Short passages, find-the-error sentences and mathematics problems in three of the four TACHS parts, each answer explained.
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Unofficial practice questions, not affiliated with Riverside Insights or the New York, Brooklyn and Rockville Centre dioceses. Bank checked October 11, 2026.
The real test: TACHS, fall 2026
Fee
$78
Retakes
None. The TACHS may be taken only once.
Who takes it
Current eighth graders applying to Catholic high schools of the Archdiocese of New York, the Diocese of Brooklyn/Queens or the Diocese of Rockville Centre.
Parts
Reading, Written Expression, Mathematics and Ability, given as 6 timed subtests.
Testing time
About 2 hours 10 minutes with directions, plus optional 5-minute breaks after each of the first three subtests.
Where and when
Online, at home. November 6, 2026, for the Archdiocese of New York; November 7, 2026, for Brooklyn/Queens and Rockville Centre.
Calculator
A basic 4-function calculator inside the test, new in 2026. Personal calculators are not allowed.
Scores
Local and national percentile ranks, sent to three high schools the student chooses. Wrong answers carry no penalty.
"Notice to students: Starting Monday, the library will stay open until 5:00 p.m. on school days. The extra hour is a trial. If fewer than ten students use it each day in October, the library will go back to closing at 4:00 p.m. Students who stay must sign in at the front desk and arrange their own ride home, because the late bus leaves at 4:15 p.m." As it is used in the notice, what does "trial" mean?TACHS Student Handbook 2026, page 28: Reading, a word in context. "trial" read in Wiktionary
"Notice to students: Starting Monday, the library will stay open until 5:00 p.m. on school days. The extra hour is a trial. If fewer than ten students use it each day in October, the library will go back to closing at 4:00 p.m. Students who stay must sign in at the front desk and arrange their own ride home, because the late bus leaves at 4:15 p.m." What must a student who stays for the extra hour do?TACHS Student Handbook 2026, page 28: Reading, informational material. Passage made up for this page
"Notice to students: Starting Monday, the library will stay open until 5:00 p.m. on school days. The extra hour is a trial. If fewer than ten students use it each day in October, the library will go back to closing at 4:00 p.m. Students who stay must sign in at the front desk and arrange their own ride home, because the late bus leaves at 4:15 p.m." What would most likely keep the library open until 5:00 p.m. after October?TACHS Student Handbook 2026, page 28: Reading, informational material. Passage made up for this page
Show all 120 questions (117 more)
Reading: informational texts, continued
"Notice to students: Starting Monday, the library will stay open until 5:00 p.m. on school days. The extra hour is a trial. If fewer than ten students use it each day in October, the library will go back to closing at 4:00 p.m. Students who stay must sign in at the front desk and arrange their own ride home, because the late bus leaves at 4:15 p.m." Why does the notice mention the late bus?TACHS Student Handbook 2026, page 28: Reading, informational material. Passage made up for this page
"Sunlight looks white, but it is made of all the colors of the rainbow. Light travels in waves, and blue light travels in shorter waves than red light. When sunlight reaches Earth's atmosphere, the gases and particles in the air scatter it in all directions. Blue light is scattered more than the other colors, which is why the sky looks blue most of the time. Near sunset the light passes through more air, and more reds and yellows reach your eyes." According to the passage, why does the sky look blue most of the time?TACHS Student Handbook 2026, page 28: Reading. Passage facts: "Why Is the Sky Blue?", NASA Space Place
"Sunlight looks white, but it is made of all the colors of the rainbow. Light travels in waves, and blue light travels in shorter waves than red light. When sunlight reaches Earth's atmosphere, the gases and particles in the air scatter it in all directions. Blue light is scattered more than the other colors, which is why the sky looks blue most of the time. Near sunset the light passes through more air, and more reds and yellows reach your eyes." As it is used in the passage, what does "scatter" mean?TACHS Student Handbook 2026, page 28: Reading, a word in context. "scatter" read in Wiktionary
"Sunlight looks white, but it is made of all the colors of the rainbow. Light travels in waves, and blue light travels in shorter waves than red light. When sunlight reaches Earth's atmosphere, the gases and particles in the air scatter it in all directions. Blue light is scattered more than the other colors, which is why the sky looks blue most of the time. Near sunset the light passes through more air, and more reds and yellows reach your eyes." Based on the passage, why is a sunset often red or yellow?TACHS Student Handbook 2026, page 28: Reading. Passage facts: "Why Is the Sky Blue?", NASA Space Place
