MCVSD Summer Seminar — Week 1 (Sessions 1–5)

Daily format (mirrors the bootcamp structure):

• Tutorial & worked examples — ~45 min (read together, work the examples on paper)
• Timed Problem Set — 12 questions, 30 minutes, no calculator
• Review answer key together — ~15 min. Log every miss in the error notebook.

SESSION 1 — Integers, Order of Operations, Fractions & Decimals

Tutorial

Integers. Subtracting a negative = adding: 7 − (−3) = 10. Same signs multiply/divide to positive, opposite signs to negative: (−6)(−4) = 24, but (−6)(4) = −24.

Order of operations (PEMDAS). Parentheses → Exponents → Multiply/Divide left to right → Add/Subtract left to right. The #1 careless error: doing addition before a division that comes first left-to-right.

Fractions. Add/subtract: common denominator. Multiply: straight across (simplify first when possible). Divide: keep–change–flip (multiply by the reciprocal). Mixed numbers: convert to improper fractions before multiplying or dividing.

Worked Example 1: 4 + 3 × (7 − 5)³ ÷ 6 Parentheses: 2. Exponent: 8. Then left to right: 3 × 8 = 24, 24 ÷ 6 = 4. Finally 4 + 4 = 8.

Worked Example 2: 3 1/3 ÷ 5/6 Convert: 10/3. Keep–change–flip: 10/3 × 6/5 = 60/15 = 4.

Worked Example 3: −9 + 4 − (−7) = −5 + 7 = 2.

Timed Problem Set 1 (12 questions, 30 minutes)

1. −12 + 7 = A) −19 B) −5 C) 5 D) 19 2. −4 − (−9) = A) −13 B) −5 C) 5 D) 13 3. (−6)(−3) − 8 = A) −26 B) 10 C) −10 D) 26 4. 48 ÷ (−8) + (−3)² = A) 3 B) −15 C) 15 D) −3 5. 5 + 2 × (9 − 4)² ÷ 10 = A) 7.5 B) 10 C) 17.5 D) 55 6. 3/5 + 1/4 = A) 4/9 B) 4/20 C) 17/20 D) 13/20 7. 4 2/3 − 1 5/6 = A) 2 5/6 B) 3 1/6 C) 2 1/2 D) 3 1/2 8. 3/8 × 2/9 = A) 5/17 B) 1/12 C) 6/17 D) 27/16 9. 1 3/4 ÷ 7/8 = A) 1 1/2 B) 2 C) 49/32 D) 1 17/32 10. Order from least to greatest: −1.5, −1 2/3, −1.06, −7/5 A) −1 2/3, −1.5, −7/5, −1.06 B) −1.06, −7/5, −1.5, −1 2/3 C) −1.5, −1 2/3, −1.06, −7/5 D) −1 2/3, −7/5, −1.5, −1.06 11. |−15| + |4| − |−6| = A) 5 B) 13 C) 25 D) 17 12. At dawn the temperature was −8°F. It rose 15° by noon, then fell 4° by dusk. Dusk temperature? A) 3°F B) 11°F C) −27°F D) 7°F

SESSION 2 — Ratios, Rates, Proportions & Percents

Tutorial

Unit rate = amount per ONE unit: divide. 270 miles in 4.5 hours → 270 ÷ 4.5 = 60 mph.

Proportions. Set up matching units in matching positions, cross-multiply: a/b = c/d → ad = bc.

Percent of a number: convert to decimal and multiply. 30% of 48 = 0.30 × 48. Percent change = change ÷ original. (Original is always the “before” number — the most-tested trap.) Discount then tax: multiply step by step. 20% off = ×0.80; then 7% tax = ×1.07. Never add/subtract percents of different bases. Simple interest: I = p × r × t (principal × rate as decimal × time in years).

Worked Example 1: A map scale is 1 inch = 40 miles. Two towns are 3.25 inches apart. Distance = 3.25 × 40 = 130 miles.

Worked Example 2: A $60 item increases to $75. Percent change = 15/60 = 0.25 = 25% increase.

