# 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
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.
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
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