Probability

ENEM 2021 – Solved mathematics: questions 166 to 180

Source: INEP – proof and template of the 2nd day, Notebook 5 – Yellow (1st application). The ENEM Mathematics and Technologies test 2021 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 Percentage increase C 167 Histogram and accumulated frequency C 168 Caesar cipher and letter frequency C 169 Statistics: median C 170 Percentage: reservoir volume D 171 Weighted average D 172 Weighted average and linear system C 173 Coefficient of variation E 174 Comparison of means E 175 Weighted average: monthly revenue B 176 Algebraic expression with percentage A 177 Probability of the complementary event B 178 Combinatorial analysis (cancelled) Canceled 179 Powers of the golden ratio E 180 Orthogonal projection of the cube E Question 166: Increase in sales of antidepressants Statement Depression is characterized by an imbalance in brain chemistry. The Neurons in a depressed person do not respond well to stimuli from neurotransmitters. Medicines that combat depression aim to restore brain chemistry. With the gradual increase in cases of depression, the sale of these medicines is increasingly evolving, as illustrated by the graphic.

September 26, 2026 Read

ENEM 2022 – Solved mathematics: questions 151 to 165

Source: INEP – proof and template of the 2nd day, Notebook 5 – Yellow (1st application). The ENEM Mathematics and Technologies test 2022 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 Graph reading and 2nd degree equation E 152 Odds: World Series C 153 Median from bar chart D 154 Proportion: game pack E 155 Linear system and maximization E 156 Proportionality and percentage C 157 Multiplicative principle B 158 Cube planning D 159 Checksum: remainder of division C 160 Scale A 161 Counting days in a tournament B 162 Odds: bingo E 163 Folding and symmetry C 164 Arithmetic mean B 165 Orthogonal projection onto the sphere E Question 151: How many times does the piston speed cancel out Statement A machine in operation has its temperature T monitored using a graphic record over time t. This machine has a piston whose speed V varies with the temperature T of the machine, according to the expression $V = T^2 - 4$. After the machine works during the time interval of 10 hours, its operator analyzes the graphic record, shown in the figure, to assess the need for possible adjustments, knowing that the machine malfunctions when the piston speed drops.

September 26, 2026 Read

ENEM 2023 – Solved mathematics: questions 136 to 150

Source: INEP – proof and template of the 2nd day, Notebook 5 – Yellow. The ENEM Mathematics and Technologies test 2023 was administered on the 2nd day and will from question 136 to 180. This post addresses questions 136 to 150. 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 136 Proportion and rounding up D 137 Trigonometry in the right triangle C 138 Scale E 139 Tables: caloric expenditure C 140 Discount proportion and percentage A 141 Conversion between calendars C 142 Pythagoras and the law of cosines: areas of circles C 143 Units of measurement B 144 Arithmetic progressions: sales comparison D 145 Statistics: mean, median and mode E 146 Cylinder flow and volume C 147 Capable arc (inscribed angle) B 148 Magic triangle and arithmetic progression E 149 Probability with weights E 150 Cylinder volume and water consumption A Question 136: Packets of bread for the walk (proportion) Statement Some studies prove that carbohydrates provide the body with energy, preserve the structural proteins of muscles during activity physics and also give strength to the brain to coordinate movements, which in fact has a positive impact on the practitioner’s development. The ideal is to consume 1 grams of carbohydrates for every minute of walking.

September 26, 2026 Read

ENEM 2023 – Solved mathematics: questions 151 to 165

Source: INEP – proof and template of the 2nd day, Notebook 5 – Yellow. The ENEM Mathematics and Technologies test 2023 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 Percentage: daycare waiting list B 152 Sequences: pentagonal numbers E 153 Periodic functions: Ferris wheel A 154 Scatter and percentage plot B 155 Profit, revenue and cost D 156 Exponential growth D 157 Multiplicative principle and probability A 158 Conditional probability in steps A 159 Geometric progression D 160 Quadratic function: minimum value D 161 Percentage and algebraic expression A 162 Graph reading (parametric curve) B 163 Logarithms: sound level in decibels B 164 Volume of cone, frustum and cylinder B 165 Weighted average C Question 151: New rooms for the daycare center (percentage) Statement In January last year, the management of a factory opened a daycare center for children of its employees, with 10 rooms, each with the capacity to serve 10 children each year. Vacancies are drawn among employees’ children. registered, while those not included in the draw form a waiting list. Last year, the waiting list had 400 names, and this year, that number grew 10%.

