Question 1

Which of the following best defines a rational number?

Accepted Answer

A number that can be written as a fraction $$\frac{a}{b}$$, where $$a$$ and $$b$$ are integers and $$b 
eq 0$$

Question 2

Which of the following is an example of a rational number?

Accepted Answer

$$\frac{7}{3}$$

Question 3

Simplify: $$-2 + (-8) - (-5)$$

Accepted Answer

Question 4

Simplify: $$-(-4)^2$$

Accepted Answer

$$-16$$

Question 5

Are the terms $$-8a^5$$ and $$8a^5$$ like terms? Why or why not?

Accepted Answer

Yes, because they have the same variable part and exponent

Question 6

Find the degree of each term and the degree of the polynomial: $$5x^2y$$ - $$5yx^3 + 4$$ + $$9y^2x$

Accepted Answer

Degrees: $$5x^2y$ is 3, -5yx^3$ is 4, 4$ is 0, 9y^2$x is 3$$; Degree of polynomial: 4

Question 7

Simplify: $$1 + 2(7 - 9)^3$ - 42$$

Accepted Answer

$$-57$$

Question 8

Simplify: $$7x^2 + 3$$ + $$9x^2 - 10$

Accepted Answer

$$16x^2 - 7$

Question 9

Add: $$-3(w + 7) + 5(w + 1)$$

Accepted Answer

Question 10

Expand: $$(x - 2)^2$

Accepted Answer

$$x^2 - 4x + 4$

Question 11

A store sells an item for $$60$$ retail, which is $$20\%$$ more than the wholesale price. What is the wholesale price?

Accepted Answer

$$50$$

Question 12

Evaluate $$P = 2L + 2W$$ for $$L = 5$$ and $$W = 4$$

Accepted Answer

$$18$$

Question 13

Simplify using positive exponents: $$(-3xy^2a)^3$

Accepted Answer

$$-27x^3y^6$a^3$$

Question 14

Solve for $$x$$: $$3x - 2 = -x - 5 + 4x$$

Accepted Answer

$$x = 1$$

Question 15

Expand: $$(x + y + z)^2$

Accepted Answer

$$x^2$$ + $$y^2$$ + $$z^2 + 2xy + 2xz + 2yz$

Question 16

How many terms are in the expression $$(x^2$$ - $$4y)(y^2 - 15xy$$)$$ after expansion?

Accepted Answer

4

Question 17

Simplify using positive exponents: $$\frac{12mn$$^{-7}$$}{4m$$^{-2}$$n^{-3}$$}$

Accepted Answer

Question 18

Solve for $$x$$: $$6 - (5x - 2) \u003e 14 + x$$

Accepted Answer

$$x \u003c -1$$

Question 19

Bonus: Algebraically show that $$0.9999\ldots is $$equal to $$1.$$

Accepted Answer

Let $$x = 0.9999\ldots. $$Then $$10x = 9.9999\ldots. $$Subtract $$x$$ from $$10x$$: $$10x - x = 9.9999\ldots - 0.9999\ldots = 9. So$$ $$9x = 9$$, and $$x = 1.$$

Step-by-Step Guidance for Math 0001 Exam #1A (Beginning Algebra)

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