SAT problem solving数学17套练习题
SAT problem solving数学17套练习题
SAT problem solving数学1
1. Of the following, which is greater than ? ?
A. 2/5
B. 4/7
C. 4/9
D. 5/11
E. 6/13
2. If an object travels at five feet per second, how many feet does it travel in one hour?
A. 30
B. 300
C. 720
D. 1800
E. 18000
3. What is the average (arithmetic mean) of all the multiples of ten from 10 to 190 inclusive?
A. 90
B. 95
C. 100
D. 105
E. 110
4. A cubical block of metal weighs 6 pounds. How much will another cube of the same metal weigh if its sides are twice as long?
A. 48
B. 32
C. 24
D. 18
E. 12
5. In a class of 78 students 41 are taking French, 22 are taking German and 9 students are taking both French and German. How many students are not enrolled in either course?
A. 6
B. 15
C. 24
D. 33
E. 54
6.If f(x) = │(x2 –50)│, what is the value of f(-5) ?
A. 75
B. 25
C. 0
D. -25
E. -75
7.( √2 - √3 )2 =
A. 5 - 2√6
B. 5 - √6
C. 1 - 2√6
D. 1 - √2
E. 1
8. 230 + 230 + 230 + 230 =
A. 8120
B. 830
C. 232
D. 230
E. 226
9. Amy has to visit towns B and C in any order. The roads connecting these towns with her home are shown on the diagram. How many different routes can she take starting from A and returning to A, going through both B and C (but not more than once through each) and not travelling any road twice on the same trip?
A. 10
B. 8
C. 6
D. 4
E. 2
10. In the figure above AD = 4, AB = 3 and CD = 9. What is the area of triangle AEC ?
A. 18
B. 13.5
C. 9
D. 4.5
E. 3
参考答案
1.Correct Answer: B
Explanation:
One way to deal with fractions is to convert them all to decimals. (Using your calculator, divide the numerator by the denominator).
In this case all you would need to do is to see which is greater than 0.5.
Otherwise to see which is greater than ?, double the numerator and see if the result is greater than the denominator. In B, the correct answer, doubling the numerator gives us 8, which is bigger than 7.
2.Correct Answer: E
Explanation:
If an object travels at 5 feet per second it covers 5x60 feet in one minute, and 5x60x60 feet in one hour. Answer = 18000 (E)
3.Correct Answer: C
Explanation:
You could add up all the multiples of 10 (10 + 20 + 30 ....+190), and divide by the number of terms (19). Or you could realize that the average of an evenly spaced series of numbers is equal to the value of the middle term (or the average of the two middle terms if there are an even number of terms). The middle term out of 19 is the tenth term in the series = 100.
4.Correct Answer: A
Explanation:
If you double the sides of a cube, the ratio of the surface areas of the old and new cubes will be 1: 4. The ratio of the volumes of the old and new cubes will be 1: 8.
Weight is proportional to volume. So, If the first weighs 6 pounds, the second weighs 6x8 pounds =48.
5.Correct Answer: C
Explanation:
You could solve this by drawing a Venn diagram. A simpler way is to realize that you can subtract the number of students taking both languages from the numbers taking French to find the number taking only French. Likewise find those taking only German. Then we have:Total = only French + only German + both + neither
78 = (41-9) + (22-9) + 9 + neither.
Not enrolled students = 24
6.Correct Answer: B
Explanation:
If x = -5, then (x2– 50) = 25 – 50 = -25
But the sign │x│ means the absolute value of x (the distance between the number and zero on the number line). Absolute values are always positive.
│-25 │ = 25
7.Correct Answer: A
Explanation:
Expand as for (a + b)2.
(√2 - √3)(√2 - √3) = 2 - 2(√2 + √3) + 3 = 5 - 2 √6
8.Correct Answer: C
Explanation:
All four terms are identical therefore we have 4 (230).
But 4 = 22, and so we can write 22. 230
Which is equivalent to 232
9.Correct Answer: B
Explanation:
Amy can travel clockwise or anticlockwise on the diagram.
Clockwise, she has no choice of route from A to B, a choice of one out of two routes from B to C, and a choice of one out of two routes from C back to A. This gives four possible routes. Similarly, anticlockwise she has four different routes.
Total routes = 8
10.Correct Answer: D
Explanation:
If we take AE as the base of triangle AEC, then the height is CD.
The height of the triangle is therefore, 9 (given).
To find the base we need to see that triangles AEB and CDE are similar. The ratio AB: CD, is therefore equal to the ratio AE: ED. The given information shows that the ratio is 3:9, or 1:3. Now dividing AD (4) in this ratio gives us AE as 1.
The area of AEC = ? base x height
=1/2 x 9 = 4.5
SAT problem solving数学2
1. Which of the following could be a value of x, in the diagram above?
A. 10
B. 20
C. 40
D. 50
E. any of the above
2. Helpers are needed to prepare for the fete. Each helper can make either 2 large cakes or 35 small cakes per hour. The kitchen is available for 3 hours and 20 large cakes and 700 small cakes are needed. How many helpers are required?
A. 10
B. 15
C. 20
D. 25
E. 30
3. Jo's collection contains US, Indian and British stamps. If the ratio of US to Indian stamps is 5 to 2 and the ratio of Indian to British stamps is 5 to 1, what is the ratio of US to British stamps?
A. 5 : 1
B. 10 : 5
C. 15 : 2
D. 20 : 2
E. 25 : 2
4. A 3 by 4 rectangle is inscribed in circle. What is the circumference of the circle?
A. 2.5π
B. 3π
C. 5π
D. 4π
E. 10π
5. Two sets of 4 consecutive positive integers have exactly one integer in common. The sum of the integers in the set with greater numbers is how much greater than the sum of the integers in the other set?
A. 4
B. 7
C. 8
D. 12
E. it cannot be determined from the information given.
6. If f(x) = (x + 2) / (x-2) for all integers except x=2, which of the following has the greatest value?
A. f(-1)
B. f(0)
C. f(1)
D. f(3)
E. f(4)
7. ABCD is a square of side 3, and E and F are the mid points of sides AB and BC respectively. What is the area of the quadrilateral EBFD ?
A. 2.25
B. 3
C. 4
D. 4.5
E. 6
8.If n ≠ 0, which of the following must be greater than n?
I 2n
II n2
III 2 - n
A. I only
B. II only
C. I and II only
D. II and III only
E. None
9. After being dropped a certain ball always bounces back to 2/5 of the height of its previous bounce. After the first bounce it reaches a height of 125 inches. How high (in inches) will it reach after its fourth bounce?
A. 20
B. 15
C. 8
D. 5
E. 3.2
10. n and p are integers greater than 1
5n is the square of a number
75np is the cube of a number.
The smallest value for n + p is
A. 14
B. 18
C. 20
D. 30
E. 50
参考答案
1.Correct Answer: B
Explanation:
The marked angle, ABC must be more than 90 degrees because it is the external angle of triangle BDC, and must be equal to the sum of angles BDC (90) and DCB.
Also ABC is not a straight line and must be less than 180.
Therefore 90 < 5x < 180
The only value of x which satisfies this relation is 20.
2.Correct Answer: A
Explanation:
20 large cakes will require the equivalent of 10 helpers working for one hour. 700 small cakes will require the equivalent of 20 helpers working for one hour. This means if only one hour were available we would need 30 helpers. But since three hours are available we can use 10 helpers.
