Praxis 5003 flashcards
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32 cards. Read the term and the definition here. The deck at the top of this page is optional.
- Divisibility rule for 3
- A whole number is divisible by 3 when the sum of its digits is a multiple of 3; for instance, 741 has a digit sum of 12, so 3 divides it.
- Divisibility rule for 9
- A number is divisible by 9 exactly when the sum of its digits is a multiple of 9; since 2 + 5 + 5 = 12, the number 255 is not divisible by 9.
- Least common multiple
- The smallest positive number that is a multiple of two or more given numbers; the least common multiple of 6 and 8 is 24.
- Greatest common factor
- The largest whole number that divides evenly into two or more numbers; the greatest common factor of 18 and 24 is 6, since 6 divides both with no remainder.
- Dividing by a fraction
- To divide by a fraction, multiply by its reciprocal: a/b ÷ c/d equals a/b × d/c, so 3/4 ÷ 1/2 becomes 3/4 × 2/1 = 3/2.
- Cross products in proportions
- In a proportion a/b = c/d, the cross products ad and bc are equal; this property is used to solve for an unknown value in proportional reasoning problems.
- Multiplying by powers of ten
- Multiplying a decimal by 10 moves its decimal point one place to the right for each factor of ten; dividing moves it the same number of places left.
- Percent change
- Percent change equals the amount of change divided by the original amount, multiplied by 100; an increase from 40 to 50 is a 25% increase.
- Absolute value
- The distance of a number from zero on the number line, which is always nonnegative; the absolute value of both 7 and −7 is 7.
- Slope formula
- The slope of a line through points (x1, y1) and (x2, y2) is the change in y divided by the change in x, written m = (y2 − y1)/(x2 − x1).
- Slope-intercept form
- The equation y = mx + b describes a line with slope m and y-intercept b, the point where the line crosses the y-axis.
- Distributive property
- Multiplying a sum by a factor gives the same result as multiplying each addend separately: a(b + c) = ab + ac, so 3(x + 4) = 3x + 12.
- Quadratic formula
- For ax² + bx + c = 0 with a not equal to zero, the solutions are x = (−b ± √(b² − 4ac)) ÷ (2a); it works even when the expression cannot be factored.
- Discriminant
- The expression b² − 4ac under the square root in the quadratic formula; positive means two real solutions, zero means one, and negative means no real solutions.
- Product rule for exponents
- When multiplying powers that share the same base, add the exponents: xᵃ · xᵇ = xᵃ⁺ᵇ, as in 2³ · 2⁴ = 2⁷.
- Definition of a function
- A relationship in which each input value is paired with exactly one output value; a graph represents a function if no vertical line crosses it twice.
- Proportional relationship
- A relationship in which the ratio of two quantities is constant, written y = kx, and whose graph is a straight line passing through the origin.
- Pythagorean theorem
- In a right triangle, the square of the hypotenuse equals the sum of the squares of the legs: a² + b² = c², where c is the longest side.
- Area of a circle
- The area enclosed by a circle equals pi times the square of the radius, A = πr²; a circle of radius 3 has an area of about 28.3 square units.
- Volume of a cylinder
- The volume of a cylinder equals the base area times the height, V = πr²h, where r is the radius of the circular base and h is the height.
- Interior angle sum of polygon
- For a polygon with n sides, the interior angles add to (n − 2) × 180°; the five angles of a pentagon total 540°.
- Complementary angles
- Two angles whose measures add to 90°; the complement of a 35° angle is a 55° angle.
- Supplementary angles
- Two angles whose measures add to 180°; angles that form a straight line are supplementary, so the supplement of 110° is 70°.
- Scale factor and area
- When two figures are similar with linear scale factor k, their areas compare by the factor k² and their volumes compare by the factor k³.
- Surface area of rectangular prism
- The total area of all six faces of a box: SA = 2(lw + lh + wh), where l, w, and h are the prism's length, width, and height.
- Mean
- The arithmetic average, found by adding all data values and dividing by the number of values; the mean of 4, 8, and 12 is 8.
- Median
- The middle value when data are ordered from least to greatest; with an even number of values it is the mean of the two middle values.
- Mode
- The value that occurs most often in a data set; a set can have more than one mode, or none if all values occur equally often.
- Range of a data set
- The difference between the greatest and the least values in a data set; for the data 3, 7, 8, and 12, the range is 9.
- Complement rule
- The probability that an event does not occur equals 1 minus the probability that it does occur: P(not A) = 1 − P(A).
- Independent events
- Two events are independent when the outcome of one does not change the probability of the other; then P(A and B) = P(A) × P(B).
- Interquartile range
- The difference between the third quartile and the first quartile, IQR = Q3 − Q1, which measures the spread of the middle 50% of the data.