PERT Math flashcards
PERT 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.
- Slope formula
- The slope between points (x1,y1) and (x2,y2) is (y2-y1)/(x2-x1); it measures vertical change per horizontal change.
- Slope-intercept form
- An equation written as y = mx + b, where m is the slope and b is the y-intercept of the line.
- Point-slope form
- An equation written as y - y1 = m(x - x1); it uses a known point (x1,y1) and slope m.
- Parallel line slopes
- Two nonvertical lines are parallel exactly when their slopes are equal; vertical lines are parallel to other vertical lines.
- Perpendicular line slopes
- Two lines are perpendicular when their slopes are negative reciprocals; their product equals -1, and vertical is perpendicular to horizontal.
- Inequality reversal rule
- When you multiply or divide both sides of an inequality by a negative number, reverse the inequality symbol.
- Absolute value inequality
- For a > 0, |x| < a means -a < x < a, while |x| > a means x < -a or x > a.
- No-solution linear system
- A system of two linear equations has no solution when the lines are parallel and distinct, meaning they have equal slopes but different intercepts.
- Distributive property
- For real numbers a, b, and c, a(b + c) = ab + ac; it lets you multiply a factor across terms inside parentheses.
- Product exponent rule
- When multiplying powers with the same base, add exponents: x^a times x^b equals x^(a+b). This is the product rule.
- Power exponent rule
- When raising a power to a power, multiply exponents: (x^a)^b equals x^(a times b). This is the power rule.
- Negative exponent rule
- A nonzero base raised to a negative exponent equals the reciprocal of the base raised to the positive exponent: x^-a = 1/x^a.
- Function definition
- A function pairs each input in its domain with exactly one output; the vertical line test checks this on a graph.
- Domain restrictions
- For real-valued functions, exclude inputs making a denominator zero and require even-root radicands to be nonnegative.
- Function composition
- The composition (f ∘ g)(x) equals f(g(x)); apply g first, then apply f to that result.
- Direct vs inverse variation
- Direct variation has the form y = kx, while inverse variation has the form y = k/x, with k a nonzero constant.
- Quadratic standard form
- A quadratic equation written as ax^2 + bx + c = 0, where a is not zero and a, b, c are constants.
- Quadratic formula
- Solutions of ax^2+bx+c=0 are x = [-b ± sqrt(b^2-4ac)]/(2a), provided a is not zero. This is the quadratic formula.
- Discriminant
- The discriminant is b^2 - 4ac. Positive gives two real solutions, zero gives one real solution, negative gives no real solutions.
- Vertex of parabola
- For y = ax^2 + bx + c, the vertex x-coordinate is -b/(2a); the axis of symmetry is the vertical line x = -b/(2a).
- Vertex form
- A quadratic written as y = a(x - h)^2 + k has vertex (h, k) and axis of symmetry x = h.
- Parabola opening direction
- The graph of y = ax^2 + bx + c opens upward when a > 0 and downward when a < 0.
- Zero product property
- If the product of two factors equals zero, then at least one factor equals zero; use it after factoring a quadratic.
- Difference of squares
- The expression a^2 - b^2 factors as (a - b)(a + b), which helps solve quadratics and simplify expressions.
- Area of a circle
- The area of a circle is A = πr^2, where r is the radius and π is approximately 3.14159.
- Circumference of a circle
- The circumference of a circle is C = 2πr or C = πd, where r is radius and d is diameter.
- Pythagorean theorem
- In a right triangle with legs a and b and hypotenuse c, a^2 + b^2 = c^2.
- Triangle angle sum
- The interior angles of any triangle add to 180 degrees; complementary angles add to 90 and supplementary angles to 180.
- Volume of a cylinder
- The volume of a cylinder is V = πr^2h, where r is the base radius and h is the height.
- Similar figure scale factor
- If two similar figures have side-length ratio k, their areas have ratio k^2 and their volumes have ratio k^3.
- Mean median mode
- The mean is the sum divided by the count; the median is the middle ordered value; the mode is the most frequent value.
- Probability of independent events
- For independent events A and B, P(A and B) = P(A) times P(B); for mutually exclusive events, P(A or B) = P(A) + P(B).