DOST-SEI-Style Mathematics Practice Examination Reviewer

Vocabulary and core formula flashcards covering arithmetic, geometry, functions, limits, probability, statistics, and calculus topics from the DOST-SEI-style mathematics reviewer.

Ratio

A mathematical comparison of two quantities written as $a : b$, which is simplified by dividing both terms by their greatest common factor (GCF).

Fraction Addition and Subtraction

Operations on fractions that require finding a common denominator before combining the numerators.

Fraction Multiplication

An arithmetic operation performed by multiplying straight across the numerators and straight across the denominators.

Fraction Division

An arithmetic operation evaluated by multiplying the first fraction by the reciprocal of the second fraction.

Percentage

A proportion per hundred calculated by the formula $\text{Percentage} = (\text{part} \div \text{whole}) \times 100$, where $x\% \text{ of } N = \left(\frac{x}{100}\right)N$.

Rectangle Area

The surface area of a rectangle, calculated by multiplying length by width: $A = lw$.

Triangle Area

The surface area of a triangle, calculated as half of base times height: $A = \frac{1}{2}bh$.

Circle Area

The two-dimensional space enclosed by a circle, calculated using the formula $A = \pi r^2$.

Circumference

The boundary perimeter around a circle, given by the formula $C = 2\pi r$.

Cube Volume

The three-dimensional capacity of a cube with side length $s$, given by the formula $V = s^3$.

Distance Formula

The fundamental motion formula relating space traversed, speed, and duration: $\text{Distance} = \text{rate} \times \text{time}$.

Probability of an Event

The likelihood of a specific event occurring, calculated as $P(\text{event}) = \text{favorable outcomes} \div \text{total equally likely outcomes}$.

Mean

A measure of central tendency calculated as $\text{sum} \div \text{count}$, which is the measure most sensitive to an extremely high outlier.

Median

The middle value in a data set after sorting, or the average of the two middle values when the number of observations is even.

Mode

The data value that occurs with the highest frequency in a given set.

Range (Statistics)

A measure of statistical dispersion calculated as the difference between extreme values: $\text{maximum} - \text{minimum}$.

Function

A mathematical relation in which every single input is associated with exactly one output.

Evaluating a Function

The procedure of determining $f(a)$ by substituting the value $a$ for every occurrence of $x$ in the function expression.

Direct Substitution

The primary method used to evaluate a limit, which generally works directly for polynomial functions.

Indeterminate Form $\frac{0}{0}$

A limit outcome indicating that the expression must be factored or simplified before attempting substitution again.

Power Rule

A basic differentiation rule stating that the derivative of a variable raised to an exponent is given by $\frac{d}{dx}(x^n) = nx^{n-1}$.

Derivative of a Constant

A calculus rule stating that the derivative of any constant numerical value is $0$.

Pythagorean Theorem

A geometric relationship for right triangles with legs $a$ and $b$ and hypotenuse $c$, defined by $c^2 = a^2 + b^2$.