SAT数学：5道习题练练手(附答案和详解)

SAT数学练习题1：

-5.1x+3y=1.2

3.2x-8y=p

In the system of equations, p is a constant. Which of the following describes all values of p forwhich the system has exactly one solution?

A.p can be any number

B.p can be any number except 1.2

C.p can be any number except -1.2

D.p=1.2

答案：A

解析：

Option A is correct. After rewriting the equations inslope-intercept form (y=mx+b), the slopes of thetwo equations are different and the constant p ispart of the y-intercept. Since the slopes are differentregardless of the value of p, the lines represented by the equations must always intersect atexactly one point. So there is always one solution for any value of p.

SAT数学练习题2：

F(t)=0.95^(t/2)

The function F(t) gives the percentage, as a decimal, of information Dianna remembered t days after memorizing lines for a play. Assuming she didnot work on her lines again, what is the best interpretation of the meaning of the function Fin this context?

A.On any given day, Dianna will forget 95% of the lines 1 day after she memorizes them.

B.On any given day, Dianna will forget 95% of the lines 2 days after she memorizes them.

C.On any given day, Dianna will remember 95% of the lines 1 day after she memorizes them.

D.On any given day, Dianna will remember 95% of the lines 2 days after she memorizes them.

答案：D

解析：

Option D is correct. After 2 days, the exponent ofthe function will be 2/2=1. Dianna will remember (0.95^1)*100 or 95% of the lines.

SAT数学练习题3：

An online video gaming site with 20 million registeredusers ages 8 and older wants to find out the averagenumber of hours that all of its registered users spend playing offline video games each week. The site administerwd an online survey to 10 comma 000 of its registered users ages 16 through 18, selected at random. The survey asked the question, "How many hours do youspend playing offline video games each week?" The data collected showed that the meannumber of offline gaming hours per user was 8.3 hours per week. What characteristic of thesurvey prevents these results from being generalized to all of the site's users?

A.The age criteria for selecting the users who were surveyed

B.The size of the sample

C.The method used to analyze the data

D.The size of the population

答案：A

解析：

Option A is correct. The results can be generalizedonly to the population that was randomly sampled.

SAT数学练习题4:

While driving from Orlando, Florida, to Tampa, Florida, a family travels 4 miles in 5 minutes. If theytravel at the same rate for the next half hour, approximately how many miles will they travel inthat half hour?

A.20 miles

B.24 miles

C.40 miles

D.48 miles

答案：B

解析：

Option B is correct. 30 minutes is six times as longas 5 minutes, so the car will travel six times as faras it traveled in 5 minutes, or 4*6 miles.

SAT数学练习题5：

y=x+a

y=-x+a

In the system of equations above, a is a positive constant. If the system is graphed in the xy-plane, which of the following best describes the two lines?

A.Both equations represent the same line.

B.The lines are parallel.

C.The lines are perpendicular.

D.The lines intersect but are not perpendicular.

答案：C

解析：

Let's examine the slope and y-intercept of bothgraphs.

Both equations are written in slope-intercept form: y=mx+b

where m is the graph's slope and b is the graph's y-intercept.

The graph of the first equation, y=x+a, has a slope of 1 and its y-intercept is a.

The graph of the second equation, y=-x+a, has a slope of -1. Its y-intercept is also a. Therefore, the y-intercepts are the same; the slope of the first equation's graph is thenegative of the reciprocal of the slope of the second equation's graph (the reciprocal of 1/1 is 1/1), which means that the lines are perpendicular.

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