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【天道原创】2013年SAT官方每日一题1月-2月汇总之数学选择题

【天道原创】2013年SAT官方每日一题1月-2月汇总之数学选择题
【天道原创】2013年SAT官方每日一题1月-2月汇总之数学选择题

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目录

1月题目 (6)

1月答案解析 (11)

2月题目 (17)

2月答案解析 (21)

1月题目

1月1日

答案解析

In the figure,the slope of the line through points.What is the value of?

(A)(B)(C)(D)(E)

1月4日

答案解析

A machine can insert letters in envelopes at the rate of per minute.

Another machine can stamp the envelopes at the rate of per second.How many

such stamping machines are needed to keep up with inserting machines of this kind?

(A)(B)(C)(D)(E)

1月7日答案解析

If a number is chosen at random from the set

,what is the probability that it is a member of the solution set of both

and

?

(A)(B)(C)(D)(E)

1月10日答案解析

If

percent of

is greater than

,which of the following must be true?

(A)

(B)

(C)

(D)

(E)

1月13日答案解析

A train traveling

miles per hour for 1hour covers the same distance as a train

traveling miles per hour for how many hours?

(A)(B)(C)(D)(E)

1月16日

答案解析

The scatterplot above shows the number of items purchased at a grocery store by28customers and the total cost of each purchase.How many of these28 customers bought more than10items and spent less than$20?

(A)Four(B)Five(C)Six(D)Seven(E)Eight

1月19日

答案解析

In the-plane,the graph of the line with equation intersects the graph of

the quadratic function in exactly one point.What is the value of?

(A)(B)(C)(D)(E)

1月22日

答案解析

If,and,what is?

(A)(B)(C)(D)(E)

1月25日

答案解析

A jar contains only red marbles and green marbles.If a marble is selected at

random from the jar,the probability that a red marble will be selected is.If there are green marbles in the jar,how many red marbles are there in the jar?

(A)(B)(C)(D)(E)

1月28日

答案解析

If the function is defined by,where, for which of the following values of is undefined?

(A)None

(B)only

(C)only

(D)and only

(E),,and

1月31日

答案解析

If it is now4:00p.m.Saturday,in hours from now,what time and day will it be? (Assume no daylight saving time changes in the period.)

(A)5:00a.m.Saturday

(B)1:00a.m.Sunday

(C)5:00p.m.Tuesday

(D)1:00a.m.Wednesday

(E)5:00a.m.Wednesday

1月答案解析

1月1日

The correct answer is B

The slope of a line in a coordinate plane is given by the fraction whose numerator is

the change in between any two points on the line and whose denominator is the change in between the same points on the line.

The question asks for the value of,which is the-coordinate of point.

The change in between points and is.The change in between

these points is.Since the slope is,it follows that.Solving this equation gives.Therefore,,and.

1月4日

The correct answer is A

First you can change minute to seconds so that the ratios are both in envelopes per second.One inserting machine inserts letters at the rate

of per seconds,or per second.So machines would insert letters

per second.

Let be the number of stamping machines needed to keep up with18inserting

machines.Then,since one machine stamps3envelopes per second,machines

stamp envelopes per second.You can write the equation,which gives.

1月7日

The correct answer is C

If and,then.The numbers from the

listed set that satisfy these inequalities are and.There are five elements in the listed set,so the probability of a number chosen at random from the set being a member of the solution set of both inequalities is.

1月10日

The correct answer is A

If percent of is greater than,then.It follows that,and so.

1月13日

The correct answer is B

When the speed of a train in miles per hour is multiplied by the travel time in hours, the distance traveled by the train is obtained.The distance that the first train travels

is miles per hour times hour,which is https://www.wendangku.net/doc/5d7819084.html,ing the variable for the

travel time,in hours,of the second train,the distance that the second train travels

is miles per hour times hours,which is miles.Since the two trains travel

the same distance,,which gives hours,the travel time of the second train.

1月16日

The correct answer is A

Drawing the vertical line"Number of Items=10"and the horizontal line"Total Cost ="$20"divides the scatterplot into four regions,as shown in the figure below.

The lower right region lies below the line"Total Cost=$20"and to the right of the line"Number of Items=10."Thus the points in this region are exactly the points that represent a purchase of more than10items at a total cost of less than$20. (Note that the points on the line"Number of Items=10"represent a purchase of

exactly10items,not more than10items and,thus,do not meet the given conditions.)There are four points in the lower right region.Therefore,four of the customers bought more than10items and spent less than$20.

1月19日

The correct answer is B

The graph in the-plane of the quadratic function is a

parabola.If the graph of the line with equation intersects the graph of this parabola in exactly one point,that point must be the vertex of the parabola,and

the-coordinate of the point must be.The graph

of intersects the-axis at and,

so the-coordinate of the vertex of the parabola is halfway

between and on the-axis at.Thus the-coordinate of the

vertex is.Therefore,if the graph of the line with

equation intersects the graph of the quadratic

function in exactly one point,the value of must be.

1月22日

The correct answer is E

If,and,then.

Therefore,.

1月25日

The correct answer is D

Choice(D)is correct.Let be the number of red marbles in the jar.

The probability of selecting a red marble is equal to the number of red marbles divided by the total number of marbles.Since the probability of selecting a red

marble is,it follows that.There are green

marbles and red marbles,so the previous equation becomes.This

simplifies to,or.Therefore,the number of red marbles,,is.

