Download ACT FORMULA SHEET and more Summaries Algebra in PDF only on Docsity! 1 ACT FORMULA SHEET Arithmetic and Algebra Properties of Exponents and Radicals an ∙ am = an+m an __ am = an-m (an)m = anm (ab)n = anbn ( a __ b) n = a n __ bn a-n = 1 __ an 1 __ a-n = an ( a __ b) -n = ( b __ a) n n √ __ a = a 1 __n n √ __ ab = n √ __ a ∙ n √ __ b n √ _ a _ b = n √ __ a ___ n √ __ b n√ __ am = a m __n Generic Formulas Quadratic Formula: For ax2 + bx + c = 0, x = -b ± √ _____ b2-4ac ________ 2a Arithmetic Mean: Sum of Terms _____________ Number of Terms Event Probability: Desired Outcomes _____________ Possible Outcomes Distance: Distance = Rate ∙ Time Percent Growth/Decay: Original(1 ± r1)(1 ± r2)... In Percent Growth or Decay, r1, r2, ... are the percents an amount is being changed by each year, month, etc. Percent Change: New - Old _______ Old ∙ 100% Common Difference: d = an+1 - an Arithmetic Sequence/Series Geometric Sequence/Series Find the nth term: an = a1 + (n - 1)d Sum the first n terms: Sn = n __ 2 (a1 + an) Common Ratio: r = an+1 ___ an Find the nth term: an = a1r n-1 Sum the first n terms: Sn = a1 ( 1 - r n ___ 1 - r ) Combination (Order Doesn’t Matter): nCr = n! ______ r!(n - r)! Permutation (Order Does Matter): nPr = n! ______ (n - r)! Remember, n is the number of choices you have, and r is how many you are going to choose. Counting and Ordering Properties of Logarithms loga a x = x xloga y = loga y x logax + logay = loga(xy) logax - logay = loga ( x _ y) 2 Geometry The Circle Area: A = πr2 Circumference: C = 2πr Arc length: L(A,B) = θ ____ 360° ∙ 2πr Sector Area: AOB = θ ____ 360° ∙ πr 2 Equation for circle with center (h, k) and radius r: (x - h)2 + (y - k)2 = r 2 Areas Volumes Parallelogram: A = bh Trapezoid: A = 1 _ 2 (b1 + b2)h Triangle: A = 1 _ 2 bh Cube: A = 6s 2 Cube: V = s3 Rectangular Prism: V = lwh Cylinder: V = πr 2h Sphere: V = 4 _ 3πr 3 Angles Lines Sum of Interior Angles: = 180(n - 2)˚ Each Interior Angle: = 180(n - 2)˚ _______ n Sum of Exterior Angles: = 360˚ Each Exterior Angles: = 360˚ ___ n Slope of a Line: m = y2 - y1 _____ x2 - x1 Midpoint: M = ( x1 + x2 _____ 2 , y1 + y2 _____ 2 ) Distance: d = √ _____________ (x2 - x1) 2 + (y2 - y1) 2 Pythagorean’s Theorem in 3D d2 = a2 + b2 + c2
