NSE Math 10 flashcards
NSE Math 10 · 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.
- Quadratic formula
- For any equation ax² + bx + c = 0 with a ≠ 0, the solutions are x = (−b ± √(b² − 4ac)) divided by 2a.
- Discriminant
- The expression b² − 4ac from the quadratic formula. Positive means two real roots, zero means one repeated root, negative means two complex roots.
- Vertex of a parabola
- For y = ax² + bx + c, the vertex is at x = −b/(2a). It is the minimum when a > 0 and the maximum when a < 0.
- Zero product property
- If the product of two or more factors equals zero, then at least one factor must equal zero. This lets you solve factored equations one factor at a time.
- Difference of squares
- The pattern a² − b² factors as (a − b)(a + b). Recognizing it lets you factor quickly and simplify rational expressions without long division.
- Exponential growth model
- A = P(1 + r)^t gives the amount after t periods when a starting value P grows by rate r each period. Use (1 − r) for decay.
- Extraneous solution
- A value produced by squaring both sides of a radical equation that does not satisfy the original equation. Always substitute solutions back to check them.
- Function definition
- A relation pairing each input in its domain with exactly one output. On a graph, the vertical line test confirms this rule holds.
- Domain restriction
- Values excluded from a function's input. Exclude inputs making a denominator zero, and require nonnegative radicands under even roots.
- Composite function
- The function f(g(x)), found by substituting g(x) into f. Order matters, so composition is usually not commutative.
- Inverse function
- A function f⁻¹ that undoes f, so f⁻¹(f(x)) = x. Find it by swapping x and y, then solving for y.
- Even function
- A function satisfying f(−x) = f(x) for every input in its domain. Its graph is symmetric about the y-axis, as with y = x².
- Odd function
- A function satisfying f(−x) = −f(x) for every input in its domain. Its graph has rotational symmetry about the origin, as with y = x³.
- Linear versus exponential growth
- A linear function changes by a constant difference between equal input steps. An exponential function changes by a constant ratio, so it grows or decays faster.
- Distance formula
- The distance between points (x₁, y₁) and (x₂, y₂) is √((x₂ − x₁)² + (y₂ − y₁)²), derived from the Pythagorean theorem on coordinate differences.
- Perpendicular slope rule
- Two nonvertical lines are perpendicular exactly when their slopes are negative reciprocals, so the product m₁·m₂ equals −1.
- Circle equation
- (x − h)² + (y − k)² = r² describes a circle centered at (h, k) with radius r. Expanding it produces a quadratic in x and y.
- Sector area
- The area of a circle sector with central angle θ degrees is (θ/360)·πr². Arc length uses the same fraction times 2πr.
- Scale factor and area
- When two figures are similar with linear scale factor k, their areas compare as k² and their volumes as k³.
- 30-60-90 triangle
- A right triangle with acute angles 30° and 60° has side lengths in ratio x, x√3, and 2x, where 2x is the hypotenuse.
- Mean, median, mode
- Mean is the sum divided by the count. Median is the middle ordered value. Mode is the most frequent value. Each measures center differently.
- Interquartile range
- IQR = Q3 − Q1, the spread of the middle half of the data. It resists outliers better than the range does.
- Standard deviation
- A measure of typical distance of data values from the mean. Adding the same constant to every value shifts the mean but leaves it unchanged.
- Conditional probability
- P(A|B) = P(A and B)/P(B), the probability that A occurs given that B already occurred, with P(B) greater than zero.
- Independent events
- Two events are independent when one occurring does not change the other's probability. Then P(A and B) = P(A)·P(B).
- Mutually exclusive events
- Events that cannot occur together, so P(A and B) = 0. Their union probability is P(A) + P(B).
- Correlation coefficient
- A number r between −1 and 1 describing the strength and direction of a linear association. Values near zero indicate weak linear association.
- Scientific notation
- A number written as c × 10^k with 1 ≤ |c| < 10. Multiply by multiplying coefficients and adding exponents; divide by subtracting exponents.
- Rational exponent rule
- a^(m/n) equals the nth root of a raised to the m power, also written as the nth root of a^m. It connects radicals and exponents.
- Rationalizing a denominator
- Rewriting a fraction so no radical remains in the denominator. Multiply numerator and denominator by the radical or by the conjugate expression.
- Linear model interpretation
- In y = mx + b, m is the constant rate of change with units of output per input, and b is the output when the input is zero.
- Modeling cycle
- Identify the real quantity, define variables, build an equation or function, solve it, then interpret and verify the result against the original situation.