CAEC STUDY GUIDE 2026 – 2027

Divide both sides by 4: 4x / 4 = 28 / 4, so x = 7.

Add 7 to both sides: x - 7 + 7 = 15 + 7, so x = 22.

Multiply both sides by 3: (x/3) x 3 = 9 x 3, so x = 27.

The slope is 2, and the y-intercept is 3.

Combine like terms: (7x - 2x) + (4 + 6) = 5x + 10.

Subtract 2x from both sides: 3x + 2 = 14. Subtract 2 from both sides: 3x = 12. Divide both sides by 3: x = 4.

Divide both sides by 3: x <= 5.

Subtract 4 from both sides: x > 5.

Subtract 3 from both sides: 2x = 8. Divide both sides by 2: x = 4.

Add 4 to both sides: 3x = 21. Divide both sides by 3: x = 7.

Finding the value of the variable that makes the equation true. x + 5 = 12; subtract 5 from both sides: x = 7.

Terms containing the same variable raised to the same power; like terms are combined by adding or subtracting their coefficients. 3x + 5x = 8x.

A letter or symbol representing an unknown or changeable value, such as x or y.

A mathematical statement comparing two values using symbols such as , =; unlike an equation, which typically has one solution, an inequality's solution is generally a range of values.

The property stating that a(b + c) = ab + ac. Applying it: 3(x + 4) = 3x + 12.

A measure of how steep a line is, calculated as the change in y divided by the change in x (rise over run).

An expression has no equals sign, such as 3x + 5, while an equation states that two expressions are equal, such as 3x + 5 = 20.

y = mx + b, where m represents the slope of the line and b represents the y-intercept.

Substituting the solution back into the original equation verifies that it makes the equation true, helping catch any calculation errors made while solving.

Multiplying or dividing by a negative number reverses the relative order of values, so the inequality symbol must flip to remain accurate. Dividing both sides of -2x > 8 by -2 gives x < -4.

Mean = (5+6+7+8+40) / 5 = 66 / 5 = 13.2. The outlier of 40 pulls the mean well above most of the data, while the median (7) remains a more representative middle value, largely unaffected by the outlier.

Average the two middle values. Sorted: 2, 4, 8, 10. Median = (4 + 8) / 2 = 12 / 2 = 6.

Probability = 4 / (4 + 6) = 4 / 10 = 2/5 (or 0.4, or 40%).

Total sum = average x number of values = 80 x 25 = 2000 (total percentage points across all students).

25% x 400 = 0.25 x 400 = 100 students.

Multiply the individual probabilities: 1/2 x 1/2 = 1/4.

A value significantly higher or lower than the rest of the data; an outlier can significantly skew the mean, pulling it noticeably toward the extreme value.

Identify the correct row and correct column based on the specific labels needed, then locate the value at their intersection.

The likelihood of an event occurring. Probability = number of favorable outcomes / total number of possible outcomes.

A graph using rectangular bars to compare quantities across different categories.

A graph displaying the frequency of data within continuous numerical ranges (intervals), unlike a standard bar graph, which typically compares distinct, separate categories.

A graph using connected points to show how a value changes over time.

A circular chart divided into sections, each representing a proportion or percentage of the whole data set.

The sum of all values divided by the number of values. (4+8+6+10+2) / 5 = 30 / 5 = 6.

The middle value when data is arranged in order. Sorted: 2, 3, 5, 7, 9. The median is 5.

The value that appears most frequently in a data set. The mode is 4, since it appears three times.

The difference between the highest and lowest values. Range = 18 - 3 = 15.

Probability = 1 favorable outcome / 2 possible outcomes = 1/2.

Probability = 1 favorable outcome / 6 possible outcomes = 1/6.

Data and visual representations of data are commonly encountered in everyday life and work, making the ability to accurately interpret both essential for informed, practical decision-making.

Area = 1/2 x base x height = 1/2 x 12 x 7 = 1/2 x 84 = 42 square cm.

Perimeter = 4 x side length = 4 x 6 = 24 inches.

180 - 50 - 60 = 70 degrees.

b^2 = 13^2 - 5^2 = 169 - 25 = 144. b = sqrt(144) = 12.

c^2 = 3^2 + 4^2 = 9 + 16 = 25. c = sqrt(25) = 5 cm.

Two angles whose measures add up to 90 degrees. 90 - 35 = 55 degrees.

Two angles whose measures add up to 180 degrees. 180 - 110 = 70 degrees.

The amount of space inside a two-dimensional shape. Area = length x width = 10 x 4 = 40 square meters.

The total distance around the outside of a shape. Perimeter = 2(length + width) = 2(8 + 5) = 2(13) = 26 cm.

The amount of space inside a three-dimensional object. Volume = length x width x height = 5 x 3 x 4 = 60 cubic cm.

An angle measuring exactly 90 degrees.

An angle measuring exactly 180 degrees, forming a straight line.

An angle measuring less than 90 degrees.

An angle measuring more than 90 degrees but less than 180 degrees.

Area = pi r^2. Area = 3.14 x 5^2 = 3.14 x 25 = 78.5 square cm.

Area = 1/2(base1 + base2) x height. Area = 1/2(6 + 10) x 4 = 1/2(16)(4) = 32 square cm.

Circumference = 2 pi r. Circumference = 2 x 3.14 x 4 = 25.12 cm.

a^2 + b^2 = c^2, where a and b are the legs of a right triangle and c is the hypotenuse.

180 degrees.

Quick recall of formulas allows a test-taker to move directly to solving the problem, rather than spending valuable exam time trying to derive or recall the correct formula.

100,000 centimeters = 1 kilometer, and 1,000 meters = 1 kilometer. 2 x 1,000 = 2,000 m.

100 centimeters = 1 meter. 3.5 x 100 = 350 cm.

