2013 AMC amc10a 真题 答案 详解

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中英双语真题

2013 AMC 10A

Problem 1
A taxi ride costs $1.50 plus $0.25 per mile traveled. How much does a 5-mile taxi ride cost?
出租车的起步价是1.5美元，每开1英里还需额外支付0.25美元，那么5英里的里程需要支付多少美元？
(A) 2.25 (B) 2.50 (C) 2.75 (D) 3.00 (E) 3.75

Problem 2
Alice is making a batch of cookies and needs ( \frac{2}{4} ) cups of sugar. Unfortunately, her measuring cup holds only ( \frac{1}{4} ) cup of sugar. How many times must she fill that cup to get the correct amount of sugar?
Alice 正在做一些曲奇饼，需要 ( \frac{2}{4} ) 杯糖。不幸的是，她的量杯只能一次装满 ( \frac{1}{4} ) 杯的糖。那么她需要装满多少杯量杯才能得到所需要的总量的糖？
(A) 8 (B) 10 (C) 12 (D) 16 (E) 20

Problem 3
Square ABCD has side length 10. Point E is on BC, and the area of △ABE is 40. What is BE?
正方形ABCD的边长为10。点E在BC上，△ABE的面积为40。问BE的长是多少？
(A) 4 (B) 5 (C) 6 (D) 7 (E) 8

英文真题

2013 AMC 10A Problems Problem 1 A taxi ride costs $1.50 plus $0.25 per mile traveled. How much does a 5-mile taxi ride cost? (A) 2.25 (B) 2.50 (C) 2.75 (D) 3.00 (E) 3.75 Problem 2 Alice is making a batch of cookies and needs (2 \frac{1}{2}) cups of sugar. Unfortunately, her measuring cup holds only (\frac{1}{4}) cup of sugar. How many times must she fill that cup to get the correct amount of sugar? (A) 8 (B) 10 (C) 12 (D) 16 (E) 20 Problem 3 Square ABCD has side length 10. Point E is on BC, and the area of △ABE is 40. What is BE? (A) 4 (B) 5 (C) 6 (D) 7 (E) 8 Problem 4 A softball team played ten games, scoring 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 runs. They lost by one run in exactly five games. In each of their other games, they scored twice as many runs as their opponent. How many total runs did their opponents score? (A) 35 (B) 40 (C) 45 (D) 50 (E) 55 Problem 5 Tom, Dorothy, and Sammy went on a vacation and agreed to split the costs evenly. During their trip Tom paid $105, Dorothy paid $125, and Sammy paid $175. In order to share costs equally, Tom gave Sammy t dollars, and Dorothy gave Sammy d dollars. What is t - d? (A) 15 (B) 20 (C) 25 (D) 30 (E) 35 Problem 6 Joey and his five brothers are ages 3, 5, 7, 9, 11, and 13. One afternoon two of his brothers whose ages sum to 16 went to the movies, two brothers younger than 10 went to play baseball, and Joey and the 5-year-old stayed home. How old is Joey? (A) 3 (B) 7 (C) 9 (D) 11 (E) 13 Problem 7 A student must choose a program of four courses from a menu of courses consisting of English, Algebra, Geometry, History, Art, and Latin. This program must contain English and at least one mathematics course. In how many ways can this program be chosen? (A) 6 (B) 8 (C) 9 (D) 12 (E) 16

真题文字详解(英文)

Problem 1 A taxi ride costs $1.50 plus $0.25 per mile traveled. How much does a 5-mile taxi ride cost?
(A) 2.25 (B) 2.50 (C) 2.75 (D) 3.00 (E) 3.75

Solution There are five miles which need to be traveled. The cost of these five miles is $(0.25 \cdot 5)=1.25$. Adding this to 1.50, we get (C) 2.75.

Problem 2 Alice is making a batch of cookies and needs $2\frac{1}{2}$ cups of sugar. Unfortunately, her measuring cup holds only $\frac{1}{4}$ cup of sugar. How many times must she fill that cup to get the correct amount of sugar?
(A) 8 (B) 10 (C) 12 (D) 16 (E) 20

Solution To get how many cups we need, we realize that we simply need to divide the number of cups needed by the number of cups collected in her measuring cup each time. Thus, we need to evaluate the fraction $\frac{2\frac{1}{2}}{\frac{1}{4}}$. Simplifying, this is equal to $\frac{5}{2}(4)=(\textbf{(B)}\ 10)$.

Problem 3 Square ABCD has side length 10. Point E is on BC, and the area of △ABE is 40. What is BE?
(A) 4 (B) 5 (C) 6 (D) 7 (E) 8

Solution We are given that the area of △ABE is 40, and that AB = 10.
The area of a triangle is:
$A=\frac{bh}{2}$
Using AB as the height of △ABE,

真题文字详解(中英双语)

Problem 1 A taxi ride costs $1.50 plus $0.25 per mile traveled. How much does a 5-mile taxi ride cost? 一辆出租车行程的费用为$1.50加上每行驶$0.25英里的5。一辆5英里的出租车行程费用是多少？
(A) 2.25 (B) 2.50 (C) 2.75 (D) 3.00 (E) 3.75 Solution There are five miles which need to be traveled. The cost of these five miles is $(0.25 \cdot 5)=1.25$. Adding this to $1.50$, we get (C) 2.75 Problem 2 Alice is making a batch of cookies and needs $2\frac{1}{2}$ cups of sugar. Unfortunately, her measuring cup holds only $\frac{1}{4}$ cup of sugar. How many times must she fill that cup to get the correct amount of sugar? (A) 8 (B) 10 (C) 12 (D) 16 (E) 20 Solution To get how many cups we need, we realize that we simply need to divide the number of cups needed by the number of cups collected in her measuring cup each time. Thus, we need to evaluate the fraction $\frac{2\frac{1}{2}}{\frac{1}{4}}$. Simplifying, this is equal to $\frac{5}{2}(4)=(B) 10$ Problem 3 Square ABCD has side length 10. Point E is on BC, and the area of △ABE is 40. What is BE? (A) 4 (B) 5 (C) 6 (D) 7 (E) 8 Solution We are given that the area of △ABE is 40, and that AB = 10. The area of a triangle is: $A=\frac{bh}{2}$