Study guide: a worked example

Sample passage. "Many people believe honey can spoil like other foods. In truth, it almost never does. Honey holds very little water and is slightly acidic, so bacteria cannot survive in it. Archaeologists have even found honey in ancient tombs that was still safe to eat."

Question. What is the main idea of this passage?

How to work it out. The topic (one or two words) is "honey not spoiling." The main idea is the full-sentence point: honey almost never spoils because of its chemistry, its low water and slight acidity. The first sentence is a common wrong belief, not the point. The tomb sentence is a supporting detail, an interesting fact that backs up the idea but is not the idea itself.

Common mistakes

• Choosing a true but small detail (the tombs) instead of the big overall point.
• Answering with the topic ("honey") instead of a complete sentence that makes a point.

Practice tips

• Before reading the answer choices, say the main idea out loud in your own words, then find the choice that matches.
• If a choice is true but only covers one sentence of the passage, it is a detail, not the main idea.

Study guide: a worked example

Sample passage. "Do not wait until you feel thirsty to drink water. By the time thirst hits, your body is already low on fluids. Make a habit of sipping water through the day, and your energy and focus will thank you."

Question. What is the author's main purpose?

How to work it out. The author is not just sharing facts, the author wants the reader to change a habit ("Make a habit of sipping water"). The command words give it away. So the purpose is to persuade or instruct. The tone is encouraging and helpful, not playful or worried.

Common mistakes

• Confusing tone (how the writing sounds) with purpose (why it was written). They are two separate questions.
• Picking "to inform" for any passage that contains facts, even when the author is clearly arguing or telling you to act.

Practice tips

• Ask yourself: "What does the author want me to do, think, or feel after reading this?"
• Watch for opinion words ("should," "best," "must") and commands, they signal persuade or instruct.

Study guide: a worked example

Sample passage. "Maria checked her bag twice, glanced at the clock, and tapped her foot by the door. Her ride was already ten minutes late."

Question. What can you infer about how Maria feels?

How to work it out. The passage never says "Maria is anxious," but the clues add up: checking her bag twice, watching the clock, tapping her foot, and a late ride. A safe inference is that Maria feels nervous or impatient. An unsafe inference would be "Maria will miss her appointment," because the passage gives no information about an appointment.

Common mistakes

• Stretching too far beyond the clues. The most common wrong answer is an inference the text does not fully support.
• Using your own life experience or a guess instead of the actual words in the passage.

Practice tips

• For each answer choice, find the exact words in the passage that support it. If you cannot, eliminate it.
• Pick the choice that is the smallest safe step from the clues, not the most dramatic one.

Study guide: a worked example

Sample passage. "Community gardens make neighborhoods better. A 2019 study found that blocks with a shared garden had 15% less litter, and neighbors there knew twice as many people by name."

Question. Which detail is the best evidence for the claim that gardens make neighborhoods better?

How to work it out. First find the claim: "Community gardens make neighborhoods better" (the first sentence). Then find the evidence: the specific, checkable facts, the "15% less litter" and "twice as many people by name." Evidence is concrete and measurable. A sentence that just repeats the claim in other words is not evidence.

Common mistakes

• Picking a sentence that restates the claim instead of one that proves it with facts.
• Choosing a detail that sounds pleasant but does not actually connect to the point being made.

Practice tips

• Underline the claim first, then hunt only for facts, numbers, or examples that back it up.
• Strong evidence can be fact-checked. If a detail cannot be checked, it is probably an opinion, not evidence.

Study guide: a worked example

Sample sentence. "The old bridge was so decrepit that the town finally closed it; rust had eaten through the beams and several boards were missing."

Question. What does the word "decrepit" most likely mean?

How to work it out. Even if you have never seen "decrepit," the clues are right beside it: "rust had eaten through," "boards were missing," and the town "closed it." Everything points to worn out and falling apart. That is the meaning. The contrast and example clues did the work for you.

Common mistakes

• Picking a familiar word that you like but that does not fit the sentence.
• Ignoring the clue words around the unknown word and guessing blindly.

Practice tips

• Replace the hard word with your guessed meaning and reread the sentence. If it still makes sense, your guess is right.
• Use prefixes and suffixes as backup: "de-" often means down or away, which fits "decrepit."

Study guide: a worked example

Sample passage. "To register for a class, first create an account. Then verify your email address. Finally, choose your class. You cannot choose a class until your email has been verified."

