Entrance Exam

ENEM 2025 – Solved mathematics: questions 151 to 165

Source: INEP – proof and template of the 2nd day, Notebook 5 – Yellow. The ENEM Mathematics and Technologies test 2025 was administered on the 2nd day and will from question 136 to 180. This post addresses questions 151 to 165. The numbering used here is that of the Notebook 5 – Yellow; us In other notebooks the same questions appear in a different order. Template Question Subject Template 151 Polyhedra: number of vertices B 152 Proportionality: production D 153 Numeric code (rules reading) D 154 Probability: permutations D 155 Reading charts: bars and sectors B 156 Trigonometry: law of cosines and directions A 157 Statistics: mean and standard deviation D 158 Average (running pace) E 159 Tangent function: period and displacement E 160 Mesh localization (orientation) A 161 Percentage and inequality of the 1st degree B 162 Combinatorial analysis: multiplicative principle B 163 Scale E 164 Reason C 165 Percentage: cost and profit C Question 151: Vertices of the gyroelongated pentagonal dome Statement The gyroelongated pentagonal dome is a Johnson polyhedron, whose faces are regular polygons, but it is not a polyhedron of Plato, Archimedes, prism or antiprism.

September 26, 2026 Read

ENEM 2025 – Solved mathematics: questions 166 to 180

Source: INEP – proof and template of the 2nd day, Notebook 5 – Yellow. The ENEM Mathematics and Technologies test 2025 was administered on the 2nd day and will from question 136 to 180. This post addresses questions 166 to 180. The numbering used here is that of the Notebook 5 – Yellow; us In other notebooks the same questions appear in a different order. Template Question Subject Template 166 Volume Units D 167 Agricultural production and line graph A 168 Volume: cylinder minus prism B 169 Probability with data E 170 Units of measurement A 171 Sequences: expression of the general term D 172 Chart reading and fuel cost D 173 Cost Comparison E 174 Volume of the parallelepiped B 175 Spatial geometry: cylinder in prism E 176 Logarithm and quadratic function A 177 Area of the semicircle A 178 Equation: installments of financing Canceled 179 Combinatorial analysis: combinations C 180 Average speed C Question 166: Ice cream cups (volume units) Statement The owner of an ice cream shop stores ice cream in 20 000 cm³ containers. He serves the ice cream in cups, in portions of 250 mL.

September 26, 2026 Read

FUVEST 2022 – 1st phase: Mathematics solved

Source: FUVEST – General Knowledge test, version V and rectified official template of the 1st phase (applied in 12/12/2021). The 1st phase of FUVEST 2022 had 90 questions from all subjects. This post brings the 12 mathematics questions, which in test V are questions 30 to 41. In the others versions (K, Q, X and Z) the same questions appear with different numbering and another order of alternatives, so always check the version of your test.

September 26, 2026 Read

FUVEST 2022 – 2nd phase: Mathematics solved

Source: FUVEST – 2nd phase test, 2nd day (notebook with all the questions of the day), questions M01 to M06. FUVEST does not publish a template for the 2nd phase; the resolutions are ours. On the 2nd day of the 2nd phase of FUVEST 2022 each candidate received 12 discursive questions of the specific disciplines of your career. Mathematics had 6 questions (M01 to M06). Those who only did 4 math questions received M01 to M04; who only did 3, M01 to M03. Each resolution below was checked by a second path (another method or account on the computer).

September 26, 2026 Read

FUVEST 2023 – 1st phase: Mathematics solved

Source: FUVEST – proof (version V) and official answer key of the 1st phase (General Knowledge Test, applied in 04/12/2022). The 1st phase of FUVEST 2023 had 90 questions from all subjects. This post brings the mathematics questions: 21, 22, 24, 36, 58 and 84 to 90. The numbering is that of Proof V; in other versions (K, Q, X and Z) the same questions appear in another order. The question 58 is interdisciplinary (CO₂ emissions), but is resolved with graph reading and area estimation, that’s why it’s here.

September 26, 2026 Read

FUVEST 2023 – 2nd phase: Mathematics solved

Source: FUVEST – 2nd phase test, 2nd day (questions M01 to M06) and document expected approaches. The 2nd phase of FUVEST 2023 lasted two days. The 1st day was Portuguese and Writing; in 2nd day, the test had 6 questions from each subject, and Mathematics goes from M01 to M06. Each candidate answered only the subjects of their career (in some careers, only the first questions of each subject). FUVEST does not publish a template for the 2nd phase; the resolutions are ours. She disclosed an “expected approaches” document with the path expected of the candidates. Each resolution below was checked by a second path and compared to this document.

