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AMC8 1998

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AMC8 · 1998

Q1
For $x = 7$, which of the following is smallest?
当 $x = 7$ 时，下列哪个最小？
Q2
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Q3
What is $\frac{3}{8} + \frac{7}{8} \div \frac{4}{5}$?
计算 $\frac{3}{8} + \frac{7}{8} \div \frac{4}{5}$ 等于多少？
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Q4
How many triangles are in this figure? (Some triangles may overlap other triangles.)
这幅图中有多少个三角形？（有些三角形可能与其他三角形重叠。）
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Q5
Which of the following numbers is largest?
下列哪个数最大？
Q6
Dots are spaced one unit apart, horizontally and vertically. The number of square units enclosed by the polygon is
点在水平和垂直方向上相距一单位。多项式围成的平方单位数是
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Q7
$100 \times 19.98 \times 1.998 \times 1000 =$
$100 \times 19.98 \times 1.998 \times 1000 = $
Q8
A child's wading pool contains 200 gallons of water. If water evaporates at the rate of 0.5 gallons per day and no other water is added or removed, how many gallons of water will be in the pool after 30 days?
一个儿童戏水池中有 200 加仑水。如果水每天蒸发 0.5 加仑，且没有其他水加入或移除，30 天后池中水有多少加仑？
Q9
For a sale, a store owner reduces the price of a $10 scarf by 20%. Later the price is lowered again, this time by one-half the reduced price. The price is now
店主为促销将一条 10 美元的围巾降价 20%。后来价格再次降低，这次是降低已降价的一半。现在的价格是
Q10
Each of the letters W, X, Y, and Z represents a different integer in the set {1, 2, 3, 4}, but not necessarily in that order. If $\frac{W}{X} - \frac{Y}{Z} = 1$, then the sum of W and Y is
字母 W、X、Y 和 Z 各代表集合 {1, 2, 3, 4} 中的不同整数，不一定按此顺序。如果 $\frac{W}{X} - \frac{Y}{Z} = 1$，则 W 和 Y 的和是
Q11
Harry has 3 sisters and 5 brothers. His sister Harriet has S sisters and B brothers. What is the product of S and B?
Harry 有 3 个姐妹和 5 个兄弟。他的姐姐 Harriet 有 S 个姐妹和 B 个兄弟。S 和 B 的乘积是多少？
Q12
$2(1 - \frac{1}{2}) + 3(1 - \frac{1}{3}) + 4(1 - \frac{1}{4}) + \dots + 10(1 - \frac{1}{10}) =$
$2(1 - \frac{1}{2}) + 3(1 - \frac{1}{3}) + 4(1 - \frac{1}{4}) + \dots + 10(1 - \frac{1}{10}) =$
Q13
What is the ratio of the area of the shaded square to the area of the large square? (The figure is drawn to scale.)
阴影正方形的面积与大正方形的面积之比是多少？（图形按比例绘制。）
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Q14
At Annville Junior High School, 30% of the students in the Math Club are in the Science Club, and 80% of the students in the Science Club are in the Math Club. There are 15 students in the Science Club. How many students are in the Math Club?
在 Annville 初中，数学俱乐部 30% 的学生在科学俱乐部，科学俱乐部 80% 的学生在数学俱乐部。科学俱乐部有 15 名学生。数学俱乐部有多少学生？
Q15
Estimate the population of Nisos in the year 2050.
估计 2050 年 Nisos 的总人口。
Q16
Estimate the year in which the population of Nisos will be approximately 6,000.
估计 Nisos 人口大约达到 6000 年的年份。
Q17
In how many years, approximately, from 1998 will the population of Nisos be as much as Queen Irene has proclaimed that the islands can support?
大约从 1998 年起多少年后，Nisos 的人口将达到 Queen Irene 宣称岛屿所能支持的数量？
Q18
As indicated by the diagram at the right, a rectangular piece of paper is folded bottom to top, then left to right, and finally, a hole is punched at X. What does the paper look like when unfolded?
如右图所示，一张矩形纸从下折到上，然后从左折到右，最后在 X 处打一个洞。展开纸后是什么样子？
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Q19
Tamika selects two different numbers at random from the set {8, 9, 10} and adds them. Carlos takes two different numbers at random from the set {3, 5, 6} and multiplies them. What is the probability that Tamika's result is greater than Carlos' result?
Tamika 从集合 {8, 9, 10} 中随机选两个不同的数相加。Carlos 从集合 {3, 5, 6} 中随机选两个不同的数相乘。Tamika 的结果大于 Carlos 的结果的概率是多少？
Q20
Let $PQRS$ be a square piece of paper. $P$ is folded onto $R$ and then $Q$ is folded onto $S$. The area of the resulting figure is 9 square inches. Find the perimeter of square $PQRS$.
设 $PQRS$ 是一张正方形纸。将 $P$ 折到 $R$，然后将 $Q$ 折到 $S$。所得图形的面积是 9 平方英寸。求正方形 $PQRS$ 的周长。
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Q21
A $4 \times 4 \times 4$ cubical box contains 64 identical small cubes that exactly fill the box. How many of these small cubes touch a side or the bottom of the box?
一个 $4 \times 4 \times 4$ 的立方体盒子装有 64 个完全填满盒子的小立方体。其中有多少个小立方体触及盒子的侧面或底部？
Q22
Terri produces a sequence ... starts with positive integer, rules: <10 *9; even>9 /2; odd>9 -5. Sequence begins 98,49,... find 98th term.
Terri 生成一个序列……从正整数开始，规则：<10 *9；偶数>9 /2；奇数>9 -5。序列从 98,49,... 开始，求第 98 项。
Q23
If the pattern in the diagram continues, what fraction of the interior would be shaded in the eighth triangle?
如果图中的模式继续，第八个三角形的内部有几分之几被涂黑？
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Q24
A rectangular board of 8 columns has squares numbered beginning in the upper left corner and moving left to right so row one is numbered 1 through 8, row two is 9 through 16, and so on. A student shades square 1, then skips one square and hades square 3, skip two squares and shades square 6, ships 3 squares and shades square 10, and continues in this way until there is at least one shaded square in each column. What is the number of the shaded square that ¯rst achieves this result?
一个有 8 列的矩形棋盘，方格从左上角开始编号，从左到右，行一是 1 到 8，行二是 9 到 16，依此类推。学生涂黑方格 1，然后跳过一个涂黑 3，跳过两个涂黑 6，跳过三个涂黑 10，并以此类推，直到每列至少有一个涂黑方格。第一个实现此结果的涂黑方格编号是多少？
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Q25
Three generous friends, each with some cash, redistribute their money as follows: Ami gives enough money to Jan and Toy to double the amount that each has. Jan then gives enough to Ami and Toy to double their amounts. Finally, Toy gives Ami and Jan enough to double their amounts. If Toy has \$36 when they begin and $36 when they end, what is the total amount that all three friends have?
三位慷慨的朋友，各有一些现金，按以下方式重新分配金钱：Ami 给 Jan 和 Toy 足够的钱，使她们各自的金额翻倍。Jan 然后给 Ami 和 Toy 足够的钱，使她们各自的金额翻倍。最后，Toy 给 Ami 和 Jan 足够的钱，使她们各自的金额翻倍。如果 Toy 开始和结束时都有 \$36，他们三人总共有多少钱？
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