3.Correct Answer: E
Explanation:
Indian stamps are common to both ratios. Multiply both ratios by factors such that the Indian stamps are represented by the same number.
US : Indian = 5 : 2, and Indian : British = 5 : 1. Multiply the first by 5, and the second by 2.
Now US : Indian = 25 : 10, and Indian : British = 10 : 2
Hence the two ratios can be combined and US : British = 25 : 2
4.Correct Answer: C
Explanation:
Draw the diagram. The diagonal of the rectangle is the diameter of the circle. The diagonal is the hypotenuse of a 3,4,5 triangle, and is therefore, 5.
Circumference = π.diameter = 5π
5.Correct Answer: D
Explanation:
If two sets of four consecutive integers have one integer in common, the total in the combined set is 7., and we can write the sets as
n + (n + 1) + (n + 2) + (n + 3 ) and
(n + 3) + (n + 4) + (n + 5) + (n + 6)
Note that each term in the second set is 3 more than the equivalent term in the first set. Since there are four terms the total of the differences will be 4 x 3 = 12
6.Correct Answer: D
Explanation:
You can solve this by back solving – substitute the answer choices in the expression and see which gives the greatest value.sat
A (-1 + 2) / (-1-2) = -2 / 2 = -1;
B (0 + 2) / (0-2) = 2/ -2 = -1;
C (1 + 2) / (1-2) = 3/-1 = -3;
D (3 + 2) / (3-2) = 5/1 = 5;
E (4+ 2) / (4-2) = 6/2 = 3
If you had just chosen the largest value for x you would have been wrong. So although it looks a long method, it is actually quick and accurate since the numbers are really simple and you can do the math in your head.
7.Correct Answer: D
Explanation:
(Total area of square - sum of the areas of triangles ADE and DCF) will give the area of the quadrilateral
9 - (2 x ? x 3 x 1.5) = 4.5
8.Correct Answer: E
Explanation:
Remember that n could be positive negative or a fraction. Try out a few cases:
In case I, if n is -1, then 2n is less than n.
In case II, if n is a fraction such as ? then n2 will be less than n.
In case III, if n is 2, then 2-n = 0, which is less than n.
Therefore, none of the choices must be greater than n
9.Correct Answer: C
Explanation:
If after each bounce it reaches 2/5 of the previous height, then after the second bounce it will reach 2/5 x 125. After the third it will reach 2/5 x 2/5 x 125. After the fourth it will reach 2/5 x 2/5 x 2/5 x 125. This cancels down to 2 x 2 x 2 = 8
10.Correct Answer: A
Explanation:
The smallest value for n such that 5n is a square is 5.
75np can now be written as 75 x 5 x p.
This gives prime factors.... 3 x 5 x 5 x 5 x p
To make the expression a perfect cube, p will have to have factors 3 x 3 , and hence p =9
n + p = 5 + 9 = 14
SAT problem solving数学3
1. The distance from town A to town B is five miles. C is six miles from B. Which of the following could be the distance from A to C?
I 11
II 1
III 7
A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, or III.
2.√5 percent of 5√5 =
A. 0.05
B. 0.25
C. 0.5
D. 2.5
E. 25
3. If pqr = 1 , rst = 0 , and spr = 0, which of the following must be zero?
A. P
B. Q
C. R
D. S
E. T
4.
A. 1/5
B. 6/5
C. 63
D. 64 / 5
E. 64
5. -20 , -16 , -12 , -8 ....
In the sequence above, each term after the first is 4 greater than the preceding term. Which of the following could not be a term in the sequence?
A. 0
B. 200
C. 440
D. 668
E. 762
6. If f(x) = x2– 3, where x is an integer, which of the following could be a value of f(x)?
I 6
II 0
III -6
A. I only
B. I and II only
C. II and III only
D. I and III only
E. I, II and III
7. For how many integer values of n will the value of the expression 4n + 7 be an integer greater than 1 and less than 200?
A. 48
B. 49
C. 50
D. 51
E. 52
8. In the following correctly worked addition sum, A,B,C and D represent different digits, and all the digits in the sum are different. What is the sum of A,B,C and D?
A. 23
B. 22
C. 18
D. 16
E. 14
9. 12 litres of water a poured into an aquarium of dimensions 50cm length , 30cm breadth, and 40 cm height. How high (in cm) will the water rise?https://www.wendangku.net/doc/3314739514.html,
(1 litre = 1000cm3)
A. 6
B. 8
C. 10
D. 20
E. 40
10. Six years ago Anita was P times as old as Ben was. If Anita is now 17 years old, how old is Ben now in terms of P ?
A. 11/P + 6
B. P/11 +6
C. 17 - P/6
D. 17/P
E. 11.5P
参考答案
1.Correct Answer: E
Explanation:
Do not assume that AB and C are on a straight line. Make a diagram with A and B marked 5 miles apart. Draw a circle centered on B, with radius 6. C could be anywhere on this circle. The minimum distance will be 1, and maximum 11, but anywhere in between is possible.
2.Correct Answer: B
Explanation:
We can write the statement mathematically, using x to mean ‘of’ and /100 for ‘per cent’. So ( √5/100) x 5√5 = 5 x 5 /100 = 0.25
3.Correct Answer: D
Explanation:
If pqr = 1, none of these variable can be zero. Since spr = 0 , and since p and r are not zero, s must be zero. (Note that although rst = 0, and so either s or t must be zero, this is not sufficient to state which must be zero)
4.Correct Answer: E
Explanation:
65 = 64x 6
(64 x 6) - 64 = 64(6 - 1) = 64 x 5
Now, dividing by 5 will give us 64
5.Correct Answer: E
Explanation:
All terms in the sequence will be multiples of 4.
762 is not a multiple of 4
6.Correct Answer: A
Explanation:
Choice I is correct because f(x) = 6 when x=3
Choice II is incorrect because to make f(x) = 0, x2 would have to be 3. But 3 is not the square of an integer.
Choice III is incorrect because to make f(x) = 0, x2 would have to be –3 but squares cannot be negative.
(The minimum value for x2 is zero; hence, the minimum value for f(x) = -3)
7.Correct Answer: C
Explanation:
1 < 4n + 7 < 200
n can be 0, or -1
n cannot be -2 or any other negative integer or the expression 4n + 7 will be less than1.
The largest value for n will be an integer < (200 - 7) /4
193/4 = 48.25, hence 48
The number of integers between -1 and 48 inclusive is 50
8.Correct Answer: B
Explanation:
First you must realize that the sum of two 2-digit numbers cannot be more that 198 (99 + 99). Therefore in the given problem D must be 1.
Now use trial and error to satisfy the sum 5A + BC = 143
A + C must give 3 in the units place, but neither can be 1 since all the digits have to be different. Therefore A + C = 13.
With one to carry over into the tens column, 1 + 5 + B = 14, and B = 8.
A + C +
B + D = 13 + 8 + 1 = 22
9.Correct Answer: B
Explanation:
Total volume of water = 12 liters = 12 x 1000 cm3
The base of the aquarium is 50 x 30 = 1500cm3
Base of tank x height of water = volume of water
1500 x height = 12000; height = 12000 / 1500 = 8
10.Correct Answer: A
Explanation:
Let Ben’s age now be B
Anita’s age now is A.
