Formulas You’ll Need for the PSAT/NMSQT® Test
What do you need to succeed on the math section of the PSAT/NMSQT® Test?
Everything can be summarized in two sentences:
 Know your calculator.
 Know your formulas.
Why?
Well, you are going to be able to use a calculator during the PSAT/NMSQT® Math TestCalculator, but if you don’t know how to use it to get the results you want accurately and quickly, you probably won’t have the time to solve all the questions in that section.
Do I Need to Know Formulas?
For both the Calculator and the No Calculator sections, you’ll need to know the formulas. Most of them are going to be given to you, but you need to know when to use them, and how to manipulate them to get the results you need.
What’s the Best Way to Prepare?
We are here to help you! Below, you’ll find a formula chart with the essential formulas in math that you are probably going to use during your PSAT/NMSQT® Math Test.
Why don’t you start becoming familiar with them by solving the free sample exercises we have for you here?
Category  Formula  Symbols  Comment 

Heart of Algebra 
\(x+a = b \rightarrow x = ba\) \(xa = b \rightarrow x= b+a\) \(x \cdot a = b \rightarrow x = b \div a\) \(x\div a = b \rightarrow x = b \cdot a\) \(x^a = b \rightarrow x = \sqrt[a]{b}\) \(\sqrt[a]{x}=b \rightarrow x = b^a\) \(a^x = b \rightarrow \dfrac{\log{b}}{\log{a}}\) 
\(a,b\) = constants \(x\) = variable 

Heart of Algebra 
\(Ax+By=C\)  \(A, B, C\)= Constants \(y\) = dependent variable \(x\) = independent variable 
Standard Form 
Heart of Algebra 
\(y=mx+b\)  \(m\) = slope \(b\) = intercept \(y\) = dependent variable \(x\) = independent variable 
SlopeIntercept Form 
Heart of Algebra 
\(yy_1 = m(xx_1)\)  \(m\) = slope of a line \(y_n\) = dependent variable (point n) \(x_n\) = independent variable (point n) 
PointSlope Form 
Heart of Algebra 
\(m = \dfrac{y_2y_1}{x_2x_1}\)  \(m\) = slope of a line \(y_n\) = dependent variable (point n) \(x_n\) = independent variable (point n) 
Slope of a line 
Heart of Algebra 
\(f(x) = ax^2 + bx + c\)  \(a,b\) = constants \(c\) = constant (yaxis intercept) \(x\) = variable 
Standard form of Quadratic 
Heart of Algebra 
\(f(x) = a(xh)^2 + k\)  \(a\) = constant \(h\) = constant (horizontal shift) \(k\) = constant (vertical shift) \(x\) = variable 
Vertex form of Quadratic 
Heart of Algebra 
\(x=\dfrac{b\pm \sqrt{b^24ac}}{2a}\)  \(a,b\) = constants from Standard form \(c\) = constant (yaxis intercept) \(x\) = xintercept 
Quadratic formula 
Heart of Algebra 
\(x = \frac{b}{2a}\)  \(a,b\) = constants from Standard form \(x\) = axis of symmetry 
Axis of symmetry 
Heart of Algebra 
\(P=4s\)  \(P\) = Perimeter of a square \(s\) = side length 

Heart of Algebra 
\(P = 2l + 2w\)  \(P\) = Perimeter of a rectangle \(l\) = length \(w\) = width 

Heart of Algebra 
\(P = s_1 + s_2 + s_3\)  \(P\) = Perimeter of a triangle \(s_n\) = side length 

Heart of Algebra 
\(C = 2 \pi r = \pi d\)  \(C\) = Perimeter of a circle \(r\) = radius \(d\) = diameter \(\pi \approx 3.14\) 

Heart of Algebra 
\(A = s^2\)  \(A\) = Area of a square \(s\) = side length 

Heart of Algebra 
\(A = lw\)  \(A\) = Area of a rectangle \(l\) = length \(w\) = width 

Heart of Algebra 
\(A = bh\)  \(A\) = Area of a parallelogram \(b\) = base \(h\) = height 

Heart of Algebra 
\(A = \frac{1}{2}bh\)  \(A\) = Area of a triangle \(b\) = base \(h\) = height 

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

Heart of Algebra 
\(A = \pi r^2\)  \(A\) = Area of a circle \(r\) = radius \(\pi \approx 3.14\) 

Heart of Algebra 
\(V=lwh\)  \(V\) = Volume of a rectangular prism \(l\) = length \(w\) = width \(h\) = height 

Heart of Algebra 
\(V=Bh\)  \(V\) = Volume of a right prism \(B\) = area of the base \(h\) = height 

Heart of Algebra 
\(V = \pi r^2 h\)  \(V\) = Volume of a cylinder \(r\) = radius \(h\) = height \(\pi \approx 3.14\) 

Heart of Algebra 
\(V = \frac{1}{3}Bh\)  \(V\) = Volume of a pyramid \(B\) = area of the base \(h\) = height 

Heart of Algebra 
\(V = \frac{1}{3}\pi r^2 h\)  \(V\) = Volume of a cone \(r\) = radius \(h\) = height \(\pi \approx 3.14\) 

Heart of Algebra 
\(V = \frac{4}{3} \pi r^3\)  \(V\) = Volume of a sphere \(r\) = radius \(\pi \approx 3.14\) 