Worked Example 3: Ratio of cats to dogs at a shelter is 5:3, with 64 animals total. 5+3 = 8 parts; 64 ÷ 8 = 8 per part; cats = 5 × 8 = 40.

Timed Problem Set 2 (12 questions, 30 minutes)

1. A train covers 270 miles in 4.5 hours. Average speed? A) 54 mph B) 60 mph C) 62 mph D) 66 mph 2. A recipe uses 2 cups flour for every 3/4 cup sugar. How much sugar for 5 cups flour? A) 1 1/2 cups B) 1 7/8 cups C) 2 cups D) 1 3/4 cups 3. Solve: 7/12 = 21/x A) 30 B) 32 C) 36 D) 42 4. Scale: 1 in = 25 mi. A 4.5-inch map distance is how many real miles? A) 100 B) 112.5 C) 125 D) 90 5. A 15% tip on a $62 bill is how much? A) $8.30 B) $9.30 C) $9.60 D) $10.30 6. An $85 item is discounted 20%, then 7% sales tax is added. Final price? A) $68.00 B) $72.76 C) $73.95 D) $74.80 7. Attendance dropped from 84 to 63. Percent decrease? A) 21% B) 25% C) 33% D) 75% 8. 36 is 45% of what number? A) 16.2 B) 72 C) 80 D) 81 9. Simple interest on $1,200 at 3.5% per year for 2 years? A) $42 B) $84 C) $420 D) $8.40 10. The ratio of boys to girls in a club is 3:4. If there are 28 members, how many are boys? A) 7 B) 12 C) 16 D) 21 11. Which is the better buy? Brand X: 12 oz for $2.88. Brand Y: 20 oz for $4.60. A) X at $0.23/oz B) X at $0.24/oz C) Y at $0.23/oz D) Y at $0.24/oz 12. A store buys an item for $50, marks it up 40%, then puts it on sale for 10% off the marked price. Sale price? A) $63 B) $65 C) $67.50 D) $70

SESSION 3 — Reading Comprehension I: Main Idea, Inference, Evidence, Vocabulary in Context

Tutorial

Main idea = the umbrella every paragraph fits under. Wrong answers are usually too narrow (true, but only one paragraph) or too broad.

Inference = what MUST be true from the text, not what MIGHT be. If you can’t point to the sentence(s) that force the conclusion, it’s the wrong answer.

Evidence questions (“Which sentence best supports…”): answer the paired question first, then find the sentence that proves YOUR answer.

Vocabulary in context: cover the word, read the sentence, predict your own word, then match. Test each choice by substitution — the test loves words with a common meaning and a less common one, and it wants the one that fits this sentence.

Strategy for the set below: preview the question stems (10 seconds), read the passage actively (underline the point of each paragraph), then answer. Budget ~2 minutes per question.

Timed Problem Set 3 (12 questions, 30 minutes)

Read the passage, then answer questions 1–8.

The Comeback of the Osprey

(1) Fifty years ago, spotting an osprey along the Atlantic coast was a rare event. (2) The fish-hunting raptor, once common from Maine to Florida, had nearly vanished from many states. (3) The culprit was a pesticide called DDT, which washed into waterways, accumulated in fish, and concentrated in the birds that ate them. (4) DDT did not usually kill adult ospreys outright; instead, it thinned their eggshells so severely that eggs cracked under the weight of nesting parents. (5) By 1970, some coastal regions had lost ninety percent of their breeding pairs.

(6) The osprey’s recovery required two very different kinds of effort. (7) The first was legal: the United States banned most uses of DDT in 1972, allowing the chemical to slowly fade from rivers and bays. (8) The second was practical, and surprisingly humble. (9) Volunteers and biologists erected hundreds of nesting platforms — simple wooden frames on poles — in marshes where dead trees had disappeared. (10) Ospreys, unusually tolerant of human activity, adopted the platforms readily, sometimes building nests within sight of busy highways.

(11) Today the osprey is once again a familiar summer silhouette, hovering over tidal creeks before plunging feet-first for fish. (12) Scientists now monitor osprey populations for another reason: because the birds sit at the top of an aquatic food chain, their health reflects the health of the waters below them. (13) The species that once warned us about DDT has become a living instrument for measuring the recovery of our coasts.