(A - 6) = P(B - 6)
But A is 17 and therefore 11 = P(B - 6)
11/P = B-6
(11/P) + 6 = B
SAT problem solving数学4
1. If a2 = 12, then a4 =
A. 144
B. 72
C. 36
D. 24
E. 16
2. If n is even, which of the following cannot be odd?
I n + 3
II 3n
III n2 - 1
A. I only
B. II only
C. III only
D. I and II only
E. I, II and III
3. One side of a triangle has length 8 and a second side has length 5. Which of the following could be the area of the triangle?
I 24
II 20
III 5
A. I only
B. II only
C. III only
D. II and III only
E. I, II and III
4. A certain animal in the zoo has consumed 39 pounds of food in six days. If it continues to eat at the same rate, in how many more days will its total consumption be 91 pounds?
A. 12
B. 11
C. 10
D. 9
E. 8
5. A perfect cube is an integer whose cube root is an integer. For example, 27, 64 and 125 are perfect cubes. If p and q are perfect cubes, which of the following will not necessarily be a perfect cube?
A. 8p
B. pq
C. pq + 27
D. -p
E. (p - q)6
6. What is the length of the line segment in the x-y plane with end points at (-2,-2) and (2,3)?
A. 3
B. √31
C. √41
D. 7
E. 9
7. n is an integer chosen at random from the set
{5, 7, 9, 11 }
p is chosen at random from the set
{2, 6, 10, 14, 18}
What is the probability that n + p = 23 ?
A. 0.1
B. 0.2
C. 0.25
D. 0.3
E. 0.4
8. A dress on sale in a shop is marked at $D. During the discount sale its price is reduced by 15%. Staff are allowed a further 10% reduction on the discounted price. If a staff member buys the dress what will she have to pay in terms of D ?
A. 0.75D
B. 0.76D
C. 0.765D
D. 0.775D
E. 0.805D
9. All the dots in the array are 2 units apart vertically and horizontally. What is the length of the longest line segment that can be drawn joining any two points in the array without passing through any other point ?
A. 2
B. 2√2
C. 3
D. √10
E. √20
10. If the radius of the circle with centre O is 7 and the measure of angle AOB is 100, what is the best approximation to the length of arc AB ?
A. 9
B. 10
C. 11
D. 12
E. 13
参考答案
1.Correct Answer: A
Explanation:
a4 = a2 x a2 = 12 x 12 = 144
2.Correct Answer: B
Explanation:
In case I , even plus odd will give odd
In case II, odd times even will give even
In case III even squared is even, and even minus odd is odd.
(You can check this by using an easy even number like 2 in place of n)
Only case II cannot be odd.
3.Correct Answer: D
Explanation:
The maximum area of the triangle will come when the given sides are placed at right angles. If we take 8 as the base and 5 as the height the area = ? x 8 x 5 = 20
We can alter the angle between the sides to make it less or more than 90, but this will only
reduce the area. (Draw it out for yourself). Hence the area can be anything less than or equal to 20.
4.Correct Answer: E
Explanation:
Food consumed per day = 39/6.
In the remaining days it will consume 91 - 39 pounds = 52 pounds
Now divide the food by the daily consumption to find the number of days
52 / (39/6) = 52 x (6 / 39) = 8
5.Correct Answer: C
Explanation:
A perfect cube will have prime factors that are in groups of 3; for example 125 has the prime factors 5 x 5 x 5 , and 64 x 125 will also be a cube because its factors will be 4 x 4 x 4 x 5 x 5 x 5
Consider the answer choices in turn.
8 is the cube of 2, and p is a cube, and so the product will also be a cube.
pq will also be a cube as shown above.
pq is a cube and so is 27, but their sum need not be a cube. Consider the case where p =1 and q = 8, the sum of pq and 27 will be 35 which has factors 5 x 7 and is not a cube.
-p will be a cube.
Since the difference between p and q is raised to the power of 6, this expression will be a cube (with cube root = difference squared).
6.Correct Answer: C
Explanation:
Sketch a diagram and calculate the distance (hypotenuse of a right triangle) using Pythagoras theorem.
Vertical height of trian gle = 5 ; horizontal side = 4 ; hypotenuse = √(25 + 16) = √41
7.Correct Answer: A
Explanation:
Each of the integers in the first set could be combined with any from the second set, giving a total of 4 x 5 = 20 possible pairs.
Of these the combinations that could give a sum of 23 are (5 + 18), and (9 + 14)
This means that the probability of getting a sum of 23 is 2/20 = 1/10
8.Correct Answer: C
Explanation:
If the price is reduced by 15 %, then the new price will be 0.85D
If this new price is further reduced by 10%, the discounted price will be 0.9 x 0.85D = 0.765D
9.Correct Answer: E
Explanation:
The longest line segment that can be drawn without passing through any dots other than those at the beginning and end of the segment, such a line could go from the middle dot in the top row to either the bottom left or right dot. In any case the segment will be the hypotenuse of a right triangle with sides 2 and 4. Using Pythagoras theorem the hypotenuse will be √(2 2 + 4 2 ) = √20
10.Correct Answer: D
Explanation:
I f the radius is 7, the circumference = 14π
The length of the arc is 100/360 of the circumference
Taking π as 22/7 we get
(100 x 14 x 22) / (360 x 7) which reduces to 440/ 36 = 12.22 (i.e. approx. 12)
SAT problem solving数学5
1. Sheila works 8 hours per day on Monday, Wednesday and Friday, and 6 hours per day on Tuesday and Thursday. She does not work on Saturday and Sunday. She earns $324 per week. How much does she earn in dollars per hour?
A. 11
B. 10
C. 9
D. 8
E. 7
2. ABCD is a parallelogram. BD = 2. The angles of triangle BCD are all equal. What is the perimeter of the parallelogram?
A. 12
B. 9√3
C. 9
D. 8
E. 3√3
3. If the product of 6 integers is negative, at most how many of the integers can be negative?
A. 2
B. 3
C. 4
D. 5
E. 6
4. If a positive integer n, divided by 5 has a remainder 2, which of the following must be true?
I n is odd
II n + 1 cannot be a prime number
III (n + 2) divided by 7 has remainder 2
A. none
B. I only
C. I and II only
D. II and III only
E. I, II and III
5. A solid cube of side 6 is first painted pink and then cut into smaller cubes of side 2. How many of the smaller cubes have paint on exactly 2 sides?
A. 30
B. 24
C. 12
D. 8
E. 6
6. Line l contains the points (3,1) and (4,4).
If line m is a different line, parallel to line l in the same coordinate plane, which of the following could be the equation of line m?
A. y = 3x - 8
B. y = 1/3x - 3
C. y = -3x - 8
D. y = 3x + 1
E. y = -8x + 3
7. In the figure above the square has two sides which are tangent to the circle. If the area of the circle is 4a2π, what is the area of the square?
A. 2a2
B. 4a
C. 4a2
D. 16a2
E. 64a2
8. A triangle has a perimeter 13. The two shorter sides have integer lengths equal to x and x + 1. Which of the following could be the length of the other side?
A. 2
B. 4
C. 6
D. 8
E. 10
9. A machine puts c caps on bottles in m minutes. How many hours will it take to put caps on b bottles?
A. 60bm/c
B. bm/60c
C. bc/60m
D. 60b/cm
E. b/60cm
10. Paint needs to be thinned to a ratio of 2 parts paint to 1.5 parts water. The painter has by mistake added water so that he has 6 litres of paint which is half water and half paint. What must he add to make the proportions of the mixture correct?
