AFOQT Study Guide Questions with Correct Answers

AFOQT Study Guide Questions with Correct Answers Types of analogies - Answer-synonym, antonym, action, function, size, degree, amount, part to whole, member to group, units of measurement, mathematical Types of numbers - Answer-natural: greater than 0 and has no decimal or fraction Whole: natural numbers and 0 Integer: positive/negative numbers and 0 Rational: can be represented as fraction or decimal , must terminate or resolve into repeating pattern Irrational: cannot be represented as a fraction, decimal never ends or resolves into pattern (ex. pi) Real: number that can be represented by a point on a number line. Includes all rational/irrational Imaginary: includes the imaginary unit i = square root of -1. complex: in the form of a + bi where a and b are real numbers Closed number system - Answer-a system is closed under an operation if performing that operation on two elements of the system results in another element of that system Properties of number systems - Answer-adding, subtracting, and multiplying are closed. dividing is not. rational numbers are closed under all operations except division real numbers are closed under all operations complex numbers are closed under all four operations irrational numbers are not closed under any of the operations Commutative property - Answer-holds for a operation if the order doesnt matter Associative property - Answer-the elements of an operation can be regrouped without changing the result Distributive property - Answer-multiplication over addition allows a product of sums to be written as a sum of products: a(b+c)= ab + ac Identity element - Answer-operation performed with an element and the identity element the result is the element (a x 1 = a) Inverse element - Answer-operation performed with the inverse element results in the identity element a + (-a) = 0 American units - Answer-length: inch/foot/yard/mile mass: ounce/pound/ton volume: cup/pint/quart/gallon force: pound-force pressure: pound-force per square inch work and energy: cal/british thermal unit temperature: fahrenheit charge: faraday SI units - Answer-length: meter mass: gram volume: liter force: newton pressure: pascal work and energy: joule temperature: kelvin charge: coulomb metric prefixes - Answer-tera: 10^12 T giga: 10^9 G mega: 10^6 M kilo: 10^3 k hecto: 10^2 h deca: 10^1 da deci: 10^-1 d centi: 10^-2 c milli: 10^-3 m micro: 10^-6 u nano: 10^-9 n pico: 10^-12 p conversions (inch, meter, yard, mi, gal, oz, lb, cal, F) - Answer-1 inch = 2.54cm 1 meter = 3.28 ft 1 yd = .914m 1 mi = 1.61km 1 gal = 3.785 L 1 oz = 28.35 g 1 lb = .454 kg 1 cal = 4.19 J 1 degree F: 5/9 (F-32C) proper fraction - Answer-fraction that equals less than 1 improper fraction - Answer-fraction that equals more than 1 IQR - Answer-interquartile range = Q3-Q1 Measures of variation/dispersion - Answer-range, IQR, variance, standard deviation formula for standard deviations (sample/population) - Answer-pg. 33 formula for variance - Answer-pg. 33 Complement (probablility) - Answer-The probability that an event won't occur Independent probability - Answer-the probability of one occurring does not affect the probability of the other Dependent probability - Answer-the probability of one occurring does have an effect on the probability of the other conditional probability - Answer-the probability that one event occurs given that another has occurred. Mutually exclusive probability - Answer-two events cant happen at the same time Mutually inclusive probability - Answer-events share common outcomes/ can happen at same time Formula for finding nth term - Answer-pg. 38 Formula for finding partial sum - Answer-pg.38 Formula for finding X/Y intercepts and slope - Answer-X: C/A Y: C/B Slope: -A/B in Ax + By = C form Formula for slope given two points - Answer-(Y2-Y1)/(X2-X1) distance formula - Answer-pg.54 midpoint formula - Answer-pg.54 zeros/roots of a quadratic are the... - Answer-x intercepts standard form of a quadratic - Answer-Ax^2 + Bx + C axis of symmetry: x = -b/2a vertex: pg. 59 vertex form of a quadratic - Answer-y = a(x-h)^2 + k axis of symmetry: x=h vertex: (h, k) The effect of A (first term) on a parabola - Answer-if negative: opens downward if positive: opens upward if a fraction less than 1: wider if above 1: narrower How to convert standard form to vertex form - Answer-complete the square 1, move c to the left side of the equation 2. divide the entire equation through by a (to make the coefficient of x^2 be 1). 3. Take half of the coefficient of x, square it, and then add it to both sides of the equation. 4. convert the right side of the equation to a perfect binomial squared, (x + m)^2. 5. Isolate y to put the equation in proper vertex form. quadratic formula - Answer-pg. 61 if (B^2 - 4AC) is 0, + or - then... - Answer-0: only 1 real root/ vertex on x axis +: 2 real roots, 2 x intercepts -: 2 complex roots, 0 x intercepts colinear - Answer-2 points on the same line Line segment - Answer-line with 2 endpoints and a finite length ray - Answer-line with one endpoint and extends indefinitely in one direction line - Answer-extends indefinitely in both directions complementary angles - Answer-add up to 90 supplementary angles - Answer-add up to 180 convert radians to degrees - Answer-1 radian = 57.3 degrees circumference/area of a circle - Answer-C = 2*pi*r A= pi*r^2 pg.65 secant - Answer-line that crosses a circle and touches twice chord - Answer-part of the secant line that lies within the circle tangent - Answer-line that touches a circle or any curve at one point arc - Answer-any portion of a circle between two points. measured in degrees minor arc - Answer-less than 180 major arc - Answer-greater than 180 central angle - Answer-an angle with its vertex at the center of a circle sector - Answer-part of a circle and its interior that is inside the rays of a central angle inscribed angle - Answer-has a vertex on the circle and is formed by two chords circumscribed angle - Answer-rays tangent to the circle and lies on the outside formula for measurement of inscribed angle - Answer-(1/2) x the central angle with the same points formula for measurement of angles outside of the circle - Answer-pg. 67 area of a sector - Answer-pg. 66 length of an arc - Answer-pg. 66 formula for angles inside in the circle - Answer-pg.67 formula for angle formed by tangent and secant - Answer-pg. 68 area of a triangle - Answer-(1/2)*b*h angle bisector - Answer-extends from the side opposite an angle to bisect that angle altitude (triangles) - Answer-shortest distance from a vertex to a side median (triangles) - Answer-extends from and angle to bisect the opposite side centroid - Answer-where a triangles three medians meet orthocenter - Answer-formed by the intersection of a triangle's 3 altitudes. Third side rule - Answer-if b and c are two sides of a trianle, the the measure of the third side a must be between the sum of the other two sides and the difference of the other two sides: c - b a c + b Special right triangles - Answer-45-45-90: x, x, root (2)x 30-60-90: x, root (3)x, 2x Parallelogram - Answer-quadrilateral with two pairs of parallel sides formula for the sum of interior angles - Answer-(n-2) * 180 apothem - Answer-shortest distance from the polygons center to one of the sides area of a polygon - Answer-(apothem)(perimeter)/2 pg. 76 SA/Volume of prism/diagonal - Answer-pg. 78 SA/Volume of cube - Answer-pg.78 SA/Volume of sphere - Answer-pg. 78 SA/Volume of cylinder - Answer-pg. 78 Volume of cone - Answer-pg. 78 SA/Volume of pyramid - Answer-pg. 78