LFM Stats And Pure

LFM Stats And Pure

Completing the square and sketching 61

Inequalities 181

Discriminant and conditions for roots 65

Solving quadratics and applications 131

Curve Sketching 228

Factor & Remainder Theorem 61

Polynomial Division & Manipulation 35

Binomial Theorem (positive integer n) 197

Function Transformations 28

Composite & Inverse Functions 211

Partial Fractions 12

Generalised Binomial Theorem 10

Complex Numbers Arithmetic 207

Complex Numbers Argand & Loci 159

Permutations & Arrangements 255

Combinations & Selection 237

Measures of Location and Spread 181

Probability Definitions 212

Tree Diagrams 18

Principle of Inclusion/Exclusion 33

Independent Events 35

Conditional Probability 167

Discrete Probability Distributions 176

Uniform Distribution 3

Binomial Distribution 101

Geometric Distribution 8

Hypergeometric Distribution 9

Negative Binomial Distribution 1

Modelling and Hypothesis Testing 22

Hypothesis test of binomial distributions 2

Data representation 21

Continuous Probability Distributions and Random Variables 322

Continuous Uniform Random Variables 3

Geometric Probability 16

Normal Distribution 87

Approximating Binomial to Normal Distribution 4

Sign Change & Interval Methods 26

Fixed Point Iteration 9

Newton-Raphson method 6

brazil-enem 2012 Q179 View

The graph presents the behavior of formal employment created, according to CAGED, in the period from January 2010 to October 2010.
Based on the graph, the value of the integer part of the median of formal employment created in the period is
(A) 212952.
(B) 229913.
(C) 240621.
(D) 255496.
(E) 298041.

brazil-enem 2013 Q137 View

The grades of a teacher who participated in a selection process, in which the evaluation panel was composed of five members, are presented in the graph. It is known that each panel member assigned two grades to the teacher, one relating to specific knowledge in their area of work and another relating to pedagogical knowledge, and that the teacher's final grade was given by the arithmetic mean of all grades assigned by the evaluation panel.
Using a new criterion, this evaluation panel decided to discard the highest and lowest grades assigned to the teacher.
The new average, in relation to the previous average, is
(A) 0.25 point higher. (B) 1.00 point higher. (C) 1.00 point lower. (D) 1.25 points higher. (E) 2.00 points lower.

brazil-enem 2013 Q160 View

Five food companies are for sale. An entrepreneur, aiming to expand his investments, wishes to buy one of these companies. To choose which one he will buy, he analyses the profit (in millions of reais) of each one, as a function of their time (in years) of existence, deciding to buy the company that presents the highest average annual profit.
The table presents the profit (in millions of reais) accumulated over the time (in years) of existence of each company.

Company	Profit (in millions of reais)	Time (in years)
F	24	3.0
G	24	2.0
H	25	2.5
M	15	1.5
P	9	1.5

The entrepreneur decided to buy the company
(A) F. (B) G. (C) H. (D) M. (E) P.

brazil-enem 2013 Q162 View

A survey was conducted in the 200 hotels in a city, in which the values, in reais, of the daily rates for a standard double room and the number of hotels for each daily rate value were noted. The daily rate values were: $\mathrm{A} = \mathrm{R}\$ 200{,}00$; $\mathrm{B} = \mathrm{R}\$ 300{,}00$; $\mathrm{C} = \mathrm{R}\$ 400{,}00$ and $\mathrm{D} = \mathrm{R}\$ 600{,}00$. In the graph, the areas represent the numbers of hotels surveyed, in percentage, for each daily rate value.
The median value of the daily rate, in reais, for the standard double room in this city, is
(A) 300.00. (B) 345.00. (C) 350.00. (D) 375.00. (E) 400.00.

brazil-enem 2015 Q142 View

QUESTION 142
A student scored the following grades in four tests: 6.0, 7.5, 8.0, and 4.5. The arithmetic mean of the student's grades is
(A) 6.0
(B) 6.5
(C) 7.0
(D) 7.5
(E) 8.0

brazil-enem 2015 Q169 View

QUESTION 169
The median of the data set $\{3, 7, 5, 9, 1, 6, 4\}$ is
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

brazil-enem 2016 Q160 View

The graph shows the average daily oil production in Brazil, in million barrels, in the period from 2004 to 2010.
Estimates made at that time indicated that the average daily oil production in Brazil in 2012 would be 10\% higher than the average of the three last years shown in the graph.
If these estimates had been confirmed, the average daily oil production in Brazil, in million barrels, in 2012, would have been equal to
(A) 1.940.
(B) 2.134.
(C) 2.167.
(D) 2.420.
(E) 6.402.