"Sunlight looks white, but it is made of all the colors of the rainbow. Light travels in waves, and blue light travels in shorter waves than red light. When sunlight reaches Earth's atmosphere, the gases and particles in the air scatter it in all directions. Blue light is scattered more than the other colors, which is why the sky looks blue most of the time. Near sunset the light passes through more air, and more reds and yellows reach your eyes." What is the author's main purpose in this passage?TACHS Student Handbook 2026, page 28: Reading. Passage facts: "Why Is the Sky Blue?", NASA Space Place
"Tides are very long waves that move through the ocean, pulled by the moon and the sun. When the highest part of the wave, the crest, reaches a shore, it is high tide. When the lowest part, the trough, arrives, it is low tide. The difference in height between the two is the tidal range. Few things in nature are as dependable: the water rises and falls along the coast day after day." According to the passage, what is the tidal range?TACHS Student Handbook 2026, page 28: Reading. Passage facts: "What are tides?", NOAA National Ocean Service
"Tides are very long waves that move through the ocean, pulled by the moon and the sun. When the highest part of the wave, the crest, reaches a shore, it is high tide. When the lowest part, the trough, arrives, it is low tide. The difference in height between the two is the tidal range. Few things in nature are as dependable: the water rises and falls along the coast day after day." As it is used in the passage, what does "dependable" mean?TACHS Student Handbook 2026, page 28: Reading, a word in context. "dependable" read in Wiktionary
"Tides are very long waves that move through the ocean, pulled by the moon and the sun. When the highest part of the wave, the crest, reaches a shore, it is high tide. When the lowest part, the trough, arrives, it is low tide. The difference in height between the two is the tidal range. Few things in nature are as dependable: the water rises and falls along the coast day after day." What happens when the trough of the wave reaches a shore?TACHS Student Handbook 2026, page 28: Reading. Passage facts: "What are tides?", NOAA National Ocean Service
"Tides are very long waves that move through the ocean, pulled by the moon and the sun. When the highest part of the wave, the crest, reaches a shore, it is high tide. When the lowest part, the trough, arrives, it is low tide. The difference in height between the two is the tidal range. Few things in nature are as dependable: the water rises and falls along the coast day after day." Which sentence best states the main idea of the passage?TACHS Student Handbook 2026, page 28: Reading. Passage facts: "What are tides?", NOAA National Ocean Service
"To enter the Dunmore Science Fair, first choose a question you can test, not just a topic to describe. Hand in a one-page plan by January 15 so that a teacher can approve it. Next, run your test at least three times and record every result, even the ones that surprise you. Finally, build a display that shows your question, your method and your results. The judges will ask you to explain each part." How are the directions in this passage organized?TACHS Student Handbook 2026, page 28: Reading, informational material. Passage made up for this page
"To enter the Dunmore Science Fair, first choose a question you can test, not just a topic to describe. Hand in a one-page plan by January 15 so that a teacher can approve it. Next, run your test at least three times and record every result, even the ones that surprise you. Finally, build a display that shows your question, your method and your results. The judges will ask you to explain each part." What must happen before a student begins testing?TACHS Student Handbook 2026, page 28: Reading, informational material. Passage made up for this page
"To enter the Dunmore Science Fair, first choose a question you can test, not just a topic to describe. Hand in a one-page plan by January 15 so that a teacher can approve it. Next, run your test at least three times and record every result, even the ones that surprise you. Finally, build a display that shows your question, your method and your results. The judges will ask you to explain each part." Which project question best fits the fair's first rule?TACHS Student Handbook 2026, page 28: Reading, informational material. Passage made up for this page
"To enter the Dunmore Science Fair, first choose a question you can test, not just a topic to describe. Hand in a one-page plan by January 15 so that a teacher can approve it. Next, run your test at least three times and record every result, even the ones that surprise you. Finally, build a display that shows your question, your method and your results. The judges will ask you to explain each part." Why does the passage most likely say to record results "even the ones that surprise you"?TACHS Student Handbook 2026, page 28: Reading, informational material. Passage made up for this page
