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2024 enem__day2

41 maths questions

Q136 Exponential Equations & Modelling Threshold or Tipping-Point Calculation in Applied Exponential Models View
A researcher analyzed the data on the number of new cases of a disease in a city over a period of 5 consecutive years and organized them in the table below.
YearNew cases
1200
2400
3800
41600
53200

Based on this data, the researcher modeled the number of new cases as a function of the year $x$ by the expression $f(x) = 100 \cdot 2^x$.
If this trend continues, in which year will the number of new cases first exceed 100,000?
(A) 9
(B) 10
(C) 11
(D) 12
(E) 13
Q137 Solving quadratics and applications Geometric or real-world application leading to a quadratic equation View
A company produces cylindrical cans to store food. The technical standard requires that the ratio between the height and the diameter of the base of the can must be equal to 2. A can that meets this standard has a volume of $V = 500\pi \text{ cm}^3$.
What is the height, in centimeters, of this can?
(A) 5
(B) 10
(C) 15
(D) 20
(E) 25
Q138 Measures of Location and Spread View
A survey was conducted with 200 students from a school to find out which type of music they prefer. The results are shown in the pie chart below.
Type of musicPercentage
Pop35\%
Rock25\%
Funk20\%
Sertanejo15\%
Other5\%

How many students prefer Pop or Rock?
(A) 60
(B) 80
(C) 100
(D) 120
(E) 140
Q139 Solving quadratics and applications Geometric or real-world application leading to a quadratic equation View
A person invests R\$\,2{,}000.00 in a savings account that yields 0.5\% per month in simple interest. After 12 months, this person withdraws all the money.
What is the total amount withdrawn, in reais?
(A) R\$\,2{,}100.00
(B) R\$\,2{,}110.00
(C) R\$\,2{,}120.00
(D) R\$\,2{,}130.00
(E) R\$\,2{,}140.00
Q140 Solving quadratics and applications Geometric or real-world application leading to a quadratic equation View
In a right triangle, the hypotenuse measures 10 cm and one of the legs measures 6 cm. What is the area, in square centimeters, of this triangle?
(A) 20
(B) 24
(C) 30
(D) 36
(E) 48
Q141 Travel graphs View
The graph below shows the distance traveled by a cyclist as a function of time.
Based on the graph, what is the average speed of the cyclist, in km/h?
(A) 10
(B) 15
(C) 20
(D) 25
(E) 30
Q142 Probability Definitions Finite Equally-Likely Probability Computation View
A box contains 5 red balls, 3 blue balls, and 2 green balls. One ball is drawn at random from the box.
What is the probability that the drawn ball is blue?
(A) $\dfrac{1}{10}$
(B) $\dfrac{1}{5}$
(C) $\dfrac{3}{10}$
(D) $\dfrac{2}{5}$
(E) $\dfrac{1}{2}$
Q143 Solving quadratics and applications Geometric or real-world application leading to a quadratic equation View
The sum of three consecutive even integers is 78. What is the largest of these integers?
(A) 24
(B) 26
(C) 28
(D) 30
(E) 32
Q144 Solving quadratics and applications Geometric or real-world application leading to a quadratic equation View
A rectangle has a perimeter of 36 cm and its length is twice its width. What is the area, in square centimeters, of this rectangle?
(A) 48
(B) 72
(C) 96
(D) 108
(E) 144
Q145 Roots of polynomials Vieta's formulas: compute symmetric functions of roots View
The function $f(x) = x^2 - 4x + 3$ has roots $x_1$ and $x_2$. What is the value of $x_1 + x_2$?
(A) $-4$
(B) $-3$
(C) $3$
(D) $4$
(E) $7$
Q146 Solving quadratics and applications Geometric or real-world application leading to a quadratic equation View
A store is offering a 20\% discount on all products. After the discount, a product costs R\$\,80.00. What was the original price of the product, in reais?
(A) R\$\,96.00
(B) R\$\,100.00
(C) R\$\,104.00
(D) R\$\,108.00
(E) R\$\,112.00
Q147 Arithmetic Sequences and Series Find Specific Term from Given Conditions View
In an arithmetic progression, the first term is 3 and the common difference is 4. What is the 10th term of this progression?
(A) 35
(B) 39
(C) 43
(D) 47
(E) 51
Q148 Solving quadratics and applications Geometric or real-world application leading to a quadratic equation View
A map uses a scale of 1:50,000. On the map, the distance between two cities is 8 cm. What is the real distance between the two cities, in kilometers?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
Q149 Measures of Location and Spread View
The mean of five numbers is 12. If four of the numbers are 8, 10, 14, and 16, what is the fifth number?
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
Q150 Geometric Sequences and Series Finite Geometric Sum and Term Relationships View
A geometric progression has first term 2 and common ratio 3. What is the sum of the first 4 terms?
(A) 60
(B) 70
(C) 80
(D) 90
(E) 100
Q151 Laws of Logarithms Solve a Logarithmic Equation View
