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The expression $$x^{4}+2x^{2}y^{2}+9y^{4}$$ is equivalent to which of the following?
a=3+|x-4| (-2 ≤ x ≤ 5)

What is the positive difference between the greatest and least value of a?
Set A={1, 5, 9, 13, 10}

Set B={1, 5, 9, 13, 9}

Set C={1, 5, 9, 13, 7}

Set D={1, 5, 9, 13, 5}

Which of the following statement illustrates the exact order of standard deviation of these sets of numbers from the lowest to the greatest?
The average (arithmetic mean) of the values of the homes in Town A is $100,000. The average of the values of the homes in Town B is $150,000. The number of homes in Town A is between 2 times and 3 times the number of homes in Town B. Which of the following values could be the average of the values of the homes in Town A and Town B combined?

Indicate all such values.
A's salary is 33$$\frac{1}{3}$$ percent greater than B, while B's salary is 75 percent of C.

Quantity A

A's salary

Quantity B

C's salary


x and y are nonnegative numbers.

Quantity A

$$\sqrt{xy}$$

Quantity B

$$\frac{x+y}{2}$$


Quantity A

The greatest prime factor of 50

Quantity B

The greatest prime factor of 60




In the above figure, ABCD, OAPD, OBQC are all squares, and the radius of the circle O is 1.

Quantity A

The length of the semicircle PQ

Quantity B

The sum of lengths of line segments PD, DC and CQ


The salaries of five employees A, B, C, D and E are all positive integers. If the median salary of all five employees is 2000, and the salary of C, D, and E is 2000, 4000, 5000, respectively. Which of the following could be the average salary of all five employees?

Indicate all such numbers.
An organization offers only three types of annual memberships. Basic memberships cost $50 each, standard memberships cost $70 each, and premium memberships cost $100 each. Last year, a total of 200 memberships were purchased at an average arithmetic mean) cost of $80 per membership.

Which of the following statements individually provide(s) sufficient additional information to determine the number of premium memberships purchased last year?

Indicate all such statements
$$x+\frac{1}{x}=2$$

Quantity A

$$x^{2}$$+$$\frac{1}{x^{2}}$$

Quantity B

$$x^{3}$$+$$\frac{1}{x^{3}}$$




$$k+\frac{1}{k}=3$$

Quantity A

$$k+\frac{1}{k^{2}}$$

Quantity B

$$k^{2}$$+$$\frac{1}{k^{3}}$$


$$y=x^{2}+2x-35$$ can be transformed into $$y=(x+m)(x-n)$$ where $$m$$ and $$n$$ are both integers.

Quantity A

$$m$$

Quantity B

$$n$$


What is the product of the two solutions of the equation $$3x^{2}+17x+10=0$$?
The function f is defined by f(x) =$$x^{2}$$-18x+56 for all numbers x. If r and t are two different numbers such that f(r) = f(t) = 0. What is the value of $$\frac{r+t}{2}$$?
An apple falls straight to the ground from a tree branch 8 meters above the ground. The apple's height above the ground, t seconds after it starts falling, is H meters, where H=8-4.9$$t^{2}$$ and t≥0. How many seconds after the apple starts falling does it hit the ground?

Give your answer to the nearest 0.1 second.
The electric power P in a resistor is directly proportional to the square of the electric current I flowing through the resistor. For a given resistor, if the power is 18 watts when the current is 3 amperes, what is the power, in watts, when the current is 4 amperes?

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