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1. What is the sum of all the positive integer factors of 12 ?
2. The average IQ of 4 people is 110. If three people each have an IQ of 105, what is the IQ of the fourth person ?
3. Of 60 students in a class 2/3 are girls, and 2/5 of the class are taking music lessons. What is the maximum number of girls that are not taking music lessons?
4. If 2 n + 1 = 8, what is the value of n ?
5. In the figure above, AD = AC = CB.
If the value of y is 28, what is the value of x?
6. One gallon of fuel mixture contains antifreeze in the ratio of 5 parts fuel to one part antifreeze. To this is added half a gallon of mixture which is one third antifreeze and two thirds fuel. What is the ratio of fuel to antifreeze in the final mixture? (Grid your answer as a fraction: fuel/antifreeze)
7. Two dials O and P have pointers that start from the vertical position as shown. Pointer O rotates anticlockwise at a rate of 5 degrees per second and pointer P rotates clockwise at 9 degrees per second. How many complete revolutions will P have made when O completes 335 complete revolutions?
8. What is the total surface area of 2 identical cubes which together have a volume of 1458 units?
9. N {12,18,2,6}
P {1,4,2,3}
If n and p are to be selected at random from sets N and P respectively, what is the probability that n/2p will be a member of set P?
10. If f(x) = (12 � x)3/2, and n = f(3), what is the value of 2n?
参考答案
1.Correct Answer: 28
Explanation:
The positive integer factors of 21 are: 1,12,2,4,3,6
Their sum is 28
2.Correct Answer: 125
Explanation:
If the average of four is 110, the total = 4 x 110 = 440
The sum of three with IQ 105 = 315
The fourth person must have IQ = 440 - 315 = 125
3.Correct Answer: 36
Explanation:
If 2/3 of the class of 60 are girls (=40), 1/3 must be boys (=20)
2/5 of the class (=24) are taking music.
The maximum number of girls not taking music will be when all the boys take music.
If all 20 boys take music, then only 4 girls need to take it, so 36 girls do not take music lessons.
4.Correct Answer: 2
Explanation:
8 is 2 raised to the power of 3
3 = n + 1; n =2
5.Correct Answer: 84
Explanation:
In triangle ABC angles CAB and CBA are equal (isosceles triangle). And both are 28.
Angle ACD = 56 (exterior angle = sum of two opp. interior angles)
Angles ACD and CDA are equal (isosceles triangle)
Angle DAC = 180 - 112 = 68
The angle marked x = 180 - 68 - 28 = 84
6.Correct Answer: 7/2
Explanation:
The antifreeze in the initial fuel mixture is 1/6 of one gallon.
The added mixture contains 1/3 of half a gallon = 1/6 of a gallon
The final mixture contains 1/6 + 1/6 in 1.5 gallon
2/6 antifreeze in total 9/6 gallons
Fuel in the mixture is 9/6 - 2/6 = 7/6
Ratio fuel to antifreeze = 7/6 : 2/6 = 7 : 2
Grid in as 7/2
7.Correct Answer: 603
Explanation:
When O completes 335 revolutions it will have turned through 335 x 360 degrees.
At a rate of 5 degrees per second this means 335x 360 /5 seconds
P will have turned through 9 x 335 x 360 /5 degrees in the same time
Now divide by 360 to get complete revolutions = 9 x 335 / 5 = 603
8.Correct Answer: 972
Explanation:
Volume of one cube = 1458/2 = 729; the cube root will give the side of each cube.
The cube root of this = 9 (If you do not spot this you can find the prime factors then you will see the cube root is 9)
If the side of the cube =9, the area of one face = 81. There are six faces so the surface area = 6 x 81 =486
But there are two cubes so the total surface is 2 x 486 =972
9.Correct Answer: 3/8
Explanation:
n can take four different values, each of which can be combined with the four possible values for p. This gives us 16 possible pairs.#p#分页标题#e#
Now find out how many of these pairs can give a value for n/2p which is in set P.
If n = 12 and p = 2 the expression gives 12/4 = 3 which is in set P. Similarly n=12 and p = 3 works out to 2, which is in the set.
With n = 18, p can be 3. With n = 2, p can be 1. With n = 6, p can be 1, or 3
This gives us 6 pairs out of 16 = 3/8
10.Correct Answer: 54
Explanation:
First find n by finding f(3);
f(3) = (12-3)3/2 = 93/2 = √9³ =√(9x9x9) = √9 x √9 x √9 = 27
But we are asked for 2n; 2n = 54
以上就是SAT数学考试问答题练习题(二)的详细内容，考生可针对文中介绍的方法进行有针对性的备考。