1. Which statement best expresses the main idea of the passage? A) DDT was the most destructive pesticide of the twentieth century. B) The osprey recovered thanks to a legal ban and hands-on human help, and now serves as an environmental indicator. C) Nesting platforms are the most effective tool in wildlife conservation. D) Ospreys are unusually tolerant of human activity.

2. According to the passage, DDT harmed ospreys mainly by A) poisoning the fish they ate so they starved B) killing adult birds immediately C) thinning eggshells so eggs broke in the nest D) destroying the trees they nested in

3. As used in sentence 3, accumulated most nearly means A) built up B) dissolved C) escaped D) improved

4. Which sentence best supports the idea that the osprey’s decline was severe? A) Sentence 1 B) Sentence 5 C) Sentence 9 D) Sentence 11

5. Based on sentences 8–10, the nesting-platform effort can best be described as A) expensive and controversial B) simple but effective C) scientific but unsuccessful D) illegal but tolerated

6. It can be inferred from sentence 12 that a declining osprey population today would most likely signal A) a shortage of nesting platforms B) problems in the aquatic food chain C) the return of legal DDT use D) an increase in highway traffic

7. The author’s attitude toward the osprey’s recovery is best described as A) skeptical B) indifferent C) appreciative D) alarmed

8. The phrase “a living instrument” in sentence 13 compares the osprey to A) a musical performance B) a measuring device C) a legal document D) a hunting weapon

Vocabulary in Context — Questions 9–12

9. “The captain gave explicit instructions: no one leaves the dock without a life jacket.” Explicit most nearly means A) confusing B) clearly stated C) whispered D) optional

10. “Her interest in marine biology was not a passing phase but an enduring passion.” Enduring most nearly means A) painful B) temporary C) lasting D) secret

11. “The committee tried to reconcile the two budget proposals into a single plan.” Reconcile most nearly means A) reject B) bring into agreement C) photocopy D) postpone

12. “The hikers were undaunted by the steep trail and set off at sunrise.” Undaunted most nearly means A) not discouraged B) unprepared C) exhausted D) confused

SESSION 4 — Expressions, Equations & Inequalities

Tutorial

Simplifying. Distribute carefully — the sign travels: −3(2x − 4) = −6x + 12. Then combine like terms (same variable, same exponent).

Solving equations. Undo operations in reverse order: undo add/subtract first, then multiply/divide. Variables on both sides? Move the smaller variable term across.

Translating words → algebra. “Five less than twice a number” = 2n − 5 (NOT 5 − 2n). “Four more than three times a number” = 3n + 4. “Is” means equals.

Inequalities solve exactly like equations with ONE exception: multiplying or dividing both sides by a negative number flips the inequality symbol.

Worked Example 1: Solve 2x + 7 = 4x − 9. Subtract 2x: 7 = 2x − 9. Add 9: 16 = 2x. x = 8.

Worked Example 2: Solve −x/4 ≥ 3. Multiply both sides by −4 and flip: x ≤ −12.

Worked Example 3: Tickets cost $12.50 each plus a $3 order fee. The total was $65.50. How many tickets? 12.50n + 3 = 65.50 → 12.50n = 62.50 → n = 5.

Timed Problem Set 4 (12 questions, 30 minutes)

1. Simplify: 7x − 3(2x − 4) A) x − 12 B) x + 12 C) 13x − 12 D) x + 4 2. Simplify: 4(3a + 2) − 5a A) 7a + 2 B) 12a + 8 C) 7a + 8 D) 17a + 8 3. Evaluate 2x² − 5x + 1 when x = −2. A) −17 B) 3 C) 19 D) −1 4. Solve: 5x + 9 = −16 A) −5 B) 5 C) −1.4 D) −25 5. Solve: 3(x − 4) = 21 A) 3 B) 11 C) 25/3 D) 9 6. Solve: x/5 − 2 = 6 A) 20 B) 40 C) 8/5 D) 30 7. Solve: 2x + 7 = 4x − 9 A) −8 B) 1 C) 8 D) −1 8. “Four more than three times a number is 25.” The number is A) 7 B) 9 2/3 C) 63 D) 21 9. Solve: 2x − 5 < 9 A) x < 2 B) x > 7 C) x < 7 D) x > 2 10. Solve: −x/4 ≥ 3 A) x ≥ −12 B) x ≤ −12 C) x ≥ 12 D) x ≤ 12 11. A kayak rental costs a $15 flat fee plus $8 per hour. Renting for h hours cost $47. Which equation finds h? A) 8h + 15 = 47 B) 15h + 8 = 47 C) 8(h + 15) = 47 D) 23h = 47 12. A rectangle’s length is 3 more than twice its width, and its perimeter is 36. What is the width? A) 5 B) 6 C) 10 D) 13

