SHSAT flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Main idea

The central point a passage makes about its topic, usually stated in the opening or closing lines and supported by every paragraph in the text.

Valid inference

A conclusion the passage logically forces, built only from stated details plus common knowledge, never from personal opinion or outside information.

Tone

The author's attitude toward the subject, revealed through word choice and detail; it differs from mood, which is the feeling created in the reader.

Comma splice

Two independent clauses joined only by a comma; repair it with a period, a semicolon, or a comma plus a coordinating conjunction such as 'and' or 'but'.

Dangling modifier

An introductory descriptive phrase that describes a noun not actually present in the sentence; the fix is to place the intended noun right after the comma.

Subject-verb agreement

The verb must match its subject in number; prepositional phrases in between do not change the subject, so 'the box of nails is' is correct.

Semicolon use

Joins two closely related independent clauses without a conjunction, or separates list items that already contain commas within them.

Transition: however

Signals contrast or contradiction between two ideas; the sentence that follows will oppose, limit, or qualify the statement made just before it.

Transition: therefore

Signals a result or conclusion drawn from the preceding statement; the sentence after it follows logically as a consequence of what came before.

It's vs. its

'It's' is the contraction of 'it is' or 'it has,' while 'its' is the possessive form of 'it' and never takes an apostrophe.

Fewer vs. less

'Fewer' modifies countable plural nouns, as in 'fewer chairs'; 'less' modifies uncountable amounts, as in 'less water' or 'less time.'

Superlative form

Compares three or more items and usually takes '-est' or 'most'; the comparative '-er' or 'more' applies only when exactly two items are compared.

Context clue: contrast

A nearby word such as 'but,' 'unlike,' or 'rather' signals that an unfamiliar word means the opposite of something already stated in the sentence.

Author's purpose

The reason a passage was written: to inform, persuade, entertain, or describe; the purpose is usually signaled by the passage's structure and tone.

Supporting detail

A specific fact, example, or quotation that backs up a claim; correct answer choices restate details genuinely present in the passage.

Parallel structure

Items in a list or comparison must share the same grammatical form, such as all infinitives, all gerunds, or all past-tense verbs.

Percent change

Divide the amount of change by the original amount, then multiply by 100; a positive result is an increase and a negative result is a decrease.

Slope formula

Slope equals (y₂ − y₁) divided by (x₂ − x₁) for two points on a line; it measures vertical change per unit of horizontal change.

Slope-intercept form

The equation y = mx + b, where m is the slope of the line and b is the y-intercept, the point where the line crosses the y-axis.

Pythagorean theorem

In a right triangle, a² + b² = c², where c is the hypotenuse, the side opposite the right angle, and a and b are the two legs.

45-45-90 triangle

An isosceles right triangle whose sides are in the ratio 1 : 1 : √2, so the hypotenuse equals a leg multiplied by the square root of 2.

30-60-90 triangle

Sides are in the ratio 1 : √3 : 2; the side opposite 30° is half the hypotenuse, and the side opposite 60° is that length times √3.

Area of a trapezoid

Average the lengths of the two parallel bases and multiply by the height: A = ½(b₁ + b₂)h, where h is perpendicular to both bases.

Circle circumference and area

Circumference equals 2πr and area equals πr², where r is the radius, which is half of the diameter.

Volume of a cylinder

V = πr²h, found by multiplying the area of the circular base, πr², by the height of the cylinder.

Mean vs. median

The mean is the sum of the values divided by the count; the median is the middle value once the data are ordered from least to greatest.

Range of a data set

The difference between the largest and smallest values in the set; unlike the mean, it depends only on those two extreme values.

Probability of an event

The number of favorable outcomes divided by the total number of equally likely outcomes; the result always lies between 0 and 1 inclusive.

Rate formula

Distance equals rate multiplied by time; rearrange it as rate = distance ÷ time or as time = distance ÷ rate.

Product rule for exponents

When multiplying powers that share the same base, keep the base and add the exponents: xᵃ · xᵇ = xᵃ⁺ᵇ.

Supplementary angles

Two angles whose measures add to 180 degrees; any pair of adjacent angles formed on a straight line is supplementary.

Interior angles of a polygon

A polygon with n sides has interior angles summing to (n − 2) × 180 degrees, so a triangle totals 180 and a quadrilateral 360.