OST Algebra I flashcards
OST Algebra I · 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.
- Rational number
- A number expressible as p/q where p and q are integers and q is not zero. Its decimal form terminates or repeats, unlike irrational numbers such as √2 or π.
- Negative exponent rule
- For any nonzero base a and positive n, a^(−n) equals 1 divided by a^n. A negative exponent signals a reciprocal, not a negative result.
- Rational exponent
- The expression a^(m/n) equals the n-th root of a raised to the m power, or equivalently the n-th root of a^m. The denominator gives the root index.
- Scientific notation
- A number written as a × 10^n with 1 ≤ |a| < 10 and n an integer. Multiplying adds exponents; dividing subtracts them; raising to a power multiplies the exponent.
- Percent change
- Computed as (new value − old value) divided by old value, times 100. A positive result is an increase; a negative result is a decrease relative to the original amount.
- Dimensional analysis
- A conversion method that multiplies by ratios equal to one so unwanted units cancel. For example, 60 km/h becomes about 16.7 m/s after converting kilometers and hours.
- Slope formula
- For two points (x₁, y₁) and (x₂, y₂), slope m equals (y₂ − y₁) divided by (x₂ − x₁). It measures vertical change per unit of horizontal change.
- Perpendicular line slopes
- Two nonvertical lines are perpendicular exactly when their slopes are negative reciprocals, so the product of the slopes equals −1. A horizontal and vertical line also meet at right angles.
- Quadratic formula
- For ax² + bx + c = 0 with a not zero, x equals (−b ± √(b² − 4ac)) divided by 2a. It solves any quadratic, including ones that do not factor.
- Discriminant
- The value b² − 4ac from a quadratic in standard form. Positive gives two real roots, zero gives one repeated real root, and negative gives no real roots.
- Axis of symmetry
- For y = ax² + bx + c, the vertical line x = −b/(2a) through the vertex. It divides the parabola into two mirror-image halves.
- Difference of squares
- The pattern a² − b² factors as (a − b)(a + b). Recognizing it lets you factor expressions such as x² − 49 into (x − 7)(x + 7).
- Exponential growth model
- The form y = a(1 + r)^t, where a is the starting amount, r the growth rate as a decimal, and t the number of periods. It applies when a quantity grows by a constant percent.
- System with no solution
- Two linear equations with equal slopes but different y-intercepts. Their graphs are parallel lines that never intersect, so no ordered pair satisfies both equations.
- Remainder theorem
- Dividing a polynomial by (x − k) leaves a remainder equal to the polynomial evaluated at k. A remainder of zero means (x − k) is a factor.
- Literal equation
- An equation with several variables, solved for one target variable by applying inverse operations to both sides. Example: A = P(1 + rt) solved for t gives (A/P − 1)/r.
- Vertical line test
- A graph represents a function exactly when no vertical line crosses it more than once. A second crossing means one input has two outputs.
- Horizontal line test
- A function is one-to-one, and therefore has an inverse function, exactly when no horizontal line crosses its graph more than once.
- Composite function
- The notation f(g(x)) means evaluate g at x first, then apply f to that result. Composition is generally not commutative, so f(g(x)) may differ from g(f(x)).
- Inverse function
- The function f⁻¹ undoes f, satisfying f⁻¹(f(x)) = x and f(f⁻¹(x)) = x. It exists only when f is one-to-one on its domain.
- Domain restriction
- Values excluded from a function's inputs. Exclude inputs making a denominator zero, and for even roots require the radicand to be nonnegative.
- Average rate of change
- Over the interval from a to b, it equals (f(b) − f(a)) divided by (b − a). It is the slope of the secant line through the two graph points.
- Vertical shift
- Adding k to a function, written f(x) + k, moves the graph up by k units when k is positive and down by k units when k is negative.
- Horizontal shift
- Replacing x with (x − h) moves the graph right by h units when h is positive. The sign inside the parentheses works opposite to the direction of motion.
- Arithmetic sequence formula
- The n-th term is aₙ = a₁ + (n − 1)d, where a₁ is the first term and d the constant difference between consecutive terms. It defines a linear function on term numbers.
- Exponential vs linear growth
- Linear functions change by a constant difference per step; exponential functions change by a constant ratio. Exponential graphs with base above 1 eventually outpace any linear graph.
- Median vs mean
- The median is the middle value of ordered data; the mean is the sum divided by the count. Extreme outliers shift the mean far more than the median.
- Interquartile range
- IQR equals Q3 minus Q1, the spread of the middle half of the data. It resists distortion by outliers better than the full range does.
- Standard deviation
- A measure of how far values typically lie from the mean. A larger standard deviation means greater spread; adding the same constant to every value leaves it unchanged.
- Conditional probability
- P(A | B) is the probability of A given that B occurred, computed as P(A and B) divided by P(B), with P(B) greater than zero.
- Independent events
- Two events are independent when P(A and B) equals P(A) times P(B). Equivalently, knowing one occurred does not change the other's probability.
- Correlation coefficient
- The value r ranges from −1 to 1 and measures the strength and direction of linear association. Values near ±1 are strong; values near 0 are weak.