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100+ Free TEC Admisión Practice Questions

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2026 Statistics

Key Facts: TEC Admisión Exam

60

Official Items (38 math + 22 verbal)

TEC Comité Examen de Admisión

150 min

Time Limit

TEC Indicaciones Generales 2026-2027

7,000 CRC

Registration Fee

TEC Examen de Admisión page

200–800

Score Scale

TEC Indicaciones Generales 2026-2027

The Examen de Admisión TEC — officially the Prueba de Aptitud Académica (PAA) of the Instituto Tecnológico de Costa Rica — is built and applied by TEC's Comité Examen de Admisión (CEA). It consists of exactly 38 mathematics items and 22 verbal reasoning items (60 in total), answered on paper with a pencil in a maximum of 2 hours 30 minutes, with no calculators or electronic devices allowed. There is no pass mark: the exam score (60%) and the Educación Diversificada average (40%) are combined on a 0–100 scale, standardized to a 200–800 puntaje de admisión, and ranked against per-career cut scores. The official test is in Spanish; this bank provides an English-language MCQ study adaptation.

Sample TEC Admisión Practice Questions

Try these sample questions to test your TEC Admisión exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1A digital circuit processes two input signals A and B. The output signal is given by the function f(A, B) = 3A^2 - 2AB + B^2. If A = 4 and B = -2, what is the output value of the circuit?
A.68
B.52
C.60
D.44
Explanation: Substitute A = 4 and B = -2 into the algebraic expression: f(4, -2) = 3(4^2) - 2(4)(-2) + (-2)^2 = 3(16) - 2(-8) + 4 = 48 - (-16) + 4 = 48 + 16 + 4 = 68.
2A solid rectangular metal prism measures 12 cm by 8 cm by 6 cm. It is melted down and recast into identical solid cubes of side length 2 cm. Assuming no metal is lost in the melting process, how many cubes are formed?
A.72
B.48
C.96
D.36
Explanation: Volume of the rectangular prism = length * width * height = 12 * 8 * 6 = 576 cm^3. Volume of one cube = side^3 = 2^3 = 8 cm^3. Number of cubes = Volume_prism / Volume_cube = 576 / 8 = 72 cubes.
3An engineering team tests two automated cutting lasers. Laser 1 cuts 15 meters of sheet metal in 4 minutes, while Laser 2 cuts 20 meters of sheet metal in 5 minutes. Working simultaneously, how many minutes will it take both lasers to cut a total of 155 meters of sheet metal?
A.20 minutes
B.22 minutes
C.18 minutes
D.25 minutes
Explanation: Rate of Laser 1 = 15 m / 4 min = 3.75 m/min. Rate of Laser 2 = 20 m / 5 min = 4.00 m/min. Combined cutting rate = 3.75 + 4.00 = 7.75 m/min (or 31/4 m/min). The time required to cut 155 meters is Time = 155 / 7.75 = 155 / (31/4) = (155 * 4) / 31 = 5 * 4 = 20 minutes.
4A right circular cylinder has height h and base radius r. If the radius is increased by 50% and the height is decreased by 20%, by what percentage does the volume of the cylinder change?
A.Increases by 80%
B.Increases by 30%
C.Increases by 60%
D.Decreases by 10%
Explanation: Original volume V_1 = pi * r^2 * h. New radius r_2 = 1.5r. New height h_2 = 0.8h. New volume V_2 = pi * (1.5r)^2 * (0.8h) = pi * (2.25r^2) * (0.8h) = 1.8 * pi * r^2 * h = 1.8 * V_1. The ratio V_2 / V_1 = 1.8, which represents an 80% increase.
5Consider the system of linear equations: 2x - 3y = 7 and 4x + ky = 14. For what value of the constant k does the system have infinitely many solutions?
A.-6
B.6
C.-3
D.12
Explanation: For a system of two linear equations a_1*x + b_1*y = c_1 and a_2*x + b_2*y = c_2 to have infinitely many solutions, the equations must be proportional: a_1 / a_2 = b_1 / b_2 = c_1 / c_2. Here: a_1 / a_2 = 2 / 4 = 1/2 and c_1 / c_2 = 7 / 14 = 1/2. Therefore, we must have b_1 / b_2 = -3 / k = 1/2. Cross-multiplying gives k = -3 * 2 = -6.
6A cube of wood with side length 6 cm has all six of its outer faces painted blue. The painted cube is then sliced into 216 identical small cubes of side length 1 cm. How many of these small cubes have exactly two painted faces?
A.48
B.64
C.24
D.36
Explanation: In an n x n x n cube sliced into 1 x 1 x 1 cubes: cubes with exactly two painted faces are located along the edges, excluding the corners. A cube has 12 edges. Along each edge of length n = 6, there are 2 corner cubes (which have 3 painted faces). The number of cubes with exactly two painted faces along each edge is n - 2 = 6 - 2 = 4 cubes. Since there are 12 edges: Total = 12 * (n - 2) = 12 * 4 = 48 cubes.
7If x^2 - 5x + 6 = 0 and y^2 - 7y + 12 = 0, what is the maximum possible value of the product x * y?
A.12
B.9
C.8
D.15
Explanation: Factor the first quadratic equation: x^2 - 5x + 6 = (x - 2)(x - 3) = 0, so the roots are x = 2 or x = 3. Factor the second quadratic equation: y^2 - 7y + 12 = (y - 3)(y - 4) = 0, so the roots are y = 3 or y = 4. The possible products x * y are: 2 * 3 = 6; 2 * 4 = 8; 3 * 3 = 9; and 3 * 4 = 12. The maximum possible value is 12.
8In how many distinct ways can 5 software developers and 3 data analysts be seated in a row of 8 chairs such that no two data analysts sit next to each other?
A.14,400
B.7,200
C.28,800
D.5,040
Explanation: First, seat the 5 software developers in a row. They can be arranged in 5! = 120 ways. These 5 developers create 6 potential spaces (gaps) for the data analysts to occupy (one at each end and 4 between developers): _ D _ D _ D _ D _ D _. To ensure no two analysts are adjacent, the 3 analysts must be placed into 3 of these 6 distinct spaces. The number of ways to choose and arrange the 3 analysts in these 6 spaces is the permutation P(6, 3) = 6 * 5 * 4 = 120. Total valid seating arrangements = 5! * P(6, 3) = 120 * 120 = 14,400.
9A circle is centered at the origin (0, 0) and has radius r = 5. A straight line passes through the points (0, 3) and (4, 0). What is the shortest distance from the origin to this line?
A.2.4
B.2.5
C.2.0
D.3.0
Explanation: The points (4, 0) and (0, 3) form a right triangle with the origin, where the legs along the axes are a = 4 and b = 3. The hypotenuse connecting the two points is c = sqrt(3^2 + 4^2) = sqrt(25) = 5. The shortest distance from the origin to the line is the altitude h to the hypotenuse in this right triangle. Using the area of the triangle: Area = (1/2) * 3 * 4 = 6. Alternatively, Area = (1/2) * hypotenuse * h = (1/2) * 5 * h. Setting the two equal: (5/2) * h = 6 => 5h = 12 => h = 12 / 5 = 2.4.
10The parabola y = x^2 + bx + c crosses the horizontal axis at exactly the two points (1, 0) and (5, 0). What is the value of b + c?
A.-1
B.11
C.1
D.-11
Explanation: The points where the parabola meets the horizontal axis are the roots of x^2 + bx + c = 0, so the roots are 1 and 5. For a monic quadratic, the sum of the roots equals -b and the product equals c. Sum: 1 + 5 = 6 = -b, so b = -6. Product: 1 * 5 = 5 = c. Therefore b + c = -6 + 5 = -1. (Check by expanding (x - 1)(x - 5) = x^2 - 6x + 5.)

