MCVSD Summer Seminar — Week 2 (Sessions 6–10)

Same daily format: tutorial (~45 min) → timed 12-question set (30 minutes) → review (~15 min). End the week with the full diagnostic-style mock (“Mock Test 2”).

SESSION 6 — Proportional & Linear Relationships

Tutorial

Slope = rate of change = (y₂ − y₁)/(x₂ − x₁) = rise/run. Order doesn’t matter as long as you’re consistent top and bottom.

Slope-intercept form: y = mx + b, where m = slope (rate) and b = y-intercept (starting value). In word problems: b is the one-time fee or starting amount; m is the per-unit rate.

Proportional relationships are the special case b = 0: the graph passes through the origin, and y/x is a constant (k). Equation: y = kx.

Is a point on the line? Plug it in. If both sides match, yes.

Worked Example 1: Slope through (0, 4) and (2, 10): (10−4)/(2−0) = 3. With y-intercept 4, the equation is y = 3x + 4.

Worked Example 2: A gym charges a $25 sign-up fee plus $10/month: C = 10m + 25. Six months: 60 + 25 = $85.

Worked Example 3: Table — x: 2, 4, 6; y: 5, 10, 15. Check y/x: 2.5, 2.5, 2.5. Proportional; y = 2.5x.

Timed Problem Set 6 (12 questions, 30 minutes)

1. Slope of the line through (−3, 5) and (1, −3)? A) −2 B) 2 C) −1/2 D) 1/2 2. For y = (3/4)x − 2, the slope and y-intercept are A) slope −2, intercept 3/4 B) slope 3/4, intercept −2 C) slope 3/4, intercept 2 D) slope 4/3, intercept −2 3. Which point lies on y = −3x + 4? A) (1, 7) B) (2, −2) C) (−1, 1) D) (3, 5) 4. Which table shows y proportional to x? A) x: 1,2,3 → y: 4,7,10 B) x: 2,4,5 → y: 8,16,20 C) x: 1,2,3 → y: 1,4,9 D) x: 2,3,4 → y: 5,7,9 5. A line passes through the origin with slope 4. Its equation is A) y = x + 4 B) y = 4x C) y = 4/x D) x = 4y 6. A phone plan costs $30 per month plus $0.10 per gigabyte over the limit. Which expression gives the cost with g extra gigabytes? A) 30g + 0.10 B) 0.10g + 30 C) 30.10g D) 0.10(g + 30) 7. A graph of distance vs. time is a straight line through (0, 0) and (3, 180). The slope represents A) 60 miles per hour B) 180 miles C) 3 hours per mile D) 540 miles per hour 8. The x-intercept of y = 2x − 6 is A) (0, −6) B) (3, 0) C) (−6, 0) D) (0, 3) 9. Which description guarantees a graph shows a proportional relationship? A) any straight line B) a straight line through the origin C) a line with positive slope D) a curve through the origin 10. Plan A costs y = 15x dollars for x classes. Plan B charges according to the table x: 2, 4 → y: 24, 48. Which statement is true? A) Plan A costs less per class B) Plan B costs less per class C) They cost the same per class D) Plan B has a sign-up fee 11. A line passes through (0, 4) and (2, 10). Its equation is A) y = 3x + 4 B) y = 2x + 4 C) y = 3x − 4 D) y = 4x + 3 12. In C = 12h + 20 (C = total cost, h = hours), the 20 represents A) the hourly rate B) the number of hours C) a fixed starting fee D) the maximum cost

SESSION 7 — Reading Comprehension II: Paired Passages & Argument

Tutorial

The MCVSD LA section includes paired passages — two texts on the same topic that you must compare. Attack plan:

1. Read Passage 1; write its claim in five words in the margin.
2. Read Passage 2; write its claim. Note whether it opposes, extends, or qualifies Passage 1.
3. Before the questions, answer for yourself: Where do they agree? Where exactly do they split?

Question types to expect: each author’s main claim · a point of agreement · “how would Author 2 respond to X in Passage 1” (answer using only what Author 2 actually argues — don’t invent) · tone · function of a detail · synthesis (“both passages suggest…”).

Argument anatomy: claim (the position) → evidence (facts, studies, examples) → reasoning (why the evidence supports the claim). Strong evidence is specific and relevant; weak evidence is vague, emotional, or off-topic.

Timed Problem Set 7 (12 questions, 30 minutes)

Read both passages, then answer all questions.