Question. What must you do right before choosing a class?

How to work it out. Scan the passage for the key words from the question, "choose a class." The text says you cannot choose a class "until your email has been verified," so verifying the email is the step right before. The sequence words first, then, finally confirm the order.

Common mistakes

• Answering from memory after one read instead of scanning back to the exact spot.
• Missing a small order word like "until," "before," or "after" that changes the sequence.

Practice tips

• For "locate the information" questions, scan for a key word from the question rather than rereading the whole passage.
• On a graphic or chart, read the title, the labels, and the units before you look at any numbers.

No-calculator mental-math tricks

• Multiply by 5: divide by 2, then multiply by 10. 84 × 5 = (84÷2) × 10 = 420.
• Multiply by 11 (2-digit): add the two digits and put the result between them. 36 × 11 = 3_(3+6)_6 = 396.
• Multiply by 9: multiply by 10, then subtract the number once. 7 × 9 = 70 − 7 = 63.

Key Formulas

• PEMDAS (order of operations): Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right). Example: 3 + 4 × 2 = 3 + 8 = 11, not 14.
• Absolute value: |a| = the distance of a from zero, always positive. Example: |−7| = 7, |3| = 3.
• Commutative property: a + b = b + a, and a × b = b × a. The order does not matter for addition or multiplication.
• Associative property: (a + b) + c = a + (b + c). Grouping does not matter for addition or multiplication.
• Distributive property: a × (b + c) = a × b + a × c. Example: 3 × (10 + 2) = 30 + 6 = 36.

Study guide: a worked example

Problem. Solve 24 − 6 × 3 + (8 ÷ 2).

Step by step. Follow PEMDAS. Parentheses first: (8 ÷ 2) = 4, so the problem is 24 − 6 × 3 + 4. Multiplication next: 6 × 3 = 18, so now 24 − 18 + 4. Addition and subtraction are equal rank, so work left to right: 24 − 18 = 6, then 6 + 4 = 10. The answer is 10.

Common mistakes

• Working strictly left to right and doing 24 − 6 before the multiplication.
• Doing the addition before the subtraction instead of taking them left to right.

Practice tips

• Rewrite the whole problem after each step so you never lose your place.
• Underline the parentheses and the multiply and divide signs before you begin.

Key Formulas

• Common fraction-decimal equivalents: 1/2 = 0.5, 1/3 = 0.333, 1/4 = 0.25, 1/5 = 0.2, 1/8 = 0.125, 2/3 = 0.667, 3/4 = 0.75, 3/8 = 0.375, 5/8 = 0.625, 7/8 = 0.875.
• Cross-multiply to compare fractions: to compare a/b and c/d, compute a × d and b × c. If a × d is larger, then a/b is larger. Example: compare 3/7 and 2/5: 3 × 5 = 15, 7 × 2 = 14, so 3/7 is slightly larger.

Study guide: a worked example

Problem. A recipe needs 3/4 cup of flour. You want to make 1½ times the recipe. How much flour do you need?

Step by step. "1½ times" means multiply 3/4 by 1½. First change the mixed number to an improper fraction: 1½ = 3/2. Now multiply straight across, top times top and bottom times bottom: (3 × 3) ÷ (4 × 2) = 9/8. Change the answer back to a mixed number: 9 ÷ 8 = 1 with 1 left over, so 9/8 = 1⅛ cups of flour.

Common mistakes

• Multiplying 3/4 by only the whole number 1 and forgetting the half.
• Trying to find a common denominator. You only need that for adding or subtracting, not for multiplying.

Practice tips

• Always turn mixed numbers into improper fractions before you multiply or divide.
• Simplify the answer at the end, and turn an improper fraction back into a mixed number.

Key Formulas

• Percent of a number: percent = (part ÷ whole) × 100. Example: 15 out of 60 = (15 ÷ 60) × 100 = 25%.
• Percent change: percent change = ((new − old) ÷ old) × 100. Example: price goes from $40 to $50, change = ((50 − 40) ÷ 40) × 100 = 25% increase.
• Simple interest: I = P × r × t. Variables: P = principal (starting amount), r = annual rate as a decimal, t = time in years. Example: $1,000 at 5% for 3 years = 1000 × 0.05 × 3 = $150 interest.
• Discount: sale price = original price − (original price × discount rate). Example: $80 item at 20% off = 80 − (80 × 0.20) = $64.
• Markup: selling price = cost + (cost × markup rate). Example: $50 cost with 30% markup = 50 + (50 × 0.30) = $65.

