Module 1

1.

Question 1

True or false? Ifxxis a nonzero real number andnnis a positive integer, thenx^{-n} = -x^nxn=xn.

1 point

True

False

2.

Question 2

Consider the exponential expression4^{3/2}43/2.

Which number is thebasein the expression?

1 point

44

3/23/2

22

33

3.

Question 3

Use the properties of exponents to find\dfrac{5^{11}}{(5^2)^3\cdot25}(52)325511.

If your answer is not a whole number, enter it as a decimal.

1 point

4.

Question 4

Use the properties of exponents to find\left(\dfrac{4^2\cdot 2^3}{8} ight)^{-1/2}(84223)1/2.

If your answer is not a whole number, enter it as a decimal.

1 point

5.

Question 5

Use the properties of exponents to find\left(\dfrac14 ight)^{-3/2}(41)3/2.

If your answer is not a whole number, enter it as a decimal.

1 point

6.

Question 6

Use the properties of exponents to find\dfrac{2\cdot 6^4}{3^3\cdot24}3324264.

If your answer is not a whole number, enter it as a decimal.

1 point

7.

Question 7

Simplify the expression\dfrac{\sqrt{16x^{-6}y^7}}{x^{-2}y^0}x2y016x6y7.

(Assume thatxxandyyare both nonzero real numbers)

1 point

4xy^{7/2}4xy7/2

\dfrac{4y^{7/2}}{x}x4y7/2

4x^{3/2}y^{7/2}4x3/2y7/2

4x^{3/2}4x3/2

8.

Question 8

Simplify the expression\dfrac{2a^{-4}b^{-2}}{4a^{-6}b^8}4a6b82a4b2.

(Assumeaaandbbare nonzero real numbers.)

1 point

\dfrac{a^2}{2b^{10}}2b10a2

\dfrac{b^6}{2a^{10}}2a10b6

\dfrac12 a^{2/3} b^{-1/4}21a2/3b1/4

\dfrac{1}{2a^2 b^{10}}2a2b101

9.

Question 9

Selectallof the following expressions that are equal to11.

1 point

1^010

0^000

10^{1}101

0^101

1^111

1^{10}110

10^{0}100

10.

Question 10

Letxxbe a real number. Supposemmandnnare nonzero integers.

Which of the following is equal tox^{m}xm/n?

Select all that apply.

1 point

\sqrt[n]{x^m}nxm

\left(\sqrt[n]{x} ight)^m(nx)m

Neither of these

Module 2

1.

Question 1

Solve forttin the exponential equation.

(-5)^t = -\dfrac{1}{125}(5)t=1251

Enter a number only for your answer. If your answer is not a whole number, write it as a decimal.

1 point

2.

Question 2

Findxxsuch that7^{3x} = \sqrt{7^x}73x=7x.

Enter a number only for your answer. If your answer is not a whole number, write it as a decimal.

1 point

3.

Question 3

Solve forssin the exponential equation.

6^{14-2s} = 6^{5s}6142s=65s

Enter a number only for your answer. If your answer is not a whole number, write it as a decimal.

1 point

4.

Question 4

Findvvsuch that

16^{v-1} = 2^{10v + 8}16v1=210v+8

Enter a number only for your answer. If your answer is not a whole number, write it as a decimal.

1 point

5.

Question 5

Solve forxx.

3^{2x + (1/4)} = \dfrac{1}{9^{-2 - (x/4)}}32x+(1/4)=92(x/4)1

Enter a number only for your answer. If your answer is not a whole number, write it as a decimal.

1 point

6.

Question 6

Solve foryy.

25^{2y + (1/2)} = \dfrac{5^{8y}}{25}252y+(1/2)=2558y

Enter a number only for your answer. If your answer is not a whole number, write it as a decimal.

1 point

7.

Question 7

There are approximately8.6 \times 10^{10}8.61010 neurons in the adult human brain.

Convert this number from scientific notation to standard notation.

Enter a number only (no units, no commas).

1 point

8.

Question 8

Theperihelionin a planet's orbit about the Sun is the point where the planet comes closest to the Sun.

At perihelion, the planet Venus is approximately67,700,000\text{ miles}67,700,000miles from the Sun.

Write distance in scientific notation.

1 point

67.7\times 10^{-6}\text{ miles}67.7106miles

6.77\times 10^7\text{ miles}6.77107miles

0.677\times 10^8\text{ miles}0.677108miles

6.77\times 10^{-7}\text{ miles}6.77107miles

67.7\times 10^6\text{ miles}67.7106miles

9.

Question 9

Theaphelionin a planet's orbit about the Sun is the point where the planet is farthest from the Sun.

At perihelion, the planet Earth is approximately9.14\times 10^7\text{ miles}9.14107miles from the Sun.

At aphelion, Earth is approximately9.45\times 10^7\text{ miles}9.45107miles from the Sun.

