Problem #1

If 20 percent of 40 percent of X plus 1 is equal to 10 percent of 20 percent of X, what's the value of X?

Problem #2

What is the slope of a line that passes through the points (0, 1) and (2, 3)?

Problem #3

Let

*a*^{2}b = c and

*c*^{2}d = b. What is the value of

*a*^{2} in terms of

*b* and

*d*?

Problem #4

Find the slope of a line which passes through the mid points of two lines. The first one is through (1, 2) and (3, 4). The second line is through (-5, -6) and (7, 8).

Problem #5

If [tex](x\diamond y)\odot z = (x + y)\times z[/tex], what is the value of [tex](3\diamond 2)\odot 4[/tex]?

Problem #6

If

*X* and

*Y* are consecutive positive prime numbers, that product is 143, what is the value of

*X + Y*?

Problem #7

If

*y = x + 5* and

*-mx = 4*, meet each other at the point (1, 6), what is the value of

*m*?

Problem #8

If

*y = mx + a* and

*y = nx + b*, are two lines that never meet each other, which one is true?

(

*k ∈ R, a ≠ b*)

Problem #9

The average of

*a* and

*b* is 3. What's the average of

*a*,

*b* and

*c* if c = 3?

Problem #10

If

*x = y*^{-2} and

*y*^{2} = z^{-3}, what is the value of

*z*?

Problem #11

If the sides of a triangle are three consecutive positive integers and the perimeter of the triangle is 12, what is the area of the triangle?

Problem #12

If

*a*^{2}b^{3} = 4 and [tex]b=\sqrt{2}[/tex], what is the value of

*a*.

Problem #13

If

*f(-x) = -f(x)*, what is the value of

*f(1) + f(-1)*?

Problem #14

If

* 0 < a < b < 1* then which one is false?

Problem #15

If

*p > 2* is a prime number, and

*q* is a composite even number, which of the following is odd?

Problem #17

If

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

*f(1) =?*
Problem #18

X is 10 years older than Y. In 3 years X will be 3 times older than Y. Find the sum of their ages.

Problem #19

If

*f(x) = x + 1* and

*g(x) = x - 1*, what is the value of [tex]\frac{f(x)g(x)}{f(x)+g(x)}[/tex]?

Problem #20

If

*c* is the average of

*a* and

*b*, what is the average of

*a, b,* and

*c*?