3 feet = 1 yard. 12 x 3 = 36 feet.

1,000 grams = 1 kilogram. 2.5 x 1,000 = 2,500 g.

12 inches = 1 foot. 5 x 12 = 60 inches.

1,000 milliliters = 1 liter. 0.75 x 1,000 = 750 mL.

60 minutes = 1 hour. 3.5 x 60 = 210 minutes.

16 ounces = 1 pound. 3.5 x 16 = 56 ounces.

$1,200 / 12 = $100 per payment.

7:15 PM + 2 hours = 9:15 PM. 9:15 PM + 20 minutes = 9:35 PM.

$18.50 x 32 = $592.00.

$50.00 - $24.50 = $25.50.

Discount = 25% x $80 = 0.25 x 80 = $20. Sale price = $80 - $20 = $60.

Tax = 8% x $75 = 0.08 x 75 = $6.00. Total = $75 + $6.00 = $81.00.

From 8:45 to 9:00 is 15 minutes; from 9:00 to 9:20 is 20 minutes. 15 + 20 = 35 minutes.

I = P x r x t = 1,000 x 0.05 x 2 = $100.

F = (C x 9/5) + 32. (20 x 9/5) + 32 = 36 + 32 = 68 degrees F.

C = (F - 32) x 5/9. (68 - 32) x 5/9 = 36 x 5/9 = 20 degrees C.

Interest calculated only on the original principal amount, using the formula I = P x r x t, where P is principal, r is annual interest rate, and t is time in years.

A plan tracking income against expenses. Remaining balance = $2,000 - $1,650 = $350.

First leg: 60 x 2.5 = 150 miles. Second leg: 40 x 1.5 = 60 miles. Total distance = 150 + 60 = 210 miles.

Total cost = 150 x $8 = $1,200. Total revenue = 150 x $15 = $2,250. Profit = $2,250 - $1,200 = $1,050.

Total deposits = $150 x 4 = $600. Balance before withdrawal = $500 + $600 = $1,100. Final balance = $1,100 - $200 = $900.

Any nonzero number raised to the power of 0 equals 1. 7^0 = 1.

Identifying exactly what the problem is asking, listing the known information, and solving one clear step at a time rather than attempting the entire problem at once.

Finding an approximate value using rounded numbers; it is useful because a quick estimate can help identify whether an exact calculated answer is reasonably close to expected.

A way of writing very large or very small numbers using a number between 1 and 10 multiplied by a power of 10. 4,500,000 = 4.5 x 10^6.

The largest number that divides evenly into two or more numbers. Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 18: 1, 2, 3, 6, 9, 18. The greatest common factor is 6.

A value that, when multiplied by itself, produces the original number. sqrt(64) = 8, since 8 x 8 = 64.

A number indicating how many times a base number is multiplied by itself. 3^4 = 3 x 3 x 3 x 3 = 81.

The smallest number that is a multiple of two or more numbers. Multiples of 4: 4, 8, 12, 16. Multiples of 6: 6, 12, 18. The least common multiple is 12.

sqrt(81) = 9, since 9 x 9 = 81.

Look at the tens digit; if it is 5 or greater, round up; if less than 5, round down. 362 rounds to 400.

Look at the ones digit; if it is 5 or greater, round up; if less than 5, round down. 47 rounds to 50.

Subtract the smaller absolute value from the larger and keep the sign of the larger value. 12 + (-7) = 5.

Add the absolute values and keep the negative sign. -5 + (-8) = -13.

A negative times a positive equals a negative. -5 x 4 = -20.

A negative times a negative equals a positive. -6 x -3 = 18.

Subtracting a negative number is the same as adding its positive value. 10 - (-4) = 10 + 4 = 14.

Showing each step helps catch calculation errors along the way and, on many assessments, can earn partial credit even if the final answer is not entirely correct.

By writing the decimal digits as the numerator over the appropriate power of ten as the denominator, then simplifying.

By dividing the numerator by the denominator.

Multiply the whole number by the denominator, add the numerator, and place that result over the original denominator.

Divide the numerator by the denominator; the quotient becomes the whole number, and the remainder becomes the new numerator over the original denominator.

Rewriting a fraction in its lowest terms by dividing the numerator and denominator by their greatest common factor.

Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right).

A shared denominator between two or more fractions; a common denominator is required before adding or subtracting because the fractions must represent parts of the same-sized whole.

A number expressed using a decimal point to represent a value that includes a fractional part based on powers of ten.

A number representing a part of a whole; the numerator represents the number of parts being considered, and the denominator represents the total number of equal parts.

A number combining a whole number and a proper fraction, such as 2 1/2, unlike an improper fraction, which has a numerator larger than or equal to its denominator.

A fraction flipped so that its numerator and denominator are switched; it is used in fraction division by multiplying the first fraction by the reciprocal of the second.

A fraction with a different numerator and denominator but the same overall value as the original; equivalent fractions can be created by multiplying or dividing both the numerator and denominator by the same number.

A fraction in which the numerator is greater than or equal to the denominator; it can be converted into a mixed number.

The bottom number of a fraction, representing the total number of equal parts in the whole.

The top number of a fraction, representing how many parts are being considered.

The standard sequence for solving a mathematical expression with multiple operations; the acronym PEMDAS is commonly used to remember this order.

Add or subtract the numerators while keeping the denominator the same.

Multiply the first fraction by the reciprocal of the second fraction.

Multiply the numerators together and multiply the denominators together.

Multiplication is generally performed before addition.

Multiply the decimal by 100 (or move the decimal point two places right). 0.6 x 100 = 60%.

Divide the numerator by the denominator, then multiply by 100. 3 / 4 = 0.75; 0.75 x 100 = 75%.

