MCVSD-Style Diagnostic Test

Format matches the real exam: two multiple-choice sections. Time each strictly.

Scoring guide (out of 25 per section): 22+ = strong; 18–21 = solid, targeted review needed; 14–17 = foundational gaps to address; below 14 = start with fundamentals in that subject. Log the topic of every miss — that list drives the 10-session plan.

SECTION 1 — MATHEMATICS (50 minutes)

1. −8 + 15 − (−4) = A) 3 B) 11 C) 19 D) −27

2. 3 + 6 × (5 − 3)² ÷ 4 = A) 9 B) 12 C) 4.5 D) 21

3. 2/3 + 3/4 = A) 5/7 B) 5/12 C) 1 5/12 D) 1 1/2

4. 2 1/2 ÷ 5/8 = A) 1 9/16 B) 4 C) 25/16 D) 3 1/8

5. Which value is greatest? A) 0.45 B) 4/9 C) 44% D) 0.4449

6. |−7| − |3 − 9| = A) −13 B) 1 C) 13 D) −1

7. A car travels 342 miles on 9.5 gallons of gas. What is its mileage in miles per gallon? A) 34 B) 35 C) 36 D) 38

8. Solve for x: 5/8 = x/56 A) 30 B) 35 C) 40 D) 45

9. A $48 jacket is discounted 30%. What is the sale price? A) $14.40 B) $33.60 C) $34.60 D) $36.00

10. A team’s wins increased from 60 to 75. What was the percent increase? A) 15% B) 20% C) 25% D) 30%

11. How much simple interest does $500 earn at 4% per year for 3 years? A) $20 B) $40 C) $60 D) $80

12. Simplify: 3(2x − 5) + 4x A) 10x − 5 B) 6x − 15 C) 10x − 15 D) 6x + 4x − 5

13. Solve: 4x − 7 = 21 A) 3.5 B) 5 C) 7 D) 28

14. Solve: x/3 + 5 = 11 A) 2 B) 18 C) 48 D) 6

15. “Five less than twice a number is 19.” What is the number? A) 7 B) 12 C) 24 D) 43

16. Solve the inequality: −3x > 12 A) x > −4 B) x < −4 C) x > 4 D) x < 4

17. What is the slope of the line through (2, 3) and (6, 11)? A) 1/2 B) 2 C) 4 D) 8

18. Which point lies on the line y = −2x + 7? A) (3, 1) B) (1, 4) C) (2, −3) D) (0, −7)

19. Which table shows a proportional relationship between x and y? A) x: 1, 2, 3 → y: 3, 5, 7 B) x: 2, 4, 6 → y: 5, 10, 15 C) x: 1, 2, 3 → y: 2, 4, 7 D) x: 2, 3, 4 → y: 6, 8, 10

20. A triangle has base 10 cm and height 7 cm. What is its area? A) 17 cm² B) 35 cm² C) 70 cm² D) 34 cm²

21. A bag holds 4 red, 3 blue, and 5 green marbles. What is the probability of drawing a blue marble? A) 1/3 B) 1/4 C) 3/9 D) 1/12

22. Two parallel lines are cut by a transversal. One angle measures 65°. What is the measure of the co-interior (same-side interior) angle paired with it? A) 25° B) 65° C) 115° D) 125°

23. What is the volume of a cylinder with radius 3 in and height 10 in? (Use π ≈ 3.14) A) 94.2 in³ B) 188.4 in³ C) 282.6 in³ D) 314 in³

24. A right triangle has legs of 9 and 12. What is the length of the hypotenuse? A) 13 B) 15 C) 21 D) 225

25. The mean of five numbers is 14. Four of the numbers are 10, 12, 15, and 18. What is the fifth number? A) 13 B) 14 C) 15 D) 16

SECTION 2 — LANGUAGE ARTS (50 minutes)

Passage A — Read the passage, then answer questions 1–8.

