MCVSD Extra Drills — Week 1 (Sessions 1–5)

How to use: these are supplements, not homework for its own sake. After each session’s main problem set, assign the matching drill only if accuracy was under ~80%, or use them later in the summer as refreshers. Each drill: 10 questions, 20 minutes, no calculator.

DRILL 1 — Integers, Order of Operations, Fractions (pairs with Session 1)

1. −7 + (−5) = A) −12 B) −2 C) 2 D) 12 2. −3 − 8 + 10 = A) −21 B) −1 C) 1 D) 15 3. (−4)² − 4² = A) −32 B) 0 C) 32 D) −8 4. 36 ÷ (−4) × (−2) = A) −18 B) 18 C) −4.5 D) 4.5 5. 10 − 2 × 3² = A) 72 B) −8 C) 24 D) 4 6. 7/10 − 2/5 = A) 5/5 B) 3/10 C) 1/2 D) 5/10 7. 1 1/2 × 2 2/3 = A) 4 B) 2 2/6 C) 3 1/3 D) 2 5/6 8. 5/6 ÷ 10 = A) 50/6 B) 1/12 C) 12 D) 25/3 9. Which number is between 3/8 and 1/2? A) 0.36 B) 0.42 C) 0.52 D) 5/16 10. A diver at −30 feet ascends 12 feet, then descends 7 feet. Final depth? A) −49 ft B) −25 ft C) −11 ft D) −35 ft

Answers
  1. A — Two negatives combine: −12.
  2. B — −3 − 8 = −11; −11 + 10 = −1.
  3. B — (−4)² = 16 and 4² = 16, so 16 − 16 = 0. The parentheses make the first one positive.
  4. B — Left to right: 36 ÷ (−4) = −9; (−9)(−2) = 18.
  5. B — Exponent first: 3² = 9; 2 × 9 = 18; 10 − 18 = −8.
  6. B — 7/10 − 4/10 = 3/10.
  7. A — 3/2 × 8/3 = 24/6 = 4.
  8. B — 5/6 × 1/10 = 5/60 = 1/12.
  9. B — 3/8 = 0.375 and 1/2 = 0.5; only 0.42 fits between.
  10. B — −30 + 12 − 7 = −25 ft.

DRILL 2 — Ratios, Rates & Percents (pairs with Session 2)

1. A car uses 8 gallons to travel 216 miles. Miles per gallon? A) 25 B) 26 C) 27 D) 28 2. Solve: 3/x = 12/28 A) 6 B) 7 C) 8 D) 9 3. Paint is mixed with blue and white in a 5:2 ratio. In 35 quarts of the mixture, how many quarts are blue? A) 10 B) 20 C) 25 D) 30 4. 40% of 85 = A) 32 B) 34 C) 36 D) 44 5. 18 is what percent of 40? A) 40% B) 42% C) 45% D) 50% 6. A $64 item is marked up 25%. New price? A) $80 B) $89 C) $76 D) $96 7. 120 decreased by 35% is A) 42 B) 78 C) 85 D) 95 8. A $32 purchase has 6% sales tax added. Total? A) $33.92 B) $34.12 C) $33.20 D) $38.00 9. Simple interest on $750 at 4% per year for 2 years? A) $30 B) $54 C) $60 D) $600 10. A map uses 1.5 inches = 60 miles. How many miles is 2.75 inches? A) 100 B) 105 C) 110 D) 120

Answers
  1. C — 216 ÷ 8 = 27.
  2. B — 12x = 84 → x = 7. (Or: 12/28 = 3/7.)
  3. C — 7 parts total; 35 ÷ 7 = 5; blue = 5 × 5 = 25.
  4. B — 0.40 × 85 = 34.
  5. C — 18/40 = 0.45 = 45%.
  6. A — 64 × 1.25 = 80.
  7. B — 120 × 0.65 = 78.
  8. A — 32 × 1.06 = 33.92.
  9. C — 750 × 0.04 × 2 = 60.
  10. C — Scale: 60 ÷ 1.5 = 40 miles per inch; 2.75 × 40 = 110.

DRILL 3 — Reading Comprehension (pairs with Session 3)

Read the passage, then answer questions 1–7.

Messengers on Wings

(1) Before radios were reliable on the battlefield, armies of the First World War trusted some of their most urgent messages to pigeons. (2) A homing pigeon, released far from its loft, will fly home across unfamiliar country with astonishing accuracy — a skill scientists still do not fully understand, though it seems to involve the sun, landmarks, and possibly Earth’s magnetic field. (3) Soldiers carried the birds to the front lines in wicker baskets; when telephone wires were cut by shellfire, a message was rolled into a small canister, clipped to a pigeon’s leg, and the bird was tossed into the sky.

(4) The work was dangerous for the messengers. (5) Pigeons flew through smoke, storms, and gunfire aimed specifically at them, because both sides knew what a gray blur heading home might carry. (6) Some birds completed dozens of missions; a few became famous, credited with delivering messages that guided rescues of trapped soldiers. (7) Armies valued the birds enough to punish anyone who harmed one.

(8) Radio eventually made the pigeon post obsolete, but the birds left a mark on military history out of all proportion to their size. (9) In an age of satellites, it is worth remembering that one of war’s most reliable communication systems weighed less than a pound and asked for nothing but the way home.

