ACT Prep Exam Latest with complete solution

ACT Prep Exam Latest with complete solution Acceleration - ANSWER The rate of change of velocity Acidic - ANSWER Having a pH less than 7 Acute - ANSWER (adj.) refers to an angle that is less than 90 degrees; (adj.) refers to a triangle with angles that are all less than 90 degrees; sharp; quick and precise; intense Aerobic Respiration - ANSWER The breakdown of glucose in the body of an animal to supply muscles with oxygen. Aerosol - ANSWER Solid or liquid particles suspended in gas Alkalinity - ANSWER Having a pH greater than 7 (contrast with acidic, which is having a pH less than 7). Amino Acids - ANSWER Various organic compounds that link together to form proteins. Anatomical - ANSWER Related to the structure of an organism Antigen - ANSWER A substance such as a toxin or enzyme capable of eliciting an immune response. Antitoxin - ANSWER An antibody created for and capable of neneutralizing a toxin Bacteria - ANSWER Single-celled microorganisms Basalt - ANSWER Solidified lava; a dense, gray, fine-grained igneous rock Biomass - ANSWER Total mass of all the living matter within a given area Biosynthesis - ANSWER The production of a chemical compound within the body Boiling Point - ANSWER The temperature a liquid must be to change states from liquid to gas Capillary - ANSWER A very slim tube; one of a network of extremely small blood vessels Carbohydrate - ANSWER Sugars and starches that serve as a major energy source for animals Catalyst - ANSWER An agent that causes or speeds up a chemical reaction Celsius - ANSWER A temperature scale in which the freezing point of water is 0 degrees and the boiling point is 100 degrees under normal atmospheric conditions Cerebral Edema - ANSWER Brain swelling Chlorophyll - ANSWER A green pigment produced in response to sunlight during photosynthesis. Cholesterol - ANSWER A soft, waxy compound found in the body and in the food we eat. Collinear - ANSWER 23 of 450 Collinear Passing through or lying on the same straight line. Comet - ANSWER A celestial body, having an elongated, curved vapor tail, which is seen only in that part of its orbit that is relatively close to the sun Common Difference - ANSWER The equal distance between one number in an arithmetic sequence and the next (for example, the common difference between 4, 6, and 8 is 2.). Common Ratio - ANSWER The ratio of one term and the next in a geometric sequence (for example, the common ratio between 2, 4, and 8 is 4/2 and 8/4, or 2.) Compressibility - ANSWER The ease with which pressure can alter the volume of matter Congruent - ANSWER Equal in length or measure Cos - ANSWER Abbreviation of cosine Cosine - ANSWER The ratio of the adjacent side (with respect to the angle of reference) to the hypotenuse in a right triangle Cube - ANSWER A term raised to the third power; a regular solid having six congruent faces Cubic Inch - ANSWER The volume of a cube with edges that all measure one inch. Cylindrical - ANSWER Having the shape of a cylinder, or a solid with circular ends and straight sides Diagonal - ANSWER A line segment joining two nonadjacent vertices of a polygon or solid (polyhedron). Dilute - ANSWER To weaken the strength of a solution Directly Proportional - ANSWER Increasing or decreasing together or with the same ratio Ecology - ANSWER The field of science that concentrates on relationships between organisms and their environments Emissions - ANSWER Things that are discharged (often gases into the air). Emit - ANSWER To release particles such as light, heat, or gases. Epicanthic Fold - ANSWER A fold of skin of the upper eyelid that only partly covers the eye's inner corner Equilibrium - ANSWER A state of balance Erosion - ANSWER The wearing away of an object by outside forces, like wind or water Evaporate - ANSWER To draw away moisture and convert into vapor Experimental Variables - ANSWER Elements of an experiment that are changed (distinguished from the constant, which is held the same in order to produce significant results). Fahrenheit - ANSWER A temperature scale in which the freezing point of water is 32 degrees and the boiling point is 212 degrees under normal atmospheric conditions Fermentation - ANSWER The chemical process of breaking down an organic substance into simpler substances such as the fermentation of sugar to alcohol Friction - ANSWER The force resistant to motion Galvanism - ANSWER A direct electrical current produced by chemical reactions Gas - ANSWER A fluid (such as