"To the editor: The town plans to replace the grass field behind Hale School with a parking lot. I ask the council to reconsider. The field is the only open space within a mile where children can play. The lot would hold forty cars, yet it would sit nearly empty except during two football games a year. Paving the field would solve a small problem by creating a larger one." As it is used in the letter, what does "reconsider" mean?TACHS Student Handbook 2026, page 28: Reading, a word in context. "reconsider" read in Wiktionary
"To the editor: The town plans to replace the grass field behind Hale School with a parking lot. I ask the council to reconsider. The field is the only open space within a mile where children can play. The lot would hold forty cars, yet it would sit nearly empty except during two football games a year. Paving the field would solve a small problem by creating a larger one." In the last sentence, what is the "small problem"?TACHS Student Handbook 2026, page 28: Reading, informational material. Passage made up for this page
"To the editor: The town plans to replace the grass field behind Hale School with a parking lot. I ask the council to reconsider. The field is the only open space within a mile where children can play. The lot would hold forty cars, yet it would sit nearly empty except during two football games a year. Paving the field would solve a small problem by creating a larger one." What is the author's purpose in writing this letter?TACHS Student Handbook 2026, page 28: Reading, informational material. Passage made up for this page
"To the editor: The town plans to replace the grass field behind Hale School with a parking lot. I ask the council to reconsider. The field is the only open space within a mile where children can play. The lot would hold forty cars, yet it would sit nearly empty except during two football games a year. Paving the field would solve a small problem by creating a larger one." Which sentence from the letter is an opinion, not a fact that could be checked?TACHS Student Handbook 2026, page 28: Reading, informational material. Passage made up for this page
"When the Carver Street bridge closed for repairs last spring, sixth grader Amara Diaz noticed her neighbors walking an extra mile to reach the grocery store. She drew a map of a shorter route through the park and taped copies to lampposts. Within a week the city had printed her map on real signs. 'I just wanted my grandmother to get her groceries,' Amara said." What do Amara's words at the end show about her?TACHS Student Handbook 2026, page 28: Reading, informational material. Passage made up for this page
"When the Carver Street bridge closed for repairs last spring, sixth grader Amara Diaz noticed her neighbors walking an extra mile to reach the grocery store. She drew a map of a shorter route through the park and taped copies to lampposts. Within a week the city had printed her map on real signs. 'I just wanted my grandmother to get her groceries,' Amara said." What does the city's choice to print the map on signs suggest?TACHS Student Handbook 2026, page 28: Reading, informational material. Passage made up for this page
"When the Carver Street bridge closed for repairs last spring, sixth grader Amara Diaz noticed her neighbors walking an extra mile to reach the grocery store. She drew a map of a shorter route through the park and taped copies to lampposts. Within a week the city had printed her map on real signs. 'I just wanted my grandmother to get her groceries,' Amara said." Which title best fits this passage?TACHS Student Handbook 2026, page 28: Reading, informational material. Passage made up for this page
"When the Carver Street bridge closed for repairs last spring, sixth grader Amara Diaz noticed her neighbors walking an extra mile to reach the grocery store. She drew a map of a shorter route through the park and taped copies to lampposts. Within a week the city had printed her map on real signs. 'I just wanted my grandmother to get her groceries,' Amara said." Why did Amara draw the map?TACHS Student Handbook 2026, page 28: Reading, informational material. Passage made up for this page
Reading: literary texts 16
"The first snow came early that year, and Eli, the hired boy, was sent alone to bring the sheep down from the high pasture. At the gate he counted them twice: nineteen. There should have been twenty. The sky was already the color of slate. Eli looked at the warm lights of the farmhouse below, then turned back up the trail, calling into the wind." What does "the color of slate" tell the reader about the sky?TACHS Student Handbook 2026, page 28: Reading, a word in context. "slate" read in Wiktionary
"The first snow came early that year, and Eli, the hired boy, was sent alone to bring the sheep down from the high pasture. At the gate he counted them twice: nineteen. There should have been twenty. The sky was already the color of slate. Eli looked at the warm lights of the farmhouse below, then turned back up the trail, calling into the wind." What does Eli's choice at the end show about him?TACHS Student Handbook 2026, page 28: Reading, literary material. Passage made up for this page