Advanced Math 
\((a \pm b)^2 = a^2 \pm 2ab + b^2\)  \(a,b\) = constants or variables  Square of a sum or difference 
Advanced Math 
\(a^2b^2 = (a+b)\cdot(ab)\)  \(a,b\) = constants or variable  Difference of squares 
Advanced Math 
\(a^3  b^3 = (ab)\cdot(a^2 + ab + b^2)\)  \(a,b\) = constants or variables  Difference of cubes 
Advanced Math 
\(a^3+b^3 = (a+b) \cdot (a^2  ab + b^2)\)  \(a,b\) = constants or variables  Difference of cubes 
Advanced Math 
\(\frac{a}{b} + \frac{c}{d} = \frac{ad + cb}{bd}\)  \(a,b,c,d\) = any real number  Remember to simplify the fraction (if possible) 
Advanced Math 
\(\frac{a}{b} \cdot \frac{c}{d} = \frac{ac}{bd}\)  \(a,b,c,d\) = any real number  Remember to simplify the fraction (if possible) 
Advanced Math 
\(\frac{a}{b} \div \frac{c}{d} = \frac{ad}{bc}\)  \(a,b,c,d\) = any real number  Remember to simplify the fraction (if possible) 
Advanced Math 
\(a \frac{b}{c} = \frac{ac+b}{c}\)  \(a,b,c\) = any real number  Remember to simplify the fraction (if possible) 
Advanced Math 
\(x^a \cdot x^b = x^{a+b}\)  \(a,b,x\) = any real number  
Advanced Math 
\(\dfrac{x^a}{x^b} = x^{ab}\)  \(a,b,x\) = any real number  
Advanced Math 
\((x^a)^b = x^{a\cdot b}\)  \(a,b,x\) = any real number  
Advanced Math 
\((xy)^a = x^a \cdot y^a\)  \(a,x,y\) = any real number  
Advanced Math 
\(x^1 = x\)  \(x\) = any real number  
Advanced Math 
\(x^0 = 1\)  \(x\) = any real number (\(x\ne 0\))  
Advanced Math 
\(x^{a} = \frac{1}{x^a}\)  \(a,x\) = any real number (\(x\ne 0\))  
Advanced Math 
\(x^{\frac{a}{b}} = \sqrt[b]{x^a} = (\sqrt[b]{x})^a\)  \(a,b,x\) = any real number  
Advanced Math 
\(a^x = b \rightarrow \log _a b = x\)  \(a,b,x\) = any real number  
Advanced Math 
\(\ln (x) = \log _e x\)  \(x\) = any real number \(e \approx 2.718\) = Euler’s number 

Advanced Math 
\(a^{\log_a x} = x\)  \(a,x\) = any real number  
Advanced Math 
\(\log (a\cdot b) = \log (a) + \log (b)\)  \(a,b\) = any real number  
Advanced Math 
\(\log (a\div b) = \log (a)  \log (b)\)  \(a,b\) = any real number  
Advanced Math 
\(\log (a^b) = b \cdot \log (a)\)  \(a,b\) = any real number  
Advanced Math 
\(\log_a x = \log_b x \cdot \log_a b\)  \(a,b,x\) = any real number  
Advanced Math 
\(\log_a b = \dfrac{\log_x b}{\log_x a}\)  \(a,b,x\) = any real number  
Advanced Math 
\(\log_a a = 1\)  \(a\) = any real number (\(a\ne 0\))  
Advanced Math 
\(\log (1) = 0\)  
Problem Solving and Data Analytics 
\(a\cdot b \% = a \cdot \frac{b}{100}\)  \(a\) = any real number \(b \%\) = any percent 
Remember to simplify (if possible) 
Problem Solving and Data Analytics 
\(\% = \dfrac{\lvert b  a \rvert}{b} \cdot 100 = \frac{c}{b} \cdot 100\)  \(\% = \%\) increase or decrease \(a\) = new value \(b\) = original value \(c\) = amount of change 

Problem Solving and Data Analytics 
\(\overline{x} = \dfrac{\Sigma x_i}{n}\)  \(\overline{x}\) = mean \(x_i\) = value of each measurement \(n\) = number of measurements 

Problem Solving and Data Analytics 
\(Md = (\frac{n+1}{2})^{th}\) term  \(Md\) = Median \(n\) = number of measurements (odd) 

Problem Solving and Data Analytics 
\(Md = \dfrac{(\frac{n}{2})^{th} \text{ term } + (\frac{n}{2} + 1)^{th} \text{ term}}{2}\)  \(Md\) = Median \(n\) = number of measurements (even) 

Problem Solving and Data Analytics 
\(s = \sqrt{\dfrac{\Sigma (x_i  \overline{x})^2}{n1}}\)  \(s\) = standard deviation \(\overline{x}\) = mean \(x_i\) = value of each measurement \(n\) = number of measurements 

Problem Solving and Data Analytics 
\(V = s^2\)  \(V\) = Variance \(s\) = standard deviation 

Problem Solving and Data Analytics 
\(CV = RSD = 100 \cdot s \div \overline{x}\)  \(CV\) = Coefficient of variation \(RSD\) = Relative standard deviation \(s\) = standard deviation 

Problem Solving and Data Analytics 
\(p=\frac{d}{t}\)  \(p\) = probability of an event \(d\) = desired event \(t\) = total number of possible events 
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