Quiz about M4 Unit 1 (Fundamental Skills) Study Guide

Question 1

Simplify each expression. Write all answers with positive exponents and in standard form. 1. $$\left( \frac{8a^4b^5}{12a^5b^2} \right)^2$$

Accepted Answer

$$\frac{16b^6}{9a^2}$$

Answer

$$\frac{16a^2}{9b^6}$$

Answer

$$\frac{64a^8b^{10}}{144a^{10}b^4}$$

Answer

$$\frac{4b^3}{3a}$$

Question 2

Simplify each expression. Write all answers with positive exponents and in standard form. 2. $$\left( \frac{1}{4}x^3y^2 \right)^{-2}(-4x^{-1}y)^3$$

Accepted Answer

$$4x^6y^4$$

Answer

$$x^6y^5$$

Answer

$$16x^2y^4$$

Answer

$$-4x^6y^4$$

Question 3

Simplify each expression. Write all answers with positive exponents and in standard form. 3. $$(5k^2-7k+9)-(-2k+6k^2+11)$$

Accepted Answer

$$-k^2-5k-2$$

Answer

$$k^2-5k-2$$

Answer

$$-k^2 + 5k + 2$$

Answer

$$7k^2-5k-2$$

Question 4

Simplify each expression. Write all answers with positive exponents and in standard form. 4. $$-5s^5t^3(3s^5t-7s)+4s^3 \cdot 2s^6t^4$$

Accepted Answer

$$-15s^{10}t^4+35s^6t^3+8s^9t^4$$

Answer

$$-15s^{10}t^3+35s^6t^3+8s^9t^4$$

Answer

$$-15s^{10}t^4-35s^6t^3+8s^9t^4$$

Answer

$$-15s^{10}t^4+35s^6t^3+8s^9t^3$$

Question 5

Simplify each expression. Write all answers with positive exponents and in standard form. 6. $$(2r-5)^3$$

Accepted Answer

$$8r^3-60r^2+150r-125$$

Answer

$$8r^3-30r^2+75r-25$$

Answer

$$8r^3-40r^2+100r-125$$

Answer

$$8r^3-50r^2+125r-100$$

Question 6

Completely factor each expression. 7. $$12w^3+26w^2-10w$$

Accepted Answer

$$2w(6w^2+13w-5)$$

Answer

$$$ 2w(6w^2+13w+5) $$$

Answer

$$2w(6w^2-13w-5)$$

Answer

$$2w(6w^2-13w+5)$$

Question 7

Completely factor each expression. 8. $$64c^4-121d^6$$

Accepted Answer

$$(8c^2-11d^3)(8c^2+11d^3)$$

Answer

$$(4c^2-11d^3)(4c^2+11d^3)$$

Answer

$$(8c^2-121d^3)(8c^2+121d^3)$$

Answer

$$(64c^2-121d^3)$$

Question 8

Completely factor each expression. 10. $$32m-162m^5$$

Accepted Answer

$$$ 32m(1-5.0625m^4) $$$

Answer

$$2m(16-81m^4)$$

Answer

$$2(16m-81m^5)$$

Answer

$$32m(1-162m^4)$$

Question 9

Completely factor each expression. 11. $$x^4+9x^2-112$$

Accepted Answer

$$(x^2+16)(x^2-7)$$

Answer

$$(x^2-16)(x^2+7)$$

Answer

$$(x^2+14)(x^2-8)$$

Answer

$$(x^2+8)(x^2-14)$$

Question 10

Completely factor each expression. 12. $$8v^3+20v^2-18v-45$$

Accepted Answer

$$(2v+5)(4v^2-9)$$

Answer

$$(2v-5)(4v^2+9)$$

Answer

$$(4v+5)(2v^2-9)$$

Answer

$$(2v+9)(4v^2-5)$$

Question 11

Simplify each expression. 13. $$(10m^3 + 20m^2) / (15m^2 + 15m^2 - 30m)$$

Accepted Answer

(2m(m+2))/(3(m-1)(m+1))

Answer

(2m(m-2))/(3(m+1)(m-1))

Answer

(m(m+2))/(3(m-1)(m+1))

Answer

(2m(m+2))/(3(m+1)(m-1))

Question 12

Simplify each expression. 14. $$(8a^3 + 24a^2) / (18a + 54) · (5a^2 + 43a + 24) / (10a^2 + 6a)$$

Accepted Answer

$$\frac{5a^2 + 43a + 24}{18(5a+3)}$$

Answer

$$\frac{8a^3 + 24a^2}{10a^2 + 6a}$$

Answer

$$\frac{5a^2 + 43a + 24}{10a^2 + 6a}$$

Answer

$$\frac{8a^3 + 24a^2}{18a + 54}$$

Question 13

Simplify each expression. $$\frac{3p+1}{p^2-1}$$ - $$\frac{1}{p+1}$$

Accepted Answer

2/(p-1)