Living Light

(1) On a summer night, the wake of a boat can glow an eerie blue-green, as if the ocean itself were electrified. (2) The source is not electricity but bioluminescence — light produced by living organisms through a chemical reaction. (3) When a molecule called luciferin combines with oxygen, aided by an enzyme, energy is released in the form of light rather than heat. (4) Scientists sometimes call it “cold light” because almost none of the energy is wasted as warmth, making it far more efficient than an ordinary light bulb.

(5) Bioluminescence is surprisingly common in the ocean. (6) Researchers estimate that in the deep sea, where sunlight never penetrates, a majority of animals can produce their own light. (7) They use it for strikingly different purposes. (8) The anglerfish dangles a glowing lure to attract prey in the darkness. (9) Certain squid release luminous clouds to confuse predators, much as other squid release ink. (10) Some small crustaceans flash patterns of light to signal potential mates. (11) For creatures of the deep, light is not decoration; it is a language, a weapon, and a disguise.

(12) The phenomenon has practical value for humans as well. (13) Doctors have borrowed light-producing genes from jellyfish to “tag” cells, allowing them to watch diseases spread — and treatments work — inside living tissue. (14) Engineers are even studying bioluminescent chemistry in hopes of designing lighting that wastes less energy. (15) The glow that startles a swimmer at midnight may one day help illuminate a laboratory breakthrough, or a city street.

1. Which sentence best states the main idea of the passage? A) Bioluminescence is a rare ability found only in deep-sea fish. B) Bioluminescence is a chemical form of light with many natural uses and growing human applications. C) The anglerfish is the most efficient light-producing animal in the ocean. D) Scientists have finally explained why the ocean glows at night.

2. According to the passage, bioluminescence is called “cold light” because A) it only occurs in cold, deep water B) the reaction requires low temperatures C) very little of the energy is released as heat D) the light appears blue-green in color

3. Based on sentences 8–10, the author organizes that portion of the passage by A) presenting a series of examples B) comparing an argument with a counterargument C) describing events in chronological order D) stating a problem and offering a solution

4. As used in sentence 6, the word penetrates most nearly means A) attacks B) reaches C) reflects D) warms

5. Which statement can best be inferred from sentence 11? A) Deep-sea animals depend heavily on light for survival tasks. B) Deep-sea animals decorate themselves to attract mates. C) All deep-sea animals use light the same way. D) Light is less important in the deep sea than sound.

6. Which sentence provides the best evidence that bioluminescence benefits medicine? A) Sentence 4 B) Sentence 9 C) Sentence 13 D) Sentence 15

7. The author’s primary purpose in this passage is to A) persuade readers to protect deep-sea habitats B) inform readers about a natural phenomenon and its uses C) entertain readers with a story about a night swim D) argue that bioluminescent lighting should replace light bulbs

8. The phrase “a language, a weapon, and a disguise” (sentence 11) refers to light’s use for A) signaling, hunting, and escaping predators B) heating, cooling, and camouflage C) navigation, migration, and rest D) medicine, engineering, and research

Paired Passages — Read both passages, then answer questions 9–15.

Passage 1

Our town should approve the proposed offshore wind farm. The turbines would generate clean electricity for thousands of homes, reducing the pollution that contributes to climate change — the greatest long-term threat to coastal communities like ours. Construction would bring hundreds of jobs, and studies of existing wind farms show that turbine foundations can act like artificial reefs, attracting fish and shellfish. Critics worry about the view, but the turbines would sit more than ten miles from shore, appearing smaller than a thumbnail on the horizon. We cannot claim to love our coastline while rejecting the very projects designed to protect it.

Passage 2

Enthusiasm for the offshore wind proposal is understandable, but the town should demand better answers before approving it. Fishing families worry that construction noise and buried cables will disrupt the grounds their livelihoods depend on, and researchers acknowledge that long-term effects on migrating whales remain uncertain. Tourism, our largest industry, depends on an unspoiled horizon; even distant turbines are visible on clear days. Clean energy is a worthy goal, but a project this large deserves careful, independent study — not a rushed vote. Protecting the coast means asking hard questions, even about projects wearing a green label.