"The first snow came early that year, and Eli, the hired boy, was sent alone to bring the sheep down from the high pasture. At the gate he counted them twice: nineteen. There should have been twenty. The sky was already the color of slate. Eli looked at the warm lights of the farmhouse below, then turned back up the trail, calling into the wind." What problem does Eli discover at the gate?TACHS Student Handbook 2026, page 28: Reading, literary material. Passage made up for this page
"The first snow came early that year, and Eli, the hired boy, was sent alone to bring the sheep down from the high pasture. At the gate he counted them twice: nineteen. There should have been twenty. The sky was already the color of slate. Eli looked at the warm lights of the farmhouse below, then turned back up the trail, calling into the wind." Why does the author mention the warm lights of the farmhouse?TACHS Student Handbook 2026, page 28: Reading, literary material. Passage made up for this page
"The old dog knows the mail truck's sound / before it climbs the hill; / he lifts one ear, then both, then waits / beside the windowsill. // He does not bark the way he did / when he was quick and thin; / he only thumps his tail to say / the world is coming in." How has the dog changed since he was young?TACHS Student Handbook 2026, page 28: Reading, literary material. Passage made up for this page
"The old dog knows the mail truck's sound / before it climbs the hill; / he lifts one ear, then both, then waits / beside the windowsill. // He does not bark the way he did / when he was quick and thin; / he only thumps his tail to say / the world is coming in." In the last line, what does "the world is coming in" most likely refer to?TACHS Student Handbook 2026, page 28: Reading, literary material. Passage made up for this page
"The old dog knows the mail truck's sound / before it climbs the hill; / he lifts one ear, then both, then waits / beside the windowsill. // He does not bark the way he did / when he was quick and thin; / he only thumps his tail to say / the world is coming in." Which word best describes the speaker's attitude toward the dog?TACHS Student Handbook 2026, page 28: Reading, literary material. Passage made up for this page
"The old dog knows the mail truck's sound / before it climbs the hill; / he lifts one ear, then both, then waits / beside the windowsill. // He does not bark the way he did / when he was quick and thin; / he only thumps his tail to say / the world is coming in." Which words show the dog listening closely?TACHS Student Handbook 2026, page 28: Reading, literary material. Passage made up for this page
"Tomás held the trumpet case on his knees the whole bus ride, as if it might leap out the window. At the audition door he heard another student playing the same piece, faster and cleaner than he ever had. He almost turned around. Then he remembered his sister's advice: play it the way you mean it, not the way they expect it. He wiped his palms on his jeans and knocked." What does his sister's advice mean?TACHS Student Handbook 2026, page 28: Reading, literary material. Passage made up for this page
"Tomás held the trumpet case on his knees the whole bus ride, as if it might leap out the window. At the audition door he heard another student playing the same piece, faster and cleaner than he ever had. He almost turned around. Then he remembered his sister's advice: play it the way you mean it, not the way they expect it. He wiped his palms on his jeans and knocked." What does the last sentence show about Tomás?TACHS Student Handbook 2026, page 28: Reading, literary material. Passage made up for this page
"Tomás held the trumpet case on his knees the whole bus ride, as if it might leap out the window. At the audition door he heard another student playing the same piece, faster and cleaner than he ever had. He almost turned around. Then he remembered his sister's advice: play it the way you mean it, not the way they expect it. He wiped his palms on his jeans and knocked." Which word best describes Tomás during the bus ride?TACHS Student Handbook 2026, page 28: Reading, literary material. Passage made up for this page
"Tomás held the trumpet case on his knees the whole bus ride, as if it might leap out the window. At the audition door he heard another student playing the same piece, faster and cleaner than he ever had. He almost turned around. Then he remembered his sister's advice: play it the way you mean it, not the way they expect it. He wiped his palms on his jeans and knocked." Why does Tomás almost turn around?TACHS Student Handbook 2026, page 28: Reading, literary material. Passage made up for this page
"'You can't fix it with tape,' Wren said, looking at the kite's snapped spar. Her grandfather said nothing. He slid a drinking straw over the break, wound thread around it and handed the kite back. It flew crooked, pulling left all afternoon. Wren decided she liked it better that way. A kite that flew straight, she thought, could belong to anybody." How does Wren's grandfather answer her remark?TACHS Student Handbook 2026, page 28: Reading, literary material. Passage made up for this page