Answer

$$\frac{3p+1}{p^2+1}$$

Answer

(2p)/(p-1)

Answer

1/(p-1)

Question 14

Simplify each expression. 17. 3x/(2x-3) - 3/(x+6)

Accepted Answer

$$(3x^2+12x+9)/((2x-3)(x+6))$$

Answer

$$(3x^2-12x+9)/((2x-3)(x+6))$$

Answer

$$(3x^2+9x-18)/((2x-3)(x+6))$$

Answer

$$(3x^2-9x-18)/((2x-3)(x+6))$$

Question 15

Simplify each expression. 18. $$(1/2 - r^2/18) / (1/3 - 1/r)$$

Accepted Answer

-r(3+r)/6

Answer

r(3-r)/6

Answer

$$\frac{r^2-3}{6r}$$

Answer

$$\frac{3r+r^2}{6}$$

Question 16

Simplify each expression. 21. $$-5\sqrt{64m^{11}}$$

Accepted Answer

$$-40m^5\sqrt{m}$$

Answer

$$-40m^6\sqrt{m}$$

Answer

$$-40m^5\sqrt{m^2}$$

Answer

$$-5m^5\sqrt{64m}$$

Question 17

Rewrite in exponential form: $$\sqrt{2}k^5$$

Accepted Answer

$$2^{1/2}k^{5/2}$$

Answer

$$2^{1/2}k^{10}$$

Answer

$$2k^{5/2}$$

Answer

$$2^{5/2}k^{1/2}$$

Question 18

Rewrite in simplest radical form: $$(24x^7)^{1/3}$$

Accepted Answer

$$2\sqrt[3]{3}x^2\sqrt[3]{x}$$

Answer

$$2x^2∛12x$$

Answer

$$∛24x^7$$

Answer

$$6x^3∛x$$

Question 19

Simplify each expression. Write your answer in simplest radical form. 30. $$k^{1/4} · k^{3/2}$$

Accepted Answer

$$k^{7/4}$$

Answer

$$k^{5/8}$$

Answer

$$k^{3/4}$$

Answer

$$k^{2}$$

Question 20

Simplify each expression. Write your answer in simplest radical form. 31. $$(u^3 / u^2)^{1/5} · (u^{-5} / u^6)^{1/6}$$

Accepted Answer

$$u^{-41/30}$$

Answer

$$u^{-7/30}$$

Answer

$$u^{1/2}$$

Answer

$$u^{-1/30}$$

Question 21

Simplify each expression. $$i^{52}$$

Accepted Answer

$$i^0 = 1$$

Answer

$$i^1 = i$$

Answer

$$i^2 = -1$$

Answer

$$i^3 = -i$$

Question 22

Simplify each expression. 33. $$(-3i)^3 · 2i^{12}$$

Accepted Answer

-54i

Answer

54i

Answer

-6i

Answer

6i

Question 23

Simplify each expression. 34. -i(5 - i) + 2(3 - 7i)

Accepted Answer

11 - 9i

Answer

-11 + 9i

Answer

5 - 13i

Answer

-1 - 7i

Question 24

Simplify each expression. $$(-2 + 9i)^2$$

Accepted Answer

-77 - 36i

Answer

77 + 36i

Answer

-77 + 36i

Answer

77 - 36i

Question 25

Simplify each expression. 36. (-6 - 10i) / 9i

Accepted Answer

10/9 - 2/3i

Answer

-2/3 + 10/9i

Answer

-10/9 - 2/3i

Answer

2/3 - 10/9i

Question 26

Simplify each expression. 37. (-7 - 4i) / (-8 + i)

Accepted Answer

60 + 45i / 65 = 12/13 + 9/13i

Answer

-60 - 45i / 65 = -12/13 - 9/13i

Answer

-60 + 45i / 65 = -12/13 + 9/13i

Answer

60 - 45i / 65 = 12/13 - 9/13i

Question 27

Solve each equation. 8 - 4(n - 1) = -2n + 18. Fill in the value of n.

Accepted Answer

n = 0

Answer

n = 2

Answer

n = -1

Answer

n = 4

Question 28

Solve each equation. (15/4) * (12x - 8/3) = 9(2 + 5x). Fill in the value of x.

Accepted Answer

x = 1

Answer

x = 2

Answer

x = -1

Answer

x = 0

Question 29

Solve each equation. $$\frac{5p + q^2}{7} = 8$$ (solve for q). Fill in the value of q.

