Free TEAS 7 Math Practice Test 2 — 30 Questions With Full Explanations

Question 1. Numbers & Algebra easy

A lab technician labels 3/8 of a batch of 24 specimen vials for a special study. How many vials does the technician label?

• A. 12
• B. 9 (correct)
• C. 6
• D. 8

Explanation: Multiplying 24 by 3/8 means dividing by 8 first (24 / 8 = 3) and then multiplying by 3, giving 9 vials. The 8 option divides 24 by the numerator 3 only, the 6 option uses 1/4 of the batch, and the 12 option uses half the batch rather than 3/8.

Question 2. Numbers & Algebra easy

Convert the fraction 7/8 to a decimal.

• A. 1.14
• B. 0.78
• C. 0.87
• D. 0.875 (correct)

Explanation: Divide the numerator by the denominator: 7 divided by 8 equals 0.875. The 0.78 option writes the digits side by side, 0.87 truncates 0.875 at two places instead of rounding, and 1.14 inverts the fraction by dividing 8 by 7.

Question 3. Numbers & Algebra easy

A community clinic sees 80 patients in a day, and 35% of them are children. How many of the day's patients are children?

• A. 45
• B. 28 (correct)
• C. 2.8
• D. 35

Explanation: Change 35% to 0.35 and multiply by 80: 80 x 0.35 = 28 children. The 2.8 option misplaced the decimal (multiplying by 3.5), the 35 option mistook the percent itself for a count, and the 45 option subtracted 35 from 80 instead of taking 35% of it.

Question 4. Numbers & Algebra easy

Evaluate the expression: 6 + 4 x 2 - 3.

• A. 17
• B. 14
• C. 8
• D. 11 (correct)

Explanation: Multiplication comes before addition and subtraction: 4 x 2 = 8, then 6 + 8 = 14, then 14 - 3 = 11. The 17 option worked strictly left to right, the 14 option stopped after adding 6 and 8, and the 8 option reported only the product and ignored the rest.

Question 5. Numbers & Algebra medium

Of 40 patients on a ward, 3/5 completed a satisfaction survey, and 1/4 of those preferred morning appointments. How many patients preferred morning appointments?

• A. 6 (correct)
• B. 12
• C. 16
• D. 10

Explanation: First find 3/5 of 40, which is 24 patients, then take 1/4 of 24 to get 6. The 10 option applied the 1/4 to all 40 patients instead of to the 24 survey completers, the 12 option used 3/10 of 40, and the 16 option used 2/5 of 40.

Question 6. Numbers & Algebra medium

A solution's concentration is 0.08. Express this decimal as a fraction in lowest terms.

• A. 8/10
• B. 2/25 (correct)
• C. 1/8
• D. 4/5

Explanation: The decimal 0.08 is 8 hundredths, or 8/100, which reduces by the common factor 4 to 2/25. The 8/10 and 4/5 options treat 0.08 as 0.8 (decimal misplaced), and the 1/8 option inverts the relationship between 8 and 100.

Question 7. Numbers & Algebra medium

A medical jacket is marked down 30% and now sells for $56. What was the original price?

• A. 72.80
• B. 16.80
• C. 80 (correct)
• D. 39.20

Explanation: The sale price is 70% of the original, so divide $56 by 0.70 to get $80. The 72.80 option instead added 30% of the sale price to the sale price, the 39.20 option subtracted 30% a second time to double the discount, and the 16.80 option reported the discount amount itself.

Question 8. Numbers & Algebra medium

A floor-plan drawing uses a scale of 1 cm = 4 m. A corridor measures 2.75 cm on the drawing. How long is the actual corridor?

• A. 6.75
• B. 5.5
• C. 1.4
• D. 11 (correct)

Explanation: Multiply the drawing length by the scale factor: 2.75 cm x 4 m per cm = 11 m. The 6.75 option added the numbers instead of multiplying, the 5.5 option incorrectly used a 2-cm-equals-4-m scale, and the 1.4 option divided 4 by 2.75, reversing the ratio.

Question 9. Numbers & Algebra medium

Evaluate the expression: 20 - 4 x 3 + 8 / 2.

• A. 8
• B. 16
• C. 12 (correct)
• D. 28

Explanation: Do multiplication and division before addition and subtraction: 4 x 3 = 12 and 8 / 2 = 4, so 20 - 12 + 4 = 12. The 28 option worked strictly left to right, the 8 option stopped after 20 - 12, and the 16 option answered the term 4 x 3 + 8 / 2 by itself.

Question 10. Numbers & Algebra medium

Solve for x: 5x + 9 = 3x + 21.

• A. 12
• B. 30
• C. 3.75
• D. 6 (correct)

Explanation: Subtract 3x from both sides to get 2x + 9 = 21, then subtract 9 to get 2x = 12, and divide by 2 to find x = 6. The 12 option stopped at the value of 2x, the 3.75 option combined terms with the wrong signs (8x = 30), and the 30 option added the two constants.

