Uma função $f: \mathbb{R} \to \mathbb{R}$ é definida por $f(x) = 2x^2 - 3x + 1$. O valor de $f(2)$ é
(A) 1 (B) 2 (C) 3 (D) 4 (E) 5

For the function $f ( x ) = x ( x + 1 ) ( x - 4 )$, answer the following. For the matrix $A = \left( \begin{array} { l l } 2 & 1 \\ 0 & 3 \end{array} \right)$, what is the sum of all constant values $a$ that satisfy $A \binom { 0 } { f ( a ) } = \binom { 0 } { 0 }$? [3 points]
(1) 1
(2) 2
(3) 3
(4) 4
(5) 5

Let $a, b, c$ be positive integers such that $\frac{b}{a}$ is an integer. If $a, b, c$ are in geometric progression and the arithmetic mean of $a, b, c$ is $b + 2$, then the value of $$\frac{a^2 + a - 14}{a + 1}$$ is

Let $a , b , c \in \mathbb { R }$. If $f ( x ) = a x ^ { 2 } + b x + c$ is such that $a + b + c = 3$ and $f ( x + y ) = f ( x ) + f ( y ) + x y$, $\forall x , y \in \mathbb { R }$, then $\sum _ { n = 1 } ^ { 10 } f ( n )$ is equal to:
(1) 330
(2) 165
(3) 190
(4) 255

If $\alpha$ and $\beta$ are the roots of the equation, $7x^2 - 3x - 2 = 0$, then the value of $\frac{\alpha}{1-\alpha^2} + \frac{\beta}{1-\beta^2}$ is equal to:
(1) $\frac{27}{32}$
(2) $\frac{1}{24}$
(3) $\frac{3}{8}$
(4) $\frac{27}{16}$

If $\alpha$ and $\beta$ be two roots of the equation $x ^ { 2 } - 64 x + 256 = 0$. Then the value of $\left( \frac { \alpha ^ { 3 } } { \beta ^ { 5 } } \right) ^ { \frac { 1 } { 8 } } + \left( \frac { \beta ^ { 3 } } { \alpha ^ { 5 } } \right) ^ { \frac { 1 } { 8 } }$ is :
(1) 2
(2) 3
(3) 1
(4) 4

Given that $x - 2 y = 3$, what is the value of
$$x ^ { 2 } + 4 y ^ { 2 } - 4 x y - 2 y + x - 3$$
?
A) 4
B) 5
C) 8
D) 9
E) 15

Let a and b be positive integers. The sum of the coefficients of the polynomial
$$P ( x ) = ( x + a ) \cdot ( x + b )$$
is 15. What is the sum $a + b$?
A) 10
B) 9
C) 8
D) 7
E) 6

Let $\mathbf { a }$ and $\mathbf { b }$ be real numbers such that
$$\begin{aligned} & a ^ { 2 } - a = b ^ { 2 } - b \\ & a \cdot b = - 1 \end{aligned}$$
Given this, what is the sum $a ^ { 2 } + b ^ { 2 }$?
A) 6
B) 5
C) 4
D) 3
E) 2

$$a \cdot b = \frac { 3 } { 2 }$$
Given that, what is the value of the expression $\left( a + \frac { 1 } { 2 b } \right) \left( b - \frac { 1 } { a } \right)$?
A) $\frac { 1 } { 2 }$
B) $\frac { 2 } { 3 }$
C) $\frac { 4 } { 3 }$
D) $\frac { 3 } { 4 }$
E) $\frac { 2 } { 5 }$

Given that $a ^ { 2 } + a = 1$,
$$a ^ { 4 } - 2$$
Which of the following is the equivalent of this expression in terms of $a$?
A) $- a$
B) $- a + 2$
C) $- 2 a$
D) $- 2 a + 1$
E) $- 3 a$

Let $\mathrm { a } , \mathrm { b }$ and c be prime numbers such that
$$\mathrm { ab } + \mathrm { ac } = 4 \mathrm { a } ^ { 2 } + 8$$
Given this, what is the product $\mathbf { a } \cdot \mathbf { b } \cdot \mathbf { c }$?

For positive real numbers $\mathrm{a}$, $\mathrm{b}$, and $c$ $$\begin{aligned}& \frac { a + c } { b + 2 } = \frac { c } { b } \\& \frac { a } { b } = c\end{aligned}$$ the following equalities are given.\ Accordingly, what is b?\ A) $\sqrt { 2 }$\ B) $\sqrt { 3 }$\ C) $\sqrt { 6 }$\ D) 2\ E) 3

A function $f$ on the set of real numbers is defined for every real number $x$ where $n$ is an integer as $$f ( x ) = x - n , \quad x \in [ n , n + 1 )$$ Accordingly, $$f ( 1 ) + f \left( \frac { 7 } { 3 } \right) + f \left( \frac { 13 } { 6 } \right)$$ what is this sum?\ A) $\frac { 1 } { 2 }$\ B) $\frac { 2 } { 3 }$\ C) $\frac { 7 } { 6 }$\ D) 1\ E) 2