Divide the percent by 100 (or move the decimal point two places left). 45% = 45 / 100 = 0.45.

30 / 120 = 0.25; 0.25 x 100 = 25%.

Discount amount = 20% x $40 = 0.20 x 40 = $8. Sale price = $40 - $8 = $32.

Set up the proportion 2/3 = x/9. Cross multiply: 3x = 18, so x = 6 cups of flour.

(55 - 50) / 50 x 100 = 5 / 50 x 100 = 10%.

Set up the proportion 5/7 = x/35. Cross multiply: 7x = 175, so x = 25 boys.

Multiplying the numerator of one fraction by the denominator of the other, and setting the two products equal; it is used to solve for an unknown value within a proportion.

15% x 200 = 0.15 x 200 = 30.

25% x 80 = 0.25 x 80 = 20.

A way of expressing a number as a fraction of 100; "percent" literally means "per hundred," so 45% means 45 out of 100.

A statement that two ratios are equal. Cross multiply: 3 x 20 = 4 x x, so 60 = 4x, so x = 15.

A comparison of two quantities. 8:12 simplifies to 2:3 by dividing both numbers by their greatest common factor, 4.

A rate expressed per single unit of the second quantity. 240 miles / 4 hours = 60 miles per hour.

Percent decrease = (old value - new value) / old value x 100. (80 - 60) / 80 x 100 = 20 / 80 x 100 = 25%.

Percent increase = (new value - old value) / old value x 100. (65 - 50) / 50 x 100 = 15 / 50 x 100 = 30%.

Discount amount = 30% x $120 = 0.30 x 120 = $36. Sale price = $120 - $36 = $84.

15% x $60 = 0.15 x 60 = $9.

Understanding the concept helps a test-taker recognize which type of problem they're facing, while knowing the calculation steps ensures they can actually arrive at the correct numerical answer under exam conditions.

The arrangement of words and phrases within a sentence can affect emphasis and clarity, sometimes changing how a reader interprets the intended meaning.

Words such as "therefore," "thus," and "in conclusion" signal that a summarizing or concluding point is being made.

Words such as "however," "although," and "nevertheless" signal a contrast or exception to a previous point.

Words such as "additionally," "furthermore," and "moreover" signal that more supporting information is being added.

Reading for detail means carefully noting specific facts and information, while reading for gist means gathering only a general overall understanding.

Reading to gather a general overall sense of a passage's content; it may be sufficient when specific details are not needed, such as when quickly deciding whether a text is relevant.

Comparing the specific details and evidence each source provides, while considering the credibility and perspective of each source.

An engaged approach to reading involving behaviors such as annotating important points, asking questions, and making connections while reading, rather than passively moving through the text.

Specialized terminology specific to a particular field or subject; unfamiliar technical vocabulary may require extra attention because these terms are less likely to be already known to the reader.

A sentence containing an independent clause and at least one dependent clause; it may be more challenging because it requires tracking multiple related ideas within a single sentence.

An organized listing helping a person locate a specific item, location, or piece of information within a larger structure.

A visual representation of a physical location or route; interpreting it requires understanding symbols, scale, and spatial relationships.

A functional text listing times and events in an organized format; interpreting it requires carefully cross-referencing specific rows and columns to find accurate, relevant information.

A word or phrase that connects ideas and signals the relationship between them, such as addition, contrast, or conclusion.

Previewing these elements can provide a helpful overview of the passage's topic and structure before engaging in detailed reading.

Eliminating clearly incorrect answer choices narrows the options and increases the likelihood of selecting the correct answer, even when uncertain.

Exposure to diverse text types and topics helps build vocabulary, familiarity with different structures, and overall reading fluency over time.

Different sources may have different perspectives, access to information, or biases, all of which can lead to differing accounts of the same event.

Punctuation helps clarify how different parts of a sentence relate to one another, and misreading punctuation can lead to misunderstanding the sentence's intended meaning.

Test questions sometimes include distractor answers using familiar wording from the passage that does not actually correctly answer the specific question being asked.

Understanding the author's purpose helps the reader recognize the intent behind word choices and content, supporting more accurate and critical interpretation.

Drawing a logical conclusion based on evidence in the text combined with the reader's own reasoning, even though the conclusion is not directly stated.

The surrounding words and sentences that can help a reader figure out the meaning of an unfamiliar word.

A final judgment or decision reached based on the information presented; drawing a conclusion often involves inference, since it requires connecting details to form an overall understanding.

A hint within the surrounding text, such as a definition, example, or contrast, that helps reveal the meaning of an unfamiliar word.

An educated guess about what will happen next in a passage, based on clues already provided; like inference, it relies on using textual evidence to reason beyond what is directly stated.

A brief restatement of a passage's most important content; an effective summary captures the main idea along with the most essential supporting details, without minor details.

A specific fact, example, or piece of evidence that explains or supports the main idea.

A sentence stating the main idea of a paragraph, most commonly found at the beginning of the paragraph, though it can appear elsewhere.

The author's reason for writing; common purposes include to inform, to persuade, and to entertain.

An implicit main idea is not directly stated and must be inferred from the passage, while an explicit main idea is clearly stated outright.

Specific words, phrases, or details drawn directly from the passage; citing textual evidence is important because it grounds an inference in what the passage actually says, rather than in unsupported assumption.

The central point or most important message the author wants to convey about the topic.

Literal comprehension involves understanding what is directly stated in the text, while inferential comprehension involves understanding what is implied but not directly stated.

A fact is a statement that can be objectively verified as true, while an opinion is a personal belief or judgment that cannot be objectively proven.

A topic is the general subject a passage is about, while the main idea is the specific point the author makes about that topic.

Inference questions require noticing subtle details and connections within the text, which can be easily missed if a passage is read too quickly or superficially.