Passage 1

Middle schools should push their start times later, to 8:30 or beyond. The biology is not in dispute: as children enter adolescence, their internal clocks shift, making it genuinely difficult to fall asleep before eleven. Forcing teens into first period at 7:40 guarantees a sleep-deprived classroom. Districts that moved start times later have reported better attendance, improved grades, and fewer student athletes injured in practice. Buses can be rescheduled; habits can adjust. What cannot adjust is adolescent biology. When the science and the results both point the same direction, a district that refuses to act is choosing tradition over its students.

Passage 2

Later start times sound appealing until the whole day is examined. Push the first bell back an hour and the last bell moves too — into the late afternoon, when younger siblings need supervision, part-time jobs begin, and practice fields lose daylight. Families who depend on teens for after-school responsibilities would carry the heaviest burden. The sleep research deserves respect, but sleep can also be gained on the other end: reasonable homework loads and fewer late-night screens. Before rebuilding bus routes and family schedules around one solution, districts should ask whether they are solving sleep deprivation or simply relocating it.

1. The main claim of Passage 1 is that middle schools should A) shorten the school day B) start later in the morning C) eliminate first period D) ban late-night screens

2. The author of Passage 1 supports the claim primarily with A) quotations from parents B) biology plus results from districts that changed C) a personal story D) a survey of teachers

3. The main concern of Passage 2 is that later start times would A) violate sleep research B) shift burdens to families and after-school life C) reduce attendance D) make mornings too dark

4. As used in Passage 1, “sleep-deprived” most nearly means A) lacking sufficient sleep B) sleeping too deeply C) refusing to sleep D) sleeping at school

5. The author of Passage 2 responds to the sleep research by A) denying that it exists B) claiming it applies only to high schoolers C) accepting it but proposing other ways to gain sleep D) arguing that teens do not need sleep

6. How would the author of Passage 2 most likely respond to Passage 1’s statement that “buses can be rescheduled; habits can adjust”? A) Agree that adjustment would be quick and painless B) Point out that the adjustments fall hardest on families with after-school responsibilities C) Argue that buses should be eliminated entirely D) Concede that tradition matters more than science

7. On which point would both authors most likely agree? A) Adolescents need adequate sleep. B) School should end after dark. C) Homework should be eliminated. D) Bus routes can never change.

8. The final sentence of Passage 2 (“solving sleep deprivation or simply relocating it”) suggests the author believes a later start time might A) end sleep deprivation permanently B) move the sleep problem elsewhere in the day rather than fix it C) increase sleep for younger siblings D) have no effect on anyone

9. Which best describes the difference in how the passages treat evidence? A) Passage 1 cites outcomes from real districts; Passage 2 reasons from predicted consequences. B) Passage 1 uses only emotion; Passage 2 uses only statistics. C) Both rely entirely on personal experience. D) Passage 2 cites more scientific studies than Passage 1.

10. The tone of the final sentence of Passage 1 is best described as A) apologetic B) forceful C) uncertain D) humorous

11. As used in Passage 2, “relocating” most nearly means A) solving B) moving C) measuring D) hiding

12. Which sentence best synthesizes the two passages? A) Both authors agree the current start time is perfect. B) Both authors care about student well-being but disagree about whether changing start times is the right fix. C) Both authors believe family schedules should determine school policy. D) Neither author accepts the sleep research.

SESSION 8 — Geometry

Tutorial

Area: triangle = ½bh · rectangle = lw · trapezoid = ½(b₁ + b₂)h · circle = πr². Circumference = 2πr = πd. Composite shapes: split into pieces you know, add (or subtract cutouts).

Angles: straight line = 180° (supplementary pairs) · around a point = 360° · triangle angles sum to 180° · vertical angles are equal. Parallel lines + transversal: corresponding and alternate-interior angles are equal; same-side interior angles are supplementary.

Volume: prism = (area of base) × height → rectangular prism = lwh; cylinder = πr²h.

Pythagorean theorem (right triangles only): a² + b² = c², hypotenuse c is opposite the right angle. Memorize the triples 3-4-5 and 5-12-13 (and their multiples: 6-8-10, 9-12-15).

Similar figures: corresponding sides are proportional — set up a proportion.

Worked Example 1: Trapezoid, bases 8 and 12, height 5: ½(20)(5) = 50. Worked Example 2: Right triangle, hypotenuse 13, one leg 5: other leg = √(169 − 25) = √144 = 12. Worked Example 3: Triangle angles are 55° and 63°: third = 180 − 118 = 62°.

