competition_source_list listlengths 0 1 | difficulty stringclasses 3
values | problem stringlengths 115 1.42k | solution stringlengths 7 165 |
|---|---|---|---|
[
"其它"
] | 2 | On Kangaroo planet each kangyear has 20 kangmonths and each kangmonth has 6 kangweeks, How many kangweeks are there in one quarter of a kangyear?
Options:
(A) $$9$$
(B) $$30$$
(C) $$60$$
(D) $$90$$
(E) $$120$$
Please choose an option from A-E to answer. | (B) $$30$$ |
[
"其它"
] | 2 | In a triangle with integer side lengths, one side is three times as long as a second side, and the length of the third side is $15$. What is the greatest possible perimeter of the triangle? （2006 AMC10B, Question 10)
Options:
(A) $$43$$
(B) $$44$$
(C) $$45$$
(D) $$46$$
(E) $$47$$
Please choose an option from A-E to a... | (A) $$43$$ |
[
"其它"
] | 2 | \textbf{Sean and Evan are college roommates who have part-time jobs as servers in restaurants. The distribution of Sean's weekly income is approximately normal with mean $\textbackslash$225$ and standard deviation $\textbackslash$25$. The distribution of Evan's weekly income is approximately normal with mean $\textback... | (D) \textbf{0.303} |
[
"其它"
] | 2 | What is the smallest whole number larger than the perimeter of any triangle with a side of length $9$ and a side of length $1$? (adapted from 2015 AMC8, Question 8)
Options:
(A) $$10$$
(B) $$19$$
(C) $$20$$
(D) $$21$$
(E) $$22$$
Please choose an option from A-E to answer. | (C) $$20$$ |
[
"其它"
] | 2 | Write each of the numbers 0,1,2,3,4,5,6 in the sqaures to make the addition correct. What digit will be in the grey square? pic
Options:
(A) $$2$$
(B) $$3$$
(C) $$4$$
(D) $$5$$
(E) $$6$$
Please choose an option from A-E to answer. | (D) $$5$$ |
[
"其它"
] | 2 | On the first day of a $7-$day holiday, Judy reads $9$ pages of a book. On the second day, she reads $12$. Then each day later, she reads $3$ pages more than the day before. On the last day of the holiday, she reads the corresponding number of pages and exactly finishes reading the book. How many pages does the book hav... | (D) $$126$$ |
[
"其它"
] | 2 | In the following Figures $\left (a\right )$ and $\left (b\right )$, each number inside a small triangle is the sum of the numbers inside in the neighbouring small circles. The number inside each circle is either $1$, $2$, $3$, $4$, $5$, $6$, $7$ or $8$. The sum of whole numbers inside the circles in Figure $\left (a\r... | (B) $$52$$ |
[] | 3 | Known $$A=\frac{{{3}^{2019}}+1}{{{3}^{2020}}+1}$$，$$B=\frac{{{3}^{2020}}+1}{{{3}^{2021}}+1}$$, compare between $$A$$ and $$B$$．
Options:
(A) $A=B$
(B) $A\textgreater B$
(C) $A\textless B$
(D) All of the above
(E) None of the above
Please choose an option from A-E to answer. | (B) $A\textgreater B$ |
[
"其它"
] | 2 | What is the product of five fractions, whose denominators are $5-1$ in descending order, and the numerators are $1-5$ in ascending order？
Options:
(A) $\frac1{25}$
(B) $\frac1{2}$
(C) $\frac1{5}$
(D) $$0$$
(E) $$1$$
Please choose an option from A-E to answer. | (E) $$1$$ |
[
"其它"
] | 2 | \textbf{The height and age of each child in a random sample of children was recorded. The value of the correlation coefficient between height and age for the children in the sample was 0.8. Based on the least-squares regression line created from the data to predict the height of a child based on age, which of the follo... | (C) \textbf{The proportion of the variation in height that is explained by a regression on age is 0.64.~} |
[
"其它"
] | 4 | The zeroes of the function $f(x)=x^{2}-a x+a$ are integers. What is the sum of the possible values of $a$? (Adapted From 2015 AMC 10A Problems, Question \#23)
Options:
(A) $$2$$
(B) $$4$$
(C) $$6$$
(D) $$8$$
(E) $$7$$
Please choose an option from A-E to answer. | (B) $$4$$ |
[
"其它"
] | 2 | What is the least possible value of $(x y-1)^{2}+(x+y)^{2}$ for real numbers $x$ and $y$?
