Juainny's Review + Examples

Juainny's R&W Quick Hits

Grammar (IMPORTANT) Essentials

Comma (vibe) Rules: Lists, intro phrases, non-essential info. NO comma between Subject & Verb alone.+
Do: After checking his map, the hiker continued.
Do: The book, which was long, was good.
Don't: The hiker, continued.
Don't: The book which was long was good. (Missing commas for non-essential)
Semicolon (;) = Period (.): Joins two complete sentences. If both are options & work, eliminate both.+
Do: The sky was dark; rain began to fall.
Do: The sky was dark. Rain began to fall.
Don't: The sky was dark, rain began to fall. (Comma Splice)
Colon (:): Use before a list/explanation *if* part before is a complete sentence.+
Do: Bring three items: a pen, paper, and ID.
Don't: The items are: a pen, paper, and ID. (Part before colon isn't complete sentence)
Apostrophes: Possession (cat's, students') or Contractions (it's). Watch its vs it's.+
Do: The dog wagged its tail.
Do: It's time to go.
Don't: The dog wagged it's tail.
Don't: Its time to go.
Modifiers: Phrase at start must describe noun right after comma.+
Do: Hoping for a good grade, Maria studied hard.
Don't: Hoping for a good grade, the test was studied for by Maria. (Test wasn't hoping)
Verbs: Match subject number (He runs, They run), keep tense consistent.+
Do: The committee agrees on the plan.
Do: The members agree on the plan.
Don't: The committee agree on the plan.
Pronouns: Match noun in number (team/its, students/their). Clear antecedent.+
Do: When Jane saw Sue, she waved. (If context makes clear who 'she' is)
Don't: The report discussed the survey, but they didn't include all data. ('They' unclear)

Reading & Logic

Transitions: What's the relationship? Contrast, Cause/Effect, Addition, Example?+
Scenario: Sentence 1: Study found widget A is effective. Sentence 2: Widget B is cheaper but less tested. Good Transition: However, (Contrast) Bad Transition: Therefore, (Implies cause/effect not present)
Main Idea/Purpose: What's the author's primary claim or goal?+
Text Snippet: Describes issues with plastic bottles, mentions alternatives like reusable ones, concludes recycling isn't enough. Likely Main Idea: Reducing single-use plastic requires more than just recycling, favoring reusable options. Not Main Idea: Plastic bottles are blue. (Too specific/minor detail)
Words in Context: Look at surrounding words. Predict meaning.+
Sentence: Despite the storm's ferocity, the old house remained standing. Context Clue: "Despite" + "storm" + "remained standing" suggests ferocity means intensity/violence. Wrong Meaning based on Isolation: Quickness? (Doesn't fit context)
Data Graphics: Read title, axes, key. Find specific data. Understand trends.+
Graph: Shows rising CO2 levels over time. Question: What was the approx. CO2 level in 1990? Action: Find 1990 on X-axis, trace up to the line, read value on Y-axis. Error: Looking at the overall trend instead of the specific year asked for.

Sentence Structure Super-Basics

Importance: HIGH. Understanding basic sentence structure helps avoid fragments, run-ons, and comma splices.

Key Elements:

Independent Clause: Has a subject and a verb, expresses a complete thought. (Can stand alone as a sentence).
Ex: The cat slept.
Dependent Clause: Has a subject and verb, but starts with a subordinating conjunction (like 'because', 'although', 'when', 'if') or relative pronoun ('who', 'which', 'that') and CANNOT stand alone.
Ex: Because the cat slept...
Phrase: A group of words without a subject-verb pair, acting as a single part of speech.
Ex: on the warm windowsill (prepositional phrase). Running quickly (participial phrase).

Common Structures:

Independent Clause. (Simple Sentence)
Independent Clause; Independent Clause.
Independent Clause, [coordinating conjunction] Independent Clause. (FANBOYS: For, And, Nor, But, Or, Yet, So)
Dependent Clause, Independent Clause. (Comma needed)
Independent Clause Dependent Clause. (No comma usually needed)

Juainny's Math Hints, fun!

