Math 1

Question 1

Primes to 500

Answer 1

2, 3, 5, 7. 11, 13, 17, 19. 23, 29. 31, 37. 41, 43, 47. 53, 59. 61, 67. 71, 73, 79. 83, 89. 97
101, 103, 107, 109. 113. 127. 131, 137, 139. 149. 151, 157. 163, 167. 173, 179. 181. 191, 193, 197, 199.
211. 223, 227, 229. 233, 239. 241. 251, 257. 263, 269. 271, 277. 281, 283. 293
307. 311, 313, 317. 331, 337. 347, 349. 353, 359. 367. 373, 379. 383, 389. 397
401, 409. 419. 421. 431, 433, 439. 443, 449. 457. 461, 463, 467. 479. 487. 491, 499

Question 2

First 25 Perfect Squares

Answer 2

Perfect Square Factors
1 * 1 = 1
2 * 2 = 4
3 * 3 = 9
4 * 4 = 16
5 * 5 = 25
6 * 6 = 36
7 * 7 = 49
8 * 8 = 64
9 * 9 = 81
10 * 10 = 100

11 * 11 = 121
12 * 12 = 144
13 * 13 = 169
14 * 14 = 196
15 * 15 = 225
16 * 16 = 256
17 * 17 = 289
18 * 18 = 324
19 * 19 = 361
20 * 20 = 400

21 * 21 = 441
22 * 22 = 484
23 * 23 = 529
24 * 24 = 576
25 * 25 = 625

Question 3

What is an “Expression”

Answer 3

A combo of variables and numbers using arithmetic operations

Question 4

What is Factorization

Answer 4

Breaking a number into it’s primes.

A Factorization Tree: 36 = 2 * 2 * 3 * 3 = 2^2 * 3^2

Greatest Common Factor: Used to reduce fractions (factor both into primes, ID common factor, Replace common factors by 1)

Question 5

What is a Square Root?

Answer 5

A factor of a number that, when multiplied by itself, gives the original number
*Squaring a negative is imaginary; i.e. the square root of negative 25 is equal to five “𝑖” (Or book says squaring a negative gives you a positive, since neg * neg=pos)

√1 = 1
√2 = 1.414
√3 = 1.732
√4 = 2
√5 = 2.236
√6 = 2.449
√7 = 2.646
√8 = 2.828
√9 = 3
√10 = 3.162
√11 = 3.317
√12 = 3.464
√13 = 3.606
√14 = 3.742
√15 = 3.873
√16 = 4
√17 = 4.123
√18 = 4.243
√19 = 4.359
√20 = 4.472
√21 = 4.583
√22 = 4.690
√23 = 4.796
√24 = 4.899
√25 = 5

Question 6

Exponents: Negative numbers

Answer 6

A negative number raised to an odd power = negative number
A negative number raised to an even power = positive number

Question 7

Multiplication: product

Answer 7

Production of 2 negatives OR 2 positives = positive
Product of 1 negative and 1 positive = negative

Question 8

División: Quotient

Answer 8

Quotient of 2 negatives or two positives = positive
Quotient of one negative and one positive = negative

Question 9

Order of Operations

Answer 9

Parentheses (and brackets)
Exponents
Multiplication and División
Addition and Subtraction

Question 10

Exponents: Mult and Div, and a word on Zero

Answer 10

A^m * A^n = A^m+n
A^m / A^n = A^m-n
A^0 = 1 (anything raised to zero = 1)

Question 11

Terms

Answer 11

Quantities being added together

Question 12

Factors

Answer 12

Parts being multiplied together

Question 13

Adding and Subtracting Fractions

Answer 13

Steps:
1. Find a common denominator (first see if larger denominator is a common factor. If not, multiply denominators)
2. Anything you do to the bottom, do to the top (2/3 and 3/4 —> 12 common denominator (3x4) so 24/12 and 33/12)
3. Subtract or add numerators. Common denominator remains.
4. Reduce fraction

Question 14

Interval

Answer 14

An interval is a range of numbers between two points, which are also numbers, and all the numbers in that range.

Question 15

Interval Notation: Set Builder

Answer 15

{x|x>2} The set of all X such that x is greater than 2

Parts of Set Builder Notation
{ } The set of
X All x
| Such that
General prosperity of all numbers in that set

Question 16

Interval Notation: Interval

Answer 16

(∞,2) X is less than 2

[ ] used if number is included in set
( ) used if number is not used in set

• because infinite ∞ is not a real number, always use ()

Question 17

How do you turn a DECIMAL into a FRACTION?

Answer 17

place the decimal number over its place value. For example, in 0.6, the six is in the tenths place, so we place 6 over 10 to create the equivalent fraction, 6/10

0.36 —> 3 is tenths place, 6 is hundredth place —> 36/100. —> simplify both divisible by 4 or 9/25.

• https://www.khanacademy.org/math/cc-fourth-grade-math/imp-decimals/imp-converting-decimals-to-fractions/v/converting-decimals-to-fractions-1-ex-3

Question 18

How do you turn a FRACTION into a DECIMAL?

Answer 18

Divide the denominator by the numerator
1/2 —> 2|1. (Confusing but I can’t put a foto here) The denominator goes outside the long division sign.

Question 19

Pi

Answer 19

Pi is the ratio of circumference of any circle to its diameter.
It’s irrational
3.141592…

Question 20

Linear Equation in one Variable

Answer 20

Ax + B = 0
A is the coefficient
X is the variable
B is the constant term

Any equation where one side is a linear expression and the other side is either a constant or another linear expression. expression in the form AX+B=0 where A and B are numbers, a ≠ 0, and X is a variable.

A linear equation in one variable
Must have a variable
Variable cannot appear inside a square root, inside absolutely value bars, as a denominator or with exponent.

Question 21

Linear Inequality: What happens when we multiply or divide each side of an inequality by the same negative number?

Answer 21

The inequality sign must change direction.

Do not change the inequality sign when multiplying/dividing by a positive number, or when adding/subtracting by any number.

Question 22

Commutative Property (of Multiplication and Addition)

Answer 22

AB=BA
A+B=B+A

Question 23

Associative Property (of Multiplication and Addition)

Answer 23

(AB)C=A(BC)
(A+B)+C=A+(B+C)

Question 24

Additive Identity & Inverse

Answer 24

Additive Identity: Adding zero does not change the number
Additive Inverse: Sum of two numbers = zero

Question 25

Multiplicative Identity & Inverse

Answer 25

Multiplicative Identity: Multiplying by 1 does not change the number
Multiplicative Identity: The product of two numbers = 1 (2, 1/2) (2/3 and 3/2)

Question 26

Distributive Property

Answer 26

a(bc)=ab+a*c

Question 27

Convert Percent to Decimal

Answer 27

Drop the % symbol and move the decimal place 2 to the left:
1.35% = .0135
212% = 2.12

Question 28

Convert Decimal to Percent

Answer 28

Move the decimal two to the right and add the % symbol
0.06 = 6%
0.057 = 5.7%

Question 29

Formula of a line

Answer 29

Y = MX+B