Timed Problem Set 8 (12 questions, 30 minutes)

1. Area of a triangle with base 14 cm and height 9 cm? A) 63 cm² B) 126 cm² C) 23 cm² D) 112 cm² 2. Area of a trapezoid with bases 8 in and 12 in, height 5 in? A) 100 in² B) 50 in² C) 60 in² D) 40 in² 3. Area of a circle with radius 6 m? (π ≈ 3.14) A) 18.84 m² B) 37.68 m² C) 113.04 m² D) 452.16 m² 4. An L-shaped floor is a 10 ft × 4 ft rectangle joined to a 6 ft × 3 ft rectangle (no overlap). Total area? A) 46 ft² B) 58 ft² C) 60 ft² D) 74 ft² 5. Two angles are supplementary. One measures 47°. The other measures A) 43° B) 53° C) 133° D) 313° 6. A triangle has angles of 55° and 63°. The third angle is A) 62° B) 72° C) 118° D) 58° 7. Parallel lines are cut by a transversal. One angle measures 118°. Its alternate interior angle partner measures A) 62° B) 118° C) 90° D) 28° 8. Volume of a rectangular prism 8 cm × 5 cm × 4 cm? A) 17 cm³ B) 160 cm³ C) 320 cm³ D) 40 cm³ 9. Volume of a cylinder with radius 2 in and height 9 in? (π ≈ 3.14) A) 56.52 in³ B) 113.04 in³ C) 226.08 in³ D) 36 in³ 10. A right triangle has legs 6 and 8. The hypotenuse is A) 10 B) 14 C) 12 D) 100 11. A right triangle has hypotenuse 13 and one leg 5. The other leg is A) 8 B) 12 C) 14.3 D) 18 12. Two triangles are similar. The smaller has sides 4, 6, 8; the longest side of the larger is 20. What is its shortest side? A) 8 B) 10 C) 12 D) 16

SESSION 9 — Statistics & Probability

Tutorial

Center: mean = sum ÷ count · median = middle value of the ordered list (average the middle two if count is even) · mode = most frequent. Range = max − min. IQR = Q3 − Q1 (the box in a box plot). An extreme outlier pulls the mean toward it but barely moves the median — that’s why median is used for things like home prices.

“What must I score” problems: work with totals. Needed total = target mean × new count; subtract what’s already earned.

Probability = favorable ÷ total, always between 0 and 1. P(not A) = 1 − P(A). Independent compound events: multiply — P(A and B) = P(A) × P(B).

Predictions from samples: set the sample proportion equal to the population proportion and solve.

Sampling bias: a fair sample is random and representative. Surveying only gym members about exercise habits = biased.

Worked Example 1: After 4 tests averaging 85 (total 340), what score makes the 5-test average 87? Needed total = 5 × 87 = 435; 435 − 340 = 95. Worked Example 2: P(heads AND rolling a 5 or 6) = 1/2 × 2/6 = 1/6.

Timed Problem Set 9 (12 questions, 30 minutes)

1. Mean of 8, 12, 15, 9, 16? A) 11 B) 12 C) 13 D) 15 2. Median of 3, 7, 8, 10, 12, 14, 21? A) 8 B) 10 C) 10.7 D) 12 3. A data set is 5, 6, 6, 7, 8. If the value 40 is added, which is true? A) The mean and median both increase greatly. B) The mean increases greatly; the median changes little. C) The median increases greatly; the mean changes little. D) Neither measure changes. 4. Kai’s first 4 quiz scores average 85. What must Kai score on the 5th quiz for an 87 average? A) 89 B) 91 C) 93 D) 95 5. In a box plot, Q1 = 20 and Q3 = 35. The IQR is A) 55 B) 27.5 C) 15 D) 700 6. A bag has 5 red and 7 blue marbles. P(red) = A) 5/7 B) 7/12 C) 5/12 D) 1/2 7. A spinner has 10 equal sections; 4 are green. P(NOT green) = A) 2/5 B) 3/5 C) 4/10 D) 6/4 8. A coin is flipped and a die is rolled. P(heads AND a number greater than 4) = A) 1/6 B) 1/3 C) 1/12 D) 2/3 9. A spinner with 4 equal sections labeled A–D is spun twice. P(A both times) = A) 1/4 B) 1/8 C) 1/16 D) 1/2 10. In a random sample, 3 of 20 light bulbs are defective. In a shipment of 500, about how many defective bulbs should be expected? A) 30 B) 60 C) 75 D) 150 11. A school wants student opinions on cafeteria food. Which sample is LEAST biased? A) Students in line buying lunch B) 50 students selected at random from the roster C) Students who visit the nurse D) The first 50 students to volunteer online 12. Test scores: 4 students scored in the 60s, 7 in the 70s, 12 in the 80s, 5 in the 90s. How many students scored 80 or above? A) 12 B) 16 C) 17 D) 28

SESSION 10 — Revising & Editing + Vocabulary

Tutorial

Editing questions give you a student draft and ask for the best fix. Priorities, in order: (1) grammar must be correct, (2) the sentence must say what the writer means, (3) shorter and clearer beats longer and fancier — the test almost always prefers concise over wordy.

