Entrance Exam

ENEM 2024 – Solved mathematics: questions 151 to 165

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 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 Cylinder volume D 152 Affine function: trend line B 153 Reading Charts: Tank Filling B 154 Statistics: arithmetic mean C 155 Circular sector area E 156 Related function: price modeling B 157 Flow and percentage D 158 Proportional quantities: units C 159 Cost optimization C 160 1st degree equation C 161 Bar chart and percentage A 162 Orthogonal projection C 163 Scales and magnification A 164 Arithmetic mean B 165 Fundamental counting principle B Question 151: Larger volume of cylindrical packaging Statement An industry forms a partnership with a juice distributor to launch market two types of packaging. To manufacture these packaging, the industry has rectangular aluminum sheets, with dimensions 10 cm per 20 cm. Each of these sheets is used to form the lateral surface of the packaging, in the shape of a straight circular cylinder, which subsequently receives circular bottom and lid. The figure illustrates, depending on which of the two extensions will be used as height, the two options to form the possible packaging.

September 27, 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 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 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 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 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 2022 – Solved mathematics: questions 136 to 150

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 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 Percentage and weighted average of salaries D 137 Ratio and time unit conversion B 138 Ratio between time units A 139 Distance × time graph reading A 140 Percentage increases and discounts A 141 Guidance and mesh paths C 142 Cylinder volume E 143 Ratio between quantities in graphs B 144 Big numbers: billion E 145 Shortest path: reflection and similarity D 146 Cost Comparison A 147 Sphere volume and proportion E 148 Cone volume and percentage C 149 Percentage: 75% drop C 150 Combinatorial analysis: combinations B Question 136: Salary increase and average salary (percentage) Statement At a university, professors work who are functionally for your highest degree: master or doctor. There are currently 60 masters and 40 doctors. The monthly salaries of master teachers and doctors are, respectively, R$ 8 000,00 and R$ 12 000,00.

September 26, 2026 Read

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 2021 – 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 2021 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 Fuel performance (km/L) D 152 Areas of a parallelepiped B 153 Cylinder volume D 154 Graph of piecewise defined function A 155 Quadratic function with integer domain E 156 Matrices: reading the elements E 157 Successive percentage changes B 158 Inversely proportional quantities A 159 Optimization: lower cost D 160 Percentage: quantity reduction C 161 Trigonometric function: spring movement A 162 Definite operations and 2nd degree equation E 163 Scale C 164 Projection and ratio per thousand inhabitants D 165 Chart Reading: Monthly Profit B Question 151: Performance of the new engine Statement A car has an average performance of 16 km/L. An engineer developed a new combustion engine that saves, in relation to fuel consumption, previous engine, 0,1 L of fuel for every 20 km travelled.

September 26, 2026 Read

ENEM 2021 – Solved mathematics: questions 136 to 150

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 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 Roman numeral system D 137 Addition in binary base D 138 Area and subdivision units C 139 Combinatorial analysis: combinations A 140 Cost per user (comparison) B 141 Percentage: heart rate D 142 Fewer number of washes (inequality) C 143 Discounts: lower expense C 144 Spatial geometry: faces of the structure A 145 Octahedron flattening E 146 Perimeter of equilateral triangle D 147 Volume of the cone frustum C 148 Areas of flat figures and cost E 149 Dimensional analysis B 150 Linear system: baggage mass B Question 136: Year of foundation in Roman numerals Statement The Roman numeral system is still used to indicate chapters and volumes of books, in the designation of centuries and, in chronological order, of popes and kings of the same name. Seven letters of the alphabet are used:

September 26, 2026 Read

FUVEST 2021 – 2nd phase: Mathematics solved

Source: FUVEST 2021, 2nd phase, 2nd day (Mathematics test), questions M01 to M05. Official proof available in the FUVEST collection. FUVEST does not publish a template for the 2nd phase; The resolutions below are ours. Question 1: Parking Surveillance A rectangular parking lot has dimensions of 40 m by 100 m, where security cameras have been installed that cover specific areas. The problem involves calculating areas and percentages. The owner installed 4 security cameras distributed as shown in the figure. The cameras cover the following regions:

October 3, 2022 Read