Question 11. Numbers & Algebra medium

A department's budget rose from $1.2 million to $1.5 million over a year. What was the percent increase?

• A. 2.5%
• B. 30%
• C. 25% (correct)
• D. 20%

Explanation: Percent change uses the original value as the base: the change is 0.3 million, and 0.3 / 1.2 = 0.25, or 25%. The 20% option divided the change by the new value of 1.5 million, the 30% option used a $1.0 million base, and the 2.5% option misplaced the decimal point.

Question 12. Numbers & Algebra medium

On a unit, the ratio of nurses to patients is 2:5. If the unit has 40 patients, how many nurses are on duty?

• A. 25
• B. 16 (correct)
• C. 20
• D. 8

Explanation: The ratio 2:5 means 2 nurses for every 5 patients, so nurses = 40 x 2/5 = 16. The 8 option used only the 40 / 5 part, the 20 option assumed a 1:2 ratio, and the 25 option reversed the ratio, treating nurses as 5/8 of the total.

Question 13. Numbers & Algebra medium

Solve for x: 0.25x = 1.75.

• A. 4.375
• B. 1.5
• C. 0.7
• D. 7 (correct)

Explanation: Divide both sides by 0.25: 1.75 / 0.25 = 7. The 0.7 option misplaced the decimal in the answer, the 4.375 option multiplied 1.75 by 2.5 instead of dividing by 0.25, and the 1.5 option subtracted 0.25 from 1.75.

Question 14. Numbers & Algebra hard

A rectangular garden is 3 times as long as it is wide. Its perimeter is 64 m. What is the width of the garden?

• A. 24
• B. 8 (correct)
• C. 32
• D. 16

Explanation: If the width is w, the length is 3w, and the perimeter is 2(w + 3w) = 8w. Set 8w = 64, so w = 8 m. The 16 option divided the perimeter by 4, the 24 option reported the length instead of the width, and the 32 option took half the perimeter as the width.

Question 15. Numbers & Algebra hard

An item's price increases by 20% and then decreases by 20%. Compared with the original price, the final price is:

• A. 4% higher
• B. 4% lower (correct)
• C. the same
• D. 2% lower

Explanation: Multiplying the price by 1.20 and then by 0.80 gives 1.20 x 0.80 = 0.96, so the final price is 96% of the original, which is 4% lower. The 'same' option wrongly assumes equal percents cancel, '4% higher' reverses the direction, and '2% lower' misreads the 0.04 product.

Question 16. Numbers & Algebra hard

The sum of three consecutive whole numbers is 102. What is the smallest of the three numbers?

• A. 32
• B. 35
• C. 33 (correct)
• D. 34

Explanation: If the smallest is n, then n + (n + 1) + (n + 2) = 3n + 3 = 102, so 3n = 99 and n = 33. The 34 option reported the average, 102 / 3, which is the middle number, the 35 option is the largest of the three, and the 32 option subtracted 1 from the average.

Question 17. Measurement & Data easy

A tablet weighs 0.5 g. How many milligrams is this? (1 g = 1,000 mg)

• A. 5000
• B. 500 (correct)
• C. 50
• D. 5

Explanation: Multiply grams by 1,000 to convert to milligrams: 0.5 x 1,000 = 500 mg. The 5 option multiplied by 10 instead of 1,000, the 50 option multiplied by 100, and the 5,000 option multiplied by 10,000, each a one- or two-place decimal error.

Question 18. Measurement & Data easy

A nurse records five pulse rates during rounds: 72, 68, 75, 70, and 65 beats per minute. What is the mean pulse rate?

• A. 68
• B. 72
• C. 70 (correct)
• D. 350

Explanation: Add the five readings (72 + 68 + 75 + 70 + 65 = 350) and divide by the count, 5, to get a mean of 70. The 72 and 68 options simply listed individual values, and the 350 option reported the total sum without dividing by 5.

Question 19. Measurement & Data medium

A rectangular therapy room is 4.5 m by 3 m. What is its perimeter?

• A. 7.5
• B. 13.5
• C. 27
• D. 15 (correct)

Explanation: Perimeter is twice the sum of length and width: 2 x (4.5 + 3) = 2 x 7.5 = 15 m. The 13.5 option computed the area (4.5 x 3) instead, the 7.5 option added the sides once without doubling, and the 27 option doubled the area value.

Question 20. Measurement & Data medium

A supply box measures 8 cm by 5 cm by 3 cm. What is the volume of the box?

• A. 40
• B. 120 (correct)
• C. 16
• D. 158

Explanation: Volume of a rectangular prism is length x width x height: 8 x 5 x 3 = 120 cubic cm. The 40 option multiplied only two dimensions, the 16 option added the three dimensions, and the 158 option computed the surface area instead of the volume.

Question 21. Measurement & Data medium

Seven test scores are 72, 85, 91, 78, 85, 90, and 66. What is the median score?

