數學篇|考前必看!2020年3月北美地區SAT考前預測


來源:   時間:2020-03-13 16:04:25

數學部分考點較為固定,歷次考試的題型都沒有跳出過官方指南的范疇。下文會結合歷次考試對數學部分考點進行預測。

01.方程(組)解的個數

(1)一次方程解的個數
不管是無窮多個解還是無解,都要令左右兩邊X前系數相等。
例題:
8x-2x(c+1)=x
In the equation above, c is a constant. If the equation has infinitely many solutions, what is the value of c?
A)   3/2
B)   5/2
C)   7/2
D)   9/2
答案選:B
 
(2)一次方程組解的個數
一次方程組根據兩條直線是平行,重合還是相交,判斷解的個數。
例題:
-6.4x=4y+2.1
ky+3.2x=5.8
For what value of k does the above system of linear equations have no solutions?
答案是:2
 
(3)二次方程組解的個數
根據判別式計算方程組解的個數。
例題:
kx+y=1
y=-x2+k
The graph intersect at exactly two points. Which of the following CANNOT be the value of k?
A)   3
B)   2
C)   1
D)   0
答案是:D

02.參數含義

(1)一次函數slope和y-intercept含義
例題:
At a restaurant, n cups of tea are made by adding t tea bags to hot water. If t=n+3, how many additional tea bags are needed to make each additional cup of tea?
A)   None
B)   One
C)   Two
D)   Three
答案是:B
 
(2)指數函數參數含義
指數函數類題型注意看清楚變量的單位。
例題:
P=300(1.05)^(t/6)
The equation above can be used to model the population, in thousands, of a certain city y years after 2000. According to the model , the population is predicated to increase by 5% every n months. What is the value of n?
A)   6
B)   2
C)  12
D)  72
答案選:D

03.特殊角三角函數

三角函數也是考試重點,除了30,45,60度這幾個?嫉奶厥饨,大家對90度,180度角等特殊角的三角函數也要熟悉。
例題:
Sin(180 degree)=
A)   1
B)   -1
C)   0
D)   1/2
答案選:C

04.不等式的圖像

例題:
0<=x<=y<=8
What is the area, in the xy-plane , of the region consisting of all points that satisfy the inequality above?
答案是:32

05.多項式因式定理

如果f(a)等于0,則(x-a)是f(x)的factor.
例題:
If f(x) has roots -1,-3, and 5, which of the following is a factor of f(x)?
A)   (x+1)(x-3)
B)   (x+1)(x+5)
C)   (x+3)(x-5)
D)   (x+3)(x+5)
答案是:C

06.射影定理

射影定理是?純热,三個三角形的相似和對應邊的比例關系要非常熟悉。
例題:
\
In the xy-plane above, lines k and l are perpendicular. What is the x-coordinate of point P?
A)   5.25
B)   5.75
C)   6
D)   6.25
答案是:D

07.基本統計量

注意找median類題目一定要排序。

08.survey和experiment

survey中樣本和總體的一致性是考察重點。實驗中注意一定要把樣本隨機分成實驗組和對照組。
例題:
A community center offers a French course. This year, all students in the course were offered additional audio lessons they could take at home. The students who took these additional audio lessons did better in the course than students who didn’t take the additional audio lessons. Which of the following is an appropriate conclusion?
A)   Taking additional audio lessons will cause an improvement for any student who takes any foreign language course.
B)    Taking additional audio lessons will cause an improvement for any student who takes a French course.
C)   Taking additional audio lessons was the cause of the improvement for the students at the community center who took the French course.
D)   No conclusion about cause and effect can be made regarding students at the community center who took the additional audio lessons at home and their performance in the French course.
答案選:D

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