Study guide: a worked example

Problem. A $60 jacket is marked 25% off. Then 7% sales tax is added. What is the final total?

Step by step. Do the discount first. 25% of 60 = 0.25 × 60 = 15, so the sale price is 60 − 15 = $45. Now figure the tax on the sale price, not the original: 7% of 45 = 0.07 × 45 = 3.15. Add it on: 45 + 3.15 = $48.15. The final total is $48.15.

Common mistakes

• Adding the tax to the original $60 instead of to the discounted $45.
• Combining 25% off and 7% tax into one 18% change. Percents of different amounts cannot be added that way.

Practice tips

• Do multi-step percent problems one step at a time and label each result.
• Tax is always calculated on the price after any discount is taken off.

Key Formulas

• Slope: m = (y₂ − y₁) ÷ (x₂ − x₁). Variables: (x₁, y₁) and (x₂, y₂) are two points on the line. Example: points (1, 2) and (4, 8), slope = (8 − 2) ÷ (4 − 1) = 6 ÷ 3 = 2.
• Slope-intercept form: y = mx + b. Variables: m = slope, b = y-intercept (where the line crosses the y-axis). Example: y = 2x + 3 has slope 2 and crosses the y-axis at 3.
• Distance = rate × time: d = r × t. Example: driving 60 mph for 2.5 hours = 60 × 2.5 = 150 miles.
• Solving proportions (cross-multiply): a/b = c/d means a × d = b × c. Example: 3/4 = x/20, so 3 × 20 = 4 × x, 60 = 4x, x = 15.
• FOIL (multiplying two binomials): (a + b)(c + d) = ac + ad + bc + bd. First, Outer, Inner, Last. Example: (x + 2)(x + 5) = x² + 5x + 2x + 10 = x² + 7x + 10.

Study guide: a worked example

Problem. Solve 3x − 7 = 2x + 5.

Step by step. The goal is to get x by itself. First gather the variable terms on one side: subtract 2x from both sides. That gives 3x − 2x − 7 = 5, which simplifies to x − 7 = 5. Now move the constant: add 7 to both sides, giving x = 12. Check by plugging 12 back in: 3(12) − 7 = 29, and 2(12) + 5 = 29. Both sides match, so x = 12 is correct.

Common mistakes

• Subtracting 2x from only one side of the equation.
• Moving the 7 across the equals sign without changing it from −7 to +7.

Practice tips

• Whatever you do to one side, do the exact same thing to the other side.
• Always plug your answer back into the original equation to confirm it works.

Key Formulas

• Area of a rectangle: A = l × w. Variables: l = length, w = width. Example: 8 ft × 5 ft = 40 ft².
• Area of a triangle: A = ½ × b × h. Variables: b = base, h = height. Example: base 10, height 6, area = ½ × 10 × 6 = 30.
• Area of a circle: A = πr². Variables: r = radius. Example: r = 4, area = π × 16 ≈ 50.27.
• Perimeter of a rectangle: P = 2l + 2w. Example: l = 8, w = 5, perimeter = 16 + 10 = 26.
• Circumference of a circle: C = 2πr (or πd). Variables: r = radius, d = diameter. Example: r = 4, C = 2 × π × 4 ≈ 25.13.
• Volume of a rectangular solid: V = l × w × h. Example: 3 × 4 × 5 = 60 cubic units.
• Volume of a cylinder: V = πr²h. Example: r = 3, h = 10, V = π × 9 × 10 ≈ 282.74.
• Pythagorean theorem: a² + b² = c². Variables: a and b are the legs, c is the hypotenuse (longest side). Example: 3² + 4² = 9 + 16 = 25, so c = 5.
• Surface area of a rectangular solid: SA = 2(lw + lh + wh). Example: l = 3, w = 4, h = 5, SA = 2(12 + 15 + 20) = 94.

Study guide: a worked example

Problem. A triangular garden bed has a base of 10 feet and a height of 6 feet. What is its area?

Step by step. The area of a triangle is ½ × base × height. Multiply the base and height first: 10 × 6 = 60. Then take half of that: 60 ÷ 2 = 30. The area is 30 square feet.