A. 1 litre paint
B. 1 litre water
C. ? litre water and one litre paint
D. ? litre paint and one litre water
E. ? litre paint
参考答案
1.Correct Answer: C
Explanation:
Total hours worked = 8 x 3 + 6 x 2 = 36
Total earned = 324. Hourly wage = 324 / 36 = 9
2.Correct Answer: D
Explanation:
Since the angles of BCD are all equal, it is an equilateral triangle. Therefore. Since one side is 2, BD and CD are also 2. These sides (totaling 4 units) represent half the perimeter of the parallelogram. Total perimeter = 8.
3.Correct Answer: D
Explanation:
Multiplying two negatives (or any even multiple) results in a positive. But multiplying three negatives (or any odd multiple) gives a negative. If the result of multiplying 6 negatives is odd, the largest number of negative integers will be the largest odd number (i.e.5)
4.Correct Answer: A
Explanation:
You can find the integers which when divided by 5 have a remainder 2 by adding 2 to all multiples of 5. So we have n = 9 , 12, 17, 22 etc.
From this series we can see that n does not have to be odd.
Also n + 1 can be a prime because, for example, 12 + 1 = 13
And (n + 2) / 7 has a remainder 2 in some cases but not all.
Remember the question asks us for what MUST be true, and we see that none of the statements are true in all cases.
5.Correct Answer: C
Explanation:
When the larger cube is cut into smaller cubes, the corner cubes will have paint on three sides. The cubes in the middle of the faces will have paint on only one side, but the cubes cut from the edges will have paint on two sides. In this case, there will be only one cube one each edge (excluding the corners), and since there are 12 edges, there will be 12 cubes with paint on two sides. (Drawing a diagram will make this much clearer.)
6.Correct Answer: D
Explanation:
Slope of the line l = (4 – 1) / (4 – 3) = 3/1 = 3
Parallel lines have the same slope. In the equation of a straight line, y = mx + c, m represents the slope, so we are looking for an equation where m = 3
But both answer choices A and D have slope 3.
Now we calculate the intercept, c, for line l. Using the coordinate of one of the points on l, we get: 4 = (3 x 4) + c ; 4 – 12 = c; c = -8
Hence, answer A is the equation of line l, and answer D must be the equation of a parallel line.
7.Correct Answer: D
SAT数学综合问题
1.正整数n有奇数个因子,则n为完全平方数 2.因子个数求解公式:将整数n分解为质因子乘积形式,然后将每个质因子的幂分别加一相乘.n=a*a*a*b*b*c则因子个数=(3+1)(2+1)(1+1) eg. 200=2*2*2 * 5*5 因子个数=(3+1)(2+1)=12个 3.能被8整除的数后三位的和能被8整除;能被9整除的数各位数的和能被9整除.能被3整除的数,各位的和能被3整除. 4.多边形内角和=(n-2)x180 5.菱形面积=1/2 x 对角线乘积 6.欧拉公式：边数=面数+顶点数-2 8.三角形余玄定理 C2=A2+B2-2ABCOSβ,β为AB两条线间的夹角 9.正弦定理:A/SinA=B/SinB=C/SinC=2R(A,B,C是各边及所对应的角,R是三角形外接圆的半径) 10.Y=k 1X+B 1 ,Y=k 2 X+B 2 ，两线垂直的条件为K 1 K 2 =-1 11.N的阶乘公式: N!=1*2*3*....(N-2)*(N-1)*N 且规定0!=1 1!=1 Eg:8!=1*2*3*4*5*6*7*8 12. 熟悉一下根号2、3、5的值 sqrt(2)=1.414 sqrt(3)=1.732 sqrt(5)=2.236 13. ...2/3 as many A as B: A=2/3*B ...twice as many... A as B: A=2*B 14. 华氏温度与摄氏温度的换算 换算公式:(F-32)*5/9=C PS.常用计量单位的换算:（自己查查牛津大字典的附录吧）
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
概率论杂题1
随机题只记得一些 酒井BBS (Sat Jun 17 19:09:19 2000) Part A 1. X~N(u,a),样本X1,X 2..Xn,F=1/n*(x1+..+xn),问F是u的无偏估计吗?,并求F的pdf 2. Y1,..Yn iid , P(Yi=1)=p P(Yi=-1)=q, p+q=1 A=(X2>=2),B=(X3>=3), 求E[I(A)],E[I(AUB)],E[I(AB)],X2+2的母函数 3. 求证条件数学期望的全概率公式 4. 题设如2,求E(X2|A),E(I(A)|I(B)) Part B 1.N1,N2~Po(Xi),求E(N1|N1+N2), P(min(N1,N2)=2|N1+N2=5)的分布 2.X1,X2~Ex(Xi), 独立, U=min(X1,X2) V= 1 iff X1
SAT数学概率题常用解题技巧
SAT数学概率题常用解题技巧 SAT数学难度对于中国考生来说并不是很大，但SAT数学概率题是在SAT数学考试中相对来说比较难的一项，同学们还是比较担心的。下面为大家整理了SA T数学概率题常用解题技巧。希望能够帮助大家更好的备考SAT数学考试。 SAT数学概率题常用解题技巧： (1)In the integer 3589 the digits are all different and increase from left to right. How many integers between 4000 and 5000 have digits that are all different and that increased from left to right? 比较题目：(2)In the integer 3589 the digits are all different and increase from left to right. How many integers between 30000 and 50000 have digits that are all different and that increased from left to right? (3)If p, r, m are three different prime numbers greater than 2, and n=p*r* m, how many positive factors, including 1 and n, does n have? 比较题目：(4)If p, r, m, n, t and s are six different prime numbers greater than 2, and n=p*r*s*m*n*t, how many positive factors, including 1 and n, does n have? (5)If someone throws a dice twice, on the first time he gets a points, and on the second he gets b points, what is the probability a/b>1? 比较题目：(6)If someone throws a dice twice, what is the probability that the point he gets on one throw is bigger than the other? (7)Mr. Jones must choose 4 of the following 5 flavors of jellybean: apple, berry, coconut, kumquat, and lemon, How many different combinations of flavors can Mr. Jones choose? 以上就是为大家总结的答题数学概率题常用解题技巧的相关内容介绍。各位考生一定要注意，对SAT数学概率论部分来说，你用的方法越简单，你做对的概率越大，而且还可以在考场上省出很多时间来做更有意义的事情。
SAT 2 数学重点大全
函数，方程 ● asymptote 渐近线。当在X 的某一个值时，分式的分母为0而分子不为0， 则函数有vertical asymptote 。当X 趋向于无限大（小）的时候，Y 趋近某一个数值，则函数有horizontal asymptote 。 ● 当在X 的某一个值，分式的分子分母同时是0，则函数有一个洞。 ● 在三角函数中，注意多角度的情况 ● 极坐标polar coordinates P(r ,θ)中，r 指的是长度，θ指的是角度。 ● ))(())((x g f x g f = ● 奇偶函数应该用负X 代入计算。 ● 解等式解方程的题目都可以用图像，左边和右边两个图像的交点就是解。 ● 等式()()()05322 =-+-x x x 所有解的和是多少？ 注意2要加两次，因为它是双根。 ● 在图像计算机的window 里面，Yscl=50表示y 轴每一格间距是50。 ● 如果函数的对称轴是3-=x ，那么)3(-x f 的图像关于y 轴对称。 ● 求 21>-x x 的解集。应该分两大类0>x 和0
2020下半年SAT考试解题技巧
2020下半年SAT考试解题技巧 2020下半年SAT考试解题技巧 SAT数学概率题解题技巧，概率题是SAT数学考试中一个很重要的题型，为了协助大家更加有针对性的复习SAT数学考试，提升SAT数学题的准确率。 各位考生需要注意的是，对于SAT数学概率题来说，你用的方法越简单，你做对的概率就越大。 (1)In the integer 3589 the digits are all different and increase from left to right. How many integers between 4000 and 5000 have digits that are all different and that increased from left to right? 比较题目：(2)In the integer 3589 the digits are all different and increase from left to right. How many integers between 30000 and 50000 have digits that are all different and that increased from left to right? (3)If p, r, m are three different prime numbers greater than 2, and n=p*r* m, how many positive factors, including 1 and n, does n have? 比较题目：(4)If p, r, m, n, t and s are six different prime numbers greater than 2, and n=p*r*s*m*n*t, how many positive factors, including 1 and n, does n have? (5)If someone throws a dice twice, on the first time he gets a points, and on the second he gets b points, what is the probability a/b>1?
