temas (real numbers; fundamentals of algebra; equations and inequalities; functions and graphs; analytic geometry; geometry; trigonometry), and Prueba Específica de Computación, covering the four published areas (Internet, Windows 10, Word and Excel) in 20 objective multiple-choice items. Both are assigned separately on the FIUSAC aspirantes portal and, in the current cycle, sat online through Safe Exam Browser.
Time limit: Computación: 20 minutes maximum (FIUSAC guía temática). Matemática: not published by FIUSAC. The two tests are sat as separate sessions.
Exam / certification fees: Q0.00. Artículo 55 del Reglamento del SUN prohibits any charge for the Pruebas Específicas; only the USAC-wide Orientación Vocacional test (Q70.00) is paid. Official sources

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USAC Ingeniería Específica: Suggested Study Strategy

1Work through the seven published mathematics temas in order; the faculty's own bibliography points to CONAMAT Aritmética y Álgebra, Stewart's Precálculo, Lehmann's Álgebra and the faculty's own 'Geometría de Precálculo' by Ing. Miguel Castillo.

2Drill algebraic manipulation hardest: special products, the binomial theorem, factoring, the remainder and factor theorems, and simplifying algebraic fractions carry more of the syllabus than any other single tema.

3Practise quadratics both by factoring and by formula, and use the discriminant to predict whether the roots are real - tema 3 restricts the test to quadratics with real roots.

4For analytic geometry, be fluent with distance, midpoint, slope, the parallel and perpendicular conditions, the equation of a circle and the parabola in standard form; those six items are the whole of tema 5.

5Trigonometry stops at right triangles and the unit circle: memorise the 30-45-60 ratios, convert confidently between degrees and radians, and solve right-triangle problems. The laws of sines and cosines are not in the published tema.

6Rehearse Computación against the clock. Twenty items in twenty minutes leaves a minute per question, so recognition has to be instant.

7Know the Excel material precisely: relative versus absolute references (A1 against $A$1), operator precedence, SUM, AVERAGE, COUNT, COUNTA and IF, conditional formatting, sorting and filtering, and chart choice.

8For Word, concentrate on page setup, sections and headers/footers, tables, heading styles and automatic tables of contents, and picture text wrapping - the formatting tasks a technical report actually needs.

Frequently Asked Questions

What is the USAC Ingeniería Prueba Específica?

It is the faculty admission assessment of the Facultad de Ingeniería at the Universidad de San Carlos de Guatemala. USAC lists it as 'Matemática para ingeniería y Computación', and it is two separate tests: a candidate must obtain Satisfactorio on both before being assigned to any engineering degree programme.

Which basic tests (PCB) are required before the FIUSAC specific tests?

A Satisfactorio result on the centralised Pruebas de Conocimientos Básicos in Lenguaje and Física, administered by the Sistema de Ubicación y Nivelación (SUN), plus a valid Tarjeta de Orientación Vocacional (NOV). The FIUSAC assignment system validates both automatically from the NOV number.

How many questions and how much time does the real assessment allow?

FIUSAC publishes this for the Computación test only: 20 objective multiple-choice questions with a maximum duration of 20 minutes. For Matemática it publishes a seven-tema syllabus and a recommended bibliography but no item count, item format or time limit. This 100-question bank is an independent study aid covering both syllabuses in depth, not a replica of either test.

What is the passing score for the FIUSAC specific tests?

Results are published as Satisfactorio or Insatisfactorio, and FIUSAC publishes no numeric pass mark for either test. The 61-out-of-100 minimum people often quote comes from artículo 35 del Reglamento del SUN, which governs the Pruebas de Conocimientos Básicos, and from artículo 50, which governs promotion in the Programa Académico Preparatorio - neither applies to the Pruebas Específicas.

How much do the Pruebas Específicas cost?

Nothing. Artículo 55 del Reglamento del Sistema de Ubicación y Nivelación prohibits any charge for the Pruebas de Conocimientos Básicos and the Pruebas Específicas, including the materials required to sit them. The only paid step in the whole admission process is the Orientación Vocacional test, which costs Q70.00.

How long is a result valid, and how many attempts are there?

Under artículo 43 del Reglamento del SUN a Prueba Específica result is valid for two years from the date of publication. FIUSAC programmes four opportunities per admissions cycle and passing one is enough; because the two tests are tracked separately, a candidate who passes only one re-sits just the other. An Insatisfactorio result also opens the Programa Académico Preparatorio route, which FIUSAC recognises as the equivalence for Matemática, with SAE/SAP as the equivalence for Computación.

What equipment do I need for the virtual sitting?

FIUSAC delivers the specific tests through Safe Exam Browser, which requires Windows 10 or 11, a stable internet connection and working webcam, microphone and speakers. Headphones are not permitted, and since the fourth test for 2022 entry a Junta Directiva resolution (punto sexto, acta 25-21) also requires a second camera. Old SEB builds must be uninstalled before the current configuration file will run.

Is this practice question bank an official USAC examination?

No. The official tests are set and sat in Spanish by the Facultad de Ingeniería. This bank is an original English-language MCQ study adaptation written by OpenExamPrep against the faculty's published temario. It keeps the official Spanish names and interface terms, but it is not an official test, an official translation, or a simulation of the real item formats - in particular, FIUSAC does not publish the Matemática test as four-option multiple choice.