Common mistakes

• Forgetting the ½ and answering 60. A triangle is half of a rectangle with the same base and height.
• Using a slanted side as the height. The height must form a right angle with the base.

Practice tips

• Area is the space inside, measured in square units; perimeter is the distance around.
• Circle the word in the question that tells you which one is being asked for.

Key Formulas

• Distance = rate × time: d = r × t. Example: a train at 55 mph for 3 hours travels 55 × 3 = 165 miles.
• Unit rate: unit rate = total ÷ quantity. Example: $12.50 for 5 pounds = $12.50 ÷ 5 = $2.50 per pound.
• Ratio and proportion setup: write "part to part" or "part to whole" as a fraction, then set two equal fractions and cross-multiply. Example: if 3 out of 5 students passed, how many pass out of 40? 3/5 = x/40, so x = 24.
• "Is over of" percent method: is/of = %/100. Example: "What percent of 60 is 15?" becomes 15/60 = x/100, so x = 25%.

Study guide: a worked example

Problem. A nurse works 8-hour shifts and earns $24 per hour. After working 5 shifts, she spends $310 on bills. How much of that pay is left?

Step by step. Take it one step at a time. Hours worked: 8 hours × 5 shifts = 40 hours. Pay earned: 40 hours × $24 = $960. Money left after bills: $960 − $310 = $650.

Common mistakes

• Stopping after finding the $960 and forgetting to subtract the bills.
• Multiplying 8 × 24 and ignoring that there were 5 shifts.

Practice tips

• In a multi-step problem, write down each result and label what it is.
• Reread the final question to be sure you answered exactly what it asked.

Key Formulas

• Cardiac output: CO = HR × SV. Variables: HR = heart rate (beats per minute), SV = stroke volume (mL per beat). Example: HR of 72, SV of 70 mL, CO = 72 × 70 = 5,040 mL/min (about 5 L/min).
• BMI (Body Mass Index): BMI = weight (kg) ÷ height (m)². Normal range: 18.5 to 24.9. Example: 70 kg, 1.75 m tall, BMI = 70 ÷ (1.75 × 1.75) = 70 ÷ 3.0625 ≈ 22.9.
• Blood pressure normal range: about 120/80 mmHg. The top number (systolic) is pressure when the heart beats; the bottom number (diastolic) is pressure when the heart rests between beats.

Study guide: a worked example

Problem. A patient's heart beats 80 times per minute, and each beat pumps 70 mL of blood. What is the cardiac output?

Step by step. Cardiac output is heart rate multiplied by stroke volume: 80 beats × 70 mL = 5,600 mL per minute. Since 1,000 mL equals 1 liter, that is 5.6 liters per minute, which is a normal resting value.

Common mistakes

• Adding the two numbers instead of multiplying them.
• Forgetting that 1,000 mL = 1 liter when converting the final answer.

Practice tips

• Tie each term to its body system. Cardiac output belongs to the circulatory system.
• Learn the normal ranges (resting heart rate about 60 to 100, cardiac output about 5 L/min) so an odd answer stands out.

Study guide: a worked example

Problem. In pea plants, the allele for tall (T) is dominant over the allele for short (t). If two Tt plants are crossed, what fraction of the offspring is expected to be short?

Step by step. Set up a Punnett square for Tt crossed with Tt. The four possible offspring are TT, Tt, Tt, and tt. A plant looks short only when it has no dominant T, which is just the tt result. That is 1 out of 4, or 25%.

Common mistakes

• Thinking a Tt plant looks short. It is tall, because the dominant T hides the t.
• Mixing up genotype (the pair of letters) with phenotype (the trait you can see).

Practice tips

• A recessive trait shows up only when both alleles are recessive.
• Draw the Punnett square every time instead of trying to guess the ratio.

Study guide: a worked example

Question. Sand and mud settle at the bottom of a lake. Over thousands of years the layers are pressed together and harden into rock. What type of rock has formed?

How to work it out. Match the rock type to its action word. Igneous rock cools from melted rock. Sedimentary rock forms from pressed-together layers (sediment). Metamorphic rock is existing rock changed by heat and pressure. Pressed layers means the answer is sedimentary rock.

Common mistakes

• Mixing up metamorphic and sedimentary. Metamorphic needs heat and pressure to change a rock that already exists; sedimentary is simply pressed layers.
• Confusing weather (today's conditions) with climate (the average pattern over many years).

