AP Pre-calculus

2021-09-15 :: Future Perfect Team

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Question 1

$\dfrac{x+2}{x^2-16}\cdot\dfrac{4x+16}{2x+4}$ equals

$\dfrac{1}{2x+4}$

$\dfrac{2}{x-4}$

$\dfrac{2x+4}{x^2-16}$

$\dfrac{2}{x}$

None of the above

Question 2

Let $f(x)=x^2+kx-1$. If $f(2)=5$, then $k$ is

$4$

$1$

$-\dfrac{22}{5}$

$2$

None of the above

Question 3

If $x>0$ then $\sqrt{25x^2-16x^2}$ equals

$x$

$5x$

$9x$

$3x^2$

$3x$

Question 4

The are of the rectangle pictured below is

$17$

$78$

$39$

$34$

Insufficient information

Question 5

How many distinct real solutions are there to $(x^2+1)^5(x-3)^6=0$

None

One

Two

Eleven

Sixteen

Question 6

$$(x^2\sqrt{y^5})x^{-3}=$$

$x^{-6}y^{3/2}$

$x^{-6}y^{2}\sqrt{y}$

$\dfrac{y^2\sqrt{y}}{x}$

$x^{-6}y^{15/2}$

Both $x^{-6}y^{5/2}$ and $x^{-6}y^2\sqrt{y}$

Question 7

Simplify $\dfrac{1-\frac{4}{x^2}}{1+\frac{2}{x}}$

$\dfrac{x}{x+2}$

$\dfrac{x}{x-2}$

$\dfrac{x-2}{x}$

$\dfrac{x+2}{x}$

None of the above

Question 8

The graph of $x^2+y=9$ is

Question 9

If $a(x+b)=bx-c$, then $x=$

$\dfrac{ab+c}{b-a}$

$\dfrac{ab+c}{b+a}$

$\dfrac{ab-c}{b+a}$

$\dfrac{b+c}{b-a}$

None of the above

Question 10

If $2<x<3$, what can be said about the quantity $\dfrac{x^2-9}{(x-4)^3}$

It is positive

It is negative

Its sign depends on where $x$ lies in this interval

The quantity is undefined for some of those $x$ values

None of the above

Question 11

A function $f$ has the property that $f(a+b)=f(a)f(b)$ for all $a$ and $b$.

If $f(1)=2$ then $f(3)=$

$2$

$6$

$8$

$9$

Insufficient information

Question 12

An equation for the line joining the points $(1,1)$ and $4,10$ is

$y=3x$

$y=\dfrac{1}{3}x+\dfrac{2}{3}$

$y=3x-2$

$y=2x+2$

None of the above

Question 13

The solutions to $|3x-1|=8$ are

$x=3$ only

$x=-3$ only

$x=3$ and $x=-\dfrac{7}{3}$

$x=-3$ and $x=\dfrac{7}{3}$

None of the above

Question 14

$$\frac{x}{3y}+\frac{x}{4y}=$$

$\dfrac{2x}{7y}$

$\dfrac{2x}{12y}$

$\dfrac{7x}{12y^2}$

$\dfrac{7x}{6y}$

None of the above

Question 15

$$(-8)^{5/3}=$$

$-32$

$\dfrac{1}{32}$

$64$

$\sqrt[3]{-40}$

None of the above

Question 16

If $f(x)$ is a function whose graph is the parabola sketched below, then $f(x)<0$

when $x<0$

when $x<1$

when $x<-1$ or $x>3$

when $-1<x<3$

for no $x$ values

Question 17

The graph of $y=x^2+3x-1$ crosses the $x$ axis at

$-\dfrac{3}{2}+\dfrac{\sqrt{5}}{2}$ and $-\dfrac{3}{2}-\dfrac{\sqrt{5}}{2}$

$-\dfrac{3}{2}+\dfrac{\sqrt{13}}{2}$ and $-\dfrac{3}{2}+\dfrac{\sqrt{13}}{2}$

$1$ and $-3$

$-1$

The graph does not cross the $x$ axis

Question 18

$$\frac{\sin(x)+x}{x}=$$

$\sin+1$

$1+\cos(x)$

$1+x$

$1+\dfrac{\sin(x)}{x}$

$1+\sin(x)$