1月28日

The correct answer is C

If,then.If,

then.If,

then,which is not

defined because division by is undefined.Therefore,of the three values,,,

and,the only one for which is undefined is.Thus the correct response is only.

1月31日

The correct answer is E

Since each day has hours,divide by to find the number of

complete intervals in

hours and the number of hours remaining

after the intervals have been accounted for.When is divided

by ,

the

quotient

is

and

the

remainder

is

.

The complete intervals tell you that days,or one full week

plus

days,go by,bringing you to Tuesday at 4:00p.m.The

additional hours

take you into the next day,Wednesday.The hours will end at 5:00a.m.on

Wednesday.

2月题目

2月3日

答案解析

The function,defined for,is graphed above.For how many different values of is?

(A)None

(B)One

(C)Two

(D)Three

(E)Four

2月6日

答案解析

If triangle above is congruent to triangle(not shown),which of the following must be the length of one side of triangle?

(A)18

(B)

(C)

(D)

(E)It cannot be determined from the information given.

2月9日

答案解析

The cars in a car service use a total of gallons of gasoline per week.If each of the

cars uses the same amount of gasoline,then,at this rate,which of the following

represents the number of gallons used by of the cars in weeks?

(A)(B)(C)(D)(E)

2月12日

答案解析

Read the following SAT test question and then click on a button to select your answer.

In the-plane,line passes through the points and,where. What is the slope of line?

(A)(B)(C)(D)(E)

2月15日

答案解析

First,is subtracted from and the square root of the difference is taken.Then,5is added to the result,giving a final result of.What is the value of?

(A)(B)(C)(D)16(E)

2月18日

答案解析

If is the set of positive integers that are multiples of,and if is the set of positive

integers that are multiples of,how many integers are in the intersection of and?

(A)None

(B)One

(C)Seven

(D)Thirteen

(E)More than thirteen

2月21日

答案解析

A florist buys roses at a piece and sells them for a piece.If there are no other expenses,how many roses must be sold in order to make a profit of?

(A)(B)(C)(D)(E)

2月24日

答案解析

What is the equation of the line parallel to the-axis and four units above the-axis?

(A)(B)(C)(D)(E)

2月27日

答案解析

If,,and are numbers such that and,then is equal to which of the following?

(A)(B)(C)(D)(E)

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练习题: 1:还有数列题:a1=2,a2=6,a n=a n-1/a n-2,求a150. 解答: a n=a n-1/a n-2,所以a n-1=a n-2/a n-3,带入前式得a n=1/a n-3,然后再拆一遍得到a n=a n-6,也就是说,这个数列是以6为周期的,则a150=a144=...=a6,利用a1,a2可以 =1/3. 计算出a 6 如果实在想不到这个方法,可以写几项看看很快就会发现a150=a144,大胆推测该数列是以6为周期得,然后写出a1-a13(也就是写到你能看出来规律),不难发现a6=a12,a7=a13,然后那,稍微数数,就可以知道a150=a6了,同样计算得1/3. 2:问摄氏升高30度华氏升高的度数与62比大小. key:F=30*9/5=54<62 3:那道费波拉契数列的题:已知,a1=1 a2=1 a n=a n-1+a n-2,问a1,a2,a3,a6四项的平均数和a1,a3,a4,a5四项的平均数大小比较。 解答:费波契那数列就是第三项是前两项的和,依此类推得到a1-a6为: 1 1 2 3 5 8 13 21 a1+a2+a3+a6=12, a1+a3+a4+a5=11,所以为大于. 4:满足x^2+y^2<=100的整数对(x,y)有多少? key: 按照X的可能情况顺序写出: X= Y= 11-9 21-9 31-9 41-9 51-8 61-8 71-7 81-6 91-4 =>My answer:加起来=69 5:24,36,90,100四个数中,该数除以它的所有的质因子,最后的结果是质数的是那个:Key:90

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新SAT 数学OG 数学题目详细讲解 第一题: Content: Heart of Algebra Key: B Objective: You must make a connection between the graphical form of a relationship and a numerical description of a key feature. Explanation: Choice B is correct. The slope of a line can be determined by finding the difference in the y-coordinates divided by the difference in the x-coordinates for any two points on the line. Using the points indicated, the slope of line l is - 3/2. Translating line l moves all the points on the line the same distance in the same direction, and the image will be a line parallel to £. Therefore, the slope of the image is also - 3/2. 第二题:

Content: Passport to Advanced Math Key: A Objective: You must complete operations with multipleterms and manipulate an equation to isolate the variable of interest. Explanation: Choice A is correct. Multiplying both sidesof the equation by the denominators of the rational expressions in the equation gives 2y = 4a - 4. You should then divide both sides by 2 to isolate the y variable, yielding the equation y = 2a - 2. 第三题: Content: Heart of Algebra Key: D Objective: You must interpret the slope of an equationin relation to the realworld situation it models. Also, when themodels are created from data, you must recognize that these models only estimate the independent variable, y, for a given value of x. Explanation: Choice D is correct. When an equation is written in the form y = mx + b, the coefficient of the x-term (in this case 0.8636) is theslope. The slope of this linear equation gives the amount that the mean number of students per classroom (represented by y) changes per year (represented by x). 第四题:

sat数学考试试题

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