Formula Chart for Geometry on the SBAC Test
Geometry is literally everywhere! It’s in the shape of the stars and planets, in the food you eat, in your smartphone, and even in the icons for the apps in your smartphone. All the different shapes in the universe can be described by formulas and equations, and for Geometry on the SBAC Test, you need to know how to handle those formulas. The following chart is intended for study purposes only, as you won’t be able to use it during the actual test, but is really helpful to learn how to handle them when solving Geometry problems on the SBAC Test!
You can find free practice for the SBAC at Union Test Prep.
And you can find our other four formula charts for this test here:
Geometry Formulas for the SBAC
Category  Formula  Symbols  Comment 

Transformations  \((x,y)\rightarrow(x, y)\)  Reflection xaxis  
Transformations  \((x,y)\rightarrow(x, y)\)  Reflection yaxis  
Transformations  \((x,y)\rightarrow(x, y)\)  Reflection Origin  
Transformations  \((x,y)\rightarrow(y, x)\)  Reflection line y = x  
Transformations  \((x,y)\rightarrow(y, x)\)  Reflection line y = x  
Transformations  \((x,y)\rightarrow(y, x)\)  Rotation \(90^o\) Counterclockwise  
Transformations  \((x,y)\rightarrow(x, y)\)  Rotation \(180^o\) Counterclockwise  
Transformations  \((x,y)\rightarrow(x+a, y+b)\)  Translation  
Transformations  \((x,y)\rightarrow(rx, ry)\)  Dilation (r = scale factor)  
Right Triangles  \(a^2+b^2=c^2\)  a, b = legs of a right triangle c = hypotenuse of a right triangle 
Pythagorean Theorem 
Coordinates  \(y = m \cdot x + b\)  y = dependent variable m = slope x = independent variable b = yaxis intercept 
SlopeIntercept Form of a line: Try to convert any given linear equation to this form. 
Coordinates  \(m= \frac{(y_2y_1)}{(x_2x_1)}\)  \(m\) = slope \(y_n\) = dependent variable at point n \(x_n\) = independent variable at point n 
This is a rearranged version of the pointslope form. 
Coordinates  \(yy_1=m(xx_1)\)  \((x_1, y_1)\) = point on the line y = dependent variable x = independent variable m = slope 
Pointslope form of a line 
Coordinates  \(d=\sqrt{(y_2y_1)^2 +(x_2x_1)^2}\)  d = distance between two points \(y_n\) = y value at point n \(x_n\) = x value at point n 

Coordinates  \((x_m, y_m) = (\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2})\)  \(x_m\) = x value at the midpoint \(y_m\) = y value at the midpoint \(y_n\) = y value at point n \(x_n\) = x value at point n 

Volume  \(V=l \cdot w \cdot h\)  V = volume of rectangular prism l = length w = width h = height 

Volume  \(V = \frac{1}{3} \cdot l \cdot w \cdot h\)  V = volume of pyramid l = length w = width h = height 

Volume  \(V = \pi \cdot r^2 \cdot h\)  V = volume of a cylinder r = radius h = height 

Volume  \(V= \frac{4}{3} \cdot \pi \cdot r^3\)  V = volume of a sphere r = radius 

Circles  \(C = 2 \cdot \pi \cdot r\) \(C = \pi \cdot d\) 
C = circumference (perimeter) r = radius d = diameter \(\pi\) = 3.14 

Circles  \(s = r \cdot \theta\)  s = arc length r = radius \(\theta\) = central angle (radians 

Circles  \(A = \pi \cdot r^2\)  A = area of a circle r = radius 

Conic Sections  \((xh)^2 + (yk)^2 = r^2\)  \((h, k)\) = center of circle r = radius 
Standard form of a circle 
Conic Sections  \((xh)^2 = 4p \cdot (yk)\)  \((h, k)\) = vertex of a parabola p = distance from vertex to directrix 
Parabola that opens up or down 
Conic Sections  \((yk)^2 = 4p \cdot (xh)\)  \((h, k)\) = vertex of a parabola p = distance from vertex to directrix 
Parabola that opens left or right 
Shapes  \(A=\frac{1}{2} \cdot b \cdot h\)  A = area of a triangle b = base h = height 

Shapes  \(A = s^2\)  A = area of a square s = side length 

Shapes  \(A=l \cdot w\)  A = area of a rectangle l = length w = width 

Shapes  \(A=h \cdot \frac{(b_1+b_2)}{2}\)  A = area of a trapezoid \(b_n\) = base n h = height 
Trigonometry
\[sin\ \theta = \frac{\text{opposite}}{\text{hypotenuse}} = \frac {1}{ csc\ \theta}\] \[cos\ \theta = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac {1}{ sec\ \theta}\] \[tan\ \theta = \frac{\text{opposite}}{\text{adjacent}} = \frac {1}{ cot\ \theta}\]Keep Reading
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