All the facts, formulas, and tips you need โ organized by subject. Pick your subject and get unstuck fast!
( ) โ Exponents โ ร รท โ + โ
Remember with: Please Excuse My Dear Aunt Sally (Parentheses, Exponents, Multiply, Divide, Add, Subtract)
ร 9 trick: fingers! Hold up 10 fingers. Fold the Nth finger. Left = tens digit, Right = ones digit.
ร 11 (up to 9): the digit appears twice. 11 ร 7 = 77
a/b รท c/d = a/b ร d/c
Keep, Change, Flip โ Keep the first fraction, Change รท to ร, Flip the second fraction.
A = length ร width
A = ยฝ ร base ร height
A = ฯ ร rยฒ
ฯ โ 3.14 | r = radius
P = 2l + 2w
C = 2ฯr or ฯd
d = diameter = 2r
aยฒ + bยฒ = cยฒ
Only for right triangles. c = hypotenuse (longest side)
Part / Whole ร 100 = %
Example: 18 out of 25 = 18/25 ร 100 = 72%
Fraction โ Decimal: divide top by bottom | Decimal โ Percent: multiply by 100
Example: 3/4 = 0.75 = 75%
Stuck on a problem? Work backwards! Start from the answer you DO know and see what question it answers. This "reverse engineering" unlocks hard problems fast.
Who โ characters | What โ the main event | Where โ the setting | When โ the time | Why โ the reason / conflict
Plot: what happens | Setting: when & where | Characters: who | Conflict: the problem | Theme: the big message | Resolution: how it ends
The main idea is what the whole paragraph is mostly about. Supporting details are the examples, facts, or reasons that explain it. Often the first or last sentence gives you the main idea.
When you're confused, stop and summarize the last paragraph in ONE sentence. If you can't, reread it. Understanding each paragraph builds a bridge to the whole story!
My Very Eager Mother Just Served Us Noodles
Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune
Evaporation โ Condensation โ Precipitation โ Collection โ repeat
Crust โ Mantle โ Outer Core (liquid) โ Inner Core (solid)
Every science question asks: What happened? Why did it happen? What would happen if you changed something? If you can answer all three, you truly understand the concept!
Legislative (Congress = Senate + House) โ Makes laws
Executive (President) โ Enforces laws
Judicial (Supreme Court) โ Interprets laws
1st: Freedom of speech, religion, press, assembly, petition
2nd: Right to bear arms | 3rd: No quartering soldiers
4th: Protection from unreasonable search | 5th: Due process, no self-incrimination
Each branch can limit the power of the others. Congress can override a veto. The President appoints judges. The Courts can strike down laws. No single branch becomes too powerful.
1776 โ Declaration of Independence | 1787 โ Constitution written | 1861โ1865 โ Civil War | 1865 โ 13th Amendment (abolishes slavery) | 1920 โ Women's right to vote (19th Amendment) | 1964 โ Civil Rights Act | 1969 โ Moon landing
Always ask WHY โ why did people do this? What problem were they solving? History makes so much more sense when you understand the people behind the events.
[Topic] + [Claim] + [3 Reasons]
Example: "Exercise is important for children because it builds strong bodies, improves focus, and boosts happiness."
whispered, exclaimed, argued, replied, announced, insisted, wondered, admitted, pleaded, declared
Adding: furthermore, in addition, also | Contrasting: however, on the other hand, although | Concluding: therefore, as a result, in conclusion | Sequence: first, next, then, finally
Show, don't tell! Instead of "She was sad," write "Her shoulders drooped and she stared at the floor, blinking fast." Your reader should FEEL it โ not just know it.
I = P ร r ร t
P = principal | r = rate | t = time (years)
A = P(1 + r/n)^(nt)
n = times compounded per year | Money grows on top of money!
Years to double = 72 รท rate%
At 8% return: 72 รท 8 = 9 years to double your money
50% Needs | 30% Wants | 20% Savings
The best time to start saving is today. Even $1 a week invested wisely grows into something amazing over 20 years. Compound interest is like a snowball rolling downhill โ it gets bigger and bigger the longer it rolls!