#math archive

[math-journal]

Scientific Notation

Standard Form: 100

SN: 1 x 10^2

Decimal Form: 0.01

SN: 1 x 10^(-2)

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REMEMBER: non-exponent # first, then exponent number

HACK: think of counting exponents as # of times you move decimal point over. Draw it out and count it physically, even Silly Wizards do it 😜

<<< + exponents

>>>> - exponents

[math-journal]

Mid Unit Reminder

General

(1st inside)^ (exponents 2nd)

Remember PEMDAS

Solving equations with #’s

Ex. (3x + x + y)^3 , x=1, y=2

1st (simplify)^later

(4x + y) ^3

2nd (simplified)^NOW

(4^3)(x^3) + (y^3)

3rd equation solution —> plug in

(4^3)(1^3) + (2^3)

4th solve

256 + 1 + 8

5th solution

266

[math-journal]

Unit 11

Property of Exponents

“a” and “b” —> real #’s

“x” and “y” —> integers

Integer —> whole numbers with no fractions

Remember

[math-journal]

Mappy’s Review Problems

Silly wizard edition

[math-journal]

Application Problem Steps

*sometimes people split up step 1 into 2 steps from unknowns and unknowns

[math-journal]

Solving Absolute Value

Definition: distance from zero

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Solve

Isolate Absolute Value

Rewrite in 2 equations: one (+) and one (-)

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Complex example

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[math-journal]

Inequalities

6 > 3 (6 is greater than 3)

6 ≥ 3 (6 is greater than or equal to 3)

Graphing on a line:

Notation:

> or < —-> o (open dot) or ( )

≥ or ≤ —> . (closed dot) or [ ]

Graph:

*remove arrow for bracket

Double Check

Check endpoint (x > 6, ep: 6)

Pick # in solution (ex. 7)

General Flipping Hack

When flipping an inequality,

6 > x —> x __ 6

make sure arrow keeps pointing toward or away from variable as originally

6 > x , points toward x

x < 6

Multiplying & Dividing

When dividing by a negative,

flip the inequality sign when divided by negative

Practice

[math-journal]

6 Step Application Question

1) Sketch

2) Variables

Ex. W=width, L=Length

3) Equation

4) Solve

5) Check

6) Answer

Ex. Width =___ m, Length = __ m

Written out ok