A passage may have one overall main idea while individual paragraphs each support that main idea with their own more specific point, so recognizing the difference helps avoid confusing a supporting detail with the passage's central message.

A valid inference must be reasonably supported by what the text actually states or implies, distinguishing it from an unsupported guess.

The correct main idea must accurately and completely reflect the passage's central point, not simply be a true but incomplete or overly general statement.

Identifying the main points and key details in each text separately, then directly comparing similarities and differences between them.

The way an author reveals a character's personality and traits, generally through direct characterization or indirect characterization.

Reading a text slowly and carefully to fully understand its details and nuances; it is necessary when deep, precise comprehension is required, such as for detailed or complex passages.

A method in which the author explicitly states a character's traits directly to the reader.

Practical, everyday text designed to help a reader accomplish a specific task or convey specific practical information.

A category of literature defined by its style, form, or content; common genres include fiction, nonfiction, poetry, and drama.

A method in which a character's traits are revealed through their actions, dialogue, thoughts, or how other characters react to them, rather than through direct statements.

The sequence of events in a story; it typically includes exposition, rising action, climax, falling action, and resolution.

The stage in which the story's conflicts are resolved and loose ends are tied up.

Quickly searching a text for specific information, such as a name or date, unlike skimming, which aims to get a general overall impression of the whole text.

Quickly reading through a text to get a general sense of its content; it can be useful when trying to get an overview before reading in detail.

The underlying message or central idea about life that a story conveys, distinct from the plot, which is the actual sequence of events in the story.

The main character of a story, around whom the central conflict typically revolves.

A visual arrangement of data or information; it can supplement surrounding text by presenting complex information in an organized, easy-to-reference format.

A character or force that opposes the protagonist, creating the central conflict of the story.

The turning point or moment of highest tension in a story.

The opening stage of a story, introducing the characters, setting, and initial situation.

Fiction is imaginative writing based on invented characters or events, while nonfiction presents factual information about real people, events, or topics.

Many real-world and test materials combine text with visual data, so effectively interpreting both together is necessary for a complete and accurate understanding.

Missing a step or detail in functional text, such as instructions, could result in an error or incomplete task, since these texts are typically meant to be followed precisely.

Language used to express meaning beyond its literal interpretation, often to create a vivid or imaginative effect, unlike literal language, which means exactly what it states.

A perspective in which the narrator is a participant in the story, identifiable through the use of pronouns such as "I" and "we."

The overall feeling or atmosphere a piece of writing creates for the reader, distinct from tone, which reflects the author's own attitude.

The perspective from which a text is told; common perspectives include first-person and third-person.

The way an author organizes information within a text; recognizing the structure helps a reader anticipate and follow the flow of ideas.

A perspective in which the narrator is an outside observer, referring to characters using pronouns such as "he," "she," or "they," rather than participating directly as "I."

The author's attitude toward the subject or audience, conveyed through word choice and writing style.

A visual representation used to organize information; it can support comprehension by helping a reader visually see relationships and structure within the content.

A direct comparison between two unlike things without using "like" or "as," stating that one thing actually is another.

An original, firsthand source of information created at the time of an event, such as a letter, diary, or photograph.

A source that interprets, analyzes, or discusses information from primary sources, rather than being an original, firsthand account.

A comparison between two unlike things using the words "like" or "as."

A structure that explains why something happened (the cause) and what resulted from it (the effect).

A structure that presents events or steps in the order in which they occur.

A structure that examines the similarities and differences between two or more subjects.

A structure that presents detailed characteristics, features, or examples about a topic, without necessarily following a strict sequence or comparison.

A structure that presents a problem and then describes one or more possible solutions to that problem.

Words such as "because," "as a result," "therefore," and "consequently."

Words such as "first," "next," "then," and "finally."

Words such as "similarly," "however," "in contrast," and "on the other hand."

Assessing whether a source is trustworthy and reliable; factors to consider include the author's expertise, the source's reputation, and potential bias.

"Again" or "back"; for example, "rewrite" means to write again.

"Not" or the opposite of; for example, "unhappy" means not happy.

"Capable of" or "able to be"; for example, "readable" means able to be read.

A one-sided or prejudiced perspective within a text; recognizing bias helps a reader critically evaluate whether the presented information is balanced and fair.

The emotional or cultural association a word carries beyond its literal definition, distinct from denotation, which is the word's literal meaning.

The literal, dictionary definition of a word.

Facts, examples, statistics, or expert opinions used to support the validity of a claim.

The main position or assertion an author is trying to persuade the reader to accept.

An opposing viewpoint acknowledged within a persuasive piece; an author might include one to address potential objections and strengthen their own argument's credibility.

An error in reasoning that weakens the validity of an argument; critical readers should be alert to fallacies because they can make a weak argument appear more convincing than it actually is.

A word part added to the beginning of a base word, generally changing or adding to the word's meaning.

The core part of a word that carries its basic meaning; understanding common roots is useful because it can help a reader determine the meaning of many related, unfamiliar words.

A word part added to the end of a base word, often changing the word's part of speech or meaning.

A word with a similar meaning to another word; recognizing synonyms can help a reader infer the meaning of an unfamiliar word based on a more familiar one nearby.

A word with the opposite meaning of another word, unlike a synonym, which shares a similar meaning.

A position supported by reasoning and evidence, typically including a claim, supporting evidence, and reasoning connecting the two.

Summarizing condenses the main points of a passage into a much shorter form, while paraphrasing restates the full content of a passage in different words, without necessarily shortening it.

Using the same wording without proper attribution, even when claiming to summarize or paraphrase, can constitute plagiarism rather than genuinely restating the content in one's own words.

Even though both words describe careful spending, "frugal" generally carries a positive connotation while "stingy" carries a negative one, illustrating how word choice can shape a reader's impression beyond literal meaning.