SESSION 5 — Grammar & Usage I

Tutorial

Subject–verb agreement. Find the true subject; ignore prepositional phrases between it and the verb. Each, every, either, neither, everyone are singular: “Each of the players is ready.”

Pronouns. Case: subjects use I/he/she/we/they; objects (after verbs and prepositions) use me/him/her/us/them — “handed it to Maya and me.” A pronoun must clearly match one antecedent in number: “Every student must bring his or her (not their, on this test) permission slip.”

Its vs. it’s: it’s = it is. Their/there/they’re; your/you’re. Possessive pronouns never take apostrophes.

Sentences. A fragment lacks a subject + verb + complete thought (dependent clauses starting with because, although, when can’t stand alone). A run-on/comma splice jams two complete sentences together; fix with a period, a semicolon, or a comma + conjunction (and, but, so).

Commas. After introductory clauses/phrases (“After the storm passed, …”); around nonessential interrupters; between items in a series. A comma alone can NEVER join two complete sentences.

Tense consistency. Keep the timeline steady unless meaning requires a change.

Timed Problem Set 5 (12 questions, 30 minutes)

1. “The box of supplies __ in the hallway.” A) were B) are C) is D) have been 2. “Neither of the answers __ correct.” A) are B) is C) were D) seem 3. “The team celebrated __ victory after the final whistle.” A) they’re B) their C) there D) its’ 4. Choose the correct pronoun: “My brother and __ built the model rocket.” A) me B) I C) myself D) us 5. Choose the correct pronoun: “The counselor spoke with Jordan and __ about the schedule.” A) I B) she C) me D) they 6. Which is a complete sentence? A) Although the ferry arrived early. B) Running along the shoreline at dawn. C) The ferry arrived early. D) Because we packed the night before. 7. Which correctly fixes this comma splice? “The tide was low, we walked to the sandbar.” A) The tide was low we walked to the sandbar. B) The tide was low, so we walked to the sandbar. C) The tide was low, we walked, to the sandbar. D) The tide, was low, we walked to the sandbar. 8. Which sentence is punctuated correctly? A) When the bell rang the students, packed their bags. B) When the bell rang, the students packed their bags. C) When, the bell rang the students packed their bags. D) When the bell, rang the students packed their bags. 9. Which sentence uses consistent verb tense? A) He opened his notebook and begins to write. B) He opens his notebook and began to write. C) He opened his notebook and began to write. D) He will open his notebook and wrote quickly. 10. Choose the correct word: “__ going to need warmer jackets for the night hike.” A) Their B) There C) They’re D) Theirs 11. Which sentence is correct? A) The dog wagged it’s tail. B) The dog wagged its tail. C) The dog wagged its’ tail. D) The dogs wagged it’s tails. 12. Which revision best fixes the misplaced modifier? “Covered in barnacles, the biologist examined the old buoy.” A) The biologist examined the old buoy covered in barnacles. B) Covered in barnacles, the old buoy examined the biologist. C) The biologist, covered in barnacles examined the old buoy. D) Examining the old buoy, barnacles covered the biologist.

End of Week 1 checkpoint

Tally the week’s five problem sets (60 questions). Under 70% in any single session’s topic → repeat that tutorial and pull extra problems from mySWOTs/Khan Academy on that skill before starting Week 2. Take the weekend off from new material; a 20-minute review of the error notebook is enough.