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If $p=3x+4$ and $v=x+5$, which of the following is equivalent to $p\nu-2p+\nu$ ?
Difficulty: Medium
A:

$3x^{2}+12x+7$

B:

$3x^{2}+14x+17$

C:

$3x^{2}+19x+20$

D:

$3x^{2}+26x+33$

$x^{2}-x-1=0$

What values satisfy the equation above?
Difficulty: Medium
A:

$x=1$ and $x=2$

B:

$x=-\frac{1}{2}$ and $x=\frac{3}{2}$

C:

$x=\frac{1+\sqrt{5}}{2}$ and $=\frac{1-\sqrt{5}}{2}$

D:

$x=\frac{-1+\sqrt{5}}{2}$ and $x=\frac{-1-\sqrt{5}}{2}$

$(x+5)+(2x-3)$

Which of the following is equivalent to the given expression?
Difficulty: Easy
A:

$3x-2$

B:

$3x+2$

C:

$3x-8$

D:

$3x+8$

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Which expression is equivalent to $\frac{8x(x-7)-3(x-7)}{2x-14}$, where $x>7$?
Difficulty: Medium
A:

$\frac{x-7}{5}$

B:

$\frac{8x-3}{2}$

C:

$\frac{8x^{2}-3x-14}{2x-14}$

D:

$\frac{8x^{2}-3x-77}{2x-14}$

$x=49$

$y=\sqrt{x}+9$

The graphs of the given equations intersect at the point $(x,y)$ in the $xy$-plane. What is the value of $y$?
Difficulty: Easy
A:

16

B:

40

C:

81

D:

130

$h(x)=2(x-4)^{2}-32$

The quadratic function $h$ is defined as shown. In the $xy$-plane, the graph of $y=h(x)$ intersects the $x$-axis at the points $(0,0)$ and $(t,0)$, where $t$ is a constant. What is the value of $t$?
Difficulty: Hard
A:

1

B:

2

C:

4

D:

8

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The function $\bm{f}$ is defined by $\bm{f}(\bm{x})=(-8)(2)^{x}+22$. What is the $y$-intercept of the graph of $\bm{y}=\bm{f}(\bm{x})$ in the xy-plane?
Difficulty: Hard
A:

$(0,14)$

B:

$(0,2)$

C:

$(0,22)$

D:

$(0,-8)$

$x^{2}-2x-9=0$

One solution to the given equation can be written as $1+\sqrt{k}$, where $k$ is a constant. What is the value of $k$?
Difficulty: Hard
A:

8

B:

10

C:

20

D:

40

$\bm{f}(\bm{x})=9,000(0.66)^{x}$

The given function $f$ models the number of advertisements a company sent to its clients each year, where $\bm{x}$ represents the number of years since 1997, and $0\leq\bm{x}\leq 5$. If $y=\bm{f}(\bm{x})$ is graphed in the $xy$-plane, which of the following is the best interpretation of the $y$-intercept of the graph in this context?
Difficulty: Hard
A:

The minimum estimated number of advertisements the company sent to its clients during the 5 years was 1,708.

B:

The minimum estimated number of advertisements the company sent to its clients during the 5 years was 9,000.

C:

The estimated number of advertisements the company sent to its clients in 1997 was 1,708.

D:

The estimated number of advertisements the company sent to its clients in 1997 was 9,000.

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The first term of a sequence is 9. Each term after the first is 4 times the preceding term. If $w$ represents the $n$th term of the sequence, which equation gives $w$ in terms of $n$?
Difficulty: Hard
A:

$w=4(9^{n})$

B:

$w=4(9^{n-1})$

C:

$w=9(4^{n})$

D:

$w=9(4^{n-1})$

$x-y=1$

$x+y=x^{2}-3$

Which ordered pair is a solution to the system of equations above?
Difficulty: Hard
A:

$(1+\sqrt{3},\sqrt{3})$

B:

$(\sqrt{3},-\sqrt{3})$

C:

$(1+\sqrt{5},\sqrt{5})$

D:

$(\sqrt{5},-1+\sqrt{5})$

Which of the following is equivalent to the expression $x^{4}-x^{2}-6$?
Difficulty: Medium
A:

$(x^{2}+1)(x^{2}-6)$

B:

$(x^{2}+2)(x^{2}-3)$

C:

$(x^{2}+3)(x^{2}-2)$

D:

$(x^{2}+6)(x^{2}-1)$

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$(2x+5)^{2}-(x-2)+2(x+3)$

Which of the following is equivalent to the expression above?
Difficulty: Medium
A:

$4x^{2}+21x+33$

B:

$4x^{2}+21x+29$

C:

$4x^{2}+x+29$

D:

$4x^{2}+x+33$

Time (years) Total amount (dollars)
0 604.00
1 606.42
2 608.84


Lisa opened a savings account at a bank. The table shows the exponential relationship between the time $t$, in years, since Lisa opened the account and the total amount $n$, in dollars, in the account. If Lisa made no additional deposits or withdrawals, which of the following equations best represents the relationship between $t$ and $n$?
Difficulty: Medium
A:

$n=(1+604)^{t}$

B:

$n=(1+0.004)^{t}$

C:

$n=604(1+0.004)^{t}$

D:

$n=0.004(1+604)^{t}$

$(ax+3)(5x^{2}-bx+4)=20x^{3}-9x^{2}-2x+12$

The equation above is true for all $x$, where $a$ and $b$ are constants. What is the value of $ab$?
Difficulty: Hard
A:

18

B:

20

C:

24

D:

40

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