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 $x = 1$.

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

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, $9y^2x$ 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: $-3(w + 7) + 5(w + 1)$

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

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

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

Question 18

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

Accepted Answer

$x < -1$

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)

Study Guide - Practice Questions