Practice tips

• Tie each term to one verb: igneous = cooled, sedimentary = pressed, metamorphic = changed.
• For the water cycle, remember the order: evaporation, condensation, precipitation, collection.

Study guide: a worked example

Question. A gardener wants to find out whether a new plant food makes tomato plants grow taller. She gives the new food to 10 plants and gives nothing extra to 10 similar plants. What is the hypothesis, and which group is the control?

How to work it out. A hypothesis is a testable "if, then" prediction: "If tomato plants are given the new plant food, then they will grow taller." The control group is the one that gets no treatment, the 10 plants given nothing extra. The control gives her something to compare against.

Common mistakes

• Confusing a hypothesis (one testable guess) with a theory (a well-supported explanation backed by lots of evidence).
• Forgetting the control group, or thinking the control is the group that gets the treatment. It is the opposite.

Practice tips

• Memorize the steps in order: observe, question, hypothesis, experiment, analyze data, conclude.
• The control is always the "no change" version. Everything kept the same in both groups is a constant.

Key Formulas

• Mean (average): mean = sum of all values ÷ how many values there are. Example: for 4, 6, 8, 10, the mean = (4 + 6 + 8 + 10) ÷ 4 = 28 ÷ 4 = 7.
• Median (middle): sort the values from low to high, then take the middle one. If there is an even count, average the two middle values. Example: for 3, 5, 8, the median is 5.
• Mode (most common): the value that appears most often. Example: for 2, 4, 4, 7, 9, the mode is 4. A set can have no mode or more than one.
• Range (spread): range = largest value − smallest value. Example: for 3, 5, 8, 12, the range = 12 − 3 = 9.
• Percent error: percent error = (|measured value − actual value| ÷ actual value) × 100. Example: you measure 48 but the actual value is 50, so percent error = (2 ÷ 50) × 100 = 4%.

Study guide: a worked example

Problem. A student records these test scores: 70, 85, 85, 90, 100. Find the mean, the median, and the mode.

Step by step. Mean (average): add them all and divide by how many there are. (70 + 85 + 85 + 90 + 100) = 430, and 430 ÷ 5 = 86. Median (middle): the scores are already sorted, and the middle of five values is the third one, 85. Mode (most common): 85 appears twice, more than any other score, so the mode is 85.

Common mistakes

• Forgetting to put the numbers in order before picking the median.
• Dividing by the wrong count when finding the mean.

Practice tips

• Always sort the numbers from low to high first.
• Remember: mean is the average, median is the middle, mode is the most frequent.

Study guide: a worked example

Problem. Choose the correct verb: "The box of medical supplies (was / were) left in the hallway."

Step by step. Find the true subject. The subject is "box," not "supplies." The phrase "of medical supplies" just describes the box and does not change what the subject is. "Box" is singular, so it needs the singular verb "was." The correct sentence is "The box of medical supplies was left in the hallway."

Common mistakes

• Matching the verb to the closest noun ("supplies") instead of the real subject.
• Assuming a sentence with plural-sounding words must take a plural verb.

Practice tips

• Cross out the phrase between the subject and the verb, then check that they agree.
• The subject of a sentence is never the noun inside a prepositional phrase.

Study guide: a worked example

Problem. Find and fix the error: "She studied all night, she still felt nervous before the exam."

Step by step. Check each side of the comma. "She studied all night" is a complete sentence, and "she still felt nervous before the exam" is also a complete sentence. Two complete sentences joined by only a comma is a comma splice. Fix it three possible ways: a period, a semicolon, or a comma plus a conjunction. The clearest fix here is "She studied all night, but she still felt nervous before the exam."

Common mistakes

• Believing a comma by itself can join two complete sentences.
• Calling it a fragment. It is the opposite problem: two full sentences, not too little.

Practice tips

• Test whether each side of the comma could stand alone as its own sentence.
• If both sides can stand alone, you need a period, a semicolon, or a comma plus a conjunction.

Study guide: a worked example

Problem. Add the missing comma: "After the long shift the nurse finally sat down."

Step by step. "After the long shift" is an introductory phrase. It sets the scene before the main part of the sentence begins. An introductory word or phrase is followed by a comma. The corrected sentence is "After the long shift, the nurse finally sat down."

