AEPA Mathematics (NT304) flashcards
AEPA Mathematics (NT304) · Build recall with a focused review session.
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- Divisibility rule for 3
- A whole number is divisible by 3 exactly when the sum of its digits is divisible by 3. For example, 4,821 has digit sum 15, so it is divisible by 3.
- Greatest common factor
- The largest positive integer that divides two or more given integers with no remainder. It simplifies fractions and factors polynomials, and satisfies GCF(a,b) times LCM(a,b) equals a times b.
- Slope formula
- For two points (x1, y1) and (x2, y2), slope m equals (y2 minus y1) divided by (x2 minus x1). It measures the constant rate of change of a linear function.
- Quadratic formula
- The solutions of ax squared plus bx plus c equals 0 are x equals negative b plus or minus the square root of b squared minus 4ac, all divided by 2a, provided a is not zero.
- Pythagorean theorem
- In a right triangle, the square of the hypotenuse equals the sum of the squares of the two legs: a squared plus b squared equals c squared, where c is the hypotenuse.
- Interior angle sum
- The interior angles of a polygon with n sides sum to (n minus 2) times 180 degrees. A triangle sums to 180 degrees and a quadrilateral to 360 degrees.
- Combinations formula
- The number of unordered selections of r objects from n distinct objects is n factorial divided by r factorial times (n minus r) factorial, written nCr. Order does not matter.
- Conditional probability
- The probability of event A given that event B has occurred equals the probability of both A and B divided by the probability of B, assuming B has nonzero probability.
- Absolute value
- The absolute value of a number is its distance from zero on the number line, so it is never negative. The expression |a minus b| gives the distance between a and b.
- Scientific notation
- A number written as a coefficient between 1 and 10 (inclusive of 1, exclusive of 10) multiplied by a power of 10. Multiplying adds exponents; dividing subtracts them.
- Discriminant
- For a quadratic ax squared plus bx plus c, the discriminant is b squared minus 4ac. Positive gives two real roots, zero gives one, and negative gives no real roots.
- 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. Dividing subtracts exponents.
- Similar figures
- Figures with equal corresponding angles and proportional corresponding side lengths. The ratio of areas equals the square of the scale factor and volumes the cube.
- Circle area and circumference
- A circle of radius r has area pi times r squared and circumference 2 times pi times r (or pi times the diameter). Pi is approximately 3.14159.
- Permutations formula
- The number of ordered arrangements of r objects chosen from n distinct objects is n factorial divided by (n minus r) factorial, written nPr. Order matters.
- Expected value
- The sum of each possible outcome multiplied by its probability. It represents the long-run average result of repeating a random experiment many times.
- Order of operations
- Evaluate grouping symbols first, then exponents and roots, then multiplication and division left to right, then addition and subtraction left to right.
- Rational number
- A number expressible as a fraction a over b where a and b are integers and b is not zero. Its decimal form terminates or repeats.
- Point-slope form
- An equation of a line written as y minus y1 equals m times (x minus x1), where m is the slope and (x1, y1) is a point on the line.
- Logarithm definition
- The equation log base b of x equals y means b raised to the y power equals x, with b positive and not equal to 1 and x positive.
- Volume of a sphere
- The volume enclosed by a sphere of radius r is four-thirds times pi times r cubed. Its surface area is 4 times pi times r squared.
- Triangle congruence criteria
- Two triangles are congruent if SSS, SAS, ASA, AAS, or (for right triangles) HL conditions hold. SSA does not guarantee congruence.
- Normal distribution rule
- In a normal distribution about 68 percent of values lie within one standard deviation of the mean, 95 percent within two, and 99.7 percent within three.
- Mutually exclusive events
- Events that cannot occur at the same time, so their joint probability is zero. For such events, P(A or B) equals P(A) plus P(B).
- Unit rate
- A rate expressed with a denominator of 1, found by dividing the first quantity by the second. It is the constant of proportionality in proportional relationships.
- Distributive property
- Multiplying a sum by a factor gives the same result as multiplying each addend by the factor and adding: a(b plus c) equals ab plus ac.
- Vertex of a parabola
- For y equals ax squared plus bx plus c, the vertex occurs at x equals negative b divided by 2a. It is the maximum if a is negative, minimum if a is positive.
- Arithmetic sequence
- A sequence with a constant difference d between consecutive terms. The nth term is a1 plus (n minus 1) times d.
- Area of a trapezoid
- The area of a trapezoid equals one-half times the sum of the two parallel bases times the height: A equals one-half (b1 plus b2) h.
- Inscribed angle
- An angle whose vertex lies on a circle and whose sides are chords. Its measure is half the measure of its intercepted arc.
- Standard deviation
- A measure of how spread out data are, equal to the square root of the variance. Adding a constant to every value leaves it unchanged.
- Euler's formula
- For a connected planar graph, the number of vertices minus the number of edges plus the number of faces equals 2, counting the outer region as a face.