# Formulas for Science on the CSET® Multiple Subjects Test

One thing you have to keep in mind when preparing for Science on this test (or any test) is that science has its own language. The language of science is precise and quantitative (uses numbers and equations). You may think that this would make science dull, plain, and boring, but in reality, once you get to know the language, it can be as beautiful as a romance language, such as French!

Each equation shows the beauty that is to be found in nature, and how everything—even sunsets, snowflakes, or the patterns in a butterfly—can be described using the language of science. The following set of essential formulas is not only designed to help you succeed at the CSET®, but also to give you a glimpse into the beauty of science.

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Formula Symbols Comment
$$Du=Su \cdot \dfrac{Du}{Su}=Su \cdot CF$$ Du = Desired Unit
Su = Starting Unit
CF = Conversion Factor
Multiple steps may
be needed.
$$a \cdot b\% =a \cdot \frac{b}{100}$$
a = any real number
b% = any percent
Remember to simplify
if possible.
$$\% = \frac{\vert b-a \vert }{b} \cdot 100= \frac{c}{b} \cdot 100$$
% = % increase or decrease
a = new value
b = original value
c = amount of change

$$d= \frac{m}{v}$$ d = density ($$\frac{g}{cm^3}$$)
m = mass (g)
v = volume ($$cm^3$$)

$$m_r=m_p$$ $$m_r$$ = total mass of reactants
$$n_p$$ = total mass of products
Law of Conservation
of Mass
$$^A_ZX$$
A = Mass Number
Z = Atomic Number = Number of protons
X = Atom symbol

$$A=Z+N$$
A = Mass Number
Z = Atomic Number = Number of protons
N = Number of neutrons

$$pH=-log[H_3O^+]$$ pH = measure of acidity based on concentration of $$H_3O^+$$
$$[H_3O^+]$$ = concentration of hydronium ions ($$\frac{mol}{L}$$)

$$14 = pH + pOH$$
pH = measure of acidity based on concentration of $$H_3O^+$$
pOH = measure of basicity based on concentration of $$OH^-$$

$$v=\dfrac{d}{t}$$
v = Velocity ($$\frac{m}{s}$$)
d = distance (displacement) (m)
t = time (s)

$$v = v_o + a \cdot t$$
v = Velocity ($$\frac{m}{s}$$)
$$v_o$$ = initial velocity ($$\frac{m}{s}$$)
a = acceleration ($$\frac{m}{s^2}$$)
t = time (s)

$$PE_g = m \cdot g \cdot h$$
$$PE_g$$ = Gravitational Potential Energy (J)
m = mass (kg)
g = acceleration of gravity ($$\frac{m}{s^2}$$)
h = height

$$KE= \frac{1}{2} \cdot (m \cdot v^2)$$ KE = Kinetic Energy (J)
m = mass (kg)
v = velocity ($$\frac{m}{s}$$)

$$PE_e = \frac{1}{2} \cdot (k \cdot x^2)$$ $$PE_e$$ = Elastic Potential Energy
k = spring constant ($$\frac{N}{m}$$)
x = distance stretched or compressed

$$U = KE + PE$$ U = Total Energy (J)
KE = Kinetic Energy (J)
PE = Potential Energy (J)

$$Q=m \cdot c \cdot \Delta t$$ Q = Quantity of transferred heat
m = mass (g)
c = specific heat constant ($$\frac{J}{g \cdot K}$$)
$$\Delta t$$ = change in temperature (K)

$$\lambda = \dfrac{c}{f}$$
$$\lambda$$ = wavelength (m)
c = speed of light ($$\frac{m}{s}$$)
f = frequency $$\frac{1}{s}$$ or Hz