Start with the math. Build the chemistry.
No recent math prerequisite? This free review is designed for students who need to rebuild confidence in arithmetic, algebra, scientific notation, and unit conversions before—or during—a chemistry course. Go at your own pace, check answers as you go, and move directly to the calculations used in your course.
Choose the right math review
General Chemistry I Math
Practice the calculations most often used with atomic masses, reactions, gases, solutions, energy, and introductory laboratory work.
- Moles, molar mass, and stoichiometry
- Empirical formulas and limiting reactants
- Molarity, dilutions, gas laws, and thermochemistry
- Photons, percent yield, and lab graphs
General Chemistry II Math
Advance into exponential and logarithmic calculations, equilibrium models, acid–base systems, kinetics, and electrochemistry.
- Equilibrium constants, Q, and ICE tables
- pH, pKa, buffers, titrations, and Ksp
- Rate laws, first-order decay, and Arrhenius
- Thermodynamics, Nernst equation, and solutions
Math foundations: learn or refresh the essentials
Each card explains a skill, models one calculation, and gives you a short independent check. You can review a single skill without doing the whole page.
Order of operations
Work through grouping, exponents, multiplication/division, then addition/subtraction.
Try it: Calculate (8 − 2)² ÷ 3.
Check your answer
(6²) ÷ 3 = 36 ÷ 3 = 12.
Signed numbers
Negative signs matter when subtracting or multiplying.
Try it: Evaluate −6 + 2(−3).
Check your answer
−6 − 6 = −12.
Fractions and decimals
A fraction is division; its top and bottom both carry information.
Try it: Convert 7/20 to a decimal.
Check your answer
7 ÷ 20 = 0.35.
Percentages
Divide the part by the whole, then multiply by 100%.
Try it: A sample contains 12 g salt in 80 g of solution. What is mass percent?
Check your answer
(12/80) × 100% = 15%.
Scientific notation
Write a number as a coefficient from 1 to less than 10 times a power of ten.
Try it: Write 6,300,000 in scientific notation to three significant figures.
Check your answer
6.30 × 106.
Exponents and square roots
Multiplying like powers adds exponents; dividing subtracts them.
Try it: Find √(9.0 × 10−4).
Check your answer
√9.0 × √10−4 = 3.0 × 10−2.
Solve for one variable
Perform the same inverse operation on both sides to isolate the unknown.
Try it: Solve 4x + 3 = 23.
Check your answer
4x = 20, so x = 5.
Ratios and proportions
A ratio compares two quantities; keep their units with the numbers.
Try it: If 6 identical items cost $15, what do 10 cost?
Check your answer
(15/6) × 10 = $25.
SI prefixes and conversions
Use conversion factors equal to 1 so the unwanted unit cancels.
Try it: Convert 250. mL to liters.
Check your answer
250. mL × (1 L/1000 mL) = 0.250 L.
Dimensional analysis
Write units in every multiplication or division and cancel them before using the calculator.
Try it: Convert 3.50 h to minutes.
Check your answer
3.50 h × (60 min/1 h) = 2.10 × 102 min (three significant figures; 60 is exact).
Significant figures
Measured-data precision is different from an exact counting or unit-definition number.
Try it: Round 2.54 × 3.1 to the correct significant figures.
Check your answer
7.874 rounds to 7.9 (2 significant figures).
Temperature scales
Kelvin is the absolute temperature scale used in gas laws and thermodynamics.
Try it: Convert 25.0 °C to K.
Check your answer
25.0 + 273.15 = 298.15 K, reported as 298.2 K to the tenths place.
Graphs and slope
Slope equals change in y divided by change in x; include slope units.
Try it: Find the slope through (2,3) and (5,12).
Check your answer
(12 − 3)/(5 − 2) = 9/3 = 3.
Logarithms and antilogarithms
A base-10 logarithm asks which power of 10 gives a number.
Try it: If log10(x) = −4, find x.
Check your answer
x = 10−4 = 0.0001.
Calculator checking
Use parentheses, carry extra digits, inspect units, and round once at the end.
Try it: Calculate 4/(2 + 2), then compare with 4/2 + 2.
Check your answer
4/(2 + 2) = 1; 4/2 + 2 = 4.
Quick math readiness check
Try these without looking at the solutions. This is a self-check: it does not record scores or affect any college placement.
| Skill | Question | Solution |
|---|---|---|
| Decimals | 0.045 × 1000 | Reveal45 |
| Equation solving | 7x = 42 | Revealx = 6 |
| Units | 75.0 mL in L | Reveal0.0750 L |
| Scientific notation | 4.5 × 10−3 in decimal form | Reveal0.0045 |
| Percent | 12 g out of 60 g | Reveal20% |
| Significant figures | How many in 0.02030? | RevealFour: 2, 0, 3, 0 |
| Logs (for General Chemistry II) | log10(0.001) | Reveal−3 |
A no-prerequisite study plan
First session: Work through arithmetic, fractions, algebra, and scientific notation. Second session: Work through units, dimensional analysis, and significant figures. Third session: Try the General Chemistry I calculations that match your current chapter. Before General Chemistry II, revisit exponents and logarithms.
For every chemistry problem, write given → wanted → equation/conversion factors → substitute with units → calculate → reasonableness check. Avoid rounding until the final answer. If you miss a question, redo a similar one after a short delay.
Continue learning on IntoChemistry
Dimensional analysis · Significant figures · Stoichiometry lessons · Gas laws · Free worksheets
Topic placement varies between colleges. The two course tracks follow a common U.S. General Chemistry I/II sequence and are not a substitute for your instructor’s syllabus.