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LEARN IT. WORK IT. CHECK IT.
One skill at a time.
Pick a subject, follow a worked example, then try a question on your own.
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Arithmetic Reasoning. Turn words into steps. Work through percents, ratios, rates, and averages.
AR · FOUNDATION LESSON7 MIN READ
Percents: the is / of method
Recognize the part, the whole, and the percent before choosing an operation.
THE IDEA TO KEEPPart ÷ whole × 100 = percent
A percent means “out of 100.” The whole is the full amount. The part is the amount you are comparing with that whole.
“18 is what percent of 40?” gives you the part (18) and the whole (40). If the wording changes, identify those quantities by their meaning—not only by looking for the words “is” and “of.”
Missing part? Multiply the whole by the decimal percent. Missing whole? Divide the part by the decimal percent. Convert a percent to a decimal by dividing by 100.
INTERACTIVE LAB / SEE THE CONNECTION
“Percent” means out of 100.
Move the slider or enter a whole number from 0 to 100. Each highlighted square is one hundredth of the whole.
25/100fraction=0.25decimal=25%percent
LET’S DO ONE TOGETHER
18 is what percent of 40?
Try a first step in your head or on paper. Reveal the method when you’re ready.
YOUR TURN · QUICK CHECK
Take it with you: Missing percent: divide. Missing part: multiply. Missing whole: divide by the decimal percent.
PRACTICE LAB · 64 ORIGINAL QUESTIONS
Understand your answers.
Choose a skill or mix all four. Get clear explanations and revisit the lessons behind your misses.
8 questions in this set. Settings apply when you start a new set.
Paper. Pencil. One question at a time.
This is a learning tool, not a timed test simulation. Try solving by hand before looking at the explanation.
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WORD KNOWLEDGE · YOUR VOCABULARY GYM
Big words. Clear meanings.
Learn a few at a time. Say the meaning out loud, reveal the card, then decide what needs another look.
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100words in this deck
100 matching words
BSEP HANDOUT1 / 100
What does this word mean?
Abashed
Self-check honestly. There’s no grade here.
A PLAN YOU CAN ACTUALLY FOLLOW
Three weeks. Small wins.
Try five study sessions per week, about 20–30 minutes each. Repeat a week or slow the pace when you need to. This is a suggested routine, not a pass guarantee.
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WEEK 01
Build the foundation
Slow down. Learn the steps before worrying about speed.
Read Fractions & decimals and Find the closest meaning. Try each lesson check.
Read Percents. Write “part, whole, percent” beside three examples. Practice AR questions.
Read Find evidence & stated details and Use the clues in the sentence. Underline the words that support each answer.
Read Operation order & negative numbers. Work one operation per line. Review ten vocabulary cards.
Try an 8-question mixed practice set. For every miss, write the correct method in your own words.
WEEK 02
Connect the skills
Turn word problems and passages into a repeatable method.
Read Ratios. Practice both part-to-part and total-group questions.
Read Solve for x and Prefixes, roots & suffixes. Check algebra answers by substitution.
Read Find the main idea and Choose the meaning that fits. Summarize a short paragraph in one sentence.
Read Rates, prices & unit conversions. Put units beside every number.
Try 16 mixed questions. Review missed questions and explain two solutions out loud in your own words.
WEEK 03
Practice with purpose
Review weak spots and prepare questions for your recruiter.
Read Averages & multi-step problems. Write a plan before calculating.
Read Perimeter, area & volume. Use the quick reference and label every answer’s units.
Read Make a supported inference and Purpose, cause & structure. Identify the evidence behind every conclusion.
Try a 24-question mixed set in review-at-the-end mode. Write down the topics you still find difficult.
Redo missed questions, review vocabulary, and ask SPC Wagne about your next study step and official testing arrangements.
Make every miss useful. Write down the topic, the step you missed, and one way to catch the mistake next time. Print the worksheet pack for space to work.
THE STUDY DESK
Keep the essentials close.
Use these during study, then practice recalling the methods without looking. These notes are not an aid you can bring into the official test.
Skill
Rule
Example
Find a percent
part ÷ whole × 100
12 ÷ 40 × 100 = 30%
Find the part
decimal percent × whole
25% of 80 = 0.25 × 80 = 20
Find the whole
part ÷ decimal percent
18 ÷ 0.30 = 60
Ratio from a total
total ÷ sum of parts; multiply for the part needed
2:3 with 20 total → 4 per part → 8 and 12
Average
sum of values ÷ number of values
(60 + 70 + 80) ÷ 3 = 70
Distance / speed
distance = rate × time; rate = distance ÷ time
40 mph × 1.5 hours = 60 miles
Rectangle
area = length × width; perimeter = 2(length + width)
9 × 4 → area 36; perimeter 26
Triangle
area = base × perpendicular height ÷ 2
10 × 6 ÷ 2 = 30 square units
Rectangular box
volume = length × width × height
5 × 3 × 2 = 30 cubic units
Circle
area = πr²; circumference = 2πr
r is radius; diameter = 2r; π ≈ 3.14
Right triangle
a² + b² = c²
c is the longest side: 3² + 4² = 5²
Operation order
grouping, exponents, ×/÷ left to right, +/− left to right
Arithmetic Reasoning, Word Knowledge, Paragraph Comprehension, and Mathematics Knowledge contribute to the AFQT. The ASVAB also covers other areas, including technical and spatial skills. See all subtests.
Practice results aren’t AFQT scores.
AFQT is reported as a percentile, not the percentage of these questions you get right. This hub cannot predict your score or qualification. Understand the scores.
Build your pencil-and-paper skills.
Calculators are not allowed on the ASVAB. Study without one, and check official instructions for your testing format. Read official test FAQs.
YOU DON’T HAVE TO FIGURE IT OUT ALONE.
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