ACT Math Reference sheet

Standard Form

$$Ax+By+C=0$$

Slope Intercept Form

$$y=mx+b$$

Point Slope Form

$$y-y<em>1= m(x-x</em>1)$$

Slope

$$m=\frac{y<em>2-y</em>1}{x<em>2-x</em>1}$$

General form of a quadratic

$$ax^2+bx+c=0$$

Quadratic Formula

$$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$

Midpoint Formula

$$(\frac{x<em>1+x</em>2}{2}, \frac{y<em>1+y</em>2}{2})$$

Distance Formula

$$d=\sqrt{(x<em>2-x</em>1)² + (y<em>2-y</em>1)²}$$

Area of a triangle

$$A=\frac{1}{2}bh$$

Area of a parallelogram

$$A=bh$$

Area of a trapezoid

$$A=\frac{1}{2}(b<em>1+b</em>2)h$$

Volume of a prism

$$V=Bh$$

Surface area of a prism

$$SA=2B+Ph$$

Volume of a circular cylinder

$$V=\pi r^2 h$$

Volume of a Pyramid

$$V=\frac{1}{3}Bh$$

Volume of a Circular Cone

$$V=\frac{1}{3}\pi r^2 h$$

Volume of a Sphere

$$V=\frac{4}{3}\pi r^3$$

Degree Measure of a regular polygon

$$\frac{180(n-2)}{n}$$

Sum of Degree Measures in a polygon

$$180(n-2)$$

Center Radius Form of a circle

$$(x-h)²+(y-k)²=r²$$

Area of a Circle

$$A=\pi r^2$$

Circumference of a circle

$$C=2\pi r$$

Pythagorean Theorem

$$a²+b²=c²$$

Trig Ratios

SohCahToa

Arithmetic Sequence

$$A<em>n=A</em>1+(n-1)d$$

Sum of an arithmetic series

$$S<em>n=\frac{n}{2}(a</em>1+a_n)$$

Simple Interest

$$I=prt$$

Compound Interest

$$A=p(1+\frac{r}{n})^{nt}$$

Distance, rate, time

$$D=rt$$

Direct variation

Y= kx. K= variation constant

Cos 0

1

Sin 30

½

Cos 30

sqrt 3/2

Tan 30

Sqrt 3/3

Sin 45

Sqrt 2/2

Cos 45

Sqrt 2/2

Tan 45

1

Sin 60

Sqrt 3/2

Cos 60

½

Tan 60

Sqrt 3

Sin 90

1

Cos 90

0

Tan 90

Undefined