Eight planets: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune.

Crust, mantle, outer core, and inner core.

Igneous, sedimentary, and metamorphic rock, each forming through a different process involving cooling magma, compressed sediment, or heat and pressure.

The tilt of Earth's axis as it orbits the sun, causing different regions to receive varying amounts of direct sunlight throughout the year.

The process by which water vapor cools and changes back into liquid water, forming clouds, the reverse of evaporation.

The process by which liquid water is heated and changes into water vapor, rising into the atmosphere.

The theory that Earth's outer surface is divided into large plates that slowly move over time.

Water falling from clouds back to Earth's surface, in forms such as rain, snow, or hail.

A rock formed when an existing rock is transformed by intense heat and pressure without melting.

A celestial body that orbits a star, is roughly spherical due to its own gravity, and has cleared its orbital path of other debris.

A rock formed from compressed and cemented layers of sediment over time.

A sudden shaking of the ground caused by the release of energy, generally resulting from movement along a fault where tectonic plates meet.

A rock formed from the cooling and solidification of molten magma or lava.

The natural process by which certain atmospheric gases trap heat from the sun, keeping the Earth warm enough to support life.

The continuous transformation of rocks among three main types through processes such as heat, pressure, and weathering.

A collection of planets, moons, and other objects orbiting a central star; our solar system orbits the sun.

The continuous movement of water through evaporation, condensation, precipitation, and collection.

The thin, solid outermost layer of the Earth, on which we live.

Weather refers to short-term atmospheric conditions in a specific place, while climate refers to long-term average weather patterns over a larger region and time span.

Increased greenhouse gas emissions from human activity have been linked to an enhanced greenhouse effect, contributing to broader changes in global climate.

Inputs are carbon dioxide, water, and light energy; outputs are glucose and oxygen.

Systems such as the circulatory, respiratory, digestive, and nervous systems, each performing specialized functions that together support overall bodily function.

The process by which cells convert glucose and oxygen into energy, carbon dioxide, and water; it is essentially the reverse of photosynthesis.

Deoxyribonucleic acid, a molecule carrying the genetic instructions for an organism's development, functioning, and reproduction.

The maintenance of a stable internal environment; it is important because many bodily processes function properly only within a relatively narrow, stable range.

The process by which plants use sunlight to convert carbon dioxide and water into glucose and oxygen.

The smallest basic structural and functional unit of all living organisms.

An organism that obtains energy by eating other organisms; general types include herbivores (plant-eaters), carnivores (meat-eaters), and omnivores (eat both).

An organism that breaks down dead organic material, returning nutrients back into the ecosystem.

A sequence showing how energy passes from one organism to another through feeding relationships.

A segment of DNA that codes for a specific trait, passed from parent to offspring.

An organism, such as a plant, that produces its own energy through photosynthesis, forming the base of most food chains.

A community of living organisms interacting with each other and their physical environment.

A membrane-bound structure within a eukaryotic cell that houses the cell's genetic material (DNA) and controls cellular activity.

A dominant trait will be expressed if at least one copy of the gene is present, while a recessive trait is only expressed if two copies of the recessive gene are present.

A prokaryotic cell lacks a nucleus and membrane-bound organelles, while a eukaryotic cell contains a true nucleus and membrane-bound organelles.

Kingdom, phylum, class, order, family, genus, and species.

Transporting blood, oxygen, and nutrients throughout the body.

Breaking down food into nutrients the body can absorb and use for energy.

Facilitating the exchange of oxygen and carbon dioxide between the body and the environment.

Solid, liquid, and gas, distinguished generally by how tightly and how freely their particles are arranged and able to move.

Protons, neutrons, and electrons.

A push or pull acting on an object, which can cause the object to accelerate, decelerate, or change direction.

Anything that has mass and takes up space (volume).

A process in which substances are transformed into new substances; indications may include a color change, temperature change, gas production, or formation of a solid precipitate.

A state of matter with no fixed shape or volume, in which particles are widely spaced and move freely, unlike the closer arrangement in a liquid.

A state of matter with a fixed volume but no fixed shape, in which particles are close together but can move past one another, unlike the fixed positions in a solid.

A subatomic particle located in the nucleus, carrying no electrical charge (neutral).

A subatomic particle located in the nucleus, carrying a positive charge.

A basic mechanical device that changes the direction or magnitude of a force, making work easier to perform.

A state of matter with a fixed shape and volume, in which particles are tightly packed and vibrate in place.

The smallest basic unit of an element, consisting of a nucleus containing protons and neutrons, surrounded by orbiting electrons.

A subatomic particle orbiting the nucleus, carrying a negative charge.

A pure substance made of only one type of atom; the periodic table organizes all known elements based on their atomic structure and properties.

A rigid bar pivoting on a fixed point (fulcrum), such as a seesaw; it makes work easier by allowing a smaller applied force to move a larger load.

An object at rest stays at rest, and an object in motion stays in motion at a constant velocity, unless acted upon by an external force.

Force equals mass times acceleration (F = ma), describing how the acceleration of an object depends on the net force applied and the object's mass.

For every force one object exerts on a second object, the second object exerts an equal force in the opposite direction back on the first.

A physical change alters a substance's form without changing its chemical composition, while a chemical change results in the formation of a new substance with different chemical properties.

Kinetic energy is the energy of motion, while potential energy is stored energy based on an object's position or condition.

Nutrients required in relatively large amounts by the body, typically including carbohydrates, proteins, and fats.

Ask a question, conduct background research, form a hypothesis, test the hypothesis through experimentation, analyze the data, and draw a conclusion.

Considerations such as privacy, fairness, safety, and environmental impact often arise when evaluating how a new technology may affect individuals and society.