2016新SAT考试深度解析(样题预览)
2016新SAT考试难度大幅度提升（样题预览） 深圳跨文化交流中心整理 美国时间2014年4月16日凌晨五点三十分，北京时间2014年4月16日下午五点三十分，美国大学委员会第一时间发布新SAT考试样题，全部样题共208页，除部分样题之外，还对考试的整体设计思路、考试的能力要求等进行了详细阐释，在现阶段起到类似《官方指南》的作用。 新SAT难度大幅增加，则说明将对中国考生的综合能力提出更高的要求。 2016新SAT考试难度大幅度提升（样题预览）
2016新SAT考试难度大幅度提升（样题预览） 新SAT考试内容变更： 1.从考试时间上讲，从原先的3小时45分钟，调整为3小时，另外加可选择写作部分时间为50分钟。 2.考试内容由原来的三部分“批判性阅读”，“数学”，“写作”，改为两部分“基于证据的阅读和写作”以及“数学”，而“写作”则作为可选择项。 3.考试分数也由600分-2400调整为400到1600分，可选项“写作”独立打分，分别根据三个要求打2-8分。
新SAT阅读内容变更 ①具体内容上来看SAT阅读填空部分完全取消，由之前的三个section、67道题目(19道填空、48道阅)，每题五个选项，总共70分钟，改变为52道题，每题4个选项，总共65分钟。篇章也由两个短单、一对短双、三个中长单、一对长双改为四个长单和一套长双构成。 ②新SAT阅读部分取消了词汇填空题，所有题目全部以passage-based的形式出现。当前SAT考试的阅读部分的总计67题中，有19题是词汇填空。根据我们的经验，19道词汇填空题部分题目中国学生往往只要下功夫背熟词汇一般可以在7分钟内完成，并且可以保持相当的准确率。这意味着每个篇章阅读题的解题时间是（70－7）／（67－19）= 1.31秒，而在新SAT下，每个篇章阅读题目的解题时间是65／52=1.25秒。别小看这个细小的变化。因为本来SAT对速度的要求就很高，在此基础上的任何提高都是苛刻的要求。 ③阅读文章内容选取上更加广泛，包含文学、历史、科学和社会研究,更趋向于和学生的学业以及就业关联度更密切的内容。 ④会增加图表数据分析，更加偏重考察考生在将来的学术生活的实际应用能力。原来的语法和词汇在新SAT中要求以文章为背景，考查文章中单词、短语和语言的使用，更加注重考生对上下文的理解和把握！这意味着纯文学内容的比重将下降，而科学类的或职业相关的说明性论证型文章比重将增加。 ⑤在新SAT框架下，文学部分会出现一篇阅读，占总题量的1/5。其余4篇阅读平均分布在历史/社会研究和自然科学两个领域。部分文章会出现插图，并要求学生结合插图进行解题。这样的变化对理科思维的学生而言是利好，对文艺青年不是好事情。 ⑥在当前版本的SAT下，小说阅读常常只需要掌握大概，把握其主要情绪即可迅速解题，而无需去理清文章的内在逻辑结构，而新版本的SAT则更加强调了对文章整体的逻辑脉
美国“高考”SAT考试的数学题
美国“高考”SAT考试的数学题 数学第一部分 时间（25分钟） 16个问题 说明：这部分包含有两种类型的问题。你将有25分钟时间来完成他们。对于1—8，在所给选项中选出一个最佳答案，然后再答题卡上填上相应的圆圈，你可以使用任何可用的草稿纸空间。 注释：1、可以使用计算器。 2、所有使用的数字均为实数。 3、在测试中，问题中所提供的数字或图表都包含一定的信息，这对于解题很有帮助。 所有图表都是比较准确的，除非在某些具体问题中，图表没有按比例绘制。所有数字都呈现于平面上，除非另有说明。 4、除非另有规定，对于任何函数f 的值域都是所有实数x 的集合，并使得f(x) 是实数。 可能用到的公式： 1、If 4(t+u) + 3 =19, then t+u= 如果4(t+u) + 3 =19, 那么t+u= A 3 B 4 C 5 D 6 E 7 2、如图，三条直线相交于一点。如果f=85, e=25, 那么a 的值是多少？
A 60 B 65 C 70 D 75 E 85 3、如果玛丽开车行驶n 英里用了t 小时，那么下列哪个可以表示她行驶的平均速度，英里/小时？ A n/t B t/n C 1/nt D nt E n2t 4、如果a 是一个奇数，b 是一个偶数，那么选项中哪一个是奇数？ A 3b B a+3 C 2(a+b) D a+2b E 2a+b 5、在平面坐标内，F(-2,1),G(1,4), H(4,1)在以P为圆心的圆上，那么点P的坐标是什么？ A（0,0） B（1,1） C（1,2） D（1，-2） E（2.5,2.5） 6、如图，如果-3≤x≤6，那么x 有几个值，使得f(x)=2?
