Free Printable PreCal SOS #3 Practice

1.

Simplify:
(-3i)(4i)(-5i)

a)

-60i

b)

60

c)

-60

d)

60i

2.

i¹³

a)

-1

b)

1

c)

i

d)

-i

3.

(3i)(-2+4i)

a)

-6+12i

b)

-12-6i

c)

-2+7i

d)

12+6i

4.

Simplify 2√-32

a)

2i√32

b)

4i√2

c)

8i√2

d)

-16i√2

5.

2(x - 8)² + 40 = 16

a)

x = 8 ± 2i√3

b)

x = 8 ± √-12

c)

x = -8 ± 2i√3

d)

x = 8 ± 3i√2

6.

⅖(x + 3)² + 8 = -32

a)

x = 3 ± 10i

b)

x = ±13i

c)

x = -3 ± 10i

d)

x = ±i√10

7.

Solve the following equation by completing the square:
n² = 18n + 40

a)

{11, -11}

b)

{16, 2}

c)

{20, -2}

d)

{10, -4}

8.

Solve by completing the square:
k² − 12k + 23 = 0

a)

{6 + √13, 6 - √13}

b)

{-6 + √13, -6 - √13}

c)

{6 + √59, 6 - √59}

d)

{-6 + √59, -6 - √59}

9.

Solve Using the Quadratic Formula
x² + 4x - 40 = -8

a)

-10 & -4

b)

-4 & 10

c)

-8 & 4

d)

8 & -4

10.

If the discriminant is a perfect square you will have.....

a)

two real solutions

b)

two irrational solutions

c)

one solution

d)

two imaginary solutions

11.

If the discriminant is zero you will have

a)

no real solutions

b)

two real solutions

c)

1 real solution

d)

1 imaginary solution

12.

If the discriminant is negative, you will have....

a)

two real solutions

b)

two irrational solutions

c)

two imaginary solutions

d)

one solution

13.

What are the factors of
25x² - 81?

a)

(5x - 9)(5x + 9)

b)

(5x - 9)(5x - 9)

c)

(5x + 9)(5x + 9)

d)

Cannot be factored

14.

Factor 4b⁵+4b³+16b²

a)

4b³(b⁴+b²+4b)

b)

4b³(b⁴+4b+5)

c)

4(b⁵+b³+4b²)

d)

4b²(b³+b+4)

15.

Factor completely:
3x² + 5x - 12

a)

(3x + 4)(x-3)

b)

(3x - 4)(x + 3)

c)

(3x + 3)(x -4)

d)

(3x - 3)(x + 4)

16.

Factor by grouping:
3x³-x²+6x-2

a)

(x²+2)(3x+1)

b)

(x²+2)(3x-1)

c)

(3x³+6x)(x²-2)

d)

none of the aboe

17.

g(x)=3x+4
h(x)=3x-1
Find g(h(x))

a)

-9x+11

b)

4x²+4x

c)

9x+1

d)

9x+11

18.

For f(x) = 2x²-1, what is and (f ° f)(-2) ?

a)

7

b)

97

c)

13

d)

6

19.

Given f and g in the graph,

what is f(g(2)) ?

a)

3

b)

8

c)

1

d)

4

20.

Which is the inverse of the table?

a)

b)

c)

d)

21.

$g\left(x\right)=-7x^5+7$ Find the inverse of the function.

a)

$g^{-1}\left(x\right)=^5\sqrt{\frac{x-7}{7}}$

b)

$g^{-1}\left(x\right)=-^5\sqrt{\frac{x-7}{7}}$

c)

$g^{-1}\left(x\right)=^5\sqrt{-\frac{x-7}{7}}$

d)

$g^{-1}\left(x\right)=-^5\sqrt{\frac{x-7}{7}}$

22.

Which function matches this graph?

a)

$f\left(x\right)=\frac{-4}{x}-2$

b)

$f\left(x\right)=\frac{-4}{x}+2$

c)

$f\left(x\right)=\frac{-4}{x-2}$

d)

$f\left(x\right)=\frac{-4}{x+2}$

23.

Which function matches this graph?

a)

$f\left(x\right)=\frac{1}{x-1}+2$

b)

$f\left(x\right)=\frac{1}{x+2}-1$

c)

$f\left(x\right)=\frac{1}{x+1}+2$

d)

$f\left(x\right)=\frac{1}{x-2}+1$

24.

