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Free TACHS Practice Test: 10 Questions Explained

Eighth graders applying to New York Catholic high schools sit the TACHS, typically in November. These ten questions come from one of our six full-length TACHS practice exams.

Take these as an interactive quiz The full TACHS exams

Question 1

What number comes just after 4,099?
  1. A. 4,010
  2. B. 5,000
  3. C. 4,100
  4. D. 4,000
Show the answer

The answer is C.

  • A is wrong: This changes the tens digit rather than counting on by one. 4,099 + 1 rolls both the tens and the units over.
  • B is wrong: This rolls the thousands over. Only 4,999 + 1 reaches 5,000.
  • D is wrong: This is smaller than 4,099. Counting up cannot give a smaller number.

Question 2

Which number is greatest?
  1. A. 0.7
  2. B. 0.07
  3. C. 0.77
  4. D. 0.707
Show the answer

The answer is C.

  • A is wrong: 0.7 is 0.70, which is less than 0.77 in the hundredths place.
  • B is wrong: This has a zero in the tenths place, making it the smallest of the four.
  • D is wrong: Having the most digits does not make a decimal largest. 0.707 is 0.70 and a little, still under 0.77.

Question 3

What is the value of 3² + 4 × 5 − 6?
  1. A. 35
  2. B. 23
  3. C. 19
  4. D. 29
Show the answer

The answer is B.

  • A is wrong: This works left to right: 3² is 9, plus 4 is 13, times 5 is 65 — or adds before multiplying. Multiplication comes before addition.
  • C is wrong: This subtracts before multiplying, or handles 3² as 3 × 2 = 6. The exponent is 3 × 3 = 9.
  • D is wrong: This adds the 6 instead of subtracting it, or leaves out a step. 9 + 20 = 29, and the −6 still has to be applied.

Question 4

Which fraction is greatest?
  1. A. 7/12
  2. B. 5/9
  3. C. 3/5
  4. D. 2/3
Show the answer

The answer is D.

  • A is wrong: About 0.583 — larger than 5/9 but smaller than both 3/5 and 2/3.
  • B is wrong: About 0.556, the smallest of the four. A large denominator does not make a fraction large.
  • C is wrong: 0.600 exactly. Close, but 2/3 is about 0.667.

Question 5

What is 3/4 + 2/3?
  1. A. 1 5/12
  2. B. 5/12
  3. C. 5/7
  4. D. 1 1/12
Show the answer

The answer is A.

  • B is wrong: This subtracts instead of adding: 9/12 − 8/12 wrongly handled. The question asks for a sum.
  • C is wrong: This adds the numerators and the denominators separately (3+2 over 4+3), which is not how fractions add.
  • D is wrong: This is 13/12, which comes from adding the numerators and one denominator wrongly. The correct sum over 12 is 17/12.

Question 6

Part 2. Look for a mistake in spelling.
  1. A. The committee agreed on the schedule.
  2. B. His argument was persuasive.
  3. C. She recieved the letter on Tuesday.
  4. D. (No mistakes)
Show the answer

The answer is C.

  • A is wrong: 'Committee' and 'schedule' are both spelled correctly here.
  • B is wrong: 'Argument' and 'persuasive' are both correct — 'argument' has no e after the u, and this one does not.
  • D is wrong: There is a mistake: 'recieved' breaks the i-before-e rule.

Question 7

Look for a mistake in spelling.
  1. A. (No mistakes)
  2. B. The rhythm was steady.
  3. C. Their absence was noticed.
  4. D. We proceeded with caution.
Show the answer

The answer is A.

  • B is wrong: 'Rhythm' is correct, unusual as it looks.
  • C is wrong: 'Absence' is correct — it ends in -ence, not -ance.
  • D is wrong: 'Proceeded' is spelled correctly, with the double e.

Question 8

Look for a mistake in spelling.
  1. A. (No mistakes)
  2. B. She apologized quickly.
  3. C. The library is separate from the school.
  4. D. It was definately the best game.
Show the answer

The answer is D.

  • A is wrong: There is a mistake: 'definately' should be 'definitely'.
  • B is wrong: 'Apologized' is spelled correctly.
  • C is wrong: 'Separate' is correct here, with an a in the middle — a common place to slip, but not this time.

Question 9

Look for a mistake in spelling.
  1. A. The restaurant was crowded.
  2. B. (No mistakes)
  3. C. We discussed the problem.
  4. D. He had a strange occurence.
Show the answer

The answer is D.

  • A is wrong: 'Restaurant' is spelled correctly, including the au.
  • B is wrong: There is a mistake: 'occurence' is missing its second r.
  • C is wrong: 'Discussed' is correct, with the double s.

Question 10

Look for a mistake in spelling.
  1. A. (No mistakes)
  2. B. We waited an hour.
  3. C. The answer was obvious.
  4. D. Their going to the park later.
Show the answer

The answer is D.

  • A is wrong: There is a mistake: 'Their' is the possessive, where 'They're' is needed.
  • B is wrong: 'Waited' and 'hour' are both spelled correctly.
  • C is wrong: 'Obvious' is correct.
Before the real one

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The TACHS practice exams See what an exam costs