Options:
(A) $$0$$
(B) $\frac{1}{4}$
(C) $\frac{1}{2}$
(D) $$1$$
(E) $$2$$
Please choose an option from A-E to answer. | (D) $$1$$ |
[
"其它"
] | 2 | \textbf{In a population of university students, 20\% of the students have experienced feelings of math anxiety. If we select 8 students, what is the probability that exactly three have experienced math anxiety?}
Options:
(A) $${8 \choose 3} (0.20)^{3} (0.80)^{8}$$
(B) $${8 \choose 3} (0.20)^{3} (0.80)^{5}$$
(C) $${5 \... | (B) $${8 \choose 3} (0.20)^{3} (0.80)^{5}$$ |
[
"其它"
] | 3 | Points $A$ and $B$ are 10 units apart. Points $B$ and $C$ are 4 units apart. Points $C$ and $D$ are 3 units apart. If $A$ and $D$ are as close as possible, then the number of units between them is ．(1996 AJHSME, Question 8)
Options:
(A) $$0$$
(B) $$3$$
(C) $$9$$
(D) $$11$$
(E) $$17$$
Please choose an option from A-E ... | (B) $$3$$ |
[
"其它"
] | 2 | There are $20$ balls of the same size in a box. Lucas says: "Half of them are red." Peter says: "The number of red balls is $5$ times that of green balls." Claire says: "There are three colors of balls in the box: red, light blue, and green." How many dark blue balls are there in the box?
Options:
(A) $$0$$
(B) $$... | (A) $$0$$ |
[
"其它"
] | 2 | Starting with some gold coins and some empty treasure chests, I tried to put $9$ gold coins in each treasure chest, but that left $2$ treasure chests empty. So instead I put 6 gold coins in each treasure chest, but then I had $3$ gold coins left over. How many gold coins did I have? ( 2017 AMC8, Questions \#17)
Option... | (C) $$45$$ |
[
"其它"
] | 2 | \textbf{A stationery store owner calculated the mean and median price of all types of pen: 5 and 3, respectively. He plans to have a 20\% off sale. What are the new mean and median of pens in that store?}
Options:
(A) \textbf{mean: 4; median: 2.4}
(B) \textbf{mean: 5; median: 2.4}
(C) \textbf{~mean: 4; median: 3}
(D) ... | (A) \textbf{mean: 4; median: 2.4} |
[
"其它"
] | 4 | The zeroes of the function $f(x)=x^{2}-a x+2 a$ are integers. What is the sum of the possible values of $a$? (2015 AMC 10A Problems, Question \#23)
Options:
(A) $$7$$
(B) $$8$$
(C) $$16$$
(D) $$18$$
(E) $$18$$
Please choose an option from A-E to answer. | (C) $$16$$ |
[
"其它"
] | 2 | In the diagram below, a circle centered at $O$ has radius $4 \text{cm}$. It is divided into $4$ regions by two chords that are perpendicular to each other at point $N$. It is known that $OM=1 \text{cm}$, $MN=2\text{cm}$. Find the value of: Area of $(I + III) -$ Area of $(II+IV)$
Options:
(A) $$0$$
(B) $$2$$
(C) $$4$$
... | (D) $$6$$ |
[
"其它"
] | 3 | Greta Grasshopper sits on a long line of lily pads in a pond. From any lily pad, Greta can jump $5$ pads to the right or $3$ pads to the left. What is the fewest number of jumps Greta must make to reach the lily pad located $2023$ pads to the right of her starting position?
Options:
(A) $$405$$
(B) $$407$$
(C) $$409$$... | (A) $$405$$ |
[] | 2 | What is the value of $$1+3+5+\cdots +2017+2019-2-4-6-\cdots -2016-2018$$?
Options:
(A) $$1010$$
(B) $$1009$$
(C) $$1008$$
(D) $$-1009$$
(E) $$-1010$$
Please choose an option from A-E to answer. | (A) $$1010$$ |
[
"其它"
] | 2 | Three fourths of a pitcher is filled with pineapple juice. The pitcher is emptied by pouring an equal amount of juice into each of 5 cups. What percent of the total capacity of the pitcher did each cup receive?~ (2020 AMC 8, Question \#5)
Options:
(A) $$5$$
(B) $$10$$
(C) $$15$$
(D) $$20$$
(E) $$25$$
Please choose an... | (C) $$15$$ |
[
"其它"
] | 3 | Let $P(x)$ be a polynomial such that when $P(x)$ is divided by $x-19$, the remainder is 99 , and when $P(x)$ is divided by $x-99$, the remainder is 19. What is the remainder when $P(x)$ is divided by $(x-19)(x-99)$? (1999 AHSME Problems, Question \#17)
Options:
(A) $-x+80$
(B) $x+80$
(C) $-x+118$
(D) $x+118$
(E) $$0$$... | (C) $-x+118$ |
[
"其它"
] | 2 | \textbf{Which of the following is/are categorical variable(s)?} \textbf{I. The mean of Grade 1 boys' heights} \textbf{II. The colors of jackets in the class} \textbf{III. The types of pens in a stationary store}
Options:
(A) I
(B) II
(C) III
(D) I, II
(E) II, III
Please choose an option from A-E to answer. | (E) II, III |
[
"其它"
] | 2 | \textbf{A statistical test involves the following null and alternative hypotheses.~} \textbf{H0: $\mu$ = 64} \textbf{Ha: $\mu$ \textgreater{} 64} \textbf{Which of the following describes a Type II error?}
Options:
(A) \textbf{Failing to reject the null hypothesis when the population mean is 64}
(B) \textbf{Failing ... | (B) \textbf{Failing to reject the null hypothesis when the population mean is greater than 64} |
[
"其它"
] | 2 | Given that $$23+25+27 +\ldots+(2k-1)=m^{2}$$, where $$k$$ and $$m$$ are whole numbers, $$k\textgreater30$$, find the value of $$m$$.
