ap calc study

21²

441

22²

484

23²

529

24²

576

11³

1331

12³

1728

4^5

1024

5^5

3125

7!

5040

standard form

2x+by=c

quadratic standard form

y=a(x-h)²+k

quadratic intercept form

y=a(x-p)(x-q)

quadratic axis of symmetry

x=-b/2a

distance fomula(physics)

d=r*t

distance formula (between two points)

d = √((x2 - x1)^2 + (y2 - y1)^2)

midpoint formula

((x1 + x2) / 2, (y1 + y2) / 2)

parallel line slope if y=mx+b

m1=m2

perpendicular line slope if y=mx+b

m1=-1/m2

Discriminant formula

b²-4ac

nature of roots >0

2 real zeros

nature of roots<0

2 imaginary roots

nature of roots=0

1 real root

Any triangle (Herom’s Formula)

√(s(s - a)(s - b)(s - c))

Equilateral triangle

((√3)/4)a²

Regular Polygon

½ (P)(apothem)

surface area of a cube

6s²

surface area of a sphere

4π(r²)

surface area of a cylinder

2π(r²)+2π(rh)

Change from log to exponential log_b (y) to x

y=b^x

Change from log to exponential ln to x

y=e^x

change from log to exponential logy to x

y=10^x

Change from exponential to log (b^x = y)

log_b (y)=x

log_10 (10) equals ?

1

log_a (1) equals?

0

log_a (a^n) equals?

n*log_a (a)=n

log_b (mn) equals?

log_b (m) + log_b (n)

log_b (m/n) = equals

log_b (m) - log_b (n)

Change of base formula: log_c (a) equals?

(log_a)/(log_c)

Factoring difference of squares (a²-b²) equals?

(a*b)(a+b)

Factoring difference of cubes (a³-b³) equals?

(a*b)(a²+ab+b²)

Factoring sum of cubes a³+b³ equals

(a+b)(a²-ab+b²)

Trig identities Double angle sin(2x) equals?

2sin(x)cos(x)

Trig identities Double angle cos(2x) equals?

cos²(x)-sin²(x); 2cos²(x)-1; 1-2sin²(x)

Power reduction: sin²(x) equals?

(1-cos²x)/2

Power reduction: cos²(x) equals?

(1+sin²x)/2

Pythagorean: sin²(x)+cos²(x) equals?

1

Pythagorean: 1+tan²x equals?

sec²(x)

Pythagorean: cot²(x)+1 equals?

csc²(x)

Reciprocal sec(x) equals?

1/(cosx)

Reciprocal cos(x)*sec(x) equals?

1

Reciprocal csc(x) equals?

1/sin(x)

Reciprocal sin(x)*csc(x) equals?

1

Even/odd sin(-x) equals?

sinx

Even/odd cos(-x)

cos(x)

Even/odd tan(-x)

tan(x)

Perfect cubes (u+v)³

(u + v)³ = u³ + 3u²v + 3uv² + v³

Perfect cubes (u-v)³

(u - v)³ = u³ - 3u²v + 3uv² - v³