The equation $\log_2(x+1) = 3$ has solution:
(A) $x = 6$
(B) $x = 7$
(C) $x = 8$
(D) $x = 9$
(E) $x = 10$
Q152 Sine and Cosine Rules Compute area of a triangle or related figure View
A triangle has sides measuring 5 cm, 12 cm, and 13 cm. What is the area, in square centimeters, of this triangle?
(A) 20
(B) 25
(C) 30
(D) 35
(E) 40
Q153 Principle of Inclusion/Exclusion View
In a class of 30 students, 18 study mathematics, 15 study physics, and 8 study both subjects. How many students study neither mathematics nor physics?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Q155 Composite & Inverse Functions Find or Apply an Inverse Function Formula View
A function $f$ is defined by $f(x) = 2x + 5$. What is the value of $f^{-1}(11)$?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Q156 Trig Graphs & Exact Values View
In a right triangle, $\sin(\theta) = \dfrac{3}{5}$. What is the value of $\cos(\theta)$?
(A) $\dfrac{1}{5}$
(B) $\dfrac{2}{5}$
(C) $\dfrac{3}{5}$
(D) $\dfrac{4}{5}$
(E) $\dfrac{5}{4}$
Q157 Permutations & Arrangements Linear Arrangement with Constraints View
How many ways can 4 people be arranged in a line?
(A) 8
(B) 12
(C) 16
(D) 20
(E) 24
Q158 Exponential Equations & Modelling Compound Interest and Financial Exponential Problems View
The compound interest on R\$\,1{,}000.00 at a rate of 10\% per year for 2 years is:
(A) R\$\,100.00
(B) R\$\,200.00
(C) R\$\,210.00
(D) R\$\,220.00
(E) R\$\,230.00
Q159 Matrices Determinant and Rank Computation View
The matrix $A = \begin{pmatrix} 2 & 1 \\ 3 & 4 \end{pmatrix}$ has determinant:
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Q160 Inequalities Solve Polynomial/Rational Inequality for Solution Set View
The solution set of the inequality $2x - 3 > 7$ is:
(A) $x > 2$
(B) $x > 3$
(C) $x > 4$
(D) $x > 5$
(E) $x > 6$
Q162 Combinations & Selection Geometric Combinatorics View
The number of diagonals of a polygon with 8 sides is:
(A) 16
(B) 18
(C) 20
(D) 22
(E) 24
Q163 Vectors Introduction & 2D Dot Product Computation View
If $\vec{u} = (1, 2)$ and $\vec{v} = (3, 4)$, what is the dot product $\vec{u} \cdot \vec{v}$?
(A) 7
(B) 9
(C) 11
(D) 13
(E) 15
Q164 Sequences and Series Evaluation of a Finite or Infinite Sum View
The distance between the points $A = (1, 2)$ and $B = (4, 6)$ is:
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Q165 Straight Lines & Coordinate Geometry Line Equation and Parametric Representation View
The equation of the line passing through the points $(0, 3)$ and $(2, 7)$ is:
(A) $y = x + 3$
(B) $y = 2x + 3$
(C) $y = 3x + 1$
(D) $y = 2x + 1$
(E) $y = x + 5$
Q166 Sequences and Series Evaluation of a Finite or Infinite Sum View
The value of $\displaystyle\sum_{k=1}^{5} k^2$ is:
(A) 45
(B) 50
(C) 55
(D) 60
(E) 65
Q168 Applied differentiation MCQ on derivative and graph interpretation View
The derivative of $f(x) = x^3 - 3x^2 + 2x$ at $x = 1$ is:
(A) $-2$
(B) $-1$
(C) $0$
(D) $1$
(E) $2$
Q169 Indefinite & Definite Integrals Definite Integral Evaluation (Computational) View
The value of $\displaystyle\int_0^2 (3x^2 + 2x)\,dx$ is:
(A) 8
(B) 10
(C) 12
(D) 14
(E) 16
Q170 Circles Circle Identification and Classification View
A circle has equation $x^2 + y^2 - 4x + 6y - 3 = 0$. What is its radius?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Q171 Simultaneous equations View
The number of solutions of the system $$\begin{cases} x + y = 5 \\ 2x + 2y = 10 \end{cases}$$ is:
(A) 0
(B) 1
(C) 2
(D) 3
(E) Infinite
Q172 Trig Graphs & Exact Values View
The value of $\cos(60^\circ) + \sin(30^\circ)$ is:
(A) 0
(B) $\dfrac{1}{2}$
(C) 1
(D) $\dfrac{3}{2}$
(E) 2
Q173 Modulus function Counting solutions satisfying modulus conditions View
The number of integers satisfying $|x - 3| \leq 2$ is:
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Q174 Combinations & Selection Basic Combination Computation View
A committee of 3 people is to be chosen from a group of 7. How many different committees are possible?
(A) 21
(B) 28
(C) 35
(D) 42
(E) 56
Q175 Laws of Logarithms Simplify or Evaluate a Logarithmic Expression View
The value of $\log_3 81$ is:
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Q176 Completing the square and sketching Vertex and parameter conditions for a quadratic graph View
The parabola $y = x^2 - 6x + 8$ has vertex at:
(A) $(2, 0)$
(B) $(3, -1)$
(C) $(3, 1)$
(D) $(4, 0)$
(E) $(6, 8)$
Q177 Indices and Surds Evaluating Expressions Using Index Laws View
The value of $2^{10}$ is:
(A) 512
(B) 1024
(C) 2048
(D) 4096
(E) 8192
Q179 Combinations & Selection Basic Combination Computation View
The value of $\binom{6}{2}$ is:
(A) 10
(B) 12
(C) 15
(D) 18
(E) 20
Q180 Differentiating Transcendental Functions Compute derivative of transcendental function View
The function $f(x) = e^{2x}$ has derivative:
(A) $e^{2x}$
(B) $2e^{x}$
(C) $2e^{2x}$
(D) $4e^{2x}$
(E) $e^{x}$