air) that is not independent in shape or volume but tends to expand Gas Chromatograph - ANSWER A device used to detect the composition of an unknown material Gastric Emptying - ANSWER The movement of the stomach's contents from the stomach to the small intestine, and finally into the colon Gravity - ANSWER The force of attraction between two bodies of mass Herbivorous - ANSWER A plant-eating organism Hydrogen Bonding - ANSWER The chemical bonding of a hydrogen atom with another electronegative atom. Hypotenuse - ANSWER The longest side of a right triangle, which is always the side opposite the right (90°) angle. Igneous Rock - ANSWER Rock that is formed by the cooling and solidification of molten magma Ignition Temperature - ANSWER The temperature that a fuel must reach before combustion can begin Infrared - ANSWER Light energy having a wavelength greater the visible range; it is experienced as heat. Interior Angle - ANSWER An angle inside of a shape (that is, all of the interior angles in a triangle have a sum of 180 degrees). Intracellular - ANSWER Within a cell or cells Isosceles Triangle - ANSWER A triangle with two congruent sides and two congruent angles Isotopes - ANSWER Two or more atoms with an identical atomic number and differing in number of neutrons. Kelvin - ANSWER A temperature scale in which absolute zero is 0 degrees K, the freezing point of water is 273 degrees K, and the boiling point of water is 373 degrees K Law of Sines - ANSWER The relationship within a triangle of the sine of angles and the lengths of sides of a triangle. Least Common Denominator (LCD) - ANSWER The smallest number (other than 0) that is a multiple of a set of denominators (for example, the LCD of 14and16 1 4 and 1 6 is 12). Least Common Multiple (LCM) - ANSWER The smallest number that is a multiple of a set of numbers (for example, the LCM of 6 and 9 is 18). Linear - ANSWER Relating to a line Lipid - ANSWER An oily/waxy organic compound that cannot be dissolved in water Liquid - ANSWER a substance that is neither a solid nor a gas; (adj.) flowing Lithosphere - ANSWER The outer part of the Earth that includes the crust and upper mantle. Log - ANSWER Abbreviation of logarithm. Logarithms are used to indicate exponents of certain numbers called bases. By definition, logab=c if ac=b (for example, logx36=2 if x2=36. In this case, x=6.) Macrophages - ANSWER Protective cells Manometer - ANSWER A device that measures the pressure of liquids and gases. Matrix - ANSWER Rows and columns of elements arranged in a rectangle Mean (also Arithmetic Mean) - ANSWER average; found by adding all the terms in a set and dividing by the number of terms Median - ANSWER The middle value in a set of ordered numbers. If the set of numbers is even, it is the average (mean) of the two middle values. Melting Point - ANSWER The temperature at which a solid softens into a liquid. Mesosphere - ANSWER A layer of the atmosphere fifty to eighty kilometers above the Earth's surface. Metamorphism - ANSWER The process of altering solid rock by changing its temperature, pressure, and chemistry. Microorganism - ANSWER An organism of microscopic or very small size. Midpoint - ANSWER The point that divides a line segment into two equal segments. Mole - ANSWER A unit of measurement for the molecular weight of a substance. Molecular Weight - ANSWER The weight of all of the atoms in a molecule. Nanometer - ANSWER One billionth of a meter. Newton - ANSWER The amount of force needed to accelerate a one-kilogram mass at a rate of one meter per second, per second. Obtuse - ANSWER An angle with a measure greater than 90 degrees but less than 180 degrees Organic Matter - ANSWER Matter that is derived from living organisms. Organism - ANSWER A living thing, either plant or animal. Parallel - ANSWER Lines in the same plane that do not intersect each other; in a coordinate plane, noncollinear lines or segments having the same slope as one another. Parallelogram - ANSWER A quadrilateral (a figure that has four sides) with opposite sides that are parallel and congruent Perimeter - ANSWER The boundary of a figure; in math, the distance from one point around the figure to the same point Perpendicular - ANSWER Lines that intersect and form 90-degree angles. pH - ANSWER A scale that measures how acidic or basic a substance is on a scale of 0 to 14. Lower numbers indicate an increasing acidity and higher numbers indicate increasing basicity. Photophores - ANSWER Organs that produce light. Photosynthesis - ANSWER The process by which plants turn carbon dioxide and water into energy with the aid of sunlight Slope Formula - ANSWER The formula used to calculate the slope of a line: (y1−y2) (x1−x2) (Note that the order of subtraction in the denominator can be reversed, giving the alternative slope formula: (y2−y1)(x2−x1) Positive Slope - ANSWER The incline of a line that slants upward (from left to right) Prime Number - ANSWER A positive integer that can only be evenly divided by 1 and itself Protein - ANSWER A compound that consists of amino acids and plays various structural, mechanical, and nutritional roles within organisms. Quadrant - ANSWER One part of a larger object that has been divided into four parts. Quadratic Equation - ANSWER An equation in the form of ax2+bx+c=0, where a≠0, and has only two solutions for x. Radian - ANSWER A unit of angle measure within a circle. Radii - ANSWER The plural form of radius Radioactive Decay - ANSWER A natural process by which an atom of a radioactive isotope spontaneously decays into another element. Radius - ANSWER A line segment with endpoints at the center of the circle and on the perimeter of the circle, equal to one-half the length of the diameter. Ratio - ANSWER A comparison between two quantities (for example, the ratio of girls to boys in the class is 1:2). Real Number Line - ANSWER An infinite line of real numbers represented on a one- dimensional graph. Real Numbers - ANSWER Numbers that can be associated with points on a number line Rectangular - ANSWER Having the shape of a rectangle (a parallelogram with four right angles). Hexagon - ANSWER A six-sided polygon. Scientific Inquiry - ANSWER Based on experiment and observation and the application of the Scientific Method; examination into facts or principles. Seedling - ANSWER A young plant grown from seed. Solid - ANSWER Neither gas nor liquid; of definite shape and volume. Solute - ANSWER A dissolved substance. Solution - ANSWER A mixture of two or more substances. Solution Set - ANSWER The set of values that make an equation true. Specific Gravity - ANSWER The ratio of the density of one substance to the density of another substance. Sphere - ANSWER A solid, round figure where all points on the surface are the same distance from the center (for example, a basketball). Spleen - ANSWER A vascular, ductless organ that is located in the left abdominal region close to the stomach. Standard (x, y) Coordinate Plane - ANSWER A plane that is formed by a horizontal x- axis and a vertical y-axis that meet at point (0,0) (also known as the Cartesian Coordinate Plane). Stratosphere - ANSWER A layer of the atmosphere between the troposphere and mesosphere. Sucrose - ANSWER A simple sugar. Suspensions - ANSWER The state of a substance when its particles are combined together but have not been dissolved in a fluid or solid Synthetic Polymer - ANSWER A human-made, repeating chain of atoms. Thermal Degradation - ANSWER A process of combustion where materials in a fuel are broken down into several by-products. Thermosphere - ANSWER The outermost layer of the atmosphere. Transversal - ANSWER A line that cuts through two or more lines. Trapezoid - ANSWER A quadrilateral (a figure with four sides) with only two parallel lines. Tropical Area - ANSWER An area near the equator that has a frost-free climate with high temperatures that can support year-round vegetation. Troposphere - ANSWER The lowest part of the Earth's atmosphere. Ultraviolet - ANSWER Situated beyond the visible spectrum. Vapor Pressure - ANSWER The pressure exerted by the molecules of vapor. Vaporize - ANSWER To change into a cloud of diffused matter. Vertices - ANSWER The plural form of vertex, which is the point of intersection of two straight lines (or line segments). Virus - ANSWER Organism that causes infection. Voltage - ANSWER A measure of the energy of an electric current. Wavelength - ANSWER The distance between repeating peaks or crests of waves. x- Intercept - ANSWER The point at which a graph of a function/relation crosses the x- axis. The x-coordinate's value when y is equal to zero. y- Intercept - ANSWER The point at which a graph of a function or relation crosses the y- axis. The y-coordinate's value when x is equal to zero. It is denoted by b in slope- intercept form. PEMDAS - ANSWER Acronym for the order the order of operations of numbers. P = Parentheses E = Exponents MD = Multiplication or Division in order from left to right AS = Addition or Subtraction in order from