SAAT flashcards
SAAT · Build recall with a focused review session.
32 cards. Read the term and the definition here. The deck at the top of this page is optional.
- Order of operations
- Evaluate grouping symbols first, then exponents, then multiplication and division left to right, then addition and subtraction left to right.
- Absolute value
- The distance of a number from zero on the number line; always nonnegative. For example, |−7| = 7 and |3 − 8| = 5.
- Percent change formula
- Percent change equals (new value minus old value) divided by old value, times 100. A positive result is an increase, a negative result a decrease.
- Negative exponent rule
- For any nonzero base x and positive integer n, x raised to the negative n equals 1 divided by x raised to the n.
- Least common multiple
- The smallest positive integer divisible by each of the given numbers; found by multiplying the highest power of each prime appearing in their factorizations.
- Slope formula
- Slope equals the change in y divided by the change in x between two points: m = (y2 − y1)/(x2 − x1). Vertical lines have undefined slope.
- Perpendicular line slopes
- Two nonvertical lines are perpendicular exactly when their slopes are negative reciprocals, so the product of the slopes equals negative one.
- Quadratic formula
- For ax² + bx + c = 0 with a nonzero, x equals negative b plus or minus the square root of b² − 4ac, all divided by 2a.
- Discriminant
- The expression b² − 4ac from a quadratic equation. Positive gives two real roots, zero gives one repeated root, negative gives no real roots.
- Vertex of a parabola
- For y = ax² + bx + c, the vertex lies at x = −b/(2a); the axis of symmetry is the vertical line through that x-value.
- Exponential growth model
- y = a·b^x where a is the initial amount and b is the growth factor. If b exceeds 1 the quantity grows; the percent rate is (b − 1) times 100.
- Inverse variation
- A relationship in which the product of two variables is constant: y = k/x. As one variable increases, the other decreases proportionally.
- Circle area and circumference
- Area equals pi times the radius squared; circumference equals two times pi times the radius. Both use the same radius from the center.
- Sector area
- The area of a pie-shaped slice of a circle: (central angle / 360) times pi times the radius squared, for the angle measured in degrees.
- Pythagorean theorem
- In a right triangle, the square of the hypotenuse equals the sum of the squares of the two legs: a² + b² = c².
- 30-60-90 triangle
- A right triangle with acute angles of 30 and 60 degrees has sides in the ratio 1 to the square root of 3 to 2.
- Sphere volume
- The volume enclosed by a sphere equals four-thirds times pi times the cube of the radius: V = (4/3)πr³.
- Similar figure scaling
- When two figures are similar with side ratio k, their areas compare as k squared and their volumes as k cubed.
- Polygon interior angle sum
- The interior angles of a polygon with n sides add to (n − 2) times 180 degrees. A quadrilateral totals 360 degrees.
- Median versus mean
- The median is the middle value of ordered data and resists outliers; the mean is the sum divided by the count and is pulled toward extreme values.
- Standard deviation shift rule
- Adding the same constant to every data value leaves the standard deviation unchanged; multiplying every value by k multiplies the standard deviation by the absolute value of k.
- Complement rule
- The probability that an event does not occur equals 1 minus the probability that it does occur, written P(not A) = 1 − P(A).
- Independent events multiplication
- If two events are independent, the probability both occur equals the product of their individual probabilities: P(A and B) = P(A)·P(B).
- Conditional probability
- The probability of event A given that B has occurred equals the probability of both divided by the probability of B: P(A|B) = P(A and B)/P(B).
- Combinations formula
- The number of unordered selections of r items from n distinct items equals n factorial divided by r factorial times (n − r) factorial.
- Normal distribution rule
- In a normal distribution roughly 68 percent of values fall within one standard deviation of the mean and about 95 percent within two.
- Main idea
- The central point that the entire passage develops and supports. A correct main idea must account for all paragraphs, not just one section.
- Inference question rule
- A valid inference must follow necessarily from stated evidence in the passage. An answer that is merely plausible but not textually supported is incorrect.
- Comma splice
- An error that joins two independent clauses with only a comma. Repair it with a period, a semicolon, or a comma plus a coordinating conjunction.
- Nonessential clause punctuation
- Information that can be removed without changing the sentence's core meaning is set off by a matched pair of commas, dashes, or parentheses.
- Dangling modifier
- An introductory descriptive phrase must modify the subject of the main clause; otherwise it appears to describe the wrong noun.
- Parallel structure
- Items joined by and, or, or a comparison must share grammatical form, such as all nouns, all gerunds, or all infinitive verbs.