brazil-enem 2016 Q162 View

A cable TV subscription seller had, in the first 7 months of the year, a monthly average of 84 subscriptions sold. Due to a company restructuring, all sellers were required to have, at the end of the year, a monthly average of 99 subscriptions sold. Faced with this, the seller was forced to increase his monthly sales average in the remaining 5 months of the year.
What should be the seller's monthly sales average in the next 5 months so that he can meet his company's requirement?
(A) 91
(B) 105
(C) 114
(D) 118
(E) 120

brazil-enem 2016 Q169 View

The board of directors of a food company decides to present a proposal for a new product to its shareholders. At this meeting, the average scores given by a group of consumers who tried the new product and two similar competing products (A and B) were presented.
The characteristic that gives the greatest relative advantage to the proposed product and that can be used by the board to encourage its production is
(A) texture.
(B) color.
(C) size.
(D) flavor.
(E) odor.

brazil-enem 2016 Q176 View

Sodium is present in most industrialized foods and can cause heart problems in people who ingest large quantities of these foods. Doctors recommend that their patients reduce sodium consumption.
Based on nutritional information from five brands of cookies (A, B, C, D and E), a graph was constructed that relates quantities of sodium with portions of different cookies.
Which of the cookie brands presented has the least amount of sodium per gram of product?
(A) A
(B) B
(C) C
(D) D
(E) E

brazil-enem 2016 Q178 View

A person is competing in a selection process for a job opening in an office. In one of the stages of this process, he must type eight texts. The number of errors made by this person in each of the typed texts is given in the table.

Text	\begin{tabular}{ c } Number
of errors

\hline I & 2 \hline II & 0 \hline III & 2 \hline IV & 2 \hline V & 6 \hline VI & 3 \hline VII & 4 \hline VIII & 5 \hline \end{tabular}
In this stage of the selection process, candidates will be evaluated by the median value of the number of errors.
The median of the number of errors made by this person is equal to
(A) 2{,}0.
(B) 2{,}5.
(C) 3{,}0.
(D) 3{,}5.
(E) 4{,}0.

brazil-enem 2017 Q151 View

The evaluation of student performance in a university course is based on the weighted average of grades obtained in the disciplines by their respective number of credits, as shown in the table:

Evaluation	Average grade (M)
Excellent	$9 < M \leq 10$
Good	$7 \leq M \leq 9$
Regular	$5 \leq M < 7$
Poor	$3 \leq M < 5$
Very Poor	$M < 3$

A certain student knows that if he obtains a ``Good'' or ``Excellent'' evaluation, he will be able to enroll in the disciplines he desires. He has already taken the exams for 4 of the 5 disciplines in which he is enrolled, but has not yet taken the exam for discipline I, as shown in the table.

Disciplines	Grades	\begin{tabular}{ c } Number
of credits

\hline I & & 12 \hline II & 8.00 & 4 \hline III & 6.00 & 8 \hline IV & 5.00 & 8 \hline V & 7.50 & 10 \hline \end{tabular}
In order to achieve his objective, the minimum grade he must obtain in discipline I is
(A) 7.00.
(B) 7.38.
(C) 7.50.
(D) 8.25.
(E) 9.00.

brazil-enem 2017 Q155 View

Three students, X, Y, and Z, are enrolled in an English course. To evaluate these students, the teacher chose to give five tests. In order to pass this course, the student must have an arithmetic mean of the grades from the five tests greater than or equal to 6. The table shows the grades each student received on each test.

Student	$\mathbf{1}^{\mathbf{st}}$	$\mathbf{2}^{\mathbf{nd}}$	$\mathbf{3}^{\mathbf{rd}}$	$\mathbf{4}^{\mathbf{th}}$	$\mathbf{5}^{\mathbf{th}}$
X	5	5	5	10	6
Y	4	9	3	9	5
Z	5	5	8	5	6

Based on the data in the table and the information given, will be/will fail
(A) only student Y.
(B) only student Z.
(C) only students X and Y.
(D) only students X and Z.
(E) students X, Y, and Z.

brazil-enem 2017 Q174 View

The graph presents the unemployment rate (in \%) for the period from March 2008 to April 2009, obtained based on data observed in the metropolitan regions of Recife, Salvador, Belo Horizonte, Rio de Janeiro, São Paulo, and Porto Alegre.
The median of this unemployment rate, in the period from March 2008 to April 2009, was
(A) $8.1\%$
(B) $8.0\%$
(C) $7.9\%$
(D) $7.7\%$
(E) $7.6\%$

brazil-enem 2024 Q138 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 music	Percentage
Pop	35\%
Rock	25\%
Funk	20\%
Sertanejo	15\%
Other	5\%

How many students prefer Pop or Rock?
(A) 60
(B) 80
(C) 100
(D) 120
(E) 140

brazil-enem 2024 Q149 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

brazil-enem 2025 Q143 View

In a school cafeteria, there are five foods sold in packages with different quantities of servings.
The nutritional information contained on the labels of these products is indicated in the images.
A student always chooses the food with the lowest total amount of sodium per package.
Which of these products should be chosen by the student?
(A) Potato chips.
(B) Salted sticks.
(C) Multigrain biscuit.
(D) Polvilho biscuit.
(E) Water and salt biscuit.

brazil-enem 2025 Q150 View

A technology company will standardize the internet connection speed it offers to its customers in ten cities. The company's management decides that its new reference speed standard will be the median of the reference speed values of connections in these ten cities. These values, in megabytes per second (MB/s), are presented in the table.