Options:
(A) $$11$$
(B) $$35$$
(C) $$41$$
(D) $$60$$
(E) None of the above
Please choose an option from A-E to answer. | (D) $$60$$ |
[
"其它"
] | 2 | Camila writes down five positive integers. The unique mode of these integers is 2 greater than their median, and the median is 2 greater than their arithmetic mean. What is the least possible value for the mode?
Options:
(A) $$5$$
(B) $$7$$
(C) $$9$$
(D) $$11$$
(E) $$13$$
Please choose an option from A-E to answer. | (D) $$11$$ |
[] | 2 | If $$a$$@$$b=\frac {a\times b}{a+b}$$ for positive integers $$a$$ and $$b$$ , what is $$5$$@$$10$$?
Options:
(A) $$\frac 3{10}$$
(B) $$1$$
(C) $$2$$
(D) $$\frac {10}3$$
(E) $$50$$
Please choose an option from A-E to answer. | (D) $$\frac {10}3$$ |
[
"其它"
] | 2 | Is it true that If an odd function has zero in its domain, then it must pass through the origin. (Hint: $0$ is in the domain, we can apply $f(-x) = -f(x)$ at $x=0$)
Options:
(A) True
(B) False
Please choose an option from A-E to answer. | (A) True |
[
"其它"
] | 2 | Lucy writes numbers from $1$ to $200$ on the blackboard. Then, she plays a game with her friend Mike. Each time they take turn to delete the first two numbers in the sequence and write their sum by the end of the sequence. For example, Lucy deletes $1$ and $2$, then writes $3$ behind $200$ for the first time. They play... | (D) $$20100$$ |
[
"其它"
] | 2 | The real numbers $c, b, a$ form an arithmetic sequence with $a \geq b \geq c \geq 0$. The quadratic $a x^{2}+b x+c$ has exactly one root. What is this root?
Options:
(A) $-7-4 \sqrt{3}$
(B) $-2-\sqrt{3}$
(C) $$-1$$
(D) $-2+\sqrt{3}$
(E) $-7+4 \sqrt{3}$
Please choose an option from A-E to answer. | (D) $-2+\sqrt{3}$ |
[
"其它"
] | 2 | In December, Tom-the-cat slept for exactly 3 weeks. Which calculations should we do in order to find how many minutes he stayed awake during this month?
Options:
(A) (31 - 7) x 3 x 24 x 60
(B) (31 - 7) x 24 x 60
(C) (31 -7 x 3) x 24 x 60
(D) (31 -7 x 3) x 24 x 60 x 60
(E) (30 -7 x 3) x 24 x 60
Please choose an option... | (B) (31 - 7) x 24 x 60 |
[
"其它"
] | 2 | What is the tens digit of $7^{2011}$? (2011 AMC 8 Problems, Question \#22)
Options:
(A) $$0$$
(B) $$1$$
(C) $$3$$
(D) $$4$$
(E) $$7$$
Please choose an option from A-E to answer. | (D) $$4$$ |
[
"其它"
] | 2 | A palindrome is a number that can be read the same forward and backward. For example, the numbers 99, 252 and 4884 are palindromes. How many 3. digit palindrome numbers are there?
Options:
(A) $$81$$
(B) $$900$$
(C) $$90$$
(D) $$9$$
(E) None of the above
Please choose an option from A-E to answer. | (C) $$90$$ |
[
"其它"
] | 2 | The arrows on the two spinners shown below are spun. Let the number $N$ equal $10$ times the number on Spinner $A$, added to the number on Spinner $B$. What is the probability that $N$ is a perfect square number? (2022 AMC 8 Problems, Question \#12)
Options:
(A) $\frac{1}{16}$
(B) $\frac{1}{8}$
(C) $\frac{1}{4}$
(D) $... | (B) $\frac{1}{8}$ |
[
"其它"
] | 2 | Half of a pitcher is filled with pineapple juice. The pitcher is emptied by pouring an equal amount of juice into each of 4 cups. What percent of the total capacity of the pitcher did each cup receive?~ (adapted from 2020 AMC 8, Question \#5)
Options:
(A) $$5$$
(B) $$10$$
(C) $$12.5$$
(D) $$15$$
(E) $$25$$
Please cho... | (C) $$12.5$$ |
[
"其它"
] | 2 | \textbf{The distribution of the number of hours worked by volunteers last year at a large hospital is approximately normal with mean 80 and standard deviation 7. Volunteers in the top 20 percent of hours worked will receive a certificate of merit. If a volunteer from last year is selected at random, which of the follow... | (B) $$0.123$$ |
[
"其它"
] | 2 | The GPAs (grade point averages) of students who take the AP Statistics exam are approximately normally distributed with a mean of 3.4 and a standard deviation of 0.3. What is the probability that a student selected at random from this group has a GPA lower than 3.0?
