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SAT考试数学考点之线性方程精讲

2016-09-26 14:02
摘要:SAT数学部分所考查的知识点,包括基础代数、数据分析&实际问题、中级代数三个部分,对于中国学生而言,这些知识点难度不大。



SAT数学部分所考查的知识点,包括基础代数、数据分析&实际问题、中级代数三个部分,对于中国学生而言,这些知识点难度不大,但部分知识点考查的方式与侧重点和国内考试有些差异,需要注意。


以下就是100留学为大家带来的SAT考试数学考点之线性方程精讲。希望对各位的备考有所帮助


1.2线性方程

线性函数的表现形式:

The general form of theequation is

The slope-intercept form is

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

The slope-point form is

直线的位置关系:

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

1line l and k are parallel if and only if theyhave the same slope;

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


例题9. f(x) = 2x – 1 and g(x) is a linearfunction 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)的斜率为,过(0,4)点,所以直线方程为:


两个方程联立,解出 x=2,y=3

答案:C


例题6.Luca’s pays $1195 per month for rent plus 10 cents per kilowatt hour (kWh) usedfor electricity. If Luca used x kWh in one month, which expression bestrepresents 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为基础费用,10cents是每kWh的增加费用,所以总费用的方程为:


答案:A.


例题7. Whichof 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是直线方程的一般形式,改写为斜截式:

,斜率为-3。再从选项中寻找斜率同样为-3的直线。

答案:B


例题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 thanf(x) for the same values of y.

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

Solution

4f(x)的图像是将y轴拉伸4倍,4f(x)=8x+8。图像与X轴的交点不变,与Y轴的交点扩大4倍,斜率也增加4倍。

答案:A



例题2. Whichof 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:

首先判断斜率:,再代入一个点计算,答案为B


练习:

|x – 3| ≤ 5

1. Which of the following inequalities isequivalent to the absolute value inequality above?

(A) –2 ≤ x ≤ 8

(B) –8 ≤ x ≤ 2

(C) x ≤ –2 or x ≥ 8

(D) x ≤ –8 or x ≥ 2

9992. Whichof the following equations could represent the linear equation above?

(A) y =–2x – 1

(B)  y =–2x + 1

(C)  y =2x – 1

(D) y = 2x+ 1


3. If f(x)is a linear function that passes through the points (4, 3) and (-4, -9), whatis the y-intercept of f(x)?

(A) (0, 2)

(B)  (2,0)

(C)  (0,-3)

(D) (-3,0)

4. Joel isa years older than Luca. In byears, Joel will be twice as old as Luca. What is Joel’s present age, in termsof a and b?

(A) –2(a – b)

(B) –2a – b

(C) 2a – b

(D) a – b


5. In the system of linear equations shown, ais a constant. If the system has no solution, what is the value of a?


A. 2

B. 3

C. 4

D. 5



3e038b846157e8b93feac42.png

6. What is the slope of the function in thegraph above?




7. If k is a rational number such that k >1, which of the following could be the graph of the equation y = key + ox + x +5?

5000b8f50457e8b95cf33c7.png


答案:

1    2    3    4    5    6    7    

A   C   C   C   C   C   A   


解析:

1.    题干:|x – 3| ≤ 5等价于什么?

解析:可以理解为x3的距离等于小于5.

2.    题干:如何表示下图的直线?

cf27bd663057e8b96c9e65c.png

解析:找出斜率和截距即可.

3.    题干:直线经过(4, 3) (-4, -9),那么y轴截距是多少?

解析:求出直线,然后得到截距.

4.    题干:JLa岁,b年后,J的年龄会是L的两倍.现在J的年龄是多少?

解析:设J现在为x岁然后根据给出的两个关系列式,即可得到x的表达式.

5.    题干:如果

无解,那么a=

解析:这种方程组相当于求两直线的交点,如果两直线不同而且平行,那么就没有交点.

6.    题干:求斜率.

8091de838057e8b97d25de2.png

解析:斜率等于My除以Ax.

7.    题干:y = key + ox + x + 5的图像是哪一个?如果k是实数,而且k>1.

解析:先移项,得到y关于x的表达式.


以上就是100留学为大家带来的SAT考试数学考点之线性方程精讲。更多SAT数学考试技巧备考内容,请继续关注100留学。

c292e2783557e8b986dd4b7.jpg



(文章内容摘选自《新SAT非官方指南》


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