Transitions: match the logic. Adding a supporting idea → in addition, furthermore. Contrast → however, on the other hand. Cause/effect → therefore, as a result. Example → for instance.

Deleting sentences: a sentence should be deleted if it strays from the paragraph’s point, even if it’s interesting or true.

Combining sentences: the best combination keeps all the meaning, avoids repetition, and doesn’t create a comma splice.

Timed Problem Set 10 (12 questions, 30 minutes)

Read this draft of a student essay. The questions refer to the numbered sentences.

(1) Last spring our class planted a rain garden beside the school parking lot. (2) A rain garden is a shallow planted basin, it collects stormwater running off pavement. (3) Without it, rainwater carries oil and litter strait into the storm drain and then to the creek. (4) Native plants was chosen because their deep roots soak up water quickly. (5) My cousin has a vegetable garden with really big tomatoes. (6) __, the garden needed almost no watering once the plants were established. (7) Volunteers measured how much runoff the garden captured during three storms. (8) The results, which surprised even our teacher were presented at the town environmental fair. (9) The garden captured more runoff in one storm. (10) Than our class had predicted for the entire month. (11) Our principal now wants to build two more rain gardens next year. (12) In my opinion, I personally think this project proves that students can make real improvements to their community.

1. Which is the best revision of sentence 2? A) A rain garden is a shallow planted basin, it collects stormwater running off pavement. B) A rain garden is a shallow planted basin that collects stormwater running off pavement. C) A rain garden is a shallow planted basin, collecting, stormwater running off pavement. D) A rain garden, is a shallow planted basin it collects stormwater running off pavement. 2. In sentence 3, which change is needed? A) Change “carries” to “carry” B) Change “strait” to “straight” C) Change “creek” to “creak” D) No change 3. In sentence 4, which change is needed? A) Change “was” to “were” B) Change “their” to “there” C) Change “roots” to “root’s” D) No change 4. What is the best way to handle sentence 5? A) Move it to the beginning of the essay B) Combine it with sentence 4 C) Delete it, because it does not support the paragraph’s topic D) Add details about the tomatoes 5. Which transition best fills the blank in sentence 6? A) However B) In addition C) For example D) On the other hand 6. Which is the best revision of sentence 8? A) The results, which surprised even our teacher, were presented at the town environmental fair. B) The results which surprised, even our teacher were presented at the town environmental fair. C) The results which surprised even our teacher, were presented, at the town environmental fair. D) No change. 7. What is the best way to combine sentences 9 and 10? A) The garden captured more runoff in one storm, than our class had predicted for the entire month. B) The garden captured more runoff in one storm than our class had predicted for the entire month. C) The garden captured more runoff. In one storm than our class had predicted for the entire month. D) The garden captured more runoff in one storm, our class had predicted for the entire month. 8. Which is the best revision of sentence 12? A) In my opinion, I personally think this project proves that students can make real improvements to their community. B) I personally think, in my opinion, that this project proves students can improve their community. C) This project proves that students can make real improvements to their community. D) No change. 9. The primary purpose of sentence 7 is to A) introduce a counterargument B) show that the garden’s impact was measured, not just assumed C) describe the appearance of the plants D) explain how storm drains work 10. “The mayor praised the students’ initiative in starting the project without being asked.” Initiative most nearly means A) confusion B) willingness to take the first step C) reluctance D) obedience 11. “Deep roots make native plants resilient during dry weeks.” Resilient most nearly means A) able to withstand difficulty B) colorful C) invisible D) fragile 12. “The data bolstered the class’s argument for building more gardens.” Bolstered most nearly means A) weakened B) strengthened C) replaced D) hid

End of program — Mock Test 2

On the final day (or the following Saturday), re-take the diagnostic file as a full timed mock, or better, use a fresh full-length mySWOTs test for each section so the questions are unseen. Compare section scores to the Week 0 baseline. Anything still under ~75% becomes the fall review list; from September on, shift to one timed practice test every 1–2 weeks while protecting those Q1 grades.