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➗ 10 questions · answers and rationales · free

TEAS math practice questions

Free TEAS math questions from both sub-areas, numbers and algebra and measurement and data: fractions, percents, ratios, equations, unit conversions, geometry and statistics, each solved step by step.

Tap an answer to check it, or open "Show the answer and rationale" under each question. Every math answer shows its steps.

Question 1 of 10 · Numbers and Algebra

Weight change over one week
PatientChange (lb)
A−1.5
B−0.75
C+0.5
D−2.25

The table shows four patients' weight changes over one week. Which patient lost the most weight?

  1. Patient B
  2. Patient A
  3. Patient C
  4. Patient D
Show the answer and rationale

Answer: D

Patient D's change of −2.25 lb is the biggest loss. Patient C gained weight (+0.5 lb), Patient B's −0.75 lb is the smallest loss, and Patient A lost 1.5 lb, less than 2.25 lb.

Step by step

  1. A loss is a negative change, so look at the negative values: −1.5, −0.75 and −2.25.
  2. The largest loss is the negative number farthest from zero: compare 1.5, 0.75 and 2.25.
  3. 2.25 is the largest, so Patient D (−2.25 lb) lost the most.

📚 Learn it: Comparing and ordering fractions, decimals and negatives

Question 2 of 10 · Measurement and Data

A cylindrical specimen container has a radius of 3 cm and a height of 10 cm. Using π ≈ 3.14, what is its volume?

  1. 188.4 cubic cm
  2. 282.6 cubic cm
  3. 1,130.4 cubic cm
  4. 94.2 cubic cm
Show the answer and rationale

Answer: B

Multiply the circular base area (3.14 × 9 = 28.26) by the height to get 282.6 cubic cm. 188.4 is the side (lateral) surface area, 2πrh, and 1,130.4 uses the diameter, 6 cm, as the radius.

Step by step

  1. Volume of a cylinder: V = πr²h.
  2. r² = 3² = 9.
  3. V = 3.14 × 9 × 10 = 3.14 × 90 = 282.6 cubic cm.

📚 Learn it: Volume and surface area

Question 3 of 10 · Numbers and Algebra

Which list shows −0.6, −2/3, −5/8 and −0.65 in order from greatest to least?

  1. −0.6, −5/8, −0.65, −2/3
  2. −2/3, −0.65, −5/8, −0.6
  3. −0.6, −0.65, −5/8, −2/3
  4. −5/8, −0.6, −0.65, −2/3
Show the answer and rationale

Answer: A

−0.6 is closest to zero, then −0.625, −0.65 and −0.667. The list starting with −2/3 is the order from least to greatest, the reverse of what was asked; the list with −0.65 before −5/8 thinks −0.65 is closer to zero than −0.625.

Step by step

  1. Convert each to a decimal with three places: −0.600, −0.667 (−2/3), −0.625 (−5/8), −0.650.
  2. For negatives, the one closest to zero is greatest.
  3. Closest to farthest from zero: −0.600, −0.625, −0.650, −0.667.
  4. Greatest to least: −0.6, −5/8, −0.65, −2/3.

📚 Learn it: Comparing and ordering fractions, decimals and negatives

Question 4 of 10 · Measurement and Data

A rectangular block is 6 cm long, 4 cm wide and 2 cm high. What is its total surface area?

  1. 48 square cm
  2. 88 square cm
  3. 44 square cm
  4. 24 square cm
Show the answer and rationale

Answer: B

Each face has a twin on the opposite side, so SA = 2 × (24 + 12 + 8) = 88 square cm. 44 counts each pair only once, and 48 is the volume (6 × 4 × 2), which is not a surface measure.

Step by step

  1. The block has three pairs of matching faces.
  2. Face areas: 6 × 4 = 24, 6 × 2 = 12, 4 × 2 = 8 (square cm).
  3. Add one of each: 24 + 12 + 8 = 44.
  4. Double for the matching pairs: 2 × 44 = 88 square cm.

📚 Learn it: Volume and surface area

Question 5 of 10 · Numbers and Algebra

What is 8 − 4 × 3 ÷ 6 + 3²?

  1. 15
  2. 12
  3. 11
  4. −3
Show the answer and rationale

Answer: A

8 − 2 + 9 = 15. The answer 12 treats 3² as 3 × 2, 11 subtracts 8 − 4 before multiplying, and −3 subtracts the sum (2 + 9) instead of working left to right.

