Formulas for Math on the CSET®: Number Sense, Algebra, and Statistics

The time has come. You have to take the CSET® Test, but you don’t remember a lot of math, or maybe you want to have a sense of what lies ahead. There are certain areas we sometimes overlook or forget about from past education. For the CSET® Test, it’s very important to have a broad and complete understanding of the different concepts in math. That’s why we’ve prepared the following chart with the essential formulas for Math on the CSET®. Stop wondering if you remember every concept, instead, print this chart and start solving the problems we have for you at Union Test Prep:

Free Math Practice for the CSET® Multiple Subjects Test

You’ll also want access to our other formula chart for the CSET® Multiple Subjects Test math section:

Formula Chart for Geometry and Measurement Problems

Formulas for Number Sense, Algebra, and Statistics

Category	Formula	Symbols	Comment
Number Sense	\(a+b=b+a\) \(a \cdot b = b \cdot a\)	a, b = any constant or variable	Commutative Property
Number Sense	\(a+(b+c)=(a+b)+c\) \(a \cdot (b \cdot c)=(a \cdot b) \cdot c\)	a, b, c = any constant or variable	Associative Property
Number Sense	\(a \cdot (b+c)=a \cdot b + a \cdot c\)	a, b, c = any constant or variable	Distributive Property
Number Sense	\(a+0=a\)	a = any constant or variable	Identity Property of Addition
Number Sense	\(a \cdot 1 = a\)	a = any constant or variable	Identity Property of Multiplication
Number Sense	\(\dfrac{a}{b} + \dfrac{c}{d} = \dfrac{(a \cdot d)+(c \cdot b)}{(b \cdot d)}\)	a, b, c, d = any real number	Remember to simplify the fraction if possible.
Number Sense	\(\dfrac{a}{b} \cdot \dfrac{c}{d}=\dfrac{(a \cdot c)}{(b \cdot d)}\)	a, b, c, d = any real number	Remember to simplify the fraction if possible.
Number Sense	\(\dfrac{a}{b} \div \dfrac{c}{d}=\dfrac{(a \cdot d)}{(b \cdot c)}\)	a, b, c, d = any real number	Remember to simplify the fraction if possible.
Number Sense	\(a\dfrac{b}{c}=\dfrac{(a \cdot c)+b}{c}\)	a, b, c = any real number	Remember to simplify the fraction if possible.
Algebra	\(x+a=b \Rightarrow x=b-a\) \(x-a=b \Rightarrow x=b+a\) \(x \cdot a=b \Rightarrow x=b \div a\) \(x \div a=b \Rightarrow x=b \cdot a\) \(x^a=b \Rightarrow x = \sqrt[a]{b}\) \(\sqrt[a]{x}= b \Rightarrow x= b^a\) \(a^x=b \Rightarrow x=\frac{log\ b}{log\ a}\)	a, b = constants x = variable
Algebra	\(x^a \cdot x^b=x^{a+b}\)	a, b, x = any real number
Algebra	\(\dfrac{x^a}{x^b}=x^{a-b}\)	a, b, x = any real number
Algebra	\((x^a)^b = x^{a \cdot b}\)	a, b, x = any real number
Algebra	\((x \cdot y)^a = x^a \cdot y^a\)	a, x, y = any real number
Algebra	\(x^1=x\)	x = any real number
Algebra	\(x^0=1\)	x = any real number
Algebra	\(x^{-a}= \dfrac{1}{x^a}\)	a, x = any real number
Algebra	\(x^{\frac {a}{b}} = \sqrt[b]{x^a} = (\sqrt[b]{x})^a\)	a, b, x = any real number
Algebra	\(\dfrac{x}{\sqrt{y}} \cdot \dfrac {\sqrt{y}}{\sqrt{y}} = \dfrac{x \sqrt{y}}{y}\)	x, y = any real number
Algebra	\(y=m \cdot x + b\)	y = dependent variable m = slope x = independent variable b = y axis intercept	Slope-Intercept Form. Try to convert any given linear equation to this form.
Quadratic Equations	\(x= \dfrac{-b \pm \sqrt{b^2-4 \cdot a \cdot c}}{2 \cdot a}\)	a, b, c = constants c = y axis intercept x = variable	Quadratic Formula for equation in form \(ax^2 + bx + c = 0\)
Statistics	\(Du=Su \cdot \dfrac{Du}{Su}=Su \cdot CF\)	Du = Desired Unit Su = Starting Unit CF = Conversion Factor	Multiple steps may be needed.
Statistics	\(a \cdot b\% =a \cdot \dfrac{b}{100}\)	a = any real number b% = any percent	Remember to simplify if possible
Statistics	\(\% = \dfrac{\vert b-a \vert }{b} \cdot 100= \dfrac{c}{b} \cdot 100\)	% = % increase or decrease a = new value b = original value c = amount of change
Statistics	\(\overline{x}= \dfrac{\Sigma x_i}{n}\)	\(\overline{x}\) = mean \(x_i\) = value of each measurement n = number of measurements
Statistics	\(Md=(\dfrac{n+1}{2})^{th} term\)	Md = median n = number of measurements (odd)
Statistics	\(Md=\dfrac{(\frac{n}{2})^{th} term + (\frac{n+1}{2})^{th} term }{2}\)	Md = median n = number of measurements (even)
Statistics	\(s=\sqrt{\Sigma(x_i-\overline{x})^2/(n-1)}\)	s = standard deviation \(\overline{x}\) = mean \(x_i\) = value of each measurement n = number of measurements
Statistics	\(V = s^2\)	v = Variance s = standard deviation
Statistics	\(CV=RSD=100 \cdot \dfrac{s}{\overline{x}}\)	CV = Coefficient of variation RSD = Relative standard deviation s = standard deviation
Statistics	\(p= \dfrac{d}{t}\)	p = probability of an event d = number of ways the desired event can occur t = total number of events