Options:
(A) $$0.0918$$
(B) $$0.4082$$
(C) $$0.9082$... | (A) $$0.0918$$ |
[] | 2 | Which is the smallest fraction in $$\frac{2020}{2021}$$, $$\frac{2021}{2022}$$, $$\frac{2022}{2023}$$ and $$\frac{2023}{2024}$$?
Options:
(A) $$\frac{2020}{2021}$$
(B) $$\frac{2021}{2022}$$
(C) $$\frac{2022}{2023}$$
(D) $$\frac{2023}{2024}$$
Please choose an option from A-E to answer. | (A) $$\frac{2020}{2021}$$ |
[
"其它"
] | 2 | What is the smallest whole number larger than the perimeter of any triangle with a side of length $12$ and a side of length $13$? (adapted from 2015 AMC8, Question 8)
Options:
(A) $$25$$
(B) $$50$$
(C) $$51$$
(D) $$49$$
(E) $$33$$
Please choose an option from A-E to answer. | (B) $$50$$ |
[
"其它"
] | 2 | Real numbers $x$ and $y$ satisfy $x+y=4$ and $x \cdot y=-2$. What is the value of $$ x+\frac{x^{3}}{y^{2}}+\frac{y^{3}}{x^{2}}+y? $$
Options:
(A) $$360$$
(B) $$400$$
(C) $$420$$
(D) $$440$$
(E) $$480$$
Please choose an option from A-E to answer. | (D) $$440$$ |
[] | 2 | Fill in the blanks with ``$$+$$'' or ``$$-$$'' to make the equation true． $$6$$~~~~ $$6$$~~~~ $$6$$~~~~ $$6$$~~~~ $$6=6$$
Options:
(A) $$+++-$$
(B) $$++++$$
(C) $$++-\/-$$
Please choose an option from A-E to answer. | (C) $$++-\/-$$ |
[
"其它"
] | 4 | Let $a, b$, and $c$ be positive integers with $a \geq b \geq c$ such that $a^{2}-b^{2}-c^{2}+a b=2011$ and $a^{2}+3 b^{2}+3 c^{2}-3 a b-2 a c-2 b c=-1997$. What is $a$?
Options:
(A) $$249$$
(B) $$250$$
(C) $$251$$
(D) $$252$$
(E) $$253$$
Please choose an option from A-E to answer. | (E) $$253$$ |
[
"其它"
] | 3 | The sum of the first $m$ positive odd integers is $212$ more than the sum of the first $n$ positive even integers. What is the sum of all possible values of $n$?
Options:
(A) $$255$$
(B) $$256$$
(C) $$257$$
(D) $$258$$
(E) $$259$$
Please choose an option from A-E to answer. | (A) $$255$$ |
[
"其它"
] | 2 | Let $A$ and $B$ be positive whole numbers. $A$ is a $2$-digit number and $B$ is a $4$-digit number. If $A+B$ and $A^{2}+B^{2}$ are both multiples of $7$, find the largest possible value of $B-A$.
Options:
(A) $$9968$$
(B) $$9982$$
(C) $$9989$$
(D) $$9996$$
(E) None of the above
Please choose an option from A-E to ans... | (B) $$9982$$ |
[
"其它"
] | 3 | Two integers are inserted into the list $3,3,8,11,28$ to double its range. The mode and median remain unchanged. What is the maximum possible sum of the two additional numbers?
Options:
(A) $$56$$
(B) $$57$$
(C) $$58$$
(D) $$60$$
(E) $$61$$
Please choose an option from A-E to answer. | (A) $$56$$ |
[
"其它"
] | 2 | \textbf{Ten percent of all trucks undergoing a certain inspection will fail the inspection. Assume that trucks are independently undergoing this inspection one at a time. The expected number of trucks inspected before a truck fails inspection is}
Options:
(A) $$2$$
(B) $$4$$
(C) $$5$$
(D) $$10$$
(E) $$20$$
Please cho... | (D) $$10$$ |
[
"其它"
] | 2 | 3, 6, , 12, 15.~~Which number should be filled in the bracket?
Options:
(A) $$10$$
(B) $$8$$
(C) $$9$$
(D) $$7$$
(E) $$11$$
Please choose an option from A-E to answer. | (C) $$9$$ |
[
"其它"
] | 2 | \textbf{Which of the following events are independent?} \textbf{P(A) = 0.7, P(B) = 0.2, P(C) = 0.1, P(B\textbar A) = 0.5, P(B\textbar C) = 0.2, P(A∩C) = 0.0}
Options:
(A) \textbf{A and B only}
(B) \textbf{A and C only}
(C) \textbf{A, B, and C}
(D) \textbf{B and C only}
(E) \textbf{None are independent}
Please choose... | (D) \textbf{B and C only} |
[
"其它"
] | 3 | In a sequence of positive integers, each term after the second is the product of the previous two terms. The sixth term in the sequence is $4000$. What is the first term?
