### Table of Contents

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

Difficulty: Medium

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

Which of the following is equivalent to the given expression?

Difficulty: Easy

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

Difficulty: Medium

##### $x=49$

$y=\sqrt{x}+9$

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

Difficulty: Easy

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

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

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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

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

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

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

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

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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

##### $x-y=1$

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

Which ordered pair is a solution to the system of equations above?

Difficulty: Hard

##### Which of the following is equivalent to the expression $x^{4}-x^{2}-6$?

Difficulty: Medium

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

Which of the following is equivalent to the expression above?

Difficulty: Medium

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

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

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

Difficulty: Hard

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