Free Printable Pre-Calculus Review Quiz

1.

When writing f(x) = |x + 2| - 3 as a piecewise-defined function, what is the equation and the domain of the piece where (x+2) is less than zero.

a)

f(x) = { 0, x<0

b)

f(x) = { -x-5, x<-2

c)

f(x) = { -x-5, x < 0

d)

f(x) = { x-1, x>-2

2.

Determine if f(x) = (sinx)(cosx) is even, odd, or neither. Show all algebraic work.

4 lines

3.

When expanding ( 2 - x ) ⁶, what is the 3rd term in the expansion?

a)

60x⁴

b)

-160x³

c)

240x²

d)

-192x

4.

List all possible rational zeros of P(x) = 2x³+ x²- 32x - 16

a)

$\pm1,\ \pm2$

b)

$\pm1,\ \pm2,\ \pm4,\ \pm8,\ \pm16$

c)

$\pm1,\ \pm\frac{1}{2},\ \pm2,\ \pm4,\ \pm8,\ \pm16$

d)

$\pm1,\ \pm\frac{1}{2},\ \pm\frac{1}{4},\ \pm\frac{1}{8},\ \pm\frac{1}{16}$

5.

ln 1 =

a)

1

b)

undefined

c)

0

d)

e

6.

The log of all numbers between 0 and 1 are

a)

positive numbers

b)

negative numbers

c)

imaginary numbers

d)

purple

7.

ln 0 =

a)

0

b)

1

c)

e

d)

undefined

8.

Solve for x: e^x = 1

a)

x = 0

b)

x = 1

c)

x = e

d)

x = -1

9.

Simplify ln e^x.

a)

1

b)

e

c)

x

d)

e^x

10.

Simplify $e^{\left(2x-\ln2\right)}$

a)

2x - ln2

b)

$\frac{1}{2}e^{2x}$

c)

$\frac{2x}{\ln2}$

d)

$\ln2e^{2x}$

11.

If f(x) = ln x, what is $f^{-1}\left(x\right)$ ?

a)

$f^{-1}\left(x\right)\ =\ \frac{1}{\ln x}$

b)

$f^{-1}\left(x\right)\ =\ \log x$

c)

$f^{-1}\left(x\right)\ =\ e^x$

d)

$f^{-1}\left(x\right)\ =\ \ln\left(-x\right)$

12.

$\csc\left(\arccos\left(-\frac{\sqrt{3}}{2}\right)\right)=$

a)

$\frac{\pi}{6}$

b)

$-\frac{1}{2}$

c)

$-\frac{\pi}{6}$

d)

2

13.

sec²x is equivalent to which of the following?

a)

tan²x + 1

b)

tan²x - 1

c)

1 - tan²x

d)

1 - cot²x

14.

Factor 27x³- 64 completely.

a)

(3x - 4) (x² + 12x - 16 )

b)

(3x - 4) (9x²+ 12x + 16 )

c)

(3x + 4) (9x²- 12x - 16 )

d)

(3x - 4) (x²- 12x + 16 )

15.

$If\ f\left(x\right)\ =\sqrt{4-x^2}\$ and $g\left(x\right)\ =\ \sqrt{3-x}$

find the domain of f [ g(x) ].

a)

( -1, 3)

b)

[ -1, $\infty$ )

c)

$\left(-\infty,\ 3\right]$

d)

[ - 1, 3 ]

16.

Describe the transformations from the graph of g(x) = x³

to the graph of f(x) = - ( x- 2)³+ 1.

a)

g is shifted 2 units to the right, 1 unit up, and reflected in the x-axis.

b)

g is shifted 2 units to the left, 1 unit up, and reflected in the x-axis.

c)

g is shifted 2 units to the right, 1 unit up, and reflected in the y-axis.

d)

g is shifted 2 units to the left, 1 unit down, and reflected in the x-axis.

Pre-Calculus Review Quiz

Total questions: 16

Worksheet time: 11mins

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