ACT math formulas

arithmetic sequence

a_n = a₁ + d(n-1)

Geometric sequence

a_n = a₁ x (d)^n-1

formula for distance (not between two points on a graph)

Distance = speed/rate x time

distance formula between two points

Distance = \sqrt {(y2 - y1)^2 + (x2 - x1)^2}

discriminant formula

b² - 4ac

If discriminant is > 0.. there are __ real solutions

2

If discriminant is = 0.. there are __ real solutions

1

If discriminant is < 0.. there are __ real solutions

no real solutions

f o g(x) is the same thing as…

f(g(x))

fg(x) is the same thing as

f(x) x g(x)

pi radians = _____ degrees

180

If a 20$ item is increasing 20% in value, how would you set the problem up?

20(1.20)

Average formula

sum of terms/ number of terms

P(event happens) + P(event does not happen) =

1

What do you do to find the probability of two independent events occurring

multiply

What do you do to find the probability of two dependent events occurring

add

P(A and B) =

P(A) x P(B)

supplementary angles add to..

180

45:45:90 ratio

x:x:x√2

30:60:90 ratio

x: x√3 : 2x

trapezoid area

(b₁+b₂)/2 x height or average of bases x height

Sum of angles in n-sided figure

180(n-2)

circle arc length =

(central angle/ 360) x circumference

A circles perimeter is its…

circumference

Circle sector area =

(central angle/360) x area

Circumference of a circle equations

pi(d) or 2(pi)(r)

Circle equation

(x-h)² + (y-k)² = r²

Vertex form of a parabola

y = a(x-h)² + k

axis of symmetry

x = …

surface area of rectangular prism

2(front and back) + 2(right and left) + 2(top and bottom)

volume of rectangular prism

V = lwh

Volume of right cylinder

V = (pi)r²h

sinx =

cos(90-x)

cos(x) =

sin(90-x)

law of sines

a/sinA=b/sinB=c/sinC

law of cosines

• a² = b² + c² − 2bc·cos(A)

• b² = a² + c² − 2ac·cos(B)

• c² = a² + b² − 2ab·cos(C)

what must always be true about the angles of an isoceles triangle

two of them are the same.

csc is the opposite of..

sin

tan = (identity)

sin/cos

period =

2(pi)/b = pi. B is the y-value at which the wave starts

Cos2theta =

costheta(costheta)-sintheta(sintheta)

how to calculte amplitude

same as physics. maximum value - midline

How to find vertical shift of a y = asin(bx) + d

vertical shift = d. d = average of max and min.