Problem #1

What is the value of x(x

^{3} - x

^{2}) if x = -2?

Problem #2

If A = (x

_{1}, y

_{1}) and B = (x

_{2}, y

_{2}), then what is the midpoint of the segment AB?

Problem #3

ABCD is square and AB=1. Find the area of the black space.

Problem #4

If

*a=c*^{2},

*b=c*^{3} and

*c* is an odd number, which one is true?

Problem #5

If

*f(x) = x*^{3} - x^{2} - x + 1, what is the value of

*f(-1)*?

Problem #6

If

*a, b, c* are positive consecutive integers, which one is true?

Problem #7

If

*ABCD* is a square and

*AB=1*, find the value of red area.

Problem #8

*f(x)=x*^{3} + 3x + 2 and

*f(a) = f(b) = 0*. Find

*a + b*.

Problem #9

If 4|a| - 3(-b)

^{3} = 5|-c|, what is the value of a in terms of

*b* and

*c*?

Problem #10

Find the sum of the units digits of the first 10 terms of the below sequence.

1, 5, 9, ..., a

_{n} = 4n - 3

Problem #11

If f(x)=3x

^{3} + 2x

^{2} + x then find f(-2)

Problem #12

If

*a, b, c* are positive consecutive odd integers and c < b < a, what is the value of

*b*^{2} in terms of

*a* and

*b*?

Problem #13

What is the value of y + x

^{2}y + xy

^{2}, if

*x = 1* and

*y = -1*?

Problem #14

Suppose A=(2, 3) and B=(x, y). Let C=(3, 4) be the midpoint of

*AB*. Find (x, y).

Problem #15

What is the average of x

^{2} + 3x + 2 and x

^{3} - x

^{2} - x + 1 for x = -1?

Problem #16

If

*f(x)=x*^{2} - 2x + 4 and

*g(x) = xf(x)*, find

*f(2) + g(-2)* = ?.

Problem #17

If f(3) = f(2) = 0, which of the following is true?

Problem #18

If A=(1, 1) and B=(2, 3), what is the distance between

*A* and

*B*?

Problem #19

Calculate the sum S = 1 + 2 + 3 + ...+ 100.

Problem #20

According to the figure, which one is true?