Algebra Essentials

(if you don't know this one...) Linear Equations: y = mx + b. Slope of Ax+By=C is -A/B.+
Q: Slope of 3x - 2y = 6? Wrong: -3 / 2 (Forgot negative in -A/B for B) Correct: -3 / (-2) = 3/2 Or solve for y: -2y = -3x + 6 => y = (3/2)x - 3. Slope (m) is 3/2.
Parallel Lines: Same slope (m), different y-intercept (b).+
Q: Which line is parallel to y = 2x + 5? (A) y=2x+5 (B) y=-1/2x+3 (C) y=2x-1 Wrong: (A) Same line (infinite solutions), not parallel. Correct: (C) Same slope (2), different y-intercept (-1 vs 5).
Perpendicular Lines: Slopes multiply to -1 (m₁ * m₂ = -1).+
Q: Slope of line perpendicular to y = (1/3)x - 4? Wrong: 1/3 (Same slope), 3 (Reciprocal but not negative) Correct: -3 Original slope m₁=1/3. Need m₂ such that (1/3)*m₂ = -1. So m₂ = -3.
Systems: Substitution/elimination. No solution=parallel. Infinite=same line.+
System: x+y=5, 2x+2y=10. Wrong: One specific solution (e.g., x=2, y=3) Correct: Infinite solutions. Second eq is 2*(first eq). They are the same line.
Quadratics: Factor, formula x = [-b ± √(b²-4ac)] / 2a, vertex a(x-h)²+k.+
Q: Solve x² - 5x + 6 = 0. Wrong Calculation: Using formula incorrectly might yield wrong roots. Correct: x=2, x=3 Factors to (x-2)(x-3) = 0. Solutions are x=2 and x=3.
Exponents: xᵃ*xᵇ=xᵃ⁺ᵇ, (xᵃ)ᵇ=xᵃᵇ, x⁻ᵃ=1/xᵃ, x⁰=1.+
Q: Simplify (2a³)². Wrong: 2a⁶ (Forgot to square the 2) or 4a⁵ (Added exponents instead of multiplying) Correct: 4a⁶ (2¹a³)² = 2¹*² * a³*² = 2²a⁶ = 4a⁶.
Radicals: Simplify (√50=5√2). Check solutions! √(a²)=|a|.+
Q: Solve √x = -3. Wrong: x=9 (Squaring both sides gives x=9, but...) Correct: No solution. The principal square root (√ symbol) cannot be negative. Checking x=9 in original: √9 = 3 ≠ -3.

Geometry & Data

Area: Circle πr², Rectangle lw, Triangle (1/2)bh.+
Q: Area of circle with diameter 10? Wrong: 100π (Used diameter instead of radius) Correct: 25π Diameter=10 => Radius r=5. Area = πr² = π(5)² = 25π.
Pythagorean Thm: Right triangles: a² + b² = c².+
Q: Legs of right triangle are 3 and 4. Hypotenuse? Wrong: √7 (Subtracted squares or added lengths) Correct: 5 3² + 4² = c² => 9 + 16 = c² => 25 = c² => c = 5.
Similar Figures: Sides ratio k => Areas ratio k² => Volumes ratio k³.+
Q: Similar triangles. Side ratio 1:3. Area ratio? Wrong: 1:3 (Used side ratio) Correct: 1:9 Area ratio = (Side ratio)² = (1/3)² = 1/9.
Percentages: %=(Part/Whole)*100. Change=(Change/Original)*100.+
Q: Price ↑ from $50 to $60. % increase? Wrong: 10% (Used change $10, but not over original) or 16.7% ($10/$60) Correct: 20% Change=$10. Original=$50. % Inc = (10/50)*100 = (1/5)*100 = 20%.
Mean, Median, Mode: Average, Middle (ordered), Most frequent.+
Data: 2, 3, 3, 5, 7. Mean: (2+3+3+5+7)/5 = 20/5 = 4. Median: Middle value = 3. Mode: Most frequent = 3. Remember to order data for median!
Probability: Favorable / Total Possible.+
Q: Roll fair 6-sided die. P(rolling even number)? Wrong: 1/6 (Prob of one specific number), 3 (Number of outcomes, not prob) Correct: 1/2 Favorable (Even) = {2, 4, 6} (3 outcomes). Total = {1, 2, 3, 4, 5, 6} (6 outcomes). P = 3/6 = 1/2.

General Tips

Read Carefully: What are they *actually* asking for?+
Q: If x=3, what is 2x+5? Wrong Answer if Misread: 3 (Just giving x) Correct: 11 Substitute x=3 into 2x+5 => 2(3)+5 = 6+5 = 11.
Use Calculator Wisely: Arithmetic, checking, graphing.+
Tip: For complex decimals or roots, use the calculator to avoid calculation errors. For systems of equations, graphing on Desmos can quickly find intersection points (solutions).
Units: Pay attention! Square lengths for area.+
Q: Convert 10 ft²/hr to ft²/min. Wrong: 600 ft²/min (Multiplied by 60 instead of dividing) Correct: 1/6 ft²/min (approx 0.167) 1 hr = 60 min. Need to divide by 60: (10 ft²/hr) * (1 hr / 60 min) = 10/60 ft²/min = 1/6 ft²/min.

Don't forget to breath— get through this one, and yo'll be fine (for next time)