Find the difference between the Earth's distance from the Sun at perihelion and aphelion, using scientific notation.

1 point

3.1\times 10^6\text{ miles}3.1106miles

3.1\text{ miles}3.1miles

31\times 10^5\text{ miles}31105miles

0.31\times 10^7\text{ miles}0.31107miles

0.31\text{ miles}0.31miles

3.1 \times 10^7\text{ miles}3.1107miles

31\text{ miles}31miles

10.

Question 10

The mass of a single grain of sand is approximately6.75\times 10^{-4} \text{ grams}6.75104grams.

There are1.5\times 10^61.5106 grains of sand in an hour glass.

Find the total mass of sand in the hourglass, in grams.

answer using standard notation (not scientific notation).

Enter a number only (no units, no commas).

1 point

Module 3

1.

Question 1

Which of the expressions below are polynomials?

Select all that apply.

1 point

x^2 - x + \dfrac{2}{x}x2x+x2

2x + 32x+3

4x^3 - 7x + \sqrt{2}4x37x+2

\sqrt{5}x^5 - \sqrt{3}x^3 + x5x53x3+x

3x^2 + 2x^{3/2} + 13x2+2x3/2+1

2.

Question 2

Consider the polynomialp(x) = 9x^2 - 7x^3 + x^5 - 8x + 6p(x)=9x27x3+x58x+6.

What is the degree ofp(x)p(x)?

Enter a number only.

1 point

3.

Question 3

Letp(x)p(x) andq(x)q(x) be two polynomials.

True or false? The degree of the sump(x) + q(x)p(x)+q(x) is the sum of the degrees ofp(x)p(x) andq(x)q(x).

1 point

True

False

4.

Question 4

True or false?

A quadratic equationax^2 + bx + c = 0ax2+bx+c=0 (whereaa,bb, andccare real numbers) has exactly two different solutions.

1 point

True

False

5.

Question 5

Find the sum of the two polynomials:

(x^5 + x^3 - 3) + (x - 2x^3 + 1)(x5+x33)+(x2x3+1)

1 point

x^5 - x^3 + x - 2x5x3+x2

x^5 + 3x^3 - x - 4x5+3x3x4

None of these

2x^5 - x^3 - 22x5x32

x^6 - x^3 - 2x6x32

6.

Question 6

Find the product:

5x^3(x^2 - 3x + 2)5x3(x23x+2)

1 point

5x^6 - 15x^3 + 10x^35x615x3+10x3

5x^5 - 15x^4 + 10x^35x515x4+10x3

5x^6 - 3x + 25x63x+2

5x^5 - 3x + 25x53x+2

None of these

7.

Question 7

Determine the product of the binomials:

(12x - 1)(4 - x^2)(12x1)(4x2)

1 point

None of these

12x^3 - x^2 - 48x + 412x3x248x+4

-11x^2 + 48x - 411x2+48x4

-12x^3 - x^2 + 48x - 412x3x2+48x4

-12x^3 + x^2 + 48x - 412x3+x2+48x4

8.

Question 8

Rewrite the quadratic as a product of linear factors:

14x^2 + x - 314x2+x3

1 point

(7x - 3)(2x + 1)(7x3)(2x+1)

(14x + 1)(x -3)(14x+1)(x3)

(14x - 3)(x + 1)(14x3)(x+1)

None of these

(7x + 1)(2x -3)(7x+1)(2x3)

9.

Question 9

Find the factorization of the cubic polynomial:

3x^3 + 12x^2 - 15x3x3+12x215x

1 point

x(x - 1)(3x + 5)x(x1)(3x+5)

3x(x - 1)(x + 5)3x(x1)(x+5)

x(3x - 5)(x + 1)x(3x5)(x+1)

3x(x - 5)(x + 1)3x(x5)(x+1)

x(3x - 1)(x + 5)x(3x1)(x+5)

10.

Question 10

Solve the polynomial equation by factoring:

2x^3 - 16x^2 + 32x = 02x316x2+32x=0.

Selectallsolutions below.

1 point

x = -4x=4

x =0x=0

x = 16x=16

x = 4x=4

x = -16x=16

x = -2x=2

x = 2x=2

Module 4

1.

Question 1

Complete the sentence.

If a quadratic polynomial has a negative leading coefficient, then its vertex is . . .

1 point

a minimum.

sometimes a minimum and sometimes a maximum.

a maximum.

2.

Question 2

True or false?

The graph of a cubic polynomial always has anxx-intercept.

1 point

True

False

3.

Question 3

A polynomial is graphed below.

Use the end behavior of the graph to determine the parity of the degree and the sign of the leading coefficient.

1 point

even degree; positive leading coefficient

even degree; negative leading coefficient

odd degree; positive leading coefficient

odd degree; negative leading coefficient

4.

Question 4

A polynomial is graphed below. Which of the polynomials from the list could correspond to the graph?

\f1.2 m 1 m