Algebra Review

• Mathematics, Economics, Basic Engineering Sciences, & ME Laws are the subjects covered.

Algebra

• For functions where f(t) = f(-t), the symmetry is even symmetry.
• Numbers with four significant figures: 0.141, 1.4140, 0.01414.
• The base of Naperian logarithm is closest to 2.72.
• If second derivative of a curve's equation equals its negative, the curve is a sinusoid.
• The law of cosines can be used to find an angle of a triangle, when only the lengths of the sides are given.
• For angles between 90° and 180°, the cosine is negative.
• The inverse natural function of cosecant is sine.
• Graphical representation of cumulative frequency distribution is called an Ogive.
• Corollaries are statements of truth that follow from a theorem with little or no proof.
• A sequence of numbers that have constant differences between successive terms is an arithmetic progression.
• A frequency curve composed of a series of rectangles is a histogram.
• Roots of a zero-equal equation are classified as a zero of a function.
• A convergent series is a sequence of decreasing numbers.
• If a = b, then b = a is illustrated by the symmetric axiom.
• For independent events A and B, the probability of B occurring is Pab/Pa, Pa is the probablility that event A will occur Is Pa and the probability that A and B will occur is Pab.
• Two or more equations are equal if they have the same solution set.
• In a square matrix, equal elements of two rows result in a zero determinant.
• Constant of variation is the ratio/product of expressions in direct/inverse relation.
• Harmonic progressions are sequences where reciprocals form arithmetic progressions.
• An array of mxn quantities representing a single number system is a matrix.
• Dyadic number system is another name for the binary number system.
• The Roman numeral MCMXCIV is equivalent to 1994.
• A sequence where each term is greater than the preceding one is a divergent series.
• Terms differing only in numeric coefficients are like terms.
• Argand diagrams are used in complex algebra to represent complex planes.
• 7 + 0i is a real number.
• Probability represents successful outcomes divided by possible outcomes.
• A two-digit number with 'x' units digit and 'y' tens digit is '10y + x'.
• Axioms are admitted truths while theorems require proof.
• A lemma is a theorem used as a step in a larger proof.
• Statements accepted without proof are postulates.
• "Product order is irrelevant" describes the commutative law of multiplication.
• If a = b, then 'b' can replace 'a' because of the substitution law.
• If a = b and b = c, then a = c illustrates the transitive law.
• Distributive laws relate addition and multiplication.
• Algebriac expressions are symbols/numbers combined by fundamental operations.
• Divergent series is one where the succeeding term is greater than the preceding term.
• Like terms differ only in numeric coefficients.
• The construction or drawing of lines admitted without proof are postulates.
• A mathematical statement neither proved nor disproved is a conjecture.
• A lemma is useful as a preliminary to proving a major theorem.
• Axioms concern equality, while theorems involve objects and constructions.
• A corollary follows directly from a theorem.
• Fallacies are mathematical statements that have neither been proved nor disproved.
• A multinomial expresses the sum of any number of terms.
• A literal equation represents known quantities with letters.
• An irradicable/irrational equation contains variables under a radical symbol.
• A redundant equation has extra, unwanted roots.
• A defective equation has fewer roots than expected.
• Open sentences include variables that become true or false with specific values.
• An arithmetic progression has consecutive terms differing by a constant.
• A rational algebraic expression is a quotient of polynomials.
• Open sentences are statements containing variables that are true or false.
• Integral rational terms have factors, not contents.
• An implicit function, A number that consists of an integer part with an integer greater than 10 for its unit digit and a decimal part less than unity that follows the decimal marker.
• Literal numbers are represented with letters.
• Conditional equations are equal for certain values of the unknown.
• A binomial contains two terms.
• Term consists of products/quotients of numbers/letters.
• The degree of polynomial is the maximum exponent.
• Compound fractions contain fractions in the numerator, denominator, or both.
• A unit fraction has unity for the numerator and a positive integer denominator.
• Proper fractions have numerators with lower absolute values, not improper.
• Binomial refers to an expression of two terms.
• Monomial refers to an algebraic expression of one term.
• Algebraic expressions consist of products and quotients of numbers and letters.
• In the absence of Pascal’s triangle, binomial term coefficients are derived by dividing the product of a term's coefficient and the exponent of "x" by one + the exponent of "y".
• Fundamental principle of counting: two things done in "m" and "n" ways yields mxn total ways.
• Permutations arrange objects in a specific order.
• The number of elements in the collection being permuted is called its degree.
• Probability is the ratio of successful outcomes to all possible outcomes.
• Probability will never equal nor exceed 1.
• Mutually exclusive events A and B have probability P(A or B) = Pa + Pb.
• For independent A and B events, the probability of B occurring is q/p, with events A has p and A and B to occur with q.
• One minus Pa is the probability that an event with possible occurrence “Pa” will not occur.
• Venn diagrams illustrate probabilistic independent/dependent concepts.
• The difference between the highest and lowest score is considered as the range.
• The second power of a standard deviation is called variance.
• Ogives are cumulative frequency distributions on step-wise functions.
• The algebraic expression consisting a sum of any number of terms is a multinomial.
• Consecutive whole numbers with 7 + Oi are considered as real numbers.
• The absolute value of a nonzero number is always positive.
• Common multiple is polynomial divisible by two or more polynomials.
• Linear factors and irreducible quadratic factors are real coefficients.
• Linear factor is the degree is the numerator is one more than the degree of numerator.
• A notation represent the product of all positive integer is Factorial.
• Goldbach conjecture that is every even integer greater than 2 can be written as the sum of two prime numbers.
• The unending hased number of integers that follows the rule that each integer is the sum of the proceding two, as Fermat numbers.
• Quod erat demonstrandum to write at the end of proof has been reached.
• Rounding off to calculate 3.1415 process is called.
• Containing the empty and original set the set of a subset call power set.
• Integre common to the original sets is the elements of Intersection.
• Is referred to sequence is defined had a final and first terms is finite sequence.
• Replaceable or absolute valuer, the series is that be absolute convergent.

