The Enem math test (Mathematics and its technologies) is the only test that presents an isolated subject, which makes it the biggest individual weight in the competition.
The test questions are objective, with 5 answer alternatives, present contextualized statements and demand a global knowledge of the student.
Contents that fall the most on the math test
See the most charged Mathematics content on Enem in the last 9 years:
1. proportional quantities
Proportional quantities, which encompass the contents of reason and proportion, rule of three, percentage and scales, is what most appears in questions of Mathematics.
The fact that this content is applied in the most varied situations of daily life, makes it much explored in Enem.
This type of calculation can appear in questions that directly cover the relationship between quantities or in problems where this calculation is used in one of the steps of its resolution.
Example
(Enem - 2017) At 5:15 pm a heavy rain begins, falling with constant intensity. A swimming pool in the shape of a rectangular parallelepiped, which was initially empty, begins to accumulate rainwater and, at 6 pm, the water level inside it reaches 20 cm in height. At that moment, the valve that releases the flow of water through a drain located at the bottom of this pool, whose flow is constant, is opened. At 6:40 pm, the rain stops and, at that exact moment, the water level in the pool dropped to 15 cm.
The moment when the water in this pool finishes draining completely is between
a) 19 h 30 min and 20 h 10 min
b) 19 h 20 min and 19 h 30 min
c) 19 h 10 min and 19 h 20 min
d) 7 pm and 7 pm 10 min
e) 18 h 40 min and 19 h
Alternative: d) 7 pm and 7 pm 10 min
2. Statistics, graphs and tables
Calculation of average, mode and median are the contents of statistic that appear most in the Mathematics test. In addition, questions involving the interpretation of graphics (statistical or not) and tables are very recurrent.
By the way, the graphics are not only present in the Mathematics test. but also from other disciplines such as Physics, Geography, Biology and Chemistry.
In the Mathematics test, the interpretation of the graph is often just one step in solving the question, and it is necessary to apply other knowledge.
Example
(Enem - 2017) Two reservoirs A and B are fed by separate pumps for a period of 20 h. The amount of water contained in each reservoir during this period can be seen in the figure.
The number of hours the two reservoirs contain the same amount of water is
to 1.
b) 2.
c) 4.
d) 5.
e) 6.
Alternative: a) 1
3. Arithmetic
Questions with simple calculations involving fractions or decimal numbers, problems related to the counting principle also appear frequently.
Example
(Enem - 2017) In a park there are two viewpoints of different heights that are accessed by a panoramic elevator. The top of lookout 1 is accessed by elevator 1, while the top of lookout 2 is accessed by elevator 2. They are within walking distance, and between the lookouts there is a cable car that connects them, which may or may not be used by the visitor.
Access to elevators has the following costs:
- Go up by elevator 1: R$ 0.15;
- Go up by elevator 2: R$ 1.80;
- Go down by elevator 1: R$ 0.10;
- Go down by elevator 2: R$ 2.30.
The cost of a cable car ticket from the top of the lookout point 1 to the top of the lookout point 2 is R$2.00, and from the top of the lookout point 2 to the top of the lookout point 1 is R$2.50.
What is the lowest cost, in real terms, for a person to visit the tops of the two viewpoints and return to the ground?
a) 2.25
b) 3.90
c) 4.35
d) 4.40
e) 4.45
Alternative: c) 4.35
4. Plane and Spatial Geometry
know how to calculate the area of main flat figures it's the volume of geometric solids it is very important, as this content appears frequently in the test.
In addition, issues involving a spatial vision, planning, Pythagorean theorem and calculation of perimeter.
Example
(Enem - 2017) A waiter needs to choose a rectangular base tray to serve four glasses of sparkling wine that need to be arranged in a single row, parallel to the longest side of the tray, and with their bases fully supported on the tray. The base and top edge of the bowls are circles with a radius of 4 cm and 5 cm, respectively.
The tray to be chosen must have a minimum area, in square centimeters, equal to
a) 192.
b) 300.
c) 304.
d) 320.
e) 400.