9. The author of Passage 1 primarily supports the wind farm because it would A) lower electric bills for residents B) reduce pollution and protect coastal communities long-term C) eliminate the need for fishing regulations D) make the horizon more attractive

10. The author of Passage 2 would most likely respond to the “artificial reef” claim in Passage 1 by A) agreeing that fish populations would certainly increase B) noting that long-term effects on marine life remain uncertain C) arguing that reefs are bad for tourism D) claiming turbines cannot function underwater

11. On which point do both authors agree? A) The turbines would be invisible from shore. B) The town should vote immediately. C) Protecting the coastline is important. D) Tourism matters more than fishing.

12. Passage 1 addresses the concern about the view mainly by A) denying that anyone cares about the horizon B) stating the turbines would appear very small from shore C) promising the turbines would be removed after ten years D) comparing turbines to lighthouses

13. Which best describes the tone of Passage 2? A) mocking and dismissive B) cautious and questioning C) enthusiastic and celebratory D) indifferent and detached

14. As used in Passage 2, “wearing a green label” most nearly suggests projects that A) are painted to blend with the sea B) are marketed as environmentally friendly C) have passed independent studies D) are funded by the town

15. The two passages differ mainly in A) whether climate change exists B) whether clean energy is a worthy goal C) whether the project should be approved now or studied further D) whether the town has a coastline

Grammar, Usage, and Vocabulary — Questions 16–25

16. Choose the correct verb: “Each of the students __ required to attend the information session.” A) are B) is C) were D) have been

17. Which sentence is punctuated correctly? A) After the storm passed, the crew inspected the dock. B) After the storm passed the crew inspected the dock. C) After the storm, passed the crew inspected the dock. D) After the storm passed the crew, inspected the dock.

18. Identify the sentence fragment. A) The tide rose quickly. B) Because the tide rose quickly. C) The tide rose, and the boats lifted. D) Quickly, the tide rose.

19. Choose the correct pronoun: “The coach handed the trophy to Maya and __.” A) I B) me C) myself D) we

20. Which revision best fixes this run-on? “The ferry was late we missed the ceremony.” A) The ferry was late, we missed the ceremony. B) The ferry was late; we missed the ceremony. C) The ferry was late we missed, the ceremony. D) The ferry, was late, we missed the ceremony.

21. Choose the correct word: “The museum changed __ hours for the summer.” A) it’s B) its C) their D) they’re

22. Which sentence maintains consistent verb tense? A) She grabbed her gear and runs to the dock. B) She grabs her gear and ran to the dock. C) She grabbed her gear and ran to the dock. D) She will grab her gear and ran to the dock.

23. “The scientist’s explanation was so lucid that even beginners understood it.” Lucid most nearly means A) lengthy B) clear C) loud D) complicated

24. “Rather than accept the first offer, the manager chose to negotiate for better terms.” Negotiate most nearly means A) refuse entirely B) discuss to reach agreement C) complain formally D) wait patiently

25. “Volunteers worked diligently through the afternoon, refusing to quit until every trail was cleared.” Diligently most nearly means A) carelessly B) occasionally C) with steady effort D) with great noise