Trigonometry

• sin(A)cos(B)-cos(A)sin(B) is equal to sin(A-B).
• The angular distance from the north pole is called coaltitude.
• csc 520° = csc 20°.
• sin 820° is 0.984
• Logarithm of negative number is imaginary.
• The sum of sine and cosine of an angle is 1.
• Number e is base to Napierian logarithm.
• Logarithmic form is when the characteristic of exponent equals 10.
• There number 2.72 to Napierian Alrogithm.
• Zero is the logarithm of 1 to any base.
• sin (270° + B) is equal to B.
• Positive number if an any Invequality is multiply revered by Both sides.
• The determent, if Interchange two rows of determinant, the sign changed.
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• Angle of line of slight above eyes are angle of elevation, below eyes are angles of the depression, triangle with same point is an inscribed triangle.
• Triangle with min perimeters call Pedal.
• Ratios of integer units are primitives unit.
• Triangle scale are equilateral
• Time in long run equal to 2.
• Triangle scale 3 angle has same tangent.
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• Sum of the three angles is always equal to two right angles.
• S =360 x273
• Sum of the angles equals the a sector for a sphere for is never.
• Triangle spheric triangle.
• L + A = - 90°
• 726 is approximately 1.2 km.
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Economics

• Private ownership is where individuals exercise rights in their interest.
• Depreciation indicates a decrease in property value over time.
• Partnerships involve two or more co-owners for profit.
• Supply is an item that offered at certain pride.
• Economic orders quantity is minimized the cost per peroid and has been constant over period.
• Market is place to gather buyer and sellers.
• Tort is that wrong with that damaged others with property.
• Working capital is a current account.
• The highest position, not by share, which is in charge under the chairman of the board.
• Book value is original cost less depreciation.
• Long run means over time by which economic value.
• Supply is offered for sale given price in any time.
• Cost is from labor and machines and expenses but can be an annuity.
• S=0.1 of assets indicates a reasonable position.
• Discount for price equal.
• Sunkcost = new cost: labor and materials.
• In any investment factor, not by to do with economic life.
• ROI = net of the market.
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