概率图模型介绍与计算
概率图模型介绍与计算 01 简单介绍 概率图模型是图论和概率论结合的产物，它的开创者是鼎鼎大名的Judea Pearl,我十分喜欢概率图模型这个工具，它是一个很有力的多变量而且变量关系可视化的建模工具，主要包括两个大方向：无向图模型和有向图模型。无向图模型又称马氏网络，它的应用很多，有典型的基于马尔科夫随机场的图像处理，图像分割，立体匹配等，也有和机器学习结合求取模型参数的结构化学习方法。严格的说他们都是在求后验概率:p(y|x)，即给定数据判定每种标签y的概率，最后选取最大的后验概率最大的标签作为预测结果。这个过程也称概率推理(probabilistic inference）。而有向图的应用也很广，有向图又称贝叶斯网络(bayes networks),说到贝叶斯就足以可以预见这个模型的应用范围咯，比如医疗诊断，绝大多数的机器学习等。但是它也有一些争议的地方，说到这就回到贝叶斯派和频率派几百年的争议这个大话题上去了，因为贝叶斯派假设了一些先验概率，而频率派认为这个先验有点主观，频率派认为模型的参数是客观存在的，假设先验分布就有点武断，用贝叶斯模型预测的结果就有点“水分”，不适用于比较严格的领域，比如精密制造，法律行业等。好吧，如果不遵循贝叶斯观点，前面讲的所有机器学习模型都可以dismiss咯，我们就通过大量数据统计先验来弥补这点“缺陷”吧。无向图和有向图的例子如（图一）所示： 图一(a)无向图（隐马尔科夫）(b)有向图 概率图模型吸取了图论和概率二者的长处，图论在许多计算领域中扮演着重要角色，比如组合优化，统计物理，经济等。图的每个节点都可看成一个变量，每个变量有N个状态（取值范围），节点之间的边表示变量之间的关系，它除了
美国SAT考试题目
https://www.wendangku.net/doc/3314739514.html, 立思辰留学介绍，美国SAT考试是美国高中生升入大学的标准化考试，分成了SAT1和SAT2两类。这两类考试题目和国内的考试相差很大，下面就为大家介绍一下美国SAT考试题目，供大家参考。 SAT1考试---推理测验(ReasoningTest)，包括阅读、写作和数学，被称为SAT或NEWSAT; SAT2考试---专项测验(SubjectTests)，有数学、物理、化学、生物、外语(包括汉语、日语、德语、法语、西班牙语)等，被统称为SAT2。 美国SAT考试题目 互联网留学360介绍，根据CollegeBoard出的官方题，数据如下： SAT数学部分考试题目有54道，其中多选题44道，填空题10道。内容包括：整数和分数;代数、几何、统计、概率;数量分析 SAT分析性阅读部分考试题目共67道：其中完成句子有19道，段落阅读有48道。阅读文章涉及内容：自然科学类，人文科学类，社会科学类，文学小说类 SAT写作部分考试题目共49道和一个短文：其中有18道句子找错，25道改句，6道改段落和一个短文。多项选择包括改错,改写句子和段落。 作文类型：议论文，需有立论和例证(作文单独评分：2-12;多项选择评分：20-80)
https://www.wendangku.net/doc/3314739514.html, 美国SAT2考试有别于SAT1，考察学生某一科目的能力，考试科目共计二十门考试。 目前SAT2分为数学、科学、语言、英语、历史与社会科学五大类。 其中数学类有数学一和数学二两门， 科学类有物理、化学、生物三门， 语言类有法语、德语、西班牙语、中文、日语、韩语、希伯莱语、拉丁语等十二门， 英语类只有英语文学一门; 历史与社会科学类有美国历史和世界历史两门。 SAT1主要测验考生的写作、阅读和数学能力，每部分满分是800分，总分是2400分;SAT2每科满分为800分。绝大部分美国名校只要求中国留学申请人提供SAT通用考试的成绩即可，个别院校及专业要求申请人提供SAT2的单科考试成绩。 以上就是对美国SAT考试题目的介绍，包括了SAT1考试和SAT2考试两类，对这两种考试题目和内容都做了介绍。大家子啊备考SAT考试的时候，可以根据自己的实际需要选择备考的方式，提高SAT成绩。
SAT考试做题技巧经验
SAT考试做题技巧经验 以下是一位SAT考试高分同学的做题技巧分析，分别从阅读、数学、写作和涂卡等方面介绍了做题经验，还谈到了对放空的态度问题。同学们在冲刺SA T考试时，可以适当参考。 考前七个礼拜开始做题，后来觉得还是可以提早些。我前期先是熟悉题目，到后来便频繁进行模考。因为真题数量有限，需要好好利用，每一套做完后我都会弄清大部分错题。 阅读部分做题的意义在于： 1.熟悉文章的风格。 2.熟悉出题者的思路。我一些同学经常文章看懂题做错，在得知选择正确选项的原因后又觉得出题人思路过于浅显直白。这说明如果能把握这种浅显直白的思路，很多题目都将唾手可得。 3.调整做题速度，掌握做题节奏。关于作一篇文章多少时间，一道题看多久，填空和阅读段落之间如何分配，都要在大量做题后才能得出答案。这一点尤其重要，因为一堆人宣称阅读做不完。 4.找到适合自己的做题顺序。个人是喜欢先做填空，然后除了短文章和对比类，其余都一边做题一边读。当然，阅读之前要先把题目中提到的行数都挑出来，与题目有关的句子之间段落就一扫而过。 谈到放空的问题，我的原则是绝不放空。因为根据概率计算，错一题扣0.25分，如果随便乱猜，最后的期望则是0分。然而，大部分情况下五个选项里都差不多有三个是可以排除的，此时期望为八分之三，表示倘若猜八题，很有可能对错各四题，即能多得三分。因此我觉得只要能排除一个以上的错误选项都不该放空。 数学部分做题的意义在于遇到尽可能多的题目，减少在真正考试时遇到不会做的题目的概率。在模考时就必须严格要求，每次都要拿到满分。 写作部分做题的意义也是在于掌握尽可能多的题目，特别是句子找错题，把所有真题都做过后可以保证考试时错两道之内。而句子改进题，题做多以后对于不恰当的句子基本上很快就可以排除掉。当然错题要弄清为什么错，我的很多错题都是在最后两周上模考班时才弄清的。 关于ESSAY，我得9分，不高。复习过程中只是觉得这玩意性价比实在太低，花同样的精力，能使前面语法题从32分提到42分的同时也许只能把ESSAY从8分提到10分。 关于涂卡，我的原则是做一面涂一面，既不像做一题涂一题那样浪费时间，又不像全部做完才涂那样冒险，是一条合适的中间路线。另外每次模考时一定都要涂卡，可以从OG上撕下来复印，否则真正考试之前即使懂得怎么涂也会由于不习惯而慌张万分，增大涂错的概率。
SAT数学知识点(一)
SAT数学知识点（一） 考试，如果一旦知道考点，对于考生就有一种如释重负的感觉。所以，面对SAT数学，文都国际教育小编将给大家分享一下基本的SAT数学知识点，希望对大家的考试有所帮助。 代数部分（heart of Algebra）：核心是线性方程（组）、线性函数、线性不等式。 1.建立、解答或解释单变量的线性方程（create, solve, or interpret linear equations of one variable） 学生根据题目背景（context）建立、解答和解释单变量（variable）的线性(linear)表达式（expression）或方程(equation)。表达式或方程有理因数（rational coefficients）。学生可能需要多个步骤简化表达式、简化方程或解出方程中的变量。 2.建立、解答或解释单变量的线性不等式（create, solve, or interpret linear inequalities of one variable） 学生根据题目背景（context）建立、解答和解释单变量（variable）的线性不等式（linear inequalities）。含有理分式的不等式（rational coefficients）。学生可能需要多个步骤简化表达式、简化方程或解出方程中的变量的值。 3.根据两个变量的线性关系建立一个线性函数（build a linear function that models a linear relationship between two quantities） 学生使用两个变量的方程（function）或函数记号（function notation）描述一个背景下的线性关系（linear relationship）。方程（equation）或有理因式函数(function with rational coefficients）。学生可能需要多个步骤建立和简化方程或函数。 4.建立、解答和解释两个变量的线性不等式组（create, solve, and interpret systems of linear inequalities in two variable） 学生通过建立、解答或解释某个背景（context）下两个变量的一个不等式（inequality）或者两个变量的一个不等式组(a system of inequality)来分析两个变量之间的一个或多个约束条件（constraints）。学生可能需要多个步骤建立不等式或者不等式用以决定某个给定点是否在解集（solution set）内。 5.建立、解答和解释含两个变量的线性方程组成的线性方程组（create, solve, and interpret systems of two liner equations in two variables）