The body's ability to resist a specific infection or disease; it can develop through prior exposure to a pathogen or through vaccination.

A process in which other experts in the field evaluate research before publication, helping ensure scientific findings meet an appropriate standard of quality and rigor.

The introduction of harmful substances into the environment; common categories include air, water, and land (soil) pollution.

Meeting present needs without compromising the ability of future generations to meet their own needs; it has become increasingly important due to growing awareness of environmental and resource limitations.

A group that does not receive the experimental treatment, serving as a baseline for comparison against the group that does.

A testable, proposed explanation for an observed phenomenon; a good hypothesis must be specific and testable through experimentation.

A natural resource that exists in a limited supply and cannot be replenished on a human timescale, such as fossil fuels, unlike a renewable resource.

A natural resource that can be replenished relatively quickly, such as solar or wind energy.

A medical preparation that stimulates the immune system to recognize and fight a specific pathogen, helping build immunity without causing the actual disease.

A factor that can be changed or measured within an experiment.

A statement describing a consistent, observed pattern in nature, generally describing what happens, while a theory more broadly explains why it happens.

A well-substantiated explanation supported by extensive evidence and repeated testing, unlike the everyday casual use of the word, which often implies mere speculation or a guess.

A systematic process for investigating questions through observation, experimentation, and analysis, used to develop reliable, evidence-based conclusions.

The independent variable is the factor deliberately changed by the researcher, while the dependent variable is the factor measured to see how it responds to that change.

Different food groups provide different essential nutrients, and a balanced diet helps ensure the body receives all the nutrients it needs to function properly.

A basic understanding of scientific concepts helps individuals make informed, evidence-based decisions in many aspects of daily life, from health choices to evaluating new technologies.

Evidence-based testing helps ensure that scientific conclusions are objectively verified and reliable, rather than simply reflecting unverified belief or influence.

Goods shifted from being made largely by hand in homes or small shops to being mass-produced in factories using machinery.

Meter (length), gram (mass), and liter (volume).

Questions about privacy, consent, and how collected data may be used, shared, or potentially misused.

The internet has dramatically increased the speed and ease with which people can access, share, and communicate information globally.

Equipment such as safety goggles, gloves, and lab coats.

Technology enabling machines to perform tasks that typically require human intelligence, such as learning, reasoning, and problem-solving.

The use of technology to perform tasks with minimal human intervention; it has significantly changed many industries by increasing efficiency while also shifting the types of jobs available.

Long-term shifts in global temperature and weather patterns.

The practice of using natural resources carefully and responsibly to prevent depletion or damage.

The ability to effectively find, evaluate, and use digital information and technology; it has become increasingly important as more aspects of daily life and work rely on digital tools.

Practices and procedures designed to protect individuals from hazards during scientific work; they are important because experiments can involve materials or conditions that pose genuine safety risks.

The process of converting used materials into new products; it helps reduce environmental impact by lowering waste and reducing the need for new raw materials.

Energy generated by converting sunlight into electricity, typically using solar panels.

Energy generated by converting the kinetic energy of wind into electricity, typically using wind turbines.

A nonrenewable energy source formed from the remains of ancient organisms; common examples include coal, oil, and natural gas.

A period of major technological and economic change beginning in the late 1700s, marked by a shift from manual production methods to machine-based manufacturing.

An era marked by the widespread shift toward digital technology, computing, and rapid information exchange.

A decimal-based system of measurement; it is widely used in science because its base-ten structure makes calculations and conversions simpler and more consistent.

The scientific consensus attributes recent climate change primarily to human activities, particularly the emission of greenhouse gases.

Science and technology increasingly shape everyday decisions and broader societal issues, making a general understanding of their interaction valuable for informed, engaged participation in modern life.

Ten provinces and three territories.

A group of large freshwater lakes along the Canada-United States border, generally associated with the province of Ontario.

A major mountain range located in western Canada, primarily in British Columbia and Alberta.

Ontario, Quebec, Nova Scotia, New Brunswick, Manitoba, British Columbia, Prince Edward Island, Saskatchewan, Alberta, and Newfoundland and Labrador.

Yukon, Northwest Territories, and Nunavut.

Price generally increases.

Price generally decreases.

Gross income is total earnings before any deductions, while net income is the amount remaining after deductions such as taxes.

A federal consumption tax applied to most goods and services sold in Canada.

A general increase in prices over time, which reduces the purchasing power of a given amount of money.

A fundamental economic principle describing the relationship between the availability of a product and consumer desire for it; this relationship generally influences the product's price.

A numerical representation of an individual's creditworthiness, used by lenders to assess the risk of extending credit.

An economic system in which decisions about production and pricing are largely guided by supply and demand, rather than centralized government control.

Ottawa, located in the province of Ontario.

The Mackenzie River, which flows through Canada's Northwest Territories.

A large geological region of ancient exposed rock covering much of central and eastern Canada.

A need is essential for basic survival, such as food or shelter, while a want is a desired but non-essential item or experience.

Quebec.

Ontario.

This knowledge supports informed decision-making in everyday financial matters and a broader understanding of the country in which one lives and participates as a citizen.

The leader of the political party that wins the most seats in a federal election generally becomes Prime Minister.

The executive branch (implements laws), the legislative branch (makes laws), and the judicial branch (interprets laws).

Federal, provincial or territorial, and municipal government.

Responsibilities such as local infrastructure, waste collection, and municipal policing or bylaws.

Responsibilities such as education, healthcare, and natural resources within that specific province or territory.

A system of government dividing power between a central (federal) government and regional (provincial or territorial) governments.

A system in which a monarch serves as the ceremonial head of state, while actual governing power rests with elected officials operating under a constitution.

An elected representative in the House of Commons, responsible for representing the interests of their specific riding.