"'You can't fix it with tape,' Wren said, looking at the kite's snapped spar. Her grandfather said nothing. He slid a drinking straw over the break, wound thread around it and handed the kite back. It flew crooked, pulling left all afternoon. Wren decided she liked it better that way. A kite that flew straight, she thought, could belong to anybody." Which idea does the passage suggest?TACHS Student Handbook 2026, page 28: Reading, literary material. Passage made up for this page
"'You can't fix it with tape,' Wren said, looking at the kite's snapped spar. Her grandfather said nothing. He slid a drinking straw over the break, wound thread around it and handed the kite back. It flew crooked, pulling left all afternoon. Wren decided she liked it better that way. A kite that flew straight, she thought, could belong to anybody." Which word best describes Wren's grandfather?TACHS Student Handbook 2026, page 28: Reading, literary material. Passage made up for this page
"'You can't fix it with tape,' Wren said, looking at the kite's snapped spar. Her grandfather said nothing. He slid a drinking straw over the break, wound thread around it and handed the kite back. It flew crooked, pulling left all afternoon. Wren decided she liked it better that way. A kite that flew straight, she thought, could belong to anybody." Why does Wren like the kite better after the repair?TACHS Student Handbook 2026, page 28: Reading, literary material. Passage made up for this page
Written Expression: the best way to say it 20
(1) ______ (2) On Mondays it serves soup made with vegetables from the school garden. (3) On Fridays students vote on the next week's menu. Which sentence best fills the blank?TACHS Student Handbook 2026, page 28: Written Expression. Common Core standard W.8.2.a
(1) Maya opened the oven door. (2) She pulls out the tray and set it on the counter. What is the best way to write sentence 2?TACHS Student Handbook 2026, page 28: Written Expression. Common Core standard L.5.1.d
(1) Our team built a bridge from craft sticks. (2) We tested it by hanging weights from the center. (3) My cousin lives near a famous bridge. (4) It held nine pounds before it cracked. Which sentence does not belong in this paragraph?TACHS Student Handbook 2026, page 28: Written Expression. Common Core standard W.8.2.b
(1) The hiking club meets every Saturday at the trailhead. (2) New members borrow boots and a pack until they buy their own. (3) Each hike ends with a shared lunch. Which sentence would best end this paragraph?TACHS Student Handbook 2026, page 28: Written Expression. Common Core standard W.8.2.f
(1) The museum opens at nine. (2) Because the line is shorter in the morning. (3) We plan to arrive early. What is the best way to fix sentence 2?TACHS Student Handbook 2026, page 28: Written Expression. Common Core standard L.4.1.f
(1) Then she poured the batter into the pan. (2) First, Ana mixed the flour and eggs. (3) Finally, she slid the pan into the oven. What is the best order for these sentences?TACHS Student Handbook 2026, page 28: Written Expression. Common Core standard W.8.3.c
A class is writing to the town council to ask for a crosswalk. Which sentence fits the letter best?TACHS Student Handbook 2026, page 28: Written Expression. Common Core standard W.8.2.e
A paragraph begins, "The later start time has helped students at Hale School." Which sentence best supports that claim?TACHS Student Handbook 2026, page 28: Written Expression. Common Core standard W.8.1.b
A report says, "The storm did things to the old barn." Which revision is the most precise?TACHS Student Handbook 2026, page 28: Written Expression. Common Core standard W.8.2.d
Four students wrote the same news for the school paper. Which sentence gives it with no wasted words?TACHS Student Handbook 2026, page 28: Written Expression. Common Core standard L.7.3.a
What is the best way to revise this sentence? "Each and every student must return back the form by Friday."TACHS Student Handbook 2026, page 28: Written Expression. Common Core standard L.7.3.a
"When Luis handed Marco the trophy, he smiled." Which revision makes clear who smiled?TACHS Student Handbook 2026, page 28: Written Expression. Common Core standard L.6.1.d
Which is the best way to combine these two sentences? "The bell rang. The students kept working."TACHS Student Handbook 2026, page 28: Written Expression. Common Core standard L.5.3.a
Which is the best way to write this sentence? "The ferry was late we missed the first act."TACHS Student Handbook 2026, page 28: Written Expression. Common Core standard L.4.1.f
Which sentence makes clear who was riding the bike?TACHS Student Handbook 2026, page 28: Written Expression. Common Core standard L.7.1.c
Which sentence puts the people who did the work first?TACHS Student Handbook 2026, page 28: Written Expression. Common Core standard L.8.3.a
Which word best fills the blank? "Neither the coach ______ the players knew the bus was late."TACHS Student Handbook 2026, page 28: Written Expression. Common Core standard L.5.1.e
Which word best fills the blank? "The box of markers ______ on the top shelf."TACHS Student Handbook 2026, page 28: Written Expression. Common Core standard L.3.1.f