SAT数学知识点范围整理
SAT数学知识点范围整理 SAT数学知识点都有哪些呢?在SAT数学备考的过程中，很多同学都认为答题数学难度不大，所以对于备考投入的时间比较少，但是小编提醒大家，在备考的时候还是要做一些SAT数学真题，长出一些常考的知识点。下面小编就为大家整理了SAT数学知识点范围整理的相关内容，供大家参考。 SAT数学考试较难部分的矩阵、统计与概率分析试题，仅涉及这些数学概念的最简单题型，国内考生通过有效的SAT备考培训与模拟测试，可很快掌握这部分试题的答题方法与技巧。 美国高考SAT不仅考察考生的学术水平、学术能力与学术素质，同时还检测考生的学术态度。考生在参加SAT考试时，不管出于何种原因，都要对在考试时答错的题承担分数上的损失。以SAT数学部分的考试为例，考生要在1小时的规定时间内，应对55道数学题。若完全答对55道数学题，则该考生可取得数学800的满分成绩;若考生每答错一道题，都要减去四分之一题所对应的分数。例如：在数学考试的55道题中，满分为800，每答对一题可约得15分，空题不答不得分也不减分，每答错一题则减去15分的四分之一即约4分。 美国高考SAT推出了新的SAT考试形式及内容，其中数学部分的考题范围与难易程度有所提高。以前的SAT数学考试程度仅相当于国内初三的数学水平，主要考学生的四则运算、因数、分数、百分数、小数及比率比值的基本知识及运算能力。这些数学的基本知识，对国内初三学生来说很简单。新SAT数学部分的试题，为了满足美国大学课程及教材的实际需要，增加了不少新的考试内容。 数学运算方面增加了连续运算、正向增量指数运算、集合论中的并集、交集及素的概念和简单计算;在代数和函数的知识上，增加了绝对值概念、有理数的等式与不等式、正负指数的计算与平方根的概念、正比和反比的变量关系、函数表达式、函数的域与围的知识、函数与简单物理模型的表达关系、线性函数及二次方程式;在几何及度量方面，加入了特殊三角形的特征分析、多种切线特征知识、简单的坐标几何学、图形与函数的相互转换与表达等等;难题方面增加了数据分析、简单的矩阵、统计及概率分析的试题。 若考生SAT数学考试的目标分数为700分，则需答对46题，剩下的9道数学题属于难题，在此时考生要特别谨慎的答题，若9道题空着不答，则考生的数学成绩为700分，并已达到目标分数;若考生采取不负责任的、瞎蒙瞎猜的答题态度，且9道题都答错，则该考生的数学成绩不是700分，而是要减去36分的664分。因此说，美国高考SAT要求考生必须以科学的、实事求是的态度来对待SAT考前培训及考试本身。
SAT数学概率题的答题技巧
文都国际教育官方网站：https://www.wendangku.net/doc/3314739514.html,/ SAT数学概率题的答题技巧 SAT数学在SAT考试中可以说是相对简单的，但还是得小心作答。今天文都国际小编为大家分享一下SAT数学考试概率题的答题技巧，供大家学习。 1.一定要认真读清楚SAT数学题目，不要在没有弄清题目意思的情况下开始解题。弄清题目中从句的结构和指代。注意插入语。把题目要你求的量画出来，可别轻视这一步，很多时候不是你理解错了，是你没把该求的求完。 2.不要在某个题目上花太长的时间。所有题目都是一个一分，不要在关键时候挑战自己，如果题目看了半天还是没有头绪，在题号上做个明显的标记，等全部题目做完再回来认真读题目，写下已知量，尝试列算式。 3.在SAT考试中SAT数学考试部分的时候没有草稿纸，在你的试卷本里计算就可以了。平时练习就要有在SAT数学试题题目旁边做标记，记录思路的习惯。写字比较大的同学要试着斯文一点，考试的时候你的“草稿”空间是有限的，要有条理的写下你的答题思路。 当然，不要十分简单的个位数加减也写上，考完以后你的试卷无法带走，你雕琢地再漂亮也无法带回家做纪念的。等全部题目做完有时间就重新读每一道题目，思考自己应该怎么做，看看之前写下的思路是否和现在想的一样。再逐行检查是否有计算错误，数字誊写错误，运算符号写错等情况。 以上就是小编给大家分享的SAT数学考试概率题的答题技巧。希望对同学们的备考有帮助。最后，小编预祝大家都能考出好成绩。 文章来源于文都国际教育：https://www.wendangku.net/doc/3314739514.html,/kaopei/20170623/8680.shtml 文都国际教育官方网站：https://www.wendangku.net/doc/3314739514.html,/
SAT数学考试全面介绍
SAT数学考试全面介绍 三立在线SAT频道为大家带来SAT数学考试全面介绍一文，希望对大家SAT备考有所帮助。更多精彩尽请关注三立在线SAT频道! 一.SAT数学考试内容介绍 SAT数学考试运算方面：在运算方面包括了连续运算、正向增量指数运算、集合论中的并集、交集及素的概念和简单计算; SAT数学考试代数和函数方面：在代数和函数的知识上，包括了绝对值概念、有理数的等式与不等式、正负指数的计算与平方根的概念、正比和反比的变量关系、函数表达式、函数的域与围的知识、函数与简单物理模型的表达关系、线性函数及二次方程式; SAT数学几何及度量方面：在几何及度量方面，包括了特殊三角形的特征分析、多种切线特征知识、简单的坐标几何学、图形与函数的相互转换与表达等等; SAT数学难题方面：难题方面增加了数据分析、简单的矩阵、统计及概率分析的试题。SAT数学考试内容中较难部分的矩阵、统计与概率分析试题，仅涉及这些数学概念的最简单题型，大家可以很快掌握这部分的技巧。 二.改革后SAT数学考试内容变化的部分 1.新SAT数学删去了大多数算术部分的内容，但是还是保留了一小部分与数据分析密切相关的内容放在problem solving and data(数据统计与分析)中。
这对中国考生来说无疑是个好消息，因为以往中国学生出错较多的排列组合问题就没有了。关于整数、小数、奇偶、质数、合数、数轴等问题也没有在新样题中出现。 2.新SAT数学中的代数部分相的题量比原来增加了一倍，其中仅线性函数与线性方程一项就单独占了一个部分，这是因为这部分也与数据统计与分析密切相关。在数据图表中，数据的趋势经常出现近似规律的线性增长或线性下降。另外线性方程也在日常应用中频频现身，使得一元一次方程的内容也在其中占据很大篇幅。 3.二次函数、一元二次方程、指数函数及其他非线性函数被归入第三大部分，除了二次函数和一元二次方程以外，指数函数与其他函数都是现行SAT数学中从未出现过的内容。一元二次方程的求根公式也在新的官方样题中频频出现，值得考生引起重视。 SAT数学的一般解题过程：读题目—理解题干意思—简化问题—转化为数学模型—运用数学知识解答—得出答案 几乎所有的题目都要经过这样一个流程，每一步的缺乏都会导致题目错误。所以我们在课堂中也会去强调解题过程中的步骤和整体思路。 SAT数学考试共80分钟，因此，长时间做题后做题的准确性与稳定性也是需要注意的问题。
SAT数学考试知识点总结
SAT数学考试知识点总结 今天文都国际小编给大家带来的是SAT数学考试的知识点，备考SAT数学的考生可以根据下面提到的知识点复习，希望对大家有帮助。 1. 给出关系式/等式，求值 例题：if n=3, and 2n + 1 = b，求b 2. 分数所占比例问题，求总数、某一项值、比例等 3. 奇偶数，质数，因子(factor)，整除等 4. 平均数，中间数，众数，几个数的和/平均值/积，求其中某个数等 5. 求最值，可能的最大值，最小值等 6. 大多少，小多少，倍数等，写关系式 7. 定义特殊符号/函数等，求值 16 函数的上升，下降问题 8. 平方，立方，平方根，立方根等，指数函数，幂函数 9. 由不等式，求解/求可能值 20 排列组合问题 21 分段计价问题 10. 数列问题：等差，等比，自定义数列，求和，某一项值，两项差值等 (1). 等差数列:通项公式an=a1+(n-1)d;前n项和Sn=na1+n(n-1)d/2 (2). 等比数列：通项公式an=a1×q(n-1) 11.一共有25个硬币(1角和1元的)，而且价值6元1角，其中1角的有21个，求1元的有多少个。 12. 周期性问题，年/月/周等 13. 通过三角形，平行四边形，多边形，平行线等，求角度，周长，面积等 14. 直角三角形a2+b2=c2;一般三角形性质的考察：两边和>第三边，两边差<第三边，大边对应大角。 15. 直线斜率，截距，两点距离等 (1). 两直线平行：k1= k2，b1 = b2 (2). 两直线垂直：k1× k2 = -1 16. 直线/图形：直线的对称问题(直线l：y =kx + b) (1). 关于x轴对称：y=-kx-b (2). 关于y轴对称：y=-kx+b