Options:
(A) $$1$$
(B) $$2$$
(C) $$4$$
(D) $$5$$
(E) $$10$$
Please choose an option from A-E to answer. | (D) $$5$$ |
[] | 2 | Compare the following pair of fractions using an inequality sign. $$A=\frac{773}{778}$$, $$B=\frac{884}{889}$$
Options:
(A) $$\frac{773}{778}\textgreater\frac{884}{889}$$
(B) $$\frac{773}{778}\textless{}\frac{884}{889}$$
(C) $$\frac{773}{778}=\frac{884}{889}$$
Please choose an option from A-E to answer. | (B) $$\frac{773}{778}\textless{}\frac{884}{889}$$ |
[
"其它"
] | 2 | David drives from his home to the airport to catch a flight. He drives $35$ miles in the first hour, but realizes that he will be $1$ hour late if he continues at this speed. He increases his speed by $15$ miles per hour for the rest of the way to the airport and arrives $30$ minutes early. How many miles is the airpor... | (C) $$210$$ |
[
"其它"
] | 2 | \textbf{A grocer would like to determine the proportion of milk cartons that have expired within 0.05 of the true proportion with a 95 percent confidence interval. What is the minimum required sample size?}
Options:
(A) $$300$$
(B) $$383$$
(C) $$384$$
(D) $$385$$
(E) $$400$$
Please choose an option from A-E to answer... | (D) $$385$$ |
[
"其它"
] | 2 | Four fair six-sided dice are rolled. What is the probability that at least three of the four dice show the same value?
Options:
(A) $\frac{1}{36}$
(B) $\frac{7}{72}$
(C) $\frac{1}{9}$
(D) $\frac{5}{36}$
(E) $\frac{1}{6}$
Please choose an option from A-E to answer. | (B) $\frac{7}{72}$ |
[
"其它"
] | 2 | For $\triangle ABC$, all of its side lengths are integers. The perimeter of $\triangle ABC$ with a side of length $12$ and a side length of $7$ is at least ．
Options:
(A) $$24$$
(B) $$25$$
(C) $$26$$
(D) $$27$$
(E) $$28$$
Please choose an option from A-E to answer. | (B) $$25$$ |
[] | 2 | What is the product of $$ \frac { 3 } { 2 } \times \frac { 4 } { 3 } \times \frac { 5 } { 4 } \times \cdots \times \frac { 2 0 0 6 } { 2 0 0 5 }$$?
Options:
(A) $$1$$
(B) $$1002$$
(C) $$1003$$
(D) $$2005$$
(E) $$2006$$
Please choose an option from A-E to answer. | (C) $$1003$$ |
[
"其它"
] | 2 | A number of students from Fibonacci Middle School are taking part in a community service project. The ratio of $8^{\text {th }}$-graders to $6^{\text {th }}$-graders is $5: 3$, and the the ratio of $8^{\text {th }}$-graders to $7^{\text {th }}$ graders is $8: 5$. What is the smallest number of students that could be pa... | (E) $$89$$ |
[
"其它"
] | 2 | Which of the following is not an algebraic expression?
Options:
(A) $$5$$
(B) $\frac{1}{h}$
(C) $3x=5y$
(D) $xyzabc$
Please choose an option from A-E to answer. | (C) $3x=5y$ |
[] | 3 | Given that $$\left[ x+0.19 \right]+\left[ x+0.20 \right]+\left[ x+0.21 \right]+\cdots \cdots +\left[ x+0.91 \right]=546$$. Find $$\left[ 100x \right]$$
Options:
(A) $$793$$
(B) $$737$$
(C) $$757$$
(D) $$743$$
(E) None of the above
Please choose an option from A-E to answer. | (D) $$743$$ |
[
"其它"
] | 2 | At an ice cream shop, a sundae is made by selecting two flavors of ice cream and topping them with fudge, whipped cream, nuts, and a cherry. The available flavors of ice cream are chocolate, vanilla, strawberry, rocky road, chocolate chip cookie dough, and mint chip. How many difference sundae combinations are possible... | (B) $$15$$ |
[
"其它"
] | 2 | \textbf{A set of 5,000 scores on a college readiness exam are known to be approximately normally distributed with a mean of 72 and a standard deviation of 6. To the nearest integer value, approximately how many scores are between 63 and 75.}
Options:
(A) $$0.6247$$
(B) $$4115$$
(C) $$3650$$
(D) $$3123$$
(E) $$3227$$
... | (D) $$3123$$ |
[
"其它"
] | 2 | The average weight of dogs that come to a certain vet\textquotesingle s office is 55.6 lbs, with a standard deviation of 2.2 lbs. If the weights are normally distributed, what percent of dogs weight more than 60 lbs?