Cities	Reference speed (MB/s)
C1	390
C2	380
C3	320
C4	390
C5	340
C6	380
C7	390
C8	400
C9	350
C10	360

The reference speed, in megabytes per second, to be adopted by this company is
(A) 360.
(B) 370.
(C) 380.
(D) 390.
(E) 400.

brazil-enem 2025 Q153 View

A language school offers courses in English, Spanish, French, and German. The graphs present the percentage distribution of enrollments, by language, in 2023, and the distribution of the number of enrollments, by language, in 2024.
To plan the activities for 2025, the school manager estimated that the total number of enrollments will be the same as in 2024, and the percentage distribution of enrollments, by language, will be equal to that recorded in 2023.
According to this estimate, the number of enrollments in the French course for the year 2025 will be
(A) 2.
(B) 12.
(C) 20.
(D) 22.
(E) 40.

brazil-enem 2025 Q155 View

In a clinical study, 55 women were randomly distributed into 5 groups of 11 people. To test a new medication, a group will be chosen in which the majority of women are between 20 and 30 years old. The other groups will take placebo or medications already on the market. The table, partially filled, provides some data related to the ages of women in these groups.

Even with the incomplete table, it was possible to select one of these groups because, with only the data presented in the table, a group was identified that certainly met the selection criterion.
The group chosen was
(A) 1.
(B) 2.
(C) 3.
(D) 4.
(E) 5.

brazil-enem 2025 Q156 View

Pace is a term used by a runner to denote his average rhythm in a race. It represents the average time, in seconds, that this runner takes to cover 1 km.
The diagram presents the time, in seconds, that a runner took to cross the marks that define the first four 1 km sections in a 5 km race, and the time spent to cover each 1 km section.
The best pace that this runner achieved in 5 km races was $281\,\mathrm{s/km}$. For him to repeat his best pace in 5 km races in this race, his time in the $5^{\text{th}}$ section should be how many seconds less than what he spent to cover the $4^{\text{th}}$ section?
(A) 1
(B) 2
(C) 8
(D) 9
(E) 15

cmi-entrance 2024 Q11 2 marks View

Let $O=(0,0,0)$, $P=(19,5,2024)$ and $Q=(x,y,z)$ be points in 3-dimensional space where $Q$ is an unknown point. Consider vector $\mathbf{u} = \overrightarrow{OP} = 19\hat{i} + 5\hat{j} + 2024\hat{k}$ and unknown vector $\mathbf{v} = \overrightarrow{OQ} = x\hat{i} + y\hat{j} + z\hat{k}$.
Instruction: for the specified set choose the correct option describing it and type in the number of that option. E.g., if you think the given set is a line, enter $\mathbf{3}$ as your answer with no full stop or any other punctuation.
$\{Q \mid \mathbf{u} \cdot \mathbf{v} = 2024(\mathbf{v} \cdot \mathbf{v})\}$. [2 points]
Options:

The empty set
A singleton set
A line
A pair of lines
A circle
A plane perpendicular to $\mathbf{u}$
A plane parallel to $\mathbf{u}$
An infinite cone
A finite cone
A sphere
None of the above

csat-suneung 2005 Q26 (Probability and Statistics) 3 marks View

The following is a stem-and-leaf plot showing the number of push-ups performed by 10 high school students in 3 minutes.
(Unit: times)

Stem	\multicolumn{3}{\|c\|}{Leaf}
1	5	9
2	3	7	8
3	2	6	6
4	1	5

Let $m$ be the mean, $n$ be the median, and $f$ be the mode of the number of push-ups. Which of the following is correct? [3 points]
(1) $m < n < f$
(2) $m < f < n$
(3) $f < m < n$
(4) $n < m < f$
(5) $n < f < m$

csat-suneung 2009 Q26b 3 marks View

(Probability and Statistics) A certain basketball player practices free throws 40 times every day. The stem-and-leaf plot below shows the number of successful free throws each day for the first 10 days, with the tens digit as the stem and the units digit as the leaf. On the 11th day, the number of successful free throws was $n$, and the average number of successful free throws for the first 11 days was equal to the mode in the stem-and-leaf plot below. What is the value of $n$? [3 points]

Stem	\multicolumn{4}{\|c\|}{Leaf}
0	9
1	7	9
2	1	4	4	6
3	0	1	3

(1) 24
(2) 26
(3) 28
(4) 30
(5) 32

csat-suneung 2010 Q26b 3 marks View

[Probability and Statistics] Which of the following is the correct shape of the graph of the function representing the median according to the value of $x$ in the following data? (where $x \geqq 0$ ) [3 points] $10 , \quad 28 , \quad x , \quad 20 , \quad 8 , \quad 2 , \quad 25 , \quad 7 , \quad 17$

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