Which word or phrase best fills the blank? "Jon studied every night for a week. ______, he felt calm on the morning of the test."TACHS Student Handbook 2026, page 28: Written Expression. Common Core standard W.8.2.c
Which word or phrase best fills the blank? "The first trail is short and flat. ______, the second climbs steeply for two miles."TACHS Student Handbook 2026, page 28: Written Expression. Common Core standard W.8.2.c
Written Expression: find the error 20
One of these sentences about a baseball season has a mistake. Which one?TACHS Student Handbook 2026, page 28: Written Expression. GPO Style Manual (2016), rule 8.8
One of these sentences about a basketball game has a mistake. Which one?TACHS Student Handbook 2026, page 28: Written Expression. Common Core standard L.3.1.f
One of these sentences about a camping trip has a mistake. Which one?TACHS Student Handbook 2026, page 28: Written Expression. GPO Style Manual (2016), rule 8.47
One of these sentences about a morning at the lake has a mistake. Which one?TACHS Student Handbook 2026, page 28: Written Expression. "go" read in Wiktionary. Common Core standard L.3.1.d
One of these sentences about a new rule has a mistake. Which one?TACHS Student Handbook 2026, page 28: Written Expression. "effect" read in Wiktionary. Common Core standard L.4.1.g
One of these sentences about a ride home has a mistake. Which one?TACHS Student Handbook 2026, page 28: Written Expression. Common Core standard L.4.1.g
One of these sentences about a school calendar has a mistake. Which one?TACHS Student Handbook 2026, page 28: Written Expression. GPO Style Manual (2016), rule 3.24
One of these sentences about a town library has a mistake. Which one?TACHS Student Handbook 2026, page 28: Written Expression. GPO Style Manual (2016), rule 8.53
One of these sentences about a town parade has a mistake. Which one?TACHS Student Handbook 2026, page 28: Written Expression. GPO Style Manual (2016), rule 3.36
One of these sentences about a trip to a museum has a mistake. Which one?TACHS Student Handbook 2026, page 28: Written Expression. GPO Style Manual (2016), rule 3.6
One of these sentences about a walk in the park has a mistake. Which one?TACHS Student Handbook 2026, page 28: Written Expression. Common Core standard L.3.1.g
One of these sentences about doing the laundry has a spelling mistake. Which one?TACHS Student Handbook 2026, page 28: Written Expression. "separate" read in Wiktionary. Common Core standard L.8.2.c
One of these sentences about holidays has a mistake. Which one?TACHS Student Handbook 2026, page 28: Written Expression. GPO Style Manual (2016), rule 3.25
One of these sentences about moving day has a mistake. Which one?TACHS Student Handbook 2026, page 28: Written Expression. Common Core standard L.6.1.a
One of these sentences about packing for a hike has a mistake. Which one?TACHS Student Handbook 2026, page 28: Written Expression. GPO Style Manual (2016), rule 8.46
One of these sentences about things that belong to someone has a mistake. Which one?TACHS Student Handbook 2026, page 28: Written Expression. GPO Style Manual (2016), rule 8.3
One of these sentences comparing things has a mistake. Which one?TACHS Student Handbook 2026, page 28: Written Expression. "than" read in Wiktionary. Common Core standard L.4.1.g
One of these sentences from a story has a mistake. Which one?TACHS Student Handbook 2026, page 28: Written Expression. GPO Style Manual (2016), rule 8.51
One of these sentences giving directions has a mistake. Which one?TACHS Student Handbook 2026, page 28: Written Expression. GPO Style Manual (2016), rule 3.23
One of these sentences spoken at soccer practice has a mistake. Which one?TACHS Student Handbook 2026, page 28: Written Expression. GPO Style Manual (2016), rule 8.48
Mathematics: number sense and operations 8
A choir has 21 altos, and they are 35% of the choir. How many singers are in the choir?TACHS Student Handbook 2026, page 28: Mathematics, number sense and operations. Common Core standard 6.RP.A.3. Answer recomputed
A diver is 23 feet below the surface of a lake. She rises 9 feet and then sinks 15 feet. Where is she now?TACHS Student Handbook 2026, page 28: Mathematics, number sense and operations. Common Core standard 7.NS.A.1. Answer recomputed
A lab report gives the width of a fiber as 0.000034 meter. Which shows that number in scientific notation?TACHS Student Handbook 2026, page 28: Mathematics, number sense and operations. Common Core standard 8.EE.A.4. Answer recomputed
A scooter is marked $85. A coupon takes 20% off, and then 8% sales tax is added to the lower price. What is the final cost?TACHS Student Handbook 2026, page 28: Mathematics, number sense and operations. Common Core standard 7.RP.A.3. Answer recomputed
A snack mix uses 2/3 cup of oats and 3/8 cup of raisins. How many cups is that in all?TACHS Student Handbook 2026, page 28: Mathematics, number sense and operations. Common Core standard 5.NF.A.1. Answer recomputed
What is the value of 7 + 36 ÷ (2 + 4) × 3 − 5?TACHS Student Handbook 2026, page 28: Mathematics, number sense and operations. Common Core standard 7.NS.A.3. Answer recomputed