Options:
(A) 66.8\%
(B) 47.2\%
(C) 33.4\%
(D) 15.9\%
(E) 2.28\%
Please choose an option from A-E to a... | (E) 2.28\% |
[] | 2 | There is a sequence of squares of some natural numbers: $1$, $4$, $9$, $16$, $\cdots$ One of the numbers in this sequence is $10^{8}$. What is the next number after $10^{8}$? ($2001$ Math Kangaroo Problem, Level $$11$$-$$12$$, Question \#$14$)
Options:
(A) $\left (10^{4}+1\right )^{2}$
(B) $\left (10^{8}+1\right )^{2}... | (A) $\left (10^{4}+1\right )^{2}$ |
[
"其它"
] | 2 | How many different four-digit numbers can be formed by rearranging the four digits in $2004$?~(2004 AMC 8 Problem, Question \#2)
Options:
(A) $$4$$
(B) $$6$$
(C) $$16$$
(D) $$24$$
(E) $$81$$
Please choose an option from A-E to answer. | (B) $$6$$ |
[
"其它"
] | 2 | The sum of the first $m$ positive odd integers is 212 more than the sum of the first $n$ positive even integers. What is the sum of all possible values of $n$ ?
Options:
(A) $$255$$
(B) $$256$$
(C) $$257$$
(D) $$258$$
(E) $$259$$
Please choose an option from A-E to answer. | (A) $$255$$ |
[
"其它"
] | 2 | What is the area of the triangle formed by the lines $y=5, y=1+x$, and $y=1-x$? (2019 AMC 8 Problems, Question \#21)
Options:
(A) $$4$$
(B) $$8$$
(C) $$10$$
(D) $$12$$
(E) $$16$$
Please choose an option from A-E to answer. | (E) $$16$$ |
[
"其它"
] | 2 | How many of the following equations are written in function form? ($1$) $2x-y=3x+1$;~($2$) $2x=-5y+2$;~($3$) $y=7x+12$;~($4$) $y+6=12x-17$;~($5$) $y=x+z+ab$
Options:
(A) $$1$$
(B) $$2$$
(C) $$3$$
(D) $$4$$
(E) $$5$$
Please choose an option from A-E to answer. | (B) $$2$$ |
[
"其它"
] | 2 | For how many values of $a$ is it true that the line $y=x+a^{2}-6$ passes through the vertex of the parabola $y=4x^{2}-8x+a^{2}$? (Adapted From 2005 AMC 12B Problem, Question \#8)
Options:
(A) $$0$$
(B) $$1$$
(C) $$2$$
(D) $$10$$
(E) infinitely many
Please choose an option from A-E to answer. | (A) $$0$$ |
[
"其它"
] | 2 | \textbf{Recently you learned that the probability of getting a critical hit on an attack in your favorite game is 15\%. You've noticed that you do 20 attacks per fight. You're interested in figuring out how likely it is that you would get 5 critical hits during a fight. Which of the following distributions should you u... | (A) \textbf{A binomial distribution with p = 0.15 and n = 20} |
[
"其它"
] | 2 | What is the smallest whole number larger than the perimeter of any triangle with a side of length $7$ and a side of length $15$? (2015 AMC8, Question 8)
Options:
(A) $$24$$
(B) $$29$$
(C) $$43$$
(D) $$44$$
(E) $$57$$
Please choose an option from A-E to answer. | (D) $$44$$ |
[
"其它"
] | 2 | A number of students from Fibonacci Middle School are taking part in a community service project. The ratio of $8^{\text {th }}$-graders to $6^{\text {th }}$-graders is $5: 3$, and the the ratio of $8^{\text {th }}$-graders to $7^{\text {th }}$ graders is $8: 5$. What is the smallest number of students that could be pa... | (D) $$89$$ |
[
"其它"
] | 2 | A box has fewer than $50$ cookies in it. The cookies can be divided evenly between $2, 3,$ or $4$ children. However, they cannot be divided evenly between $7$ children because $6$ more cookies would be needed. How many cookies are there in the box? (2021 Math Kangaroo Problem, Level 3-4, Question \#21)
Options:
(A) $$... | (D) $$36$$ |
[] | 2 | Which of the numbers below is the greatest? ($2003$ Math Kangaroo Problem, Level $9-10$, Question \#$11$)
Options:
(A) $$22222$$
(B) $2222^{2}$
(C) $222^{22}$
(D) $22^{222}$
(E) $2^{2222}$
Please choose an option from A-E to answer. | (E) $2^{2222}$ |
[
"其它"
] | 3 | Alina writes the numbers $1,2,\cdots ,9$ on a separate cards, one number per card. She wishes to divide the cards into $3$ groups of $3$ cards so that the sum of the numbers in each group will be the same. In how many ways can this be done?
Options:
(A) $$0$$
(B) $$1$$
(C) $$2$$
(D) $$3$$
(E) $$4$$
Please choose an o... | (A) $$0$$ |
[] | 2 | Which is the smallest fraction in $$\frac{2020}{2021}$$, $$\frac{2021}{2022}$$, $$\frac{2022}{2023}$$ and $$\frac{2023}{2024}$$?