Alternative: c) 304
5. Roles
In the test it is often charged affine function, quadratic function, exponential function and logarithmic function, in addition to the law of formation of a function and its graph.
Example
(Enem - 2017) To carry out the dream trip, a person needed to take out a loan in the amount of R$5,000.00. To pay the installments, you have a maximum of R$ 400.00 per month. For this loan amount, the installment amount (P) is calculated as a function of the number of installments (n) according to the formula
If necessary, use 0.005 as the approximation for log 1.013; 2.602 as an approximation for log 400; 2.525 as an approximation to log 335.
According to the given formula, the smallest number of installments whose values do not compromise the limit set by the person is by the person is
a) 12.
b) 14.
c) 15.
d) 16.
e) 17.
Alternative: d) 16
For more role exercises, see also:
- Related Function Exercises
- Quadratic Function - Exercises
- Exponential Function - Exercises
- Logarithm - Exercises
6. Probability
For this content it is not enough just to know the formulas of probability, it is essential to know how to apply them within the context proposed in the statement.
Example
(Enem - 2017) A resident of the metropolitan region has a 50% probability of being late for work when it rains in the region; if it doesn't rain, your probability of delay is 25%. For a given day, the meteorology service estimates the probability of rain in that region at 30%.
What is the probability that this resident will be late for work on the day for which the rainfall estimate was given?
a) 0.075
b) 0.150
c) 0.325
d) 0.600
e) 0.800
Alternative: c) 0.325
Math Quiz Enem
Tips for doing well on the math test
The Mathematics test is made up of questions of different difficulty levels and it is obvious that the more questions the student solves without "judging" the better.
Thus, the ideal is make the easiest questions first. Thus, the student will ensure that he will not miss these questions because he did not have time to ask them.
The questions, being contextualized, are usually very extensive. So a tip is underline the most important information, this way you avoid reading the same question several times.
Graphs, tables and infographics appear very frequently in the exam. Oftentimes, the correct interpretation of these resources is enough to get the question right.
So, before jumping to conclusions, observe the quantities involved by looking at the axes, identify the scales and units used, and see their title. All of this can make a big difference in this type of question.
As the test has many questions and little time for their resolution, the student should, whenever possible, simplify the calculations.
To gain precious minutes you can, for example, apply notable products in enhancements, do approximations, estimates and mental calculation, replace very large numbers by powers of 10 and simplify fractions.
Also read about:
- How to study for Enem
- Enem study plan
How to prepare to do well on the Mathematics test
For starters, make peace with this matter. Many students have a very bad relationship with Mathematics and end up believing that they will never be able to perform well in this subject.
Having this belief will only make your learning difficult and therefore, let yourself be involved with the charms of numbers! Trust me, you can actually learn math and you still run the risk of enjoying it.
To do this, start preparing by reviewing the contents of elementary school. These contents, in addition to being the basis for learning, are also charged at Enem.
Make it a habit to solve the exercises without using the calculator. Its use in the test is not allowed and without knowing how to perform the fundamental operations it will be very difficult to perform well.
Also, try to learn techniques that make the accounts easier, because time has a great weight in this test.
A good suggestion is to write down how many minutes it takes to do each question and always try to do it in less time.
The starting point for solving a Mathematics question is the interpretation. Mainly in Enem, where the questions are contextualized, understanding the utterance is fundamental.
In this way, reading texts on a wide range of topics every day, not just Mathematics, can help improve reading and interpretation.
And last but not least, do exercises. Try to familiarize yourself with the format of the Enem questions, solving tests from previous years.
Try to resolve the issues yourself first. If you can't solve it, don't look at the template right away. Try again after a while, being persevering is key.
As you get right the questions you ask yourself, you'll gain more confidence and enjoy learning math more, I guarantee.
Also read about:
- Subjects that most fall in Enem
- Mathematics Questions in Enem
- Enem questions
- Simulated Enem (questions commented by experts)
- Note from Enem
- Podcasts to study
