Math 2 flashcards

Perimeter of any polygon

Sum of all side lengths;

Squares 1²–12² and Cubes 1³–5³

1² = 1 … 12² = 144 and 1³ = 1 … 5³ = 125;

Order of Operations

PE(MD)(AS) = Parentheses > Exponents > Multiply/Divide > Add/Subtract (left to right);

Square Formulas

A = s² and P = 4s;

Rectangle Formulas

A = ℓ × w and P = 2ℓ + 2w;

Triangle Perimeter

P = side₁ + side₂ + side₃;

Triangle Area

A = ½ bh;

Isosceles Triangle

Has exactly two equal sides;

Equilateral Triangle

All sides equal and angles = 60°;

Trapezoid Area

A = ½ (b₁ + b₂) × h;

Circle Formulas

A = πr² and C = 2πr;

Rectangular Prism Formulas

V = ℓ w h and SA = 2ℓw + 2ℓh + 2wh;

Cube Formulas

V = s³ and SA = 6s²;

Sphere Formulas

V = (4/3)πr³ and SA = 4πr²;

Cylinder Formulas

V = πr²h and SA = 2πrh + 2πr²;

Angles in a Triangle Sum to

180°;

Pythagorean Theorem

a² + b² = c² (in a right triangle);

Distance Formula

√[(x₂ − x₁)² + (y₂ − y₁)²];

Simple Interest Formula

I = P r t (where P = principal

Percent Change Formula

New = Original ± (% change × Original);

Uniform Motion Formula

d = r t (distance = rate × time);

Constant Rate Change

new amount = starting amount + rate × time;

GCD Definition

Largest integer that divides evenly into both numbers;

LCM Definition

Smallest integer divisible by both numbers;

Example gcd(6

10)

Example lcm(6

10)

Decimal for 1/5

0.2;

Decimal for 1/4

0.25;

Decimal for 1/3

0.3̅;

Decimal for 1/2

0.5;

Decimal for 2/3

0.6̅;

Decimal for 3/4

0.75;

Interval Notation Tip

Use [ ] to include endpoints and ( ) to exclude;

Example [2

5)

Example (−∞

3.2]

Product Rule for Exponents

aᵐ × aⁿ = aᵐ⁺ⁿ;

Quotient Rule for Exponents

aᵐ / aⁿ = aᵐ⁻ⁿ;

Power of a Power Rule

(aᵐ)ⁿ = aᵐⁿ;

Zero Power Rule

a⁰ = 1 (if a ≠ 0);

Negative Exponent Rule

a⁻ⁿ = 1/aⁿ;

Reciprocal Rule

1/a⁻ⁿ = aⁿ;

Distribution of Exponent over Product

(a × b)ⁿ = aⁿ × bⁿ;

Distribution of Exponent over Quotient

(a/b)ⁿ = aⁿ / bⁿ;

Incorrect Distribution

(a + b)ⁿ ≠ aⁿ + bⁿ;

Root–Exponent Relationship

ⁿ√a = a¹⁄ⁿ;

Radical Product Rule

ⁿ√(a × b) = ⁿ√a × ⁿ√b;

Radical Quotient Rule

ⁿ√(a/b) = ⁿ√a / ⁿ√b;

Incorrect Radical Sum

ⁿ√(a + b) ≠ ⁿ√a + ⁿ√b;

Include each problem number on homework

True;

Circle or box final answers

True;

Connect equivalent expressions with equals signs

True;

Align equals signs vertically

True;

Reduce expressions to simplest form

True;

Write so classmates could follow your work

True;

Write neatly and avoid cross-outs

True;

Include diagrams for real-world problems

True;

Write symbols clearly (0 ≠ ∅)

True;

Define variables in words and symbols

True;

Always include units on real-world answers

True;

Give exact answers; don’t round mid-problem

True;

Choose intuitive variable names (ℓ for length

w for width)

Use space generously and don’t cram work

True;

Do not use arrows for transitions (→)

Use = or words instead;

Add / Plus / Sum of / Increased by / More than

+;

Decreased by / Subtract / Minus / Difference / Less than

−;

Times / Product of / Of / Multiplied by

× or ·;

Divided by / Over / Quotient of

÷ or /;

Double / Triple / Quadruple

2x / 3x / 4x;

Half of / Third of / Fourth of

x/2 / x/3 / x/4;

Greater than

;

Less than

At least / Greater than or equal to

≥;

At most / Less than or equal to

≤;

Is equal to / Represents / The same as / Is

=;

To the power of

aᵇ;

Squared / Cubed / To the nth power

a² / a³ / aⁿ;

Square root / Cube root / nth root

√a / ³√a / ⁿ√a;

Absolute value of

|x|;

Polygon prefix penta-

5 sides;

Polygon prefix hexa-

6 sides;

Polygon prefix hepta-

7 sides;

Polygon prefix octa-

8 sides;

Polygon prefix nona-

9 sides;

Polygon prefix deca-

10 sides;

What shape is this?

Square

area formula for this shape?

A=s²

What type of triangle is this?

Scalene triangle

What type of triangle is this?

Isosceles triangle

What type of triangle is this?

Equilateral triangle

What shape is this?

Rectangle

What is the area formula for this shape?

A= L x W

What is the area formula for this shape?

A= ½ ​bh

What shape is this?

Trapezoid

What is the area formula for this shape?

A= ½ (b1​+b2​)h