Options:
(A) $$\frac{2020}{2021}$$
(B) $$\frac{2021}{2022}$$
(C) $$\frac{2022}{2023}$$
(D) $$\frac{2023}{2024}$$
Please choose an option from A-E to answer. | (A) $$\frac{2020}{2021}$$ |
[
"其它"
] | 2 | \textbf{Which of the following data sets has the largest standard deviation?}
Options:
(A) \textbf{{100, 101, 102, 103, 104}}
(B) \textbf{{1000.3, 999.56, 1000.49, 1000, 998.32}}
(C) \textbf{{1, 1, 1, 1, 1}}
(D) \textbf{{5, 10, 15, 20, 25}}
(E) \textbf{{1, 2, 3, 4, 5}}
Please choose an option from A-E to answer. | (D) \textbf{{5, 10, 15, 20, 25}} |
[
"其它"
] | 2 | \textbf{Events D and E are independent, with P(D) = 0.6 and P(D and E) = 0.18. Which of the following is true?}
Options:
(A) \textbf{P(E) = 0.12}
(B) \textbf{P(E) = 0.4}
(C) \textbf{P(D or E) = 0.28}
(D) \textbf{P(D or E) = 0.72}
(E) \textbf{P(D or E) = 0.9}
Please choose an option from A-E to answer. | (D) \textbf{P(D or E) = 0.72} |
[] | 2 | If $2^{200}\times4^{1000}\times8^{40}=16^{}x$, then $x=$~\uline{~~~~~~~~~~}~.
Options:
(A) $$295$$
(B) $$520$$
(C) $$570$$
(D) $$580$$
(E) $$620$$
Please choose an option from A-E to answer. | (D) $$580$$ |
[
"其它"
] | 2 | Line $l\_1$ has equation $3 x-2 y=1$ and goes through $A=(-1,-2)$. Line $l\_2$ has equation $y=1$ and meets line $l\_1$ at point $B$. Line $l\_3$ has positive slope, goes through point $A$, and meets $l\_2$ at point $C$. The area of $\triangle A B C$ is $3$ . What is the slope of $l\_3$? (2013 AMC 12B Problems, Questio... | (B) $$\frac34$$ |
[
"其它"
] | 2 | For how many integers $x$ is the number $x^{4}-25 x^{2}+24$ negative? ( 2014 AMC 10B Problems, Question \#20)
Options:
(A) $$3$$
(B) $$6$$
(C) $$12$$
(D) $$14$$
(E) $$16$$
Please choose an option from A-E to answer. | (B) $$6$$ |
[
"其它"
] | 2 | Find the value of the expression: $$3- \frac{6}{1 \times \left (1+2\right )}- \frac{9}{\left (1+2\right ) \times \left (1+2+3\right )}-\frac{12}{\left (1+2+3\right ) \times \left (1+2+3+4\right )}- \cdots$$ $$- \frac{60}{\left (1+2+ \cdots +19\right ) \times \left (1+2+ \cdots +20\right )}$$
Options:
(A) $\frac{1}{6... | (B) $\frac{1}{70}$ |
[
"其它"
] | 3 | Let $p, q$, and $r$ be the distinct roots of the polynomial $x^{3}-22 x^{2}+80 x-67$. It is given that there exist real numbers $A, B$, and $C$ such that $$ \frac{1}{s^{3}-22 s^{2}+80 s-67}=\frac{A}{s-p}+\frac{B}{s-q}+\frac{C}{s-r} $$ for all $s \notin\textbackslash{p, q, r\textbackslash}$. What is $\frac{1}{A}+\frac{1... | (B) $$244$$ |
[
"其它"
] | 2 | On her first day of work, Janabel sold one widget. On day two, she sold three widgets. On day three, she sold five widgets, and on each succeeding day, she sold two more widgets than she had sold on the previous day. How many widgets in total had sabing $20$ days? (2015 AMC 8 Problems, Question \#9)
Options:
(A) $$39$... | (D) $$400$$ |
[
"其它"
] | 2 | Three fifths of a pitcher is filled with pineapple juice. The pitcher is emptied by pouring an equal amount of juice into each of 6 cups. What percent of the total capacity of the pitcher did each cup receive?~ (adapted from 2020 AMC 8, Question \#5)
Options:
(A) $$5$$
(B) $$10$$
(C) $$15$$
(D) $$20$$
(E) $$25$$
Plea... | (B) $$10$$ |
[
"其它"
] | 2 | A number of students from Fibonacci Middle School are taking part in a community service project. The ratio of $8^{\text {th }}$-graders to $6^{\text {th }}$-graders is $11: 6$, and the the ratio of $8^{\text {th }}$-graders to $7^{\text {th }}$ graders is $8: 13$. What is the smallest number of students that could be ... | (C) $$107$$ |
[
"其它"
] | 2 | \textbf{Scientists estimate that the distribution of the life span of the Galápagos Islands giant tortoise is approximately normal with mean 100 years and standard deviation 15 years. Based on the estimate, which of the following is closest to the age of a Galápagos Islands giant tortoise at the 90th percentile of th... | (C) \textbf{120 years} |
[
"其它"
] | 2 | \textbf{One of the values in a normal distribution is 43, and its z-score is 1.65. If the mean of the distribution is 40, what is the standard deviation of the distribution?}
Options:
(A) $$3$$
(B) $$-1.82$$
(C) $$0.55$$
(D) $$1.82$$
(E) $$-0.55$$
Please choose an option from A-E to answer. | (D) $$1.82$$ |
[
"其它"
] | 2 | Joe writes an expression $\frac59\times\frac9{13}\times\frac{13}{17}\cdots $ Following the pattern, he writes the expression with $\frac{45}{49}$ as the multiplier in the middle. What is the result of the expression?