• A. 78
• B. 81
• C. 90
• D. 85 (correct)

Explanation: Order the scores as 66, 72, 78, 85, 85, 90, 91; with 7 values the median is the 4th, which is 85. The 81 option is the mean of all seven scores instead, the 78 option is the 4th value of the unsorted list, and the 90 option is the second highest score.

Question 22. Measurement & Data hard

A training course is 1.5 miles long. How many feet is that? (1 mile = 5,280 ft)

• A. 7920 (correct)
• B. 792
• C. 3960
• D. 2640

Explanation: Multiply the mile length by 5,280 feet per mile: 1.5 x 5,280 = 7,920 feet. The 792 option misplaced the decimal by a full place, the 3,960 option used a half-mile conversion of 2,640 feet, and the 2,640 option converted only a quarter mile.

Question 23. Measurement & Data medium

A jar holds 5 red, 4 blue, and 6 green marbles. One marble is drawn at random. What is the probability that it is blue?

• A. 4/15 (correct)
• B. 11/15
• C. 5/15
• D. 4/11

Explanation: There are 15 marbles total and 4 blue ones, so the probability is 4/15. The 11/15 option is the complement, the chance of drawing a marble that is NOT blue, the 4/11 option divided blue marbles by only the red and green marbles, and the 5/15 option is the probability of red instead.

Question 24. Measurement & Data medium

A survey of 120 patients asked for one appointment preference: 45 chose morning, 35 chose evening, and 40 chose flexible. What fraction of patients chose evening?

• A. 1/3
• B. 7/24 (correct)
• C. 17/24
• D. 3/8

Explanation: Evening patients are 35 of 120, and 35/120 reduces by 5 to 7/24. The 3/8 option is the fraction that chose morning (45/120), the 1/3 option is the flexible group (40/120), and the 17/24 option combined morning and flexible patients.

Question 25. Measurement & Data hard

A medication is scheduled every 6 hours, with the first dose at 11:30 PM. What time should the next dose be given?

• A. 5:30 PM
• B. 6:30 AM
• C. 5:30 AM (correct)
• D. 12:30 AM

Explanation: Adding 6 hours to 11:30 PM crosses midnight: 11:30 PM plus 6 hours is 5:30 AM the next morning. The 5:30 PM option forgot the AM-to-PM rollover, the 12:30 AM option added only 30 minutes up to midnight, and the 6:30 AM option added 7 hours instead of 6.

Question 26. Measurement & Data medium

A spinner has 5 equal sections: 2 red, 2 blue, and 1 green. What is the probability of landing on red?

• A. 25%
• B. 40% (correct)
• C. 50%
• D. 20%

Explanation: Two of the five sections are red, so the probability is 2/5, which equals 0.40 or 40%. The 20% option used the single green section, the 50% option treated the two red sections as half of only the four colored sections, and the 25% option assumed four equal sections.

Question 27. Measurement & Data hard

A cylindrical storage tank has a radius of 2 m and a height of 5 m. Using 3.14 for pi, what is the volume of the tank?

• A. 62.8 (correct)
• B. 20
• C. 31.4
• D. 125.6

Explanation: Cylinder volume is pi x radius squared x height: 3.14 x 2 x 2 x 5 = 62.8 cubic m. The 31.4 option used pi x radius x height, dropping one factor of the radius, the 125.6 option used the diameter in place of the height, and the 20 option computed radius squared times height without pi.

Question 28. Measurement & Data hard

A course grade is made up of 60% exam and 40% lab work. A student scored 75 on the exam and 90 on the lab work. What is the student's course grade?

• A. 81 (correct)
• B. 75
• C. 84
• D. 82.5

Explanation: Multiply each score by its weight: 0.60 x 75 = 45 and 0.40 x 90 = 36, then add to get 81. The 82.5 option took a simple average of 75 and 90, the 84 option swapped the weights, and the 75 option used only the exam score and ignored the lab work.

Question 29. Measurement & Data hard

A line graph tracking monthly temperatures reads: January 20, February 25, March 35. What was the percent increase from February to March?

• A. 10%
• B. 50%
• C. 40% (correct)
• D. 28.6%

Explanation: The change from February to March is 35 - 25 = 10, and 10 divided by the original February value of 25 is 0.40, or 40%. The 28.6% option divided by the new March value of 35, the 50% option used January as the base, and the 10% option mistook the raw change for a percent.

Question 30. Measurement & Data hard

Two fair six-sided dice are rolled. What is the probability that the sum of the two dice is 7?

• A. 1/6 (correct)
• B. 1/12
• C. 1/36
• D. 1/9

Explanation: There are 36 equally likely outcomes, and 6 of them sum to 7: (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1), so the probability is 6/36 = 1/6. The 1/36 option counted only one ordered pair, the 1/12 option counted only 3 of the 6 outcomes, and the 1/9 option counted 4 pairs.