数学篇|考前必看!2020年3月北美地区SAT考前预测


来源:   时间:2020-03-13 16:04:25

数学部分考点较为固定,历次考试的题型都没有跳出过官方指南的范畴。下文会结合历次考试对数学部分考点进行预测。

01.方程(组)解的个数

(1)一次方程解的个数
不管是无穷多个解还是无解,都要令左右两边X前系数相等。
例题:
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
答案选:B
 
(2)一次方程组解的个数
一次方程组根据两条直线是平行,重合还是相交,判断解的个数。
例题:
-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)二次方程组解的个数
根据判别式计算方程组解的个数。
例题:
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

02.参数含义

(1)一次函数slope和y-intercept含义
例题:
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)指数函数参数含义
指数函数类题型注意看清楚变量的单位。
例题:
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
答案选:D

03.特殊角三角函数

三角函数也是考试重点,除了30,45,60度这几个常考的特殊角,大家对90度,180度角等特殊角的三角函数也要熟悉。
例题:
Sin(180 degree)=
A)   1
B)   -1
C)   0
D)   1/2
答案选:C

04.不等式的图像

例题:
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.多项式因式定理

如果f(a)等于0,则(x-a)是f(x)的factor.
例题:
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

射影定理是常考内容,三个三角形的相似和对应边的比例关系要非常熟悉。
例题:
\
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.基本统计量

注意找median类题目一定要排序。

08.survey和experiment

survey中样本和总体的一致性是考察重点。实验中注意一定要把样本随机分成实验组和对照组。
例题:
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.
答案选:D

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