Answer Key & Explanations

Mathematics

  1. B — −8 + 15 = 7; subtracting −4 means adding 4: 7 + 4 = 11.
  2. A — Parentheses first (5−3=2), exponent (2²=4), then 6×4÷10 left to right: 6×4=24, 24÷4=6; finally 3+6=9.
  3. C — Common denominator 12: 8/12 + 9/12 = 17/12 = 1 5/12.
  4. B — Dividing by a fraction = multiplying by its reciprocal: 5/2 × 8/5 = 40/10 = 4.
  5. A — Convert all to decimals: 0.45 vs 4/9 ≈ 0.444 vs 0.44 vs 0.4449. Greatest is 0.45.
  6. B — −7 = 7; 3−9 = −6 = 6; 7 − 6 = 1.
  7. C — 342 ÷ 9.5 = 36 mpg.
  8. B — Cross-multiply: 8x = 280, x = 35. (Or notice 56 = 8×7, so x = 5×7.)
  9. B — 30% of 48 = 14.40; 48 − 14.40 = $33.60. (Shortcut: 70% of 48.)
  10. C — Change ÷ original: 15/60 = 0.25 = 25%.
  11. C — I = prt = 500 × 0.04 × 3 = $60.
  12. C — Distribute: 6x − 15; add 4x: 10x − 15.
  13. C — Add 7: 4x = 28; divide: x = 7.
  14. B — Subtract 5: x/3 = 6; multiply by 3: x = 18.
  15. B — 2n − 5 = 19 → 2n = 24 → n = 12. (“Five less than twice” means subtract 5 FROM 2n.)
  16. B — Dividing an inequality by a negative flips the sign: x < −4.
  17. B — (11−3)/(6−2) = 8/4 = 2.
  18. A — Test each: −2(3)+7 = 1. ✓
  19. B — Proportional means y/x is constant: 5/2 = 10/4 = 15/6 = 2.5. ✓
  20. B — A = ½bh = ½(10)(7) = 35 cm².
  21. B — 3 blue out of 12 total = 3/12 = 1/4.
  22. C — Same-side interior angles are supplementary: 180 − 65 = 115°.
  23. C — V = πr²h = 3.14 × 9 × 10 = 282.6 in³.
  24. B — √(9² + 12²) = √(81+144) = √225 = 15. (A 3-4-5 triple scaled by 3.)
  25. C — Total must be 5 × 14 = 70. Given numbers sum to 55, so 70 − 55 = 15.

Language Arts

  1. B — The passage covers the chemistry, the animal uses, AND human applications; B captures all three. A, C, D are too narrow or unsupported.
  2. C — Sentence 4 says almost none of the energy is wasted as warmth.
  3. A — Anglerfish, squid, crustaceans: a list of examples of different uses.
  4. B — Sunlight never “reaches” the deep sea.
  5. A — Calling light “a language, a weapon, and a disguise” implies it’s essential for survival tasks, not decoration.
  6. C — Sentence 13 describes doctors tagging cells to track disease.
  7. B — Informational tone throughout; no call to action (rules out A and D).
  8. A — Language = signaling mates; weapon = luring prey; disguise = confusing predators.
  9. B — Passage 1 names climate change as the coast’s greatest threat and clean energy as protection.
  10. B — Passage 2’s core stance is that marine-life effects are uncertain and need study.
  11. C — Both frame their argument around protecting the coast; they disagree on how.
  12. B — “Smaller than a thumbnail on the horizon.”
  13. B — Passage 2 asks for study and “hard questions” — cautious, not mocking or enthusiastic.
  14. B — A “green label” is marketing language for environmental friendliness; the author warns labels aren’t proof.
  15. C — Both accept clean energy as a goal (eliminates B); the disagreement is approve now vs. study first.
  16. B — “Each” is singular: each… is.
  17. A — Comma after an introductory dependent clause.
  18. B — “Because the tide rose quickly” is a dependent clause with no main clause.
  19. B — Object of the preposition “to”: handed to Maya and me.
  20. B — A semicolon can join two complete sentences. A is a comma splice.
  21. B — Possessive “its” (no apostrophe); museum is singular, ruling out C/D.
  22. C — Both verbs past tense.
  23. B — Beginners understood it → clear.
  24. B — Negotiating means discussing to reach agreement on terms.
  25. C — Refusing to quit signals steady, persistent effort.

Turning the score into a plan

For each wrong answer, write down the session it maps to (Sessions 1–2: arithmetic/ratios · Session 4: equations · Session 6: linear · Session 8: geometry · Session 9: data/probability · Sessions 3/7: reading · Sessions 5/10: grammar/editing). Weak sessions get extra drill time; strong sessions can be compressed.