A system of government in which the executive branch derives its authority from, and is accountable to, an elected legislative body (Parliament).

A specific geographic area represented by one elected Member of Parliament, used to organize federal elections.

The branch responsible for implementing and enforcing laws, led by the Prime Minister and Cabinet.

The elected lower chamber of Parliament, with members chosen through federal elections held in individual electoral districts.

The branch responsible for interpreting laws and administering justice through the court system.

The branch responsible for making laws, consisting of Parliament.

The upper chamber of Parliament; senators are generally appointed, rather than elected, unlike members of the House of Commons.

Canada's federal legislative body, consisting of the House of Commons and the Senate.

18 years of age.

A federal parliamentary democracy operating under a constitutional monarchy.

The head of government, responsible for leading the executive branch and generally holding significant influence over government policy and direction.

Understanding how government functions supports informed participation in civic life, including voting and engaging with public institutions.

Ontario, Quebec, Nova Scotia, and New Brunswick.

Successive waves of immigration from Europe and, increasingly over time, from many other regions of the world, contributing significantly to Canada's demographic diversity.

Canada fought as part of the British Empire, contributing significant troops and resources to the war effort.

Canada made substantial military, industrial, and economic contributions to the Allied war effort.

The union of British North American colonies into a single federal country; it occurred in 1867.

A constitutional document guaranteeing fundamental rights and freedoms to Canadians, formally adopted in 1982.

Federal legislation, first passed in 1876, governing many aspects of First Nations status and life; it has historically been, and continues to be, widely criticized for its paternalistic and harmful impact on Indigenous peoples.

A period of significant social, political, and secular change in Quebec during the 1960s.

British legislation granting legislative independence to Canada and other dominions, marking a significant step toward full Canadian sovereignty.

A national holiday celebrated on July 1st, commemorating the anniversary of Confederation in 1867.

A Metis leader who led resistance movements, including the Red River Resistance and the North-West Resistance, and remains a significant, complex figure in Canadian and Metis history.

A major World War I battle in April 1917 in which Canadian forces achieved a significant victory; it is often considered significant to Canadian national identity as a moment of national pride and unity.

The 1867 British legislation that established the Dominion of Canada and its federal constitutional structure.

A transcontinental railway completed in 1885, connecting Canada from coast to coast and supporting national unity and westward expansion.

A government-sponsored, church-run school system that forcibly removed Indigenous children from their families, causing profound and lasting harm to Indigenous individuals, families, and communities.

John A. Macdonald, among several other key figures involved in the Confederation negotiations.

The reigning monarch of the United Kingdom, formally represented in Canada domestically by the Governor General.

John A. Macdonald.

The original Indigenous peoples of Canada, present long before European colonization, who have played a foundational and ongoing role throughout Canadian history.

A foundational understanding of national history supports informed civic participation and a broader understanding of Canada's identity and institutions.

"She likes running, to swim, and biking" lacks parallel structure; it could be corrected to "She likes running, swimming, and biking" by making all three verb forms consistent.

Using the same grammatical form for items in a series or list; it is important because inconsistent forms can make a sentence awkward or unclear.

A modifier that does not clearly refer to any specific word in the sentence at all, unlike a misplaced modifier, which is simply positioned incorrectly relative to the word it does describe.

An error using two comparative or superlative forms together, such as "more better"; it is generally considered incorrect because only one comparative or superlative form should be used at a time.

The use of two negative words within the same clause, such as "don't have no"; it is generally considered incorrect because standard English convention requires only a single negative to express negation.

A descriptive word or phrase placed too far from the word it is meant to describe, creating confusion or an unintended meaning.

An error occurring when a pronoun does not match its antecedent in number or gender.

A construction in which a word is placed between "to" and the verb, such as "to boldly go"; it was traditionally discouraged, though it is now widely accepted in modern standard usage.

"Affect" is generally used as a verb meaning to influence, while "effect" is generally used as a noun meaning a result.

"Fewer" is used with countable items, while "less" is used with uncountable quantities.

"Good" is an adjective describing a noun, while "well" is generally an adverb describing how an action is performed.

"Its" shows possession, while "it's" is a contraction of "it is" or "it has."

"Lie" means to recline and does not take a direct object, while "lay" means to place something down and does take a direct object.

"Their" shows possession, "there" indicates a location, and "they're" is a contraction of "they are."

"Then" refers to time or sequence, while "than" is used for making comparisons.

"To" indicates direction or is part of an infinitive verb, "too" means "also" or "excessively," and "two" is the number 2.

"Who" is used as a subject, while "whom" is used as an object.

"Your" shows possession, while "you're" is a contraction of "you are."

Proofreading helps catch errors that could otherwise confuse the reader or undermine the writer's credibility.

Understanding the underlying rule allows a writer to correctly apply it consistently across many different sentences, rather than relying on memorization for each individual case.

The paragraphs following the introduction, each developing a specific point or piece of evidence that supports the thesis statement.

A strong thesis statement is clear, specific, and arguable or explanatory, rather than vague or overly broad.

The logical flow and clear connection between ideas throughout a piece of writing; it is important because it helps the reader easily follow and understand the writer's overall message.

The stage in which the writer creates an initial, complete version of the piece based on the outline or plan.

The stage focused on correcting grammar, spelling, punctuation, and other surface-level errors.

The stage focused on improving the content, organization, and clarity of ideas within a draft, distinct from proofreading, which focuses on correcting surface-level errors.

The final paragraph of an essay, generally summarizing the main points and reinforcing the thesis without introducing new information.

An essay that vividly describes a person, place, object, or experience, generally aiming to create a strong sensory impression for the reader.

An engaging opening sentence or statement designed to capture the reader's interest at the start of an essay.

An essay that tells a story, typically based on a personal experience or event.