Step by step

  1. Exponent: 3² = 9.
  2. Multiply and divide left to right: 4 × 3 = 12, then 12 ÷ 6 = 2.
  3. Add and subtract left to right: 8 − 2 = 6, then 6 + 9 = 15.

📚 Learn it: Order of operations, negative numbers and absolute value

Question 6 of 10 · Measurement and Data

Steps walked by a nurse during four shifts
ShiftSteps
Monday9,800
Tuesday12,400
Wednesday10,600
Thursday11,200

How many more steps did the nurse walk on the most active shift than on the least active shift?

  1. 1,200
  2. 1,800
  3. 800
  4. 2,600
Show the answer and rationale

Answer: D

Compare the largest and smallest entries: 12,400 − 9,800 = 2,600. 1,800 compares Tuesday with Wednesday, 1,200 compares Tuesday with Thursday, and 800 compares Monday with Wednesday.

Step by step

  1. Most steps: 12,400 (Tuesday). Fewest steps: 9,800 (Monday).
  2. 12,400 − 9,800 = 2,600 steps.

📚 Learn it: Reading tables and graphs

Question 7 of 10 · Numbers and Algebra

One night the low temperature was −6°C and the next afternoon the high was 9°C. How many degrees did the temperature rise?

  1. −3°C
  2. −15°C
  3. 15°C
  4. 3°C
Show the answer and rationale

Answer: C

9 − (−6) = 15°C, which you can also see by counting 6 degrees up to zero and 9 more. The answer 3°C subtracts 9 − 6, and the negative answers reverse the order of subtraction.

Step by step

  1. Rise = high − low = 9 − (−6).
  2. Subtracting a negative is adding: 9 + 6 = 15.
  3. The temperature rose 15°C.

📚 Learn it: Order of operations, negative numbers and absolute value

Question 8 of 10 · Measurement and Data

Emergency room wait times for five patients were 10, 15, 20, 15 and 45 minutes. If the 45-minute wait is removed from the data, by how many minutes does the mean decrease?

  1. 9 minutes
  2. 6 minutes
  3. 15 minutes
  4. 21 minutes
Show the answer and rationale

Answer: B

Find both means: 21 minutes with the outlier and 15 without it, a drop of 6 minutes. 9 minutes divides 45 by 5 as if removing a value just subtracts its share, and 21 and 15 are the two means themselves, not the change.

Step by step

  1. Original mean: (10 + 15 + 20 + 15 + 45) ÷ 5 = 105 ÷ 5 = 21 minutes.
  2. New mean: (10 + 15 + 20 + 15) ÷ 4 = 60 ÷ 4 = 15 minutes.
  3. Decrease: 21 − 15 = 6 minutes.

📚 Learn it: Mean, median, mode and range

Question 9 of 10 · Numbers and Algebra

What is the mixed number 1 3/8 written as a decimal?

  1. 0.375
  2. 13.8
  3. 1.375
  4. 1.83
Show the answer and rationale

Answer: C

The whole number stays 1 and 3/8 = 3 ÷ 8 = 0.375, so the total is 1.375. The value 0.375 forgets the whole number, 1.83 writes the digits of the fraction backward, and 13.8 just strings the digits together.

Step by step

  1. Keep the whole number 1.
  2. Convert the fraction: 3 ÷ 8 = 0.375.
  3. Add: 1 + 0.375 = 1.375.

📚 Learn it: Converting fractions, decimals and percents

Question 10 of 10 · Measurement and Data

The numbers of minutes five patients waited in triage were 4, 5, 5, 6 and 30. Which statement about this data set is true?

  1. The mean is 10 and the median is 5
  2. The mean is 5 and the median is 10
  3. The mean is 10 and the median is 6
  4. The mean is 6 and the median is 5
Show the answer and rationale

Answer: A

The mean is 50 ÷ 5 = 10, while the median, the middle value, is 5. The single 30-minute wait is an outlier that drags the mean up but barely affects the median; the other choices swap the two or pick the wrong middle value.

Step by step

  1. Mean: (4 + 5 + 5 + 6 + 30) ÷ 5 = 50 ÷ 5 = 10.
  2. Median: the middle of 4, 5, 5, 6, 30 is the third value, 5.
  3. The outlier 30 pulls the mean above the median.

📚 Learn it: Spread, outliers and the shape of data

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