Which list puts 0.45, 4/9, 47% and 3/7 in order from least to greatest?TACHS Student Handbook 2026, page 28: Mathematics, number sense and operations. Common Core standard 6.NS.C.7. Answer recomputed
Which whole number is closest to √130?TACHS Student Handbook 2026, page 28: Mathematics, number sense and operations. Common Core standard 8.NS.A.2. Answer recomputed
Mathematics: algebraic patterns and connections 8
A line passes through the points (−3, −4) and (5, 2). What is its slope?TACHS Student Handbook 2026, page 28: Mathematics, algebraic patterns and connections. Common Core standard 8.EE.B.6. Answer recomputed
A machine follows one rule. It turns 2 into 3, 5 into 9 and 6 into 11. What does it turn 10 into?TACHS Student Handbook 2026, page 28: Mathematics, algebraic patterns and connections. Common Core standard 8.F.A.1. Answer recomputed
A shop rents a bike for a $6.75 fee plus $4.50 for each hour. Luz paid $29.25. For how many hours did she rent the bike?TACHS Student Handbook 2026, page 28: Mathematics, algebraic patterns and connections. Common Core standard 7.EE.B.4. Answer recomputed
A stack of chairs is 31 inches tall with one chair, 35 inches with two and 39 inches with three. If the pattern goes on, how tall is a stack of 12 chairs?TACHS Student Handbook 2026, page 28: Mathematics, algebraic patterns and connections. Common Core standard 8.F.B.4. Answer recomputed
If 5x + 9 = 2x + 30, what is the value of x?TACHS Student Handbook 2026, page 28: Mathematics, algebraic patterns and connections. Common Core standard 8.EE.C.7. Answer recomputed
What is the value of 3n² − 2m when n = 4 and m = 7?TACHS Student Handbook 2026, page 28: Mathematics, algebraic patterns and connections. Common Core standard 6.EE.A.2. Answer recomputed
Which expression is equal to 5(2y − 1) − 3y?TACHS Student Handbook 2026, page 28: Mathematics, algebraic patterns and connections. Common Core standard 7.EE.A.1. Answer recomputed
Which values of n make 4n − 6 ≥ 18 true?TACHS Student Handbook 2026, page 28: Mathematics, algebraic patterns and connections. Common Core standard 7.EE.B.4. Answer recomputed
Mathematics: data analysis, probability, statistics 8
The 26 letters of the alphabet are written on cards, one letter on each. One card is drawn without looking. What is the probability that it shows A, E, I, O or U?TACHS Student Handbook 2026, page 28: Mathematics, data analysis, probability and statistics. Common Core standard 7.SP.C.7. Answer recomputed
A jar holds 6 lemon, 9 cherry and 10 mint candies. One candy is taken without looking. What is the probability that it is cherry?TACHS Student Handbook 2026, page 28: Mathematics, data analysis, probability and statistics. Common Core standard 7.SP.C.7. Answer recomputed
A lunch special is 1 of 3 sandwiches, 1 of 4 sides and 1 of 2 drinks. How many different lunches can be chosen?TACHS Student Handbook 2026, page 28: Mathematics, data analysis, probability and statistics. Common Core standard 7.SP.C.8. Answer recomputed
A shop sold 14, 9, 22, 9, 17 and 11 muffins on six days. What is the range of the daily sales?TACHS Student Handbook 2026, page 28: Mathematics, data analysis, probability and statistics. Common Core standard 6.SP.A.3. Answer recomputed
After four quizzes Rosa has a mean score of 82. What must she score on the fifth quiz to raise her mean to 84?TACHS Student Handbook 2026, page 28: Mathematics, data analysis, probability and statistics. Common Core standard 6.SP.B.5. Answer recomputed
Five friends counted the pages they read in one evening: 24, 31, 18, 40 and 27. What is the mean number of pages?TACHS Student Handbook 2026, page 28: Mathematics, data analysis, probability and statistics. Common Core standard 6.SP.A.3. Answer recomputed
Of the 240 students at a school, 45% take the subway. How many students take the subway?TACHS Student Handbook 2026, page 28: Mathematics, data analysis, probability and statistics. Common Core standard 6.RP.A.3. Answer recomputed
Six sunflowers are 52, 47, 60, 55, 49 and 58 inches tall. What is the median height?TACHS Student Handbook 2026, page 28: Mathematics, data analysis, probability and statistics. Common Core standard 6.SP.B.5. Answer recomputed
Mathematics: geometry 8
A garden bed is a triangle with a base of 13 feet and a height of 18 feet. What is its area?TACHS Student Handbook 2026, page 28: Mathematics, geometry. Common Core standard 6.G.A.1. Answer recomputed
A photo 4 inches wide and 6 inches tall is enlarged so that it is 10 inches wide and keeps its shape. How tall is the enlargement?TACHS Student Handbook 2026, page 28: Mathematics, geometry. Common Core standard 8.G.A.4. Answer recomputed
A planter box is 45 inches long, 8 inches wide and 14 inches deep. How much soil does it hold when it is full?TACHS Student Handbook 2026, page 28: Mathematics, geometry. Common Core standard 6.G.A.2. Answer recomputed
A rectangular gate is 20 inches wide and 21 inches tall. A brace runs from one corner to the opposite corner. How long is the brace?TACHS Student Handbook 2026, page 28: Mathematics, geometry. Common Core standard 8.G.B.7. Answer recomputed