Accepted Answer

q = sqrt(56 - 5p)

Answer

q = sqrt(8 - 5p)

Answer

q = sqrt(5p - 56)

Answer

q = sqrt(56 + 5p)

Question 30

Solve each equation. 4a - 7b = ab + 3 (solve for a). Fill in the value of a.

Accepted Answer

a = (ab + 3 + 7b)/4

Answer

a = (ab - 3 - 7b)/4

Answer

a = (ab + 3 - 7b)/4

Answer

a = (ab - 3 + 7b)/4

Question 31

Solve each equation. Be sure to check for extraneous solutions. |5 - 2x| = 11. Fill in the value(s) of x.

Accepted Answer

x = -3 or x = 8

Answer

x = 3 or x = -8

Answer

x = 8 or x = 13

Answer

x = -8 or x = 3

Question 32

Solve each equation. Be sure to check for extraneous solutions. |4p - 9| = 6 + p. Fill in the value(s) of p.

Accepted Answer

p = 5 or p = -15

Answer

p = 3 or p = -9

Answer

p = 2 or p = -8

Answer

p = 7 or p = -13

Question 33

Solve each equation. Be sure to check for extraneous solutions. -7|10 + 3m| - 7 = -63. Fill in the value(s) of m.

Accepted Answer

m = 0 or m = -8

Answer

m = 1 or m = -7

Answer

m = 2 or m = -6

Answer

m = 3 or m = -5

Question 34

Solve each equation. Be sure to check for extraneous solutions. -5 - | -3 - 4x| = 11. Fill in the value(s) of x.

Accepted Answer

x = -5 or x = -1

Answer

x = 2 or x = -2

Answer

x = 1 or x = 3

Answer

x = 0 or x = -4

Question 35

Solve each equation. Simplify all irrational and complex solutions. $$2w^2 + 3w - 5 = 0$$ . Fill in the value(s) of w.

Accepted Answer

w = 1 or w = -2.5

Answer

w = 2 or w = -1.5

Answer

w = -1 or w = 2.5

Answer

w = 0 or w = -2.5

Question 36

Solve the equation: $$r^2 + 9r + 65 = -r$$

Accepted Answer

r = -5, r = -13

Answer

r = 5, r = 13

Answer

r = -1, r = -65

Answer

r = 1, r = 65

Question 37

Solve the equation: $$4y^2 - 28 = 8y$$

Accepted Answer

y = 7, y = -1

Answer

y = 2, y = -3

Answer

y = 4, y = -2

Answer

y = 1, y = -7

Question 38

How many seconds will it take the ball to reach the ground?

Accepted Answer

t = 2.25 seconds (rounded to two decimal places)

Answer

t = 1.50 seconds (rounded to two decimal places)

Answer

t = 3.00 seconds (rounded to two decimal places)

Answer

t = 4.10 seconds (rounded to two decimal places)

Question 39

Solve each equation. Be sure to check for extraneous solutions. $$7 - 2(3y)^{\frac{4}{3}} = -155$$

Accepted Answer

y = 4

Answer

y = -4

Answer

y = 2

Answer

y = -2

Question 40

Solve each equation. Be sure to check for extraneous solutions. $$(-z^2 - 8z)^{\frac{3}{2}} = 27$$

Accepted Answer

z = -1, z = -7

Answer

z = 3, z = -9

Answer

z = 0, z = -8

Answer

z = 2, z = -6

Question 41

Solve each equation. Be sure to check for extraneous solutions. 57. (k + 6)/(4 - k) = 2/(k - 4)

Accepted Answer

k = 2 (after checking for extraneous solutions)

Answer

k = 4

Answer

k = -2

Answer

k = 0

Question 42

Solve each equation. Be sure to check for extraneous solutions. 58. $$\frac{1}{2k^2} - \frac{3}{k} = \frac{1}{k^2}$$

Accepted Answer

k = -1, k = 2 (after checking for extraneous solutions)

Answer

k = 1, k = -2

Answer

k = 0, k = 3

Answer

k = 2, k = 3

Question 43

Solve each equation. Be sure to check for extraneous solutions.

Accepted Answer

u = 2 (after checking for extraneous solutions)

Answer

u = -2 (after checking for extraneous solutions)

Answer

u = 0 (after checking for extraneous solutions)

Answer

u = 4 (after checking for extraneous solutions)

Question 44

Solve each equation. Be sure to check for extraneous solutions.

Accepted Answer

y = 6 (after checking for extraneous solutions)

Answer

y = -6 (after checking for extraneous solutions)

Answer

y = 0 (after checking for extraneous solutions)

Answer

y = 12 (after checking for extraneous solutions)

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