sat难题解析
1.难题即为难度系数4,5的题目 2.应该都是做过的题目，但也请各位一定再做一遍，目标是全对，这样10月很有希望上750。错题数量>5就很不乐观了 3.认真看错题的答案和解析 1. (2013.1-27, Level 4) In this production of (A) Hamlet, the actors periodically (B) turn their back (C) to the real audience and appear to (D) address an imaginary audience on the other side of the stage. No error (E) 2. (201 3.1-28, Level 4) The Chauvet Cave, a cave in France whose(A) paintings are considered (B) among the world’s7 s6 k$ Y2 ^3 M% Q9 K# s! e oldest art, contain more than (C) 70 renderings of (D) lions prancing alongside other creatures. No error (E) 3. (2013.1-29, Level 5) What most (A) impressed my friends and I (B) as we toured the mansion was a landscape painting so vividly (C) realized that we at first thought it was (D) a window looking out onto a sunlit meadow. No error (E) 4. (2013.1-S10-12, Level 4) Some experts think that the rise of multi-language Internet forums has made learning a foreign language easier than ever before. (A)forums has made (B)forums have made (C)forums, which have made (D)forums, making (E)forums, having made 5. (2013.1-S10-13, Level 4 The African continent comprises more than 50 countries, each diverse in their cultures and languages. (A)diverse in their (B)diverse in its (C)is diverse in its (D)of them being diverse in their (E)having diversity in their 6. (2013.1-S10-14, Level 5) The 2005 movie Beowulf & Grendel was filmed in Iceland, but one might suppose it
SAT I考试包括SAT I推理测验
SAT I考试包括SAT I推理测验(Reasoning Test)和SAT II专项测验(Subject Tests)两个部分。考试时间为三小时四十五分钟，题型为选择题及写作，主要测验考生的阅读、数学及写作能力，满分是 2400分。SAT II(Subject Tests)时间一小时，大部分为选择题，主要考察考生某一专业的知识。可选择的SAT II 单科考试科目有数学、物理、化学、生物、外语(包括汉语、日语、德语、法语、西班牙语)等，学生应根据各专业和学校的要求报考。下面主要介绍SAT通用考试的考察重点： 写作 (writing) 时间:60分钟 考核内容:语法, 习惯用法和词汇选择 考核方式:多项选择题 (35分钟.);写作 (25分钟) 分数:200-800 阅读 (Critical Reading) 时间:70分钟(分为两个25分钟和一个20分钟) 考核内容:阅读能力 考核方式:阅读理解、完成句子和段落阅读理解 分数:200-800 数学 (Math section) 时间:70分钟(分为两个25分钟和一个20分钟) 考核内容:算术及应用题、代数及函数、几何及度量衡、数据分析、统计学及基础概率论 考核方式:多项选择题和运算题 分数:200-800 考试结构 SAT 分成三个部分：分析性阅读、数学、及写作;每一部分的成绩是 200 至 800 分。在每次考试中都会有一个或两个(双加试) 25 分钟的不计成绩部分
( unscored section )。不计成绩部分是为了设计未来的试题等目的。不计成绩部分可能是三部分的任何一部分。 考试题目 根据 College Board 出的官方题，数据如下： 数学部分有 54 道题，其中多选题 44 道，填空题 10 道。内容包括：整数和分数;代数、几何、统计、概率;数量分析 分析性阅读部分共 67 道题：其中完成句子有 19 道，段落阅读有 48 道。阅读文章涉及内容：自然科学类，人文科学类，社会科学类，文学小说类 写作部分共 49 道题和一个短文：其中有 18 道句子找错， 25 道改句， 6 道改段落和一个短文。多项选择包括改错 , 改写句子和段落。作文类型：议论文，需有立论和例证(作文单独评分： 2-12 ;多项选择评分： 20-80 ) 共 170 道题及一个短文。 附加部分不计成绩 , 无法与其它正常部分区分 , 时间长度是 25 分钟。附加部分可以是除写作和 10 分钟的多选题之外的任意其它部分中的一项。最好不要猜测哪一部分是不计成绩的附加部分。因为， ETS 会把附加部分和正常的部分设计得没有区别。 SAT和托福的差别? ——SAT考智力;托福考语言; TOEFL则是为申请去美国或加拿大等国家上大学或进入研究生院学习的非英语 国家学生提供的一种英语水平考试。简而言之，托福考查的是学生的语言能力，而SAT考查的是学生的逻辑推理能力。它不仅是进入本科院校的硬性条件，也是在美国社会衡量一个人是否“聪明”的标准。考SAT的意义远远超过了求学本身，也是个人思维能力的体现。 注：以前SAT成绩寄送是不可选择的，一旦选择寄送则所有历史成绩会被寄送至学校。从08年十月份开始collegeboard寄送成绩可以选择其中最好的一次寄送(如果在10月以前有过考试记录的同学则不能选择，必须全部寄送) 分数计算方法
SAT数学大纲
Number and Operations 数与运算 Arithmetic word problems (including percent, ratio, and proportion) 字符问题(百分比，比例) Properties of integers (even, odd, prime numbers, divisibility, etc.) 整数 Rational numbers 有理数 Sets (union, intersection, elements) 集合 Counting techniques 计算技术 Sequences and series (including exponential growth) 数列（指数增长） Elementary number theory 基本的理论 Algebra and Functions 代数方程式 Substitution and simplifying algebraic expressions 置换与简化代数表达式 Properties of exponents 指数 Algebraic word problems 代数 Solutions of linear equations and inequalities 线性方程和不等式 Systems of equations and inequalities 方程式和不等式 Quadratic equations 二次方程式 Rational and radical equations 有理方程式 Equations of lines 线的公式 Absolute value 绝对数 Direct and inverse variation 正反的变化 Concepts of algebraic functions 代数函数 Newly defined symbols based on commonly used operations 数学的符号 Geometry and Measurement