Praxis Middle School Math flashcards
Praxis Middle School Math · 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 from left to right, then addition and subtraction from left to right.
- Dividing by a Fraction
- To divide by a fraction, multiply by its reciprocal: a/b ÷ c/d equals a/b times d/c. Convert mixed numbers to improper fractions before dividing.
- Rational Number Definition
- A number that can be written as p/q where p and q are integers and q is not zero; its decimal form either terminates or repeats.
- GCF and LCM Product Rule
- For two positive integers, the greatest common factor multiplied by the least common multiple equals the product of the two original numbers.
- Percent Change Formula
- Percent change equals the new value minus the original value, divided by the original value, times 100. A positive result means an increase.
- Scientific Notation Form
- A number written as a times 10 to the n, where the absolute value of a is at least 1 and less than 10, and n is an integer.
- Negative Exponent Rule
- A base raised to a negative exponent equals the reciprocal of the base raised to the positive exponent: a to the negative n equals 1 over a to the n.
- Slope Formula
- The slope of the line through two points equals the change in y divided by the change in x: m = (y2 − y1)/(x2 − x1).
- Perpendicular Line Slopes
- Two nonvertical lines are perpendicular exactly when their slopes are negative reciprocals, so the product of the two slopes equals negative one.
- Quadratic Formula
- For ax² + bx + c = 0 with a not zero, x equals negative b plus or minus the square root of b² − 4ac, all divided by 2a.
- Discriminant Test
- For a quadratic, b² − 4ac greater than zero gives two real solutions, equal to zero gives one solution, and less than zero gives no real solutions.
- Difference of Squares
- a² − b² factors as (a + b)(a − b). This pattern applies whenever two perfect squares are separated by a subtraction sign.
- Exponent Product Rule
- When multiplying powers with the same base, add the exponents: a to the m times a to the n equals a to the m plus n.
- Inequality Sign Flip
- Multiplying or dividing both sides of an inequality by a negative number reverses the direction of the inequality symbol.
- Area of a Trapezoid
- Area equals one half the height times the sum of the two parallel bases: A = ½(b1 + b2)h, where h is perpendicular to the bases.
- Pythagorean Theorem
- In a right triangle, the sum of the squares of the legs equals the square of the hypotenuse: a² + b² = c², where c is the hypotenuse.
- Cone Volume Formula
- The volume of a cone is one third of the base area times the height: V = (1/3)πr²h. A pyramid follows the same one-third rule.
- Interior Angle Sum
- A polygon with n sides has interior angles summing to (n − 2) times 180 degrees. For a quadrilateral the sum is 360 degrees.
- Area Scale Factor
- If two similar figures have a linear scale factor of k, their areas compare by the factor k² and their volumes compare by k³.
- Arc Length Formula
- Arc length equals the central angle divided by 360, multiplied by the circumference 2πr. The same ratio gives sector area of the circle.
- Sphere Surface Area
- The surface area of a sphere is four times pi times the radius squared: SA = 4πr². Its volume is four thirds pi r cubed.
- Mean Versus Median
- The mean is the sum divided by the count and shifts toward outliers; the median is the middle ordered value and resists outliers.
- Interquartile Range
- The IQR equals Q3 minus Q1, the spread of the middle half of the data. Values beyond 1.5 IQR from the quartiles are outliers.
- Complement Rule
- The probability that an event does not happen equals one minus the probability that it does: P(not E) = 1 − P(E).
- Independent Events Rule
- For independent events, the probability that both occur is the product of their probabilities: P(A and B) = P(A) times P(B).
- Median of Even Data Set
- When the number of ordered data values is even, the median is the mean of the two middle values.
- Combination Formula
- The number of ways to choose r items from n items when order does not matter is n! divided by r! times (n − r)!.
- Unit Rate
- A unit rate expresses a quantity per one unit of another, found by dividing. Multiplying the unit rate scales the quantity to any amount.
- Dimensional Analysis
- Multiply by conversion factors written as fractions so unwanted units cancel and the desired unit remains. Each conversion factor equals one.
- Percent Error
- Percent error equals the absolute value of the approximate value minus the exact value, divided by the exact value, times 100.
- Combined Work Rate
- If one worker finishes a job in a hours and another in b hours, together they finish in t hours where 1/a + 1/b = 1/t.
- Counterexample
- A single example that satisfies the conditions of a statement but makes the conclusion false; it disproves a universal claim.