1. The main idea of the passage is that A) pigeons were unreliable compared to telephones B) homing pigeons served as vital battlefield messengers before radio matured C) scientists have fully explained pigeon navigation D) satellites were invented during the First World War

2. According to sentence 2, pigeon navigation A) is completely understood by scientists B) depends only on the sun C) is not yet fully explained D) fails in unfamiliar country

3. Pigeons were used when telephone wires were cut because A) radios were unreliable at the time B) soldiers preferred birds to machines C) pigeons could repair the wires D) baskets were cheaper than telephones

4. As used in sentence 8, obsolete most nearly means A) more popular B) no longer used C) extremely fast D) expensive

5. Sentence 5 suggests that enemy soldiers shot at pigeons because A) the birds damaged equipment B) they knew the birds might carry important messages C) the birds attacked soldiers D) target practice was required

6. Which sentence best supports the idea that armies took the pigeons’ role seriously? A) Sentence 1 B) Sentence 3 C) Sentence 7 D) Sentence 9

7. The final sentence’s tone is best described as A) bitter B) admiring C) mocking D) fearful

Vocabulary in Context — Questions 8–10

8. “The instructions were so ambiguous that half the class did the wrong assignment.” Ambiguous most nearly means A) unclear B) strict C) simple D) brief

9. “The lifeguard remained vigilant even when the beach was nearly empty.” Vigilant most nearly means A) relaxed B) watchful C) invisible D) cheerful

10. “Rather than hinder the project, the rain delay gave the team time to improve the design.” Hinder most nearly means A) assist B) complete C) hold back D) fund

Answers
  1. B — The passage’s arc: why pigeons were used, their dangerous service, their place in history.
  2. C — “A skill scientists still do not fully understand.”
  3. A — Sentence 1 establishes radios were unreliable; wires cut → pigeons carried the message.
  4. B — Radio replaced the pigeon post; obsolete = out of use.
  5. B — “Both sides knew what a gray blur heading home might carry.”
  6. C — Punishing anyone who harmed a bird shows how seriously armies valued them.
  7. B — “Reliable,” “asked for nothing but the way home” — admiration.
  8. A — Confusion resulted, so unclear.
  9. B — A lifeguard staying alert = watchful.
  10. C — Contrast with giving the team helpful time; hinder = hold back.

DRILL 4 — Expressions & Equations (pairs with Session 4)

1. Simplify: 9x − 4x + 6 − 10 A) 5x + 4 B) 5x − 4 C) 13x − 4 D) 5x − 16 2. Simplify: −2(3x − 5) A) −6x − 10 B) −6x + 10 C) 6x − 10 D) −6x + 5 3. Evaluate 3a − 2b when a = 4 and b = −3. A) 6 B) 18 C) −18 D) 12 4. Solve: x + 14 = 6 A) 20 B) 8 C) −8 D) −20 5. Solve: −6x = 42 A) 7 B) −7 C) 36 D) −36 6. Solve: x/4 + 3 = 10 A) 28 B) 52 C) 7/4 D) 13 7. Solve: 5x − 2 = 3x + 12 A) 5 B) 7 C) 10 D) 14 8. Solve: 8 − 2x = 20 A) 6 B) −6 C) 14 D) −14 9. “Three times the sum of a number and 4 is 27.” The number is A) 5 B) 7 2/3 C) 23/3 D) 13 10. Solve: 4 − x > 1 A) x > 3 B) x < 3 C) x > −3 D) x < −3

Answers
  1. B — 5x − 4.
  2. B — Distribute −2 to both terms: −6x + 10.
  3. B — 12 − 2(−3) = 12 + 6 = 18.
  4. C — x = 6 − 14 = −8.
  5. B — 42 ÷ (−6) = −7.
  6. A — x/4 = 7 → x = 28.
  7. B — 2x = 14 → x = 7.
  8. B — −2x = 12 → x = −6.
  9. A — 3(n + 4) = 27 → n + 4 = 9 → n = 5. “The sum” needs the parentheses.
  10. B — −x > −3; divide by −1 and flip: x < 3.

DRILL 5 — Grammar & Usage (pairs with Session 5)

1. “The list of supplies __ posted on the door.” A) were B) are C) is D) have been 2. “He __ know the combination to the equipment locker.” A) don’t B) doesn’t C) aren’t D) isn’t 3. Choose the correct pronoun: “This conversation stays between you and __.” A) I B) me C) myself D) mine 4. Choose the correct word: “__ jacket was left in the gym?” A) Who’s B) Whose C) Whos D) Whom’s 5. Which is a fragment? A) The gate opened at noon. B) While we waited in the shade near the gate. C) We waited near the gate. D) At noon, the gate opened. 6. Which correctly joins these? “The trail was muddy” + “we wore boots.” A) The trail was muddy, we wore boots. B) The trail was muddy so, we wore boots. C) The trail was muddy, so we wore boots. D) The trail was muddy we wore boots. 7. Which sentence is punctuated correctly? A) We packed sandwiches apples, and water. B) We packed sandwiches, apples, and water. C) We packed, sandwiches, apples and water. D) We packed sandwiches, apples and, water. 8. Which sentence uses consistent tense? A) The whistle blew, and the swimmers dive in. B) The whistle blows, and the swimmers dove in. C) The whistle blew, and the swimmers dove in. D) The whistle will blow, and the swimmers dove in. 9. Choose the correct word: “She performed __ on the placement test.” A) good B) well C) more good D) goodly 10. Choose the correct word: “There are __ seats available than last year.” A) less B) fewer C) lesser D) few

Answers
  1. C — Subject is “list” (singular), not “supplies.”
  2. B — Singular subject “he” takes doesn’t.
  3. B — Object of the preposition “between”: you and me.
  4. B — Whose = possessive; who’s = who is.
  5. B — A dependent clause (“While…”) with no main clause.
  6. C — Comma + coordinating conjunction. (A is a comma splice.)
  7. B — Commas between all items in a series.
  8. C — Both verbs past tense.
  9. B — “Well” is the adverb describing how she performed.
  10. B — Seats are countable → fewer. (Less is for uncountable amounts.)