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Triangle ABC is inscribed in a circle,where AB is diameter and the length of AC equals to radius R. What is the degree of ∠ABC?
AC is the diameter of a circle, and D is a point on arc ABC of that circle.

Quantity A

∠DCA

Quantity B

45°



Circle A (with radius of 4) and circle B (with radius of 3) intersect at two points.

Quantity A

The measure of the circumferential angle MAN of the chord formed by two intersection points in circle A

Quantity B

The measure of the circumferential angle MBN of the chord formed by two intersection points in circle B



Point A and point B are the centers of two circles, and their radius are 10 and 3 respectively. Point C and point D and the points of tangency of the two circles and a horizontal line. Point E and point F are the intersections between the two circles and line AB, EF=12, what is the length of CD?
The height, width and length ratio of a rectangular solid is 1:2:3, while the surface area of the entire solid is 550. What is the volume of the rectangular solid?
If 216 cubes, all of equal size, are fastened together to form one large cube, how many cubes are beneath the surface layer of the larger cube?
There is a cylindrical swimming pool with a height of 4 feet and a bottom diameter of 10 feet. Now that the water depth is 3 feet and 6 inches, how many gallons of water are in the pool? (π≈3.14,1feet=12 inches,1gallon=243 cubic inches)
Give your answer to the nearest units digit.
_______gallons
There are 500 students in a class. 450 of them take Course A, 300 of them take Course B, and 150 of them take Course C. Each student has to take at least one course, and 100 of them take all the three classes simultaneously. The number of students who take both Course A and Course B, but not Course C could be?
Indicate all such possible values.
x=1+2+3+-+100,and y=1+3+5+-+199.What is the value of y-x?
In a sequence, $$a_{1}$$=7,for any integer n greater than 1, $$a_{n}=a_{n-1}+2$$. If the last term in the sequence is 217,what's the number of integers in the sequence?

Quantity A

The sum of integers from 29 to 89, inclusive

Quantity B

The sum of integers from 30 to 90, inclusive


100 cards are marked with 100 numbers from 0 to 99. If a person draws n cards from them, then what`s the value of n such that the sum of all the numbers marked on these cards is 100?
Indicate all such values.
What is the sum of all the odds from 3 to 97,inclusive?
First step is to draw a square whose side is 1cm. Second step is to draw a square whose side is 3cm. Third step is to draw a square whose side is 5cm. At which of the following step will be taken to draw a square whose side is 43cm?
In a certain sequence, the first term is 2, and each term is -2 times the preceding term. What is the sum of the first five terms?
In a list of geometric sequence with a common ratio of 2, the first term is 2, what is the 4th term, 6th term and 8th term, respectively?all the three term.
In a sequence, $$S_{1} = 1$$, $$S_{n} = 1/7 * S_{n-1}$$, (n≥2).
Quantity A: $$S_{12}$$
Quantity B: $$S_{26}* 49^7$$
In a certain sequence an,the first term a1= 6, and each term is 3 times higher than the preceding term.

Quantity A

$$2*3^{28}$$

Quantity B

$$\frac{a_{18}}{3^(-10)}$$


In a sequence,if $$a_{n}=3a_{n-1}$$,where n is any integer greater than 1

Quantity A

$$a_{28}$$

Quantity B

$$a_{11}$$


In a sequence, $$a_{1}=1$$, $$a_{2}=2$$, for any n greater than 2, $$a_{n} =(a_(n-1)/a_(n-2) )^2$$, what is the value of $$a_{5}$$?

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