PreCalculus Practice Test

Solve the following equation:  $4\sin^2x-3=0$  on the interval  $\left[0,2\pi\right)$  .

•  $\frac{\pi}{3},\frac{2\pi}{3},\frac{4\pi}{3},\frac{5\pi}{3}$  

•  $0,\pi,\frac{3\pi}{2}$  

•  $\frac{\pi}{3},\frac{4\pi}{3}$  

•  $\frac{2\pi}{3},\frac{5\pi}{3}$  

Tags

CCSS.HSF.TF.B.7

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator:   $\frac{1}{2}\log\left(x-6\right)-\log x$  

•  $\log\sqrt{x-6}-x$  

•  $\frac{\log\sqrt{x-6}}{\log x}$  

•  $\log\ \frac{\frac{1}{2}\left(x-6\right)}{x}$  

•  $\log\frac{\sqrt{x-6}}{x}$  

Identify the center and radius of the circle:   $\left(x-2\right)^2+\left(y+5\right)^2=121$  

• (2 , 5); radius 121

• (2 , -5); radius 121

• (2 , -5); radius 11

• (-2 , -5); radius 11

Write the equation in standard form, then identify the center and radius:  $x^2+y^2-16x+4y-8=5$  

•  $\left(x-8\right)^2+\left(y+2\right)^2=81$  ; (8,-2), r =  9

•  $\left(x+8\right)^2+\left(y-2\right)^2=81$  ; (-8,2), r = 9

•  $\left(x-2\right)^2+\left(y+8\right)^2=81$  ; (2,-8), r = 81

•  $\left(x+2\right)^2+\left(y-8\right)^2=81$   ; (2,-8), r = 81

Find the value of $\sec\left(\frac{15\pi}{2}\right)$  .

• 0

• -1

• undefined

•  $-\sqrt{3}$  

Find and simplify using the Difference Quotient,  $\frac{f\left(x-h\right)-f\left(x\right)}{h}$  of the following:  $f\left(x\right)=x^2-4x+2$  

• -2x +h - 4

• -2x -h + 4

• -2x -h - 4

• -2x +h + 4

Write a vector v in terms of i and j that has a magnitude and direction angle θ are given.  $\left|\left|v\right|\right|=6\ and\ \theta=225\degree$  

•  $-3\sqrt{2}i+3\sqrt{2}j$  

•  $-3\sqrt{2}i-3\sqrt{2}j$  

•  $3\sqrt{2}i-3\sqrt{2}j$  

•  $3\sqrt{2}i+3\sqrt{2}j$  

Use a sketch to find the exact value of the expression: $\sin\left(\cos^{-1}\frac{20}{29}\right)$  

•  $\frac{\sqrt{1241}}{29}$  

•  $\frac{\sqrt{35}}{29}$  

•  $\frac{29}{20}$  

•  $\frac{21}{29}$  

Use a right triangle to write the expression as an algebraic expression.  $\tan\left(\cos^{-1}x\right)$  

•  $\frac{x\sqrt{1+x^2}}{1+x^2}$  

•  $\frac{\sqrt{1+x^2}}{x}$  

•  $\frac{\sqrt{1-x^2}}{x}$  

•  $\frac{\sqrt{1+x^2}}{1+x^2}$  

From the ground, the angle of elevation to the top of a mountain is  $35\degree$ . If the height of the mountain is 4,531 feet, which expression gives the distance from the position on the ground to the base of the mountain? 

•  $4531\tan35\degree\$  feet

•  $4531\sin35\degree$  feet

•  $\frac{4531}{\sin35\degree}$  feet

•  $\frac{4531}{\tan35\degree}$  feet

Tags

CCSS.HSG.SRT.C.8