September 26, 2026 Read

ENEM 2023 – Solved mathematics: questions 166 to 180

Source: INEP – proof and template of the 2nd day, Notebook 5 – Yellow. The ENEM Mathematics and Technologies test 2023 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 Probability of independent events C 167 Cumulative Volume Chart B 168 Numbering systems (base 2) C 169 Average of consecutive months C 170 Compound interest in installments D 171 Affine function D 172 Distance × time and trajectory graph A 173 Waiting time in line E 174 Circular sector B 175 Area of squares D 176 Graph reading A 177 Bar graph reading Canceled 178 Covering area of a staircase E 179 Location on map E 180 System of 1st degree equations B Question 166: White dots in the voucher urn (probability) Statement Aiming to attract more customers, the manager of a store announced a promotion in which each customer who makes a purchase can win a voucher to be used on your next purchase. To win your voucher, the customer needs to withdraw, at the by chance, a small ball from each of the two urns A and B made available by the manager, in which there are only black and white dots. Currently, the The probability of choosing, at random, a black ball from urn A is equal to 20% and the probability of choosing a black ball in urn B is 25%. Win the The customer who removes two black balls, one from each urn, will receive a voucher.

September 26, 2026 Read

ENEM 2024 – Solved mathematics: questions 136 to 150

Source: INEP – proof and template of the 2nd day, Notebook 5 – Yellow. The ENEM Mathematics and Technologies test 2024 was administered on the 2nd day and will from question 136 to 180. This post addresses questions 136 to 150. 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 136 Related function: production cost C 137 Statistics: median E 138 Proportional division C 139 Combinatorial analysis: combinations E 140 Probability of independent events B 141 Reason: demographic density E 142 Fractions and mixed numbers D 143 Increasing plots (logical reasoning) A 144 Arc length: pulleys and belt D 145 equilateral triangle: circumcenter C 146 Graph Reading: Sine Amplitude A 147 Areas of regular polygons A 148 Speed and furniture finding D 149 Probability without replacement E 150 Logarithm: Richter scale C Question 136: Cost of producing backpacks (related function) Statement A company produces custom school backpacks. This company has a cost total production, composed of a fixed cost, which does not depend on the number of backpacks, plus a variable cost, which is proportional to the number of backpacks produced. The total cost grows linearly, and the table shows this cost for three quantities of backpacks produced.

September 26, 2026 Read

ENEM 2025 – Solved mathematics: questions 136 to 150

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 136 to 150. 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 136 Circumference length C 137 Percentage: solution concentration E 138 Reasoning problem: discarded volume C 139 Statistics: median C 140 Multiplication and comparison A 141 Spatial geometry: faces of a polyhedron D 142 Graph reading D 143 Operations with decimals B 144 Spatial geometry: orthogonal projections E 145 Probability B 146 Reason and consumption C 147 Analytical geometry: perpendicular bisector A 148 Bar and line graph reading C 149 Percentage and graphs E 150 Scale C Question 136: Police on the bike path (length of circumference) Statement Around a circular lagoon, whose radius measures 1 km, there is a cycle path. Due to frequent bicycle thefts, the city hall plans to allocate police officers in strategic positions to patrol this cycle path, in order to make it fully protected. A point on the cycle path is considered protected if there is at least one police officer at most 200 m away from that point, positioned over the cycle path. The figure illustrates a point $P$ on the cycle path, that will be protected if there is at least one police officer positioned over the dark gray region.

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 – 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 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 – 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 – 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