An essay attempting to convince the reader to accept a particular position, unlike an expository essay, which aims to inform rather than persuade.

A sentence stating the main point or argument of an essay, guiding the direction of the entire piece.

An essay that explains or informs the reader about a topic in a clear, factual manner.

The opening paragraph of an essay, typically including a hook to engage the reader, background context, and the thesis statement.

A structured plan organizing an essay's main points and supporting details before writing begins, helping guide the drafting process.

An introduction, three body paragraphs, and a conclusion.

Prewriting (planning), drafting, revising, editing, and publishing (finalizing).

Typically at or near the end of the introduction paragraph.

Revising addresses larger issues of content and structure, while editing addresses smaller, surface-level errors, making them distinct types of review best performed separately.

Transitions between paragraphs help guide the reader smoothly from one idea to the next, maintaining overall coherence across the entire essay.

Yes, days of the week and months of the year are capitalized because they are considered proper nouns.

Proper nouns, including specific names of people, places, and organizations, must always be capitalized.

The first word of every sentence must be capitalized.

Acknowledging where borrowed information originally came from; it is important because it gives proper credit to the original source and helps avoid plagiarism.

Expressing ideas clearly using as few words as necessary; it is valuable because it helps communicate ideas efficiently and keeps the reader engaged.

A writing style characterized by proper grammar, an objective tone, and avoidance of slang or contractions, typically used in professional or academic contexts.

A more casual writing style, often including contractions, slang, and a conversational tone, unlike the more structured, objective style of formal writing.

Writing that presents factual information on a topic, unlike narrative writing, which tells a story.

The specific words a writer selects; precise, appropriate word choice matters because it directly affects how clearly and effectively an idea is communicated.

The use of unnecessary words or overly complicated phrasing; it should generally be avoided because it can obscure the writer's meaning and reduce clarity.

A brief, formal written communication used within an organization to convey information, typically addressing a specific, focused topic.

A structured written communication typically following a specific format, including a heading, greeting, body, and closing.

A formal electronic communication used in a professional context; it should generally include a clear subject line, appropriate greeting, concise body, and professional closing.

"I before e, except after c"; a common exception occurs in words such as "weird" or "science."

A longer, developed piece of writing responding to a prompt, generally requiring a clear thesis, organized supporting points, and a conclusion.

A title is capitalized when it directly precedes a person's name, but generally not when used generically without a name.

Changing the "y" to "i" and adding "es."

Adding "s" to the end of the singular noun.

Adult learners need to communicate effectively across a wide range of real-world situations, making versatile, well-rounded writing skills a genuinely valuable and broadly applicable competency.

Different audiences and purposes call for different levels of formality, and choosing the appropriate style helps ensure the writing is well-received and effective.

For, and, nor, but, or, yet, and so.

A verb tense describing an action that will happen at a later time.

A verb tense describing an action that has already happened.

A verb tense describing an action currently happening or a general truth.

The grammatical rule requiring a verb to match its subject in number, meaning a singular subject takes a singular verb, and a plural subject takes a plural verb.

The form of a verb indicating when an action takes place, whether in the past, present, or future.

A general name for a person, place, or thing, such as "city," unlike a proper noun, which names a specific person, place, or thing.

A word that connects words, phrases, or clauses within a sentence.

A verb that connects the subject to additional information about it, such as "is" or "seems," rather than expressing an action.

A word that names a person, place, thing, or idea.

A subject referring to more than one person or thing; a plural subject generally takes a plural verb form.

A word showing the relationship between a noun or pronoun and another word in the sentence, such as "in," "on," or "under."

A word that takes the place of a noun, such as "he," "she," or "it."

The specific name of a particular person, place, or thing, such as "Toronto"; proper nouns are always capitalized.

A subject referring to one person or thing; a singular subject generally takes a singular verb form.

A word that expresses an action or a state of being, serving as the core of a sentence's predicate.

A verb that expresses a physical or mental action, such as "run" or "think."

A word that describes or modifies a noun or pronoun.

A word that modifies a verb, adjective, or another adverb, unlike an adjective, which modifies only nouns or pronouns.

The noun a pronoun refers back to; a pronoun must agree in number and gender with its antecedent.

By adding a coordinating conjunction after the comma, replacing the comma with a semicolon, or separating the clauses into two distinct sentences.

By adding only an apostrophe after the final "s" of the plural noun.

By adding an apostrophe followed by "s" to the end of the singular noun.

Punctuation marks used to indicate direct speech or to signal that text is quoted directly from another source.

A punctuation mark commonly used to introduce a list, explanation, or elaboration following a complete independent clause.

An error in which two independent clauses are incorrectly joined using only a comma, without a coordinating conjunction.

A sentence containing one independent clause and at least one dependent clause, unlike a compound sentence, which joins two or more independent clauses.

A sentence containing two or more independent clauses, typically joined by a coordinating conjunction or a semicolon.

A sentence combining at least two independent clauses with at least one dependent clause.

A shortened form of two words combined into one, with the apostrophe marking the place where letters have been omitted.

A clause containing a subject and a verb but not expressing a complete thought, requiring it to be attached to an independent clause.

A sentence in which two or more independent clauses are incorrectly joined without proper punctuation or connecting words.

A punctuation mark used to join two closely related independent clauses without using a coordinating conjunction.

An incomplete sentence lacking a subject, a verb, or a complete thought.

A sentence containing only one independent clause.

A punctuation mark commonly used to show possession or to form a contraction.

A clause containing a subject and a verb that expresses a complete thought, allowing it to stand alone as a sentence.

A comma should generally be placed before the coordinating conjunction when it joins two independent clauses.

Commas should be placed between each item in a list of three or more items.

Accurately structuring and punctuating clauses helps ensure that sentences are clear, grammatically correct, and easily understood by the reader.