1. l1, l2 and l3 are three lines in spaceThe number of points at The number of points at which lines l1 and l2 intersect which lines l2 and l3 intersect1。
三條任意直線，L1和L2的交點的個數與L2和L3的交點的個數沒關。
2. The number of 1/4-inch lengths in 1a 4-inch length2，是問4英尺中有多少個1/4英尺，應該是16個，所以是A3. The maximun number of solid cubes 4having edges of length 1/2 meter thatcan be placed inside a cubical boxhaving inside edges of length 1 meter3邊長為1的立方體裡最多能放下幾個邊長為1/2的立方體，當然是8個咯4. Cube C has volume 8 cubic centimetersThe area of one of the faces of cube C 3 square centimeters4立方體體積是8，那一個面的面積當然是4咯5. Ms.Smith got an 8 percent cost-of-living raise of $20 per weekMs.Smith's new weekly salary $2605 x*0.08=20，那x+20=270>2606. On a certain number live, if -7 is a distance of 4 from n and 7 is a distance of 18from n then n=A.25B.11C.3D.-3 E-116應該是-117. For all real numbers a and b. if a•b=a(a+b), then a•(a•b)=A. a2+ab B a2+ab+a C a2+a+b D a3+a2b E a3+a2b+a2注：a2表示a平方，a3表示a立方7新定義的運算a•b=a(a+b), 那a•(a•b)=a•(aa+ab)=a(a+aa+ab)=aa+aaa+aab8.secretary typed 6 letters,each of which had either 1 or 2 pages.If the secretary typed 10 pages in all, how many of the letters had 2 pages?A 1B 2C 3D 4E 5答案是D，題目我都看不懂，是啥意思呢？這是說秘書打六封信，沒一封信要1頁或者兩頁。
如果秘書總共打了10頁，那麼有多少封信是兩頁？解答：設有x封，則2x+(6-x)=10,解得x=4.9 how many of the five numbers above are each equal to the product of an integer and an odd integer that greater than 1?這五個數是:2 6 8 14 16a.noneb.onec.twod.theree.four我覺得這道題除了2不可能,其它四個數都有可能.可答案是c,想問大家為什麼?題目意思是這5個數哪些可以是2個>1的數的積,一個是奇數,一個是整數,只有6和14的因數中有奇數,所以C.10 這句話大家看該怎樣列式子呢?這是一道圖表題.what was the approximate percent increase in personal income from 1965 to 1970?是這樣(1970-1965)/1965還是(1970-1965)/1970這樣?是這樣:(1970-1965)/19651 the sum of two numbers, x and y, equals twice their products. if x=3, what is the value of y?這道題沒大看懂?請問大家是這樣麼?x+y=2(x+y)x+y=2xy,求y.2 if x is an integer and x2(x的平方)<37,what is the greatest possible value of x minus the least possible value of x?我覺得這道題x的最大值為6,最小值為0,所以選6.a.5b.6c.10d.12e.36選D，最大為6，最小為-6.3 三角形ABC，角B＝X度，X>90 度，比較三角形的周長與3倍AC的長度的大小，答案是BAC是最大邊,所以AB+BC+AC<AC+AC+AC(3AC).2.0<p<1比較the greatest value of p(1-p)與1／2的大小，答案是C答案錯了,選B p+(1-p)>=2p(1-p)^1/2 => p(1-p)<=1/4 < 1/24 for the line with equation y=ax+b,the x-intercept os twice the y-intercept比較the slope of the line 與1／2的大小，答案是D，但算出來是－1／2呀還有截距為零的情況,所以D.5 a certain moneymarket account that had a balance of $48000 during all of last monthearned $360 in interest for the month. at what simple annual interestrate did the account earn interest last month?答案是9%,題目沒看懂意思是一個貨幣市場上個月共結餘48000，用它賺了360的利息，問以年單利計算每年利率是多少？360*12/48000=9%6 Of the positive integers that are multiples of 30 and are less than or equal to 360,what fraction are multiples of 12?a.1/6b.1/5c.1/3d.2/5e.1/2首先這道題我是對multilples of ....不大明白,這是什麼意思啊?其次這道題怎麼解呢?在小於360的30的公倍數中,也是12的公倍數的占多少?30N≤360, 得N≤12,所以共有12個數滿足題幹.又12與30的最小公倍數為60,其實此題是求是60的倍數又小於等於360所占比例,同理求出為6所以,6/12=答案E7 A certain teacher has a total ofat least 110 students enrolled in her classes.if the teachers has anaverage (arithmetic mean) of exactly 27 students enrolled per class.what is the least possible number of classes that the teacher couldhave?a.3b.4c.5d.6e.7我覺得這道題就是用110除以27就好了,可是答案是選c的是呀，110/27=4.04,如果是4個班，那麼總人數為108，還剩2個。
當然是5個班了。
8 a delivery service charges $0.02 per ounce for the first 16 ounces ofa shipment and $0.15 for eachadditional ounce of theshipment,(1pound=16ounce)the delivery charges for x shipments weighing a combimed total of the pounds vs 567.00這道題答案選的是D,不明白怎麼會無法確定呢?我是這樣算的:16×0.2+(25*16-16)×0.15...這樣對麼?因為x是個未知數，所以你無法確定它的值。
9 the cost per gram of carrots if 3 cans of carrots cost $0.90 the costper gram of onions if 5 cans of onions cost $1.50無法確定，沒有告訴1can有多少克？10 X is an integer, and the remainder when 2X is divided by 4 is 0.The remainder when X is divided by 4 0選D，當x=2，-2時，餘數為2，-2，其它情況為01 Let[X]=3, if X is an odd integer;let[X]=6, if X is an even integer.r and s are integers, 3r is odd and 5+s is odd.[r][s]3r是奇數說明r為奇數，所以[r]等於3，5+s為奇數，說明s為偶數，所以[s]=62 the value of the units' digit in 6^47(6的47次方) the value of the units' digit in 5^77(5的77次方)比較兩個數的個位，6不管多少次方個位都為6，5不管多少次方個位都為5.3 for all numbers r and s, where s/=(不等於)0, r#s=10r/s.0.01#0.01 10.01#0.01=10*0.01/0.01=10,大於1.4 1<n<5,n is an integer.the sum of the first n odd integers that are greater than zero n^2(n平方)-1說的是n個大於零的奇數和。
當n=2，1+3=4；n^2-1=3;當n=3，1+3+5=9;n^2-1=8;當n=4，1+3+5+7=16；n^2-1=15所以選A5 a^7+a^15 a^8+a^14注是a的7次方,類推呵呵比較大小題後-前=a^7(a-1)+a^14(1-a)=(a^7-a^14)(a-1)然後討論,最後結果是後-前的差<0,但當a=1時，相等。