Common mistakes

• Leaving out the comma after an introductory phrase.
• Dropping an extra comma into the middle of the main sentence where none is needed.

Practice tips

• If a sentence opens with a phrase before the subject, place a comma right after that phrase.
• Read the sentence aloud. The natural pause usually shows where the comma belongs.

How an essay is built: the three parts

Almost every essay has the same shape. Once you know the shape, you never have to wonder where something goes. Think of it as introduction, body, conclusion.

• 1. Introduction (one paragraph). It does three jobs, in order: a hook (one interesting sentence to pull the reader in), a little background (a sentence or two of context), and the thesis (your main point, always the last sentence of this paragraph).
• 2. Body (usually two or three paragraphs). Each body paragraph covers one reason or idea that supports the thesis. Each one starts with a topic sentence, then gives an example or evidence, then explains how that example proves the point.
• 3. Conclusion (one paragraph). Restate the thesis in fresh words, briefly remind the reader of the main reasons, and end with one final thought. Never add new information in the conclusion.

Common mistake: putting more than one idea in a body paragraph. If a paragraph is about two things, split it into two paragraphs.

Weak paragraph vs strong paragraph

The same idea can be written poorly or well. Read these two short body paragraphs on the same topic, then notice what changed.

What is weak: there is no real topic sentence, the words are vague ("good," "helps you"), no specific examples appear, and the sentences keep repeating the same point.

What changed: a clear topic sentence opens the paragraph, specific examples (thirty minutes of walking, heart disease, sleep, mood) replace vague claims, and a closing sentence ties everything back to the topic.

Writing a strong thesis statement

The thesis is the single most important sentence in the essay. It is your main point in one clear sentence, and it lives at the end of the introduction.

• Take a clear position. A good thesis says something a person could agree or disagree with. If no one could disagree, it is a fact, not a thesis.
• Preview your reasons. The strongest thesis hints at the reasons the body paragraphs will cover.
• Keep it to one sentence. If you need two sentences, the idea is probably too broad. Narrow it.
• Weak example: "There are many opinions about exercise." (No position, nothing to prove.)
• Strong example: "Daily walking improves health because it strengthens the heart, lifts mood, and costs nothing." (Clear position, three previewed reasons.)
• Quick test. Ask: "Could someone argue the opposite? Does this sentence tell the reader exactly what I will prove?" If yes to both, it works.

Transitions: words that connect your ideas

Transitions are signal words that show the reader how one idea relates to the next. They make writing flow instead of feeling like a list. Use them between sentences and at the start of each new paragraph.

• To add an idea: also, in addition, furthermore, moreover, another.
• To show contrast: however, on the other hand, although, in contrast, even so.
• To show cause and effect: because, therefore, as a result, consequently, so.
• To show order or sequence: first, next, then, after that, finally.
• To give an example: for example, for instance, such as, to illustrate.
• To conclude: in conclusion, overall, to sum up, in the end.

A fill-in essay template

When you feel stuck, follow this five-paragraph frame. Fill in the blanks and you have a complete essay.

Practice prompts

Try writing a short essay (even just an outline) for one of these. Use the template above. There is no single right answer; the goal is practicing the structure.

• 1. Should students be required to learn a second language? Take a position and defend it.
• 2. Describe a person who has had a positive influence on your life and explain why.
• 3. Is it better to live in a small town or a large city? Give your reasons.
• 4. Explain why nursing is a meaningful career and what it takes to succeed in it.
• 5. Should cell phones be allowed in classrooms? Argue for one side.

Study guide: a worked example

Problem. Which sentence does not belong in this paragraph? "(1) Regular exercise has many benefits. (2) It strengthens the heart and muscles. (3) It also improves sleep and mood. (4) My neighbor just bought a new car."

Step by step. Sentence 1 is the topic sentence: the paragraph is about the benefits of exercise. Sentences 2 and 3 each give a specific benefit, so they support the topic. Sentence 4 is about a neighbor buying a car, a completely different subject. It breaks the paragraph's unity, so sentence 4 does not belong.

Common mistakes

• Removing a sentence just because it is short, rather than because it is off-topic.
• Keeping an off-topic sentence because it is a true statement. Being true does not make it belong.

Practice tips

• Every sentence in a paragraph must support the topic sentence.
• For "which sentence to remove" questions, look for the one on a different subject.