Condense into a single log:

\log_65+\log_62-\log_63

a)

$\log_67$

b)

$\log_64$

c)

$\log_6\frac{10}{3}$

25.

Condense into a single log:

\log_2x+\log_27-2\log_26

a)

$\log_2\left(\frac{14x}{6}\right)$

b)

$\log_2\left(\frac{7x}{36}\right)$

c)

$\log_2\left(\frac{7x}{12}\right)$

26.

Solve for x:

\log_x\sqrt{6}=\frac{1}{2}

*Hint: Rewrite as an exponential first.

(a)

27.

Write in exponential form.
log₂(¹/₈) = -3

a)

2^-3 = ¹/₈

b)

2^1/8= -3

c)

-3² = ¹/₈

d)

-3^1/8 = 2

28.

Rewrite the equation into logarithmic form:
6² = 36

a)

log₆ 2 = 36

b)

log₆ 36 = 2

c)

ln 36 = 2

d)

6³⁶ = 2

29.

Without a calculator, evaluate log₄1

a)

¹/₄

b)

0

c)

-1

d)

not possible

30.

Without a calculator, evaluate log₁₂₅ 25

a)

²/₃

b)

³/₂

c)

¹/₆

d)

¹/₅

31.

Without a calculator, evaluate log₆ -36

a)

not possible

b)

-2

c)

2

d)

¹/2

32.

$Evaluate\ \log_864$

(a)

33.

$Evaluate\ \log_77$

(a)

34.

$Evaluate\ \log_28$

(a)

35.

$Evaluate\ \log_5\sqrt{5}$

(a)

36.

Rewrite log₂8 = 3 in exponential form

a)

2⁸ = 3

b)

2³ = 8

c)

3² = 8

d)

8³ = 2

37.

The function shown in the graph is:

a)

Even

b)

Odd

c)

Neither Even nor Odd

d)

Not a Function

38.

Is this function even, odd or neither?

a)

Even

b)

Odd

c)

Neither

39.

Solve the equation for x.

a)

x = 2

b)

x = 36

c)

x = 6

d)

x = 11

40.

7ⁿ⁺¹⁰- 8 = 6

a)

-7.374

b)

-8.643

c)

-7.360

d)

-8.853

41.

5(4)^x-2 - 29 = 6

a)

-.5609

b)

3.4036

c)

2.0674

d)

-1.0753

42.

log₂(x + 2) + log₂x = 3

a)

-4, 2

b)

-2, 4

c)

2

d)

1

43.

$\log_4x+\log_4\left(x-3\right)=1$ Solve the equation.

a)

$x=-4\ and\ x=1$

b)

$x=4$

c)

$x=1$

d)

$x=4\ and\ x=-1$

e)

$x=-1$

44.

Complete the Square and write in Vertex Form:
f(x) = x² + 6x + 5

a)

(x + 3)² - 4

b)

(x + 6)² - 4

c)

(x + 3x)² - 4

d)

(x + 3)² + 9

45.

Complete the square to write in vertex form:

y\ =\ 6x^2+12x+13

a)

$y=6\left(x+1\right)^2-7$

b)

$y\ =\ \left(6x+6\right)^2-42$

c)

$y=\left(x-6\right)^2+7$

d)

$y=\frac{13}{6}\left(x+1\right)^2+7$

46.

If $1,000 is invested at 16% interest, compounded continuously, for five years, what is the ending balance?

a)

$1,225,54

b)

$2,225.54

c)

$22,255.40

d)

$225.54

47.

Chelsea put $7500 into an account paying 5% compounded continuously. She now has $10,643.01. How long has the money been in the account?

a)

7 years

b)

6 years

c)

5 years

d)

4 years

48.

Which formula is shown?

a)

Monthly compounded interest formula

b)

Annually compounded interest formula

c)

Continuously compounded interest formula

d)

Simple interest formula

49.

Log with a base "e" (log_e) is the same thing as...

a)

e

b)

Natural Logarithm (ln)

c)

Common Logarithm (log)

d)

log₁₀

50.

Given the formula: $S\ =\ R\ \left(\frac{\left(1\ +\ i\ \right)^n-1}{i}\right)$ .

What is the meaning of $R$ ?

a)

Recycle

b)

Interest Period

c)

Periodic Payments

d)

Interest Rate

PreCal SOS #3 Practice

Total questions: 50

Worksheet time: 3hrs 58mins

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