September 26, 2026 Read

FUVEST 2024 – 1st phase: Mathematics solved

Source: FUVEST – test of the 1st phase, version V and official template (rectified in 24/11/2023), available in the FUVEST collection 2024. The 1st phase of FUVEST 2024 (General Knowledge Test, 19/11/2023) had 90 questions from all disciplines. This post only contains 12 math questions. The numbering used here is that of Proof V; In versions K, Q, X and Z the same questions appear with other numbers. Template Question Subject Template 13 Matrices: product and social network B 31 Volume of cylinder and circular segment B 33 Percentage: cost variation A 34 Statistics: mode, median, mean and range A 35 Count: digital clock reflected B 48 Cobblestone Packaging D or E (both accepted) 49 Parallelogram and trigonometry C 59 Exponential and logarithmic function (inverse) D 60 Linear system and line graph E 63 Pythagorean Tree: geometric progression and logarithm C 84 Graph Reading: Homicide Rates E 85 Triangular and oblong numbers D Question 13: Matrices and connections in a social network Statement Matrices can be used to obtain information about a social network. To understand how this can be done, let’s consider as an example a small social network made up of 4 people: $P_1, P_2, P_3, P_4$. The matrix associated with this social network is the matrix $4 \times 4$:

September 26, 2026 Read

FUVEST 2024 – 2nd phase: Mathematics solved

Here are the resolutions for M01 to M06, with the reasoning for each item and verification of the results. Use the official notebook, 2nd day to consult the statements and drawings; Below we only return the data necessary for the calculations. The explanations are copyright. The checking of answers uses the official FUVEST guide, pages 40 to 48, available in the collection of 2024. M02 requires attention: the printed data is inconsistent and the guide accepts different approaches.

September 26, 2026 Read

FUVEST 2025 – 1st phase: Mathematics solved

Source: FUVEST – General Knowledge test, version V1 and official answer key from the 1st phase (17/11/2024), available in the FUVEST collection 2025. The 1st phase of FUVEST 2025 was a General Knowledge test with 90 questions from all disciplines. This post only covers mathematics questions. The numbering used here is that of Proof V1; in versions V2, V3 and V4 the same issues appear with other numbers. Template Question Subject Template 16 Percentage: slope of ramps C 17 Distance between points on the plane C 45 Arithmetic mean E 48 Graph reading and percentage D 52 Cosine function: graph transformation D 69 Modular function and parabolas B 70 Arithmetic progression A 75 Cone Trunk Volume A 76 Volume and lateral area of cylinders D 77 Relative position of circles E Question 16: Slope of an accessible ramp (percentage) Statement The construction of a ramp that is accessible to wheelchair users must follow the ABNT NBR 9050 standard. This document regulates the inclination that the ramp must depend on the maximum difference in level of each ramp segment, according to the following table:

September 26, 2026 Read

FUVEST 2025 – 2nd phase: Mathematics solved

Source: FUVEST – 2nd phase test, 2nd day (questions M01 to M06), available in the FUVEST collection 2025. The 2nd phase of FUVEST 2025 had, on the 2nd day, specific discursive questions for career; The Mathematics test has six questions, M01 to M06. Each candidate solved only the subjects of your career (the six questions, or just the four or first three). The 2nd phase does not have a multiple choice answer sheet: FUVEST published a Answer Guide with the answers expected by the panel. The resolutions below are ours, and each The result was checked with this guide and through a second path.

September 26, 2026 Read

FUVEST 2026 – 1st phase: Mathematics solved

Source: FUVEST – test V1 and template of the General Knowledge Test (1st phase), applied in 23/11/2025. Files in FUVEST collection 2026. The 1st phase of FUVEST 2026 had 90 multiple choice questions from all disciplines. This post brings mathematics questions. The numbering used here is that of Proof V1; in versions V2, V3 and V4 the same issues appear in another order (the official template includes the correspondence table). Template Question Subject Template 3 Logical reasoning: election with tiebreaker Canceled 4 Logarithms: Shannon entropy A 6 Spatial geometry: regular pyramid E 7 Trigonometry: double arc equation D 18 Exponential function and logarithms E 30 Spatial geometry: cylinder volume B 36 Trigonometry in the right triangle E 37 Analytical geometry: circle equation A 55 Perfect numbers, primes and progressions B 74 Function graph transformations D Question 3: How many votes guarantee the election? Question canceled by FUVEST. In the official answer sheet, question 3 from Test V1 appears with an asterisk (nullified). FUVEST did not disclose the reason for the cancellation.

September 26, 2026 Read

FUVEST 2026 – 2nd phase: Mathematics solved

Source: FUVEST – test on the 2nd day of the 2nd phase (specific tests; Mathematics has questions M01 to M06) and expected Mathematics answers. Files in the FUVEST collection 2026. In the 2nd phase of FUVEST 2026, the 2nd day consisted of specific essay tests for each area; The Mathematics test has six questions, M01 to M06, each with items a), b) and c). For this test, FUVEST published the expected answers; the resolutions below are ours, we checked each one in a second way and all match the official expected answers.

September 26, 2026 Read