A regular polygon has 15 equal sides and 15 equal interior angles. What is the measure of one interior angle?TACHS Student Handbook 2026, page 28: Mathematics, geometry. Common Core standard 8.G.A.5. Answer recomputed
A round table has a diameter of 6 feet. What is the area of its top in terms of π?TACHS Student Handbook 2026, page 28: Mathematics, geometry. Common Core standard 7.G.B.4. Answer recomputed
A triangle has two equal sides, and the angle between them measures 52°. What is the measure of each of the other two angles?TACHS Student Handbook 2026, page 28: Mathematics, geometry. Common Core standard 8.G.A.5. Answer recomputed
Triangle ABC has a corner at (−4, 5). The triangle is reflected across the y-axis. Where does that corner land?TACHS Student Handbook 2026, page 28: Mathematics, geometry. Common Core standard 8.G.A.3. Answer recomputed
Mathematics: measurement 8
A 15-ounce can of beans costs $1.20. What is the price per ounce?TACHS Student Handbook 2026, page 28: Mathematics, measurement. Common Core standard 6.RP.A.2. Answer recomputed
A baker has 4 kilograms of dough and shapes it into rolls of 125 grams each. How many rolls can be made?TACHS Student Handbook 2026, page 28: Mathematics, measurement. The kilogram: "SI Units: Mass", NIST. Common Core standard 5.MD.A.1. Answer recomputed
A ferry travels 54 miles in 2 hours 15 minutes at a steady speed. What is its speed?TACHS Student Handbook 2026, page 28: Mathematics, measurement. Common Core standard 6.RP.A.3. Answer recomputed
A play begins at 10:50 a.m. and runs for 2 hours 35 minutes. At what time does it end?TACHS Student Handbook 2026, page 28: Mathematics, measurement. Common Core standard 4.MD.A.2. Answer recomputed
A rectangular flag is 4.5 feet long and 2.5 feet wide. How much ribbon is needed to trim all four edges?TACHS Student Handbook 2026, page 28: Mathematics, measurement. Common Core standard 4.MD.A.3. Answer recomputed
A swimmer covers 1.65 kilometers in practice. How far is that in meters?TACHS Student Handbook 2026, page 28: Mathematics, measurement. The kilometer: "SI Units: Length", NIST. Common Core standard 5.MD.A.1. Answer recomputed
A wall 8 feet high and 14 feet long is painted, except for a window 3 feet by 4 feet. How many square feet are painted?TACHS Student Handbook 2026, page 28: Mathematics, measurement. Common Core standard 7.G.B.6. Answer recomputed
On a plan of a park, 1 centimeter stands for 4 meters. A fence is 6.5 centimeters long on the plan. How long is the real fence?TACHS Student Handbook 2026, page 28: Mathematics, measurement. Common Core standard 7.G.A.1. Answer recomputed
Unofficial TACHS prep: 120 questions written for this site in the Reading, Written Expression and Mathematics parts the 2026 Student Handbook describes. Not affiliated with or endorsed by the Archdiocese of New York, the Diocese of Brooklyn, the Diocese of Rockville Centre or Riverside Insights.
Read the full guide
Three of the four parts are here
Reading, Written Expression and Mathematics have 40 questions each. The fourth part, Ability, is picture puzzles (figure matrices, paper folding, figure classification) and is not practiced here: this page has no figures yet. The handbook's own samples show them.
A paper test to print
For a TACHS practice test PDF, print the question sheet and choose "Save as PDF" in the print window. The first sheet has 20 questions from all three parts; the answer key is optional.
Where the questions come from
Each was written for this page from the handbook's description of its part. None comes from a real TACHS or from the handbook's sample questions. Every mathematics answer was worked out twice, and each usage answer links to the rule it follows.
Questions and answers
What is on the TACHS test?
Reading, Written Expression, Mathematics and Ability. The handbook says Mathematics draws on number sense and operations, algebraic patterns and connections, data analysis, probability and statistics, geometry and measurement, and that Ability uses spatial and figural questions.
How long is the TACHS test?
About 2 hours 10 minutes with directions, in six timed subtests, says the TACHS site. Short optional breaks come after the first three. The one accommodation offered is extended time, time and a half.
Is there an official TACHS practice test?
No. The TACHS site says official practice tests are not published and points to the sample questions in its Student Handbook. It adds that other practice tests can differ from the real exam in length, timing and format, and that is true of this one.
Can you use a calculator on the TACHS?
Yes, since 2026: a basic 4-function calculator is built into the testing platform for the questions that allow it. Personal calculators are not allowed, and the site says a student found using one is disqualified.
How is the TACHS scored?
The handbook reports local and national percentile ranks, sent to the three high schools a student chooses, and says wrong answers are not penalized. It names no pass mark. A score on this page cannot be turned into a percentile.