✓ Effortless Math · Complete ATI TEAS 7 Formula Reference

ATI TEAS 7 Math Formula & Concept Sheet

Every formula you need for the ATI TEAS 7 Math test — with illustrations, graphs, conversions, and worked relationships. Keep it open while you practice.

🔢Numbers & Percents

Order of operationsPEMDAS

Percent of a number\(part=\%\times whole\)

Percent change\(\dfrac{new-old}{old}\times100\%\)

Proportion\(\dfrac{a}{b}=\dfrac{c}{d}\Rightarrow ad=bc\)

Distance / rate / time\(d=rt\)

Scientific notation\(a\times10^{n}\)

∇Exponents & Radicals

Product rule\(x^{a}\cdot x^{b}=x^{a+b}\)

Quotient rule\(\dfrac{x^{a}}{x^{b}}=x^{a-b}\)

Power rule\((x^{a})^{b}=x^{ab}\)

Negative exponent\(x^{-a}=\dfrac{1}{x^{a}}\)

Zero exponent\(x^{0}=1\)

Radicals\(\sqrt{ab}=\sqrt{a}\,\sqrt{b}\)

📈Lines & Slope

Slope\(m=\dfrac{y_2-y_1}{x_2-x_1}\)

Slope–intercept\(y=mx+b\)

Point–slope\(y-y_1=m(x-x_1)\)

Standard form\(Ax+By=C\)

📐Area & Perimeter

Rectangle
\(A=l\,w\)
\(P=2l+2w\)

Triangle
\(A=\tfrac12 b h\)

Parallelogram
\(A=b h\)

Trapezoid
\(A=\tfrac12(b_1+b_2)h\)

Circle
\(A=\pi r^{2}\)
\(C=2\pi r\)

🧊Volume & Surface Area

Rectangular prism
\(V=lwh\)
\(SA=2(lw+lh+wh)\)

Cylinder
\(V=\pi r^{2}h\)
\(SA=2\pi r^{2}+2\pi r h\)

Cone
\(V=\tfrac13\pi r^{2}h\)

Pyramid
\(V=\tfrac13(\text{base})h\)

Sphere
\(V=\tfrac43\pi r^{3}\)
\(SA=4\pi r^{2}\)

📐Right Triangles

Pythagorean theorem
\(a^{2}+b^{2}=c^{2}\)

45°–45°–90°
legs equal; hyp \(=x\sqrt2\)

30°–60°–90°
sides \(x:x\sqrt3:2x\)

📏Conversions & Units

Length (US)1 ft = 12 in · 1 yd = 3 ft · 1 mi = 5280 ft

Weight (US)1 lb = 16 oz · 1 ton = 2000 lb

Capacity (US)1 gal = 4 qt = 8 pt = 16 cups

Metric length1 km = 1000 m · 1 m = 100 cm · 1 cm = 10 mm

Metric mass / volume1 kg = 1000 g · 1 L = 1000 mL

US ↔ Metric1 in ≈ 2.54 cm · 1 kg ≈ 2.2 lb · 1 L ≈ 1.06 qt

Temperature\(F=\tfrac95 C+32\), \(C=\tfrac59(F-32)\)

📍Coordinate Geometry

Distance\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Midpoint\(\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)\)

📉Quadratics & Functions

Quadratic formula\(x=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}\)

Standard form\(y=ax^{2}+bx+c\)

Vertex form\(y=a(x-h)^{2}+k\)

FOIL\((a+b)(c+d)=ac+ad+bc+bd\)

📊Statistics & Probability

Mean\(\dfrac{\text{sum of values}}{\text{number of values}}\)

Medianmiddle value (ordered)

Modemost frequent value

Range\(\text{max}-\text{min}\)

Probability\(\dfrac{\text{favorable}}{\text{total}}\)

Simple interest\(I=prt\)

Compound interest\(A=P\left(1+\tfrac{r}{n}\right)^{nt}\)

Note: the ATI TEAS 7 does not give you a formula sheet — these are worth memorizing. ATI® and TEAS® are registered trademarks of Assessment Technologies Institute, which has not endorsed these materials.