About the TEC Admisión Exam

The Examen de Admisión del Instituto Tecnológico de Costa Rica (TEC) evaluates mathematical reasoning, spatial perception, and verbal analysis for candidates seeking admission into undergraduate science and engineering degrees.

Assessment

60 items (38 mathematics + 22 verbal reasoning), answered on an optical answer sheet in a single session of at most 150 minutes

Time Limit

150 minutes

Passing Score

No pass mark; TEC applies a nota de corte institucional (value not published) plus per-career cut scores on the 200–800 puntaje de admisión

Exam Fee

7,000 CRC (Instituto Tecnológico de Costa Rica (TEC))

TEC Admisión Exam Content Outline

38 of 60 items (63%)

Mathematical Reasoning (Razonamiento Matemático)

Arithmetic, algebraic systems, plane geometry, 3D spatial visualization, sequences, and combinatorics.

22 of 60 items (37%)

Verbal Reasoning (Razonamiento Verbal)

Scientific reading comprehension, deductive inference, semantic precision, and textual coherence.

How to Pass the TEC Admisión Exam

What You Need to Know

  • Passing score: No pass mark; TEC applies a nota de corte institucional (value not published) plus per-career cut scores on the 200–800 puntaje de admisión
  • Assessment: 60 items (38 mathematics + 22 verbal reasoning), answered on an optical answer sheet in a single session of at most 150 minutes
  • Time limit: 150 minutes
  • Exam fee: 7,000 CRC

Keys to Passing

  • Work through all 100 available questions
  • Review every answer and explanation
  • Track weak areas and revisit them
  • Use our AI tutor for tough concepts

TEC Admisión Study Tips from Top Performers

1Manage your time carefully: with 60 questions in 150 minutes, you have an average of 2.5 minutes per question.
2Practice 3D spatial visualization, such as determining front/top/side projections and folding cubes from flat nets.
3Review quadratic equations, exponent rules, logarithms, and Euclidean geometry theorems.
4Read technical and scientific prose carefully to extract warranted deductive conclusions without adding outside assumptions.

Frequently Asked Questions

What is the official format and duration of the TEC Admission Exam?

TEC's Comité Examen de Admisión states the Prueba de Aptitud Académica is composed of 38 mathematics items and 22 verbal reasoning items, 60 in total. Candidates have a maximum of 2 hours and 30 minutes, which includes filling in the optical answer sheet, and may bring only a pencil, eraser, sharpener and their ID.

How is the TEC admission score calculated?

TEC first computes N1 = 0.6 × exam score + 0.4 × Educación Diversificada average, both on a 0–100 scale. N1 is then standardized to a 200–800 scale with mean 500 and standard deviation 100. Finally the highest score of the year is set to 800 and every other score is adjusted proportionally, producing each applicant's puntaje de admisión.

Are calculators permitted during the TEC exam?

No. All calculators, smart devices, and phones are strictly banned during the examination. All quantitative, geometric, and spatial reasoning problems are engineered to be solved by hand.

What mathematical topics are emphasized on the TEC exam?

The TEC exam places strong emphasis on algebraic manipulation, linear and quadratic systems, coordinate and Euclidean geometry, 3D solids, spatial perception (orthographic projections and cube foldings), and deductive problem-solving.

Is this practice bank administered in Spanish like the official test?

No. The official exam is administered in Spanish by TEC. This practice bank provides an English-language MCQ study adaptation of the core quantitative, spatial, and analytical skills tested on the exam.