中國(guó)數(shù)學(xué)的難度相比較于美國(guó)難很多，所以在SAT沒(méi)改革前，SAT數(shù)學(xué)滿分考生比比皆是。進(jìn)入新SAT時(shí)代后，從新SAT考試成績(jī)的數(shù)據(jù)統(tǒng)計(jì)中不難發(fā)現(xiàn)能到800分的考生是非常罕見(jiàn)的，780分以上的也是寥寥無(wú)幾，大部分都集中在700—750之間。是什么原因造成這個(gè)看似簡(jiǎn)單卻拿不到最高分的考試呢?那是因?yàn)槟銢](méi)有找到學(xué)習(xí)的正確技巧和方法。

  線性函數(shù)的表現(xiàn)形式：

  The general form of the equation is

  The slope-intercept form is

  The slope of the line is represented by m and is defined to be the ratio of, where and are any two points on the line. The y-intercept is b.

  The slope-point form is

  直線的位置關(guān)系：

  If the slopes if line l and k are each defined (that is, if neither line is a vertical line), then

  (1)line l and k are parallel if and only if they have the same slope;

  (2)Line l and line k are perpendicular if and only if the product of their slopes is -1.

  例題9. f(x) = 2x – 1 and g(x) is a linear function that is perpendicular to f(x). If (0, 4) is a point of g(x), at what point do f(x) and g(x) intersect?

  (A) (0, -1)

  (B) (1, 1)

  (C) (2, 3)

  (D) (3, 2)

  Solution：

  g(x)的斜率為，過(guò)(0,4)點(diǎn)，所以直線方程為：

  兩個(gè)方程聯(lián)立，解出 x=2, y=3。

  答案：C。

  例題6. Luca’s pays $1195 per month for rent plus 10 cents per kilowatt hour (kWh) used for electricity. If Luca used x kWh in one month, which expression best represents the amount of money in dollars Luca needs to pay for his apartment?

  (A) 1195 + 0.1x

  (B) (1195 + 0.1)x

  (C) 1195 + 10x

  (D) (1195 + 1)x

  Solution：

  1195為基礎(chǔ)費(fèi)用，10cents是每kWh的增加費(fèi)用，所以總費(fèi)用的方程為：

  答案：A.

  例題7. Which of the following equations has the same slope as 2y + 6x = 5?

  (A) x + 3y = 1

  (B) 3x = –y + 5

  (C) y – 3x = 4

  (D) 6y = 2x – 1

  Solution:

  2y + 6x = 5是直線方程的一般形式，改寫(xiě)為斜截式：

  ，斜率為-3。再?gòu)倪x項(xiàng)中尋找斜率同樣為-3的直線。

  答案：B。

  例題6. If f(x) = 2x + 2 is a linear function, which of the following is true for 4f(x)?

  (A) The slope is four times steeper than f(x).

  (B) The slope is four times less steep than f(x).

  (C) All values of x are four times greater than f(x) for the same values of y.

  (D) The slope changes, but the y-intercept remains the same as f(x).

  Solution：

  4f(x)的圖像是將y軸拉伸4倍，4f(x)=8x+8。圖像與X軸的交點(diǎn)不變，與Y軸的交點(diǎn)擴(kuò)大4倍，斜率也增加4倍。

  答案：A。

  例題2. Which of the following expressions defines f(x) in the table above?

  (A) f(x) = x + 3

  (B) f(x) = x + 3

  (C) f(x) = x

  (D) f(x) = 2x

  Solution:

  首先判斷斜率：，再代入一個(gè)點(diǎn)計(jì)算，答案為B。

  新航道上海sat培訓(xùn) 開(kāi)設(shè)有各種SAT培訓(xùn)班 ，小班教學(xué)，名師一對(duì)一指導(dǎo)，助教全程跟蹤輔導(dǎo)，直達(dá)高分不在是夢(mèng)。

請(qǐng)加COCO老師（微信號(hào)：shnc_2018）

百人留學(xué)備考群，名師答疑，助教監(jiān)督，分享最新資訊，領(lǐng)取獨(dú)家資料。掃碼免費(fèi)加入