Options:
(A) $\frac5{49}$
(B) $\frac5{89}$
(C) $\frac5{17}$
(D) $\frac1{31}$
(E) $\frac5{81}$
Please ... | (B) $\frac5{89}$ |
[
"其它"
] | 4 | What is the median of the following list of 4040 numbers: $$ 1,2,3, \ldots, 2020,1^{2}, 2^{2}, 3^{2}, \ldots, 2020^{2}$$? (2020 AMC 10A Problems, Question \#11)
Options:
(A) $$1974.5$$
(B) $$1975.5$$
(C) $$1976.5$$
(D) $$1977.5$$
(E) $$1978.5$$
Please choose an option from A-E to answer. | (C) $$1976.5$$ |
[
"其它"
] | 2 | For $\triangle ABC$, all its side lengths are integer. The primeter of $\triangle ABC$ with a side of length $2$ and a side length of $5$ is at least ．
Options:
(A) $$7$$
(B) $$8$$
(C) $$9$$
(D) $$11$$
Please choose an option from A-E to answer. | (D) $$11$$ |
[
"其它"
] | 2 | Let $f(x)=a x^{2}+b x+c$, where $a, b$, and $c$ are integers. Suppose that $f(1)=0,50\textless f(7)\textless60,70\textless f(8)\textless80$, $5000 k\textless f(100)\textless5000(k+1)$ for some integer $k$. What is $k$? (2011 AMC 12A Problems, Question 20)
Options:
(A) $$1$$
(B) $$2$$
(C) $$3$$
(D) $$4$$
(E) $$5$$
Ple... | (C) $$3$$ |
[
"其它"
] | 2 | A 95\% confidence interval for the difference between two population proportions is found to be (0.07, 0.19). Which of the following statement is (are) true? I. It is unlikely that the two populations have the same proportions. II. We are 95\% confidence that the true difference between population proportions is betw... | (C) I, II |
[
"其它"
] | 3 | Chantal and Jean start hiking from a trailhead toward a fire tower. Jean is wearing a heavy backpack and walks slower. Chantal starts walking $4$ miles per hour. Halfway to the tower, the trail becomes really steep, and Chantal slows down to $2$ miles per hour. After reaching the tower, she immediately turns around and... | (A) $\frac{12}{13}$ |
[
"其它"
] | 2 | \textbf{From a random sample of 1,005 adults in the United States, it was found that 32 percent own an e-reader. Which of the following is the appropriate 90 percent confidence interval to estimate the proportion of all adults in the United States who own an e-reader?~}
Options:
(A) \textbf{$0.32 \pm 1.960(\frac{(0.32... | (E) \textbf{$0.32 \pm 1.645\sqrt{(\frac{(0.32)(0.68)}{1,005})}$} |
[
"其它"
] | 2 | It is known that the number $2017$ is placed at $M^{\text{th}}$ row, $N^{\text{th}}$ entry. Find the value of $M+N$.
Options:
(A) $$126$$
(B) $$127$$
(C) $$128$$
(D) $$129$$
(E) $$130$$
Please choose an option from A-E to answer. | (C) $$128$$ |
[] | 2 | Fill "$$+$$" or~"$$-$$" in the blanks to make the equation true.~\uline{~~~~~~~~~~}~ $$6$$~~~~ $$6$$~~~~ $$6$$~~~~ $$6$$~~~~ $$6=6$$
Options:
(A) $$+++-$$
(B) $$++++$$
(C) $$++-\/-$$
Please choose an option from A-E to answer. | (C) $$++-\/-$$ |
[
"其它"
] | 2 | \textbf{According to a report for veterinarians in the United States, 36.5 percent of households in the United States own dogs and 30.4 percent of households in the United States own cats. If one household in the United States is selected at random, what is the probability that the selected household will own a dog or ... | (E) \textbf{Not enough information is given to determine the probability} |
[
"其它"
] | 2 | If $3^{}p+3^{4}=90$, and $2^{}r+44=76$, what is the product of $p$ and $r$? (Adapted from 2013 AMC 8 Problem, Question \#15)
Options:
(A) $$8$$
(B) $$10$$
(C) $$12$$
(D) $$15$$
(E) $$18$$
Please choose an option from A-E to answer. | (B) $$10$$ |
[
"其它"
] | 2 | What is the least possible value of $$ (x+1)(x+2)(x+3)(x+4)+2019 $$ where $x$ is a real number?
Options:
(A) $$2017$$
(B) $$2018$$
(C) $$2019$$
(D) $$2020$$
(E) $$2021$$
Please choose an option from A-E to answer. | (B) $$2018$$ |
[
"其它"
] | 2 | Avril\textquotesingle s father bought 14 books. Avril takes away 6 books. How many books does Avril\textquotesingle s father have left?
Options:
(A) $$9$$
(B) $$8$$
(C) $$7$$
Please choose an option from A-E to answer. | (B) $$8$$ |
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