ACT Math study guide

Area of Non-Right Triangle

1/2absinc

Area of Parallelogram

A=bh

Quadratic Formula

x = (-b ± √(b² - 4ac)) / (2a)

Area of Trapezoid

A=1/2(b₁+b₂)h

Area of Circular Cylinder

V = πr2h

Area of Right Circular Cylinder

SA = 2πr² + 2πrh

Area of Pyramid

A=1/3Bh

Circumference

C=πd/C=πr²

Arithmetic Sequence

a_n=a1+(n-1)d

Sum of Terms

Sn=n/2(a1+an)

Distance Formula

D=rt

Rate formula

R=d/t

Geometric Sequence

a_n = a₁ * r^(n-1)

Midpoint Formula

((x₁ + x₂)/2, (y₁ + y₂)/2)

Distance Formula

d=√((x₂ – x₁)² + (y₂ – y₁)²)

Circle Equation

(x - h)² + (y - k)² = r²

Each Interor Angles

180(n - 2)˚/n

Sum of Exterior Angles:

360˚

Sum of Interior Angles

180(n - 2)˚

Each Exterior Angles

360˚/n

Law of Sines

a/sin(A) = b/sin(B) = c/sin(C

Law of Cosines

a² = b² + c² – 2bc cos α

Special Angles-Sin

0=0 30=1/2 45=√2/2 60=√3/2 90=1

Special Angles-Cos

0=1 | 30=√3/2 | 45=√2/2 | 60=1/2 | 90=0

Special Angles-Tan

0=0 | 30=√3/3 | 45=1 | 60=√3 | 90=undef.

Special Right Triangles-45 | 45 | 90

45=x | 45=x | 90=x√2

Special Right Triangles-30 | 60 | 90

30=x | 60=x√3 | 90=2x

Log Formula

If y = log_b x, then b^y = x

Rate Proportions

Rate=Actual

What to do when you see ratio?

Write it as a fraction

When some amount is taken away from a # in a avg. question?

do avg=sum/count and subtract it from the count

How many feet in a yard

3 ft in 1 yd

Arithmetic Sum

Sn=n(a1+an)/2

Period

2pie/b

To find diagonals for rectangle

PYTHAG

Diagonal of a square

s TIMES RAD2

Venn diagram-niether nor

Subtract the “both” from each side

Area of a sector-the inside

area of sector/π r²= x/360. x/360=PART/WHOLE

Arc length-circumference

arc length/2πr=x/360. X/360=PART/WHOLE

Standard deviation

most spread out from average

a²+b²=c²

Right triangle

a²+b²<c²

Obtuse triangle

a²+b²>c²

Acute triangle

(fg)(x)

f(x) TIMES g(x)

Foci-Ellipse

two fixed interior points, and , located on the major axis, where the sum of the distances from any point on the ellipse to these two points is constant. , located on the major axis, where the sum of the distances from any point on the ellipse to these two points is constant. On the ACT, they are defined by the formula , where is the distance from the center, is the semi-major radius, and is the semi-minor radius

Ellipse equation

a2(x−h)2​+b2(y−k)2​=1 where ( (h, k) ) is the center of the ellipse, ( a ) is the semi-major axis, and ( b ) is the semi-minor axis.