Formulas for the Accuplacer Next Generation Quantitative Reasoning, Algebra, and Statistics Test
The Quantitative Reasoning, Algebra, and Statistics section of the Next Generation Accuplacer test covers a wide range of subjects. It may seem overwhelming when you’re preparing for that test, but we’ve got you covered! In the following chart, you’ll find the essential formulas you’ll need if you want to ace this section. Even though you won’t be able to use them during the test, they will serve as a summary for you. Remember to practice using these formulas to solve the sample problems we have prepared for you, and also to read our study guide for more developed content here at Union Test Prep!
Exponents
Formula  Symbols 

\(x^a \cdot x^b = x^{a+b}\)  \(a, b, x =\text{any real number}\) 
\(\dfrac{x^a}{x^b}=x^{ab}\)  \(a, b, x =\text{any real number}\) 
\((x^a)^b=x^{a \cdot b}\)  \(a, b, x =\text{any real number}\) 
\((x \cdot y)^a=x^a \cdot y^a\)  \(a, x, y =\text{any real number}\) 
\(x^1=x\)  \(x= \text{any real number}\) 
\(x^0 = 1\)  \(x = \text{any real number}\) 
\(x^{a} = \dfrac{1}{x^a}\)  \(a,x = \text{any real number}\) 
\(x^{\frac{a}{b}} = \sqrt[b]{x^a} = (\sqrt[b]{x})^a\)  \(a, b, x = \text{any real number}\) 
Logarithms
Formula  Symbols 

\(a^x = b \Rightarrow \log_a{b}=x\)  \(a, b, x = \text{any real number}\) 
\(\ln(x) = \log_e x\)  \(x = \text{any real number}\) \(e = \text{Euler's number} \approx 2.718\) 
\(a^{\log_a x}=x\)  \(a, x = \text{any real number}\) 
\(\log(a \cdot b) = \log(a) + \log(b)\)  \(a, b = \text{any real number}\) 
\(\log(a \div b) = \log(a)  \log(b)\)  \(a, b = \text{any real number}\) 
\(\log(a^b) = b \cdot \log(a)\)  \(a, b = \text{any real number}\) 
\(\log_a x = \log_b x \cdot \log_a b\)  \(a, b, x = \text{any real number}\) 
\(\log_a b = \dfrac{\log_x b}{\log_x a}\)  \(a, b,x = \text{any real number}\) 
\(\log_a a = 1\)  \(a = \text{any real number}\) 
\(\log(1) = 0\) 
Linear Equations
Formula  Symbols  Comments 

\(A\cdot x + B\cdot y = C\)  \(A, B, C = \text{any real number}\) \(y= \text{dependent variable}\) \(x = \text{independent variable}\) 
Standard Form 
\(y=m \cdot x + b\)  \(y = \text{dependent variable}\) \(m= \text{slope}\) \(x = \text{independent variable}\) \(b = y \text{intercept}\) 
SlopeIntercept Form. Try to convert linear equations to this format. 
\(m = \dfrac{y_2  y_1}{x_2  x_1}\)  \(m = \text{slope}\) \(y_n = \text{dependent variable (point n)}\) \(x_n = \text{independent variable (point n)}\) 
This is a rearranged version of the pointslope form. 
\(yy_1 = m(xx_1)\)  \(y= \text{dependent variable}\) \(x = \text{independent variable}\) \(y_1 = y \text{ value of a point on the line}\) \(x_1 = x \text{ value of a point on the line}\) \(m = \text{slope}\) 
PointSlope form 
\(x+a = b \Rightarrow x = ba\) \(xa = b \Rightarrow x = b+a\) \(x \cdot a = b \Rightarrow x = b \div a\) \(x \div a = b \Rightarrow x = b \cdot a\) \(x^a = b \Rightarrow x = \sqrt[a]{b}\) \(\sqrt[a]{x} = b \Rightarrow x = b^a\) \(a^x = b \Rightarrow x = \dfrac{\log b}{\log a}\) 
\(a, b = \text{constants}\) \(x = \text{variable}\) 
Statistics
Formula  Symbols 

\(p = \dfrac{d}{t}\)  \(p = \text{probability of an event}\) \(d = \text{desired event}\) \(t= \text{total number of possible events}\) 
\(\bar{x} = \dfrac{\sum{x_i}}{n}\)  \(\bar{x} = \text{mean}\) \(x_i = \text{value of each measurement}\) \(n = \text{number of measurements}\) 
\(s = \sqrt{\mathstrut \dfrac{\sum(x_i  \bar{x})^2}{n1}}\)  \(s = \text{standard deviation}\) \(\bar{x}=\text{mean}\) \(x_i = \text{value of each measurement}\) \(n = \text{number of measurements}\) 
\(V = s^2\)  \(V = \text{variance}\) \(s = \text{standard deviation}\) 
\(CV = RSD = 100 \cdot \dfrac{s}{\bar{x}}\)  \(CV = \text{coefficient of variation}\) \(RSD = \text{relative standard deviation}\) \(s = \text{standard deviation}\) \(\bar{x} = \text{mean}\) 
Geometry
Formula  Symbols  Comments 

\(A = s^2\)  \(A = \text{area of a square}\) \(s = \text{side length}\) 

\(A = l \cdot w\)  \(A = \text{area of a rectangle}\) \(l = \text{length}\) \(w = \text{width}\) 

\(A = \dfrac{1}{2} b \cdot h\)  \(A = \text{area of a triangle}\) \(b= \text{base}\) \(h = \text{height}\) 

\(A = \pi \cdot r^2\)  \(A = \text{area of a circle}\) \(r = \text{radius}\) 

\(A = h \cdot \dfrac{b_1+b_2}{2}\)  \(A = \text{area of a trapezoid}\) \(b_n = \text{base }n\) \(h = \text{height}\) 

\(C= 2 \pi r = \pi d\)  \(C = \text{perimeter of a circle}\) \(r = \text{radius}\) \(d = \text{diameter}\) 

\(V = s^3\)  \(V = \text{volume of a cube}\) \(s = \text{side length}\) 

\(V = l \cdot w \cdot h\)  \(V = \text{volume of a rectangular prism}\) \(l = \text{length}\) \(w = \text{width}\) \(h = \text{height}\) 

\(V = \dfrac{4}{3} \pi r^3\)  \(V = \text{volume of a sphere}\) \(r = \text{radius}\) 

\(V = \pi r^2 h\)  \(V = \text{volume of a cylinder}\) \(r = \text{radius of base}\) \(h = \text{height}\) 

\(V = \dfrac{1}{3} \pi r^2 h\)  \(V = \text{volume of a cone}\) \(r = \text{radius}\) \(h = \text{height}\) 

\(V = \dfrac{1}{3} l \cdot w \cdot h\)  \(V = \text{volume of a pyramid}\) \(l = \text{length}\) \(w = \text{width}\) \(h = \text{height}\) 

\(d= \sqrt{\mathstrut (y_2  y_1)^2 + (x_2x_1)^2}\)  \(d = \text{distance between two points}\) \(y_n = y \text{ value at point n}\) \(x_n = x \text{ value at point n}\) 

\(a^2 + b^ 2 = c^ 2\)  \(a,b = \text{legs of a right triangle}\) \(c = \text{hypotenuse of a right triangle}\) 
Pythagorean theorem 
\((xh)^2 + (yk)^2 = r^2\)  \((h,k) = \text{center of a circle}\) \(r = \text{radius}\) 
Standard form of a circle 
\(x^2 + y^2 + Ax + By + C = 0\)  \(x, y = \text{variables}\) \(A,B,C = \text{constants}\) 
General form of a circle 
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