left to right G.C.F. (Greatest Common Factor) - ANSWER The largest number that can divide each number from a set of numbers without a remainder. Ex. The G.C.F. of 8 and 12 is 4. Rational Numbers - ANSWER Numbers that can be expressed as a quotient (or fraction) of two integers. Ex. 1, -2, 3.25, 2/3 Adding Fractions - ANSWER change the fractions into the lowest common denominator and add the numerators Multiplying Fractions - ANSWER Multiply across (the numerator with the numerator and the denominator with the denominator), then reduce into lowest terms. * don't confuse this with the cross-multiplication, which is used to solve equations that are proportions. Dividing Fractions - ANSWER Multiply the first fraction by the reciprocal of the second fraction. Composite Number - ANSWER A positive integer (whole number) that can be divided evenly by at least one number other than 1 and the number itself. Ex. 4, 9, 51, 60 Percent Formula - ANSWER Percents = Part/Whole*100 Average (Mean) Formula - ANSWER Average=sum of terms/number of terms Irrational Numbers - ANSWER Numbers with infinite, non-repeating decimals that cannot be expressed as the quotient of two integers. Ex. π, √2 Percent Change Formula - ANSWER Percent Change =(final value−initial value)/initial value×100 Rate Formula - ANSWER Rate = Work/Time Speed Formula - ANSWER speed=distance/time Average Speed Formula - ANSWER Average Speed=Total Distance/Total Time Simple Interest Formula - ANSWER Simple Interest = P×N×R Where P = principal, N = number of years, R = rate expressed as a decimal Scientific Notation - ANSWER A system to express very large and very small numbers and consists of two parts: a number between 1 (included) and 10 (not included), followed by 10 raised to a positive or negative exponent e.g. 1.0*1014,6.67*10−11 Directly Proportional - ANSWER A relationship between two quantities in which they either both increase or both decrease by the same factor. If x and y are directly proportional, if you increase x by a factor of 1.5, y also increase by a factor of 1.5. x=k.y or x/y=k e.g. quantity and price of items, speed and distance etc. Inversely Proportional - ANSWER A relationship between two quantities in which if one increases by a certain factor, the other decreases by the same factor, and vice versa. If x and y are inversely proportional, if you increase x by a factor of 4, y decreases by a factor of 4. x.y=k e.g. speed and time, volume and density etc. Absolute Value - ANSWER The positive value of a quantity without regards to its sign Distance between zero and the given number on a number line Probability Formula - ANSWER Probability=Number of desired choices/number of total choices Mode - ANSWER The value that occurs most frequently in a set. Ex. The mode of {2,3,-1,5,9,-7,2,14} is 2. Base - ANSWER The number that is repeated in a power e.g. In 2 10 , 2 is the base Exponent - ANSWER The number of times the base is multiplied by itself Ex. In 2 10 , 10 is the exponent Multiplying Powers - ANSWER When you multiply powers of the same base, add the exponents x a×x b=x a+b 2 3×2 2=2 3+2=2 5 Dividing Powers - ANSWER When you divide powers of the same base, subtract the exponents x a/x b=x a−b 2 6/2 −1=2 6−(−1)=2 7 Exponents raised to a power - ANSWER If a power is raised to another exponent, then multiply all the exponents (x a)b=x a.b or (2 3) 2=2 6 Fractional Exponents - ANSWER When there is a fractional exponent, it becomes the denominator as the nth-root and the numerator as the new exponent x 1/n=n√x x m/n=n√x m 36 1/2=√36=6 27 1/3=3√27 3 432=43√=8 Zero Exponent - ANSWER Any base raised to a zero exponent equals 1. 2 0=1 x 0=1 (x 2+2x) 0=1 Negative Exponents - ANSWER With a negative exponent, take the reciprocal of the base and change the exponent to be positive x −a=1/x a Ex. 2 −3=1/2 3=1/8 Difference of Squares Formula - ANSWER a 2−b 2=(a+b)(a−b) Squares of Sum and Difference - ANSWER (a+b)2=a2+2ab+b2 (a−b)2=a2−2ab+b2 FOIL - ANSWER Multiplication of two binomials: F = First O = Outer I = Inner L = Last (a+b)(c+d)=ac+ad+bc+bd Consecutive Integers - ANSWER Integers that follow each other in order, e.g. 13, 14, 15, 16, 17 etc. These are represented algebraically by x, x + 1, x + 2, x + 3... Consecutive Odd/Even Numbers - ANSWER odd/even numbers that follow each other in order, e.g. 5, 7, 9, 11 or −4, −2, 0, 2... These can be represented algebraically by x, x + 2, x + 4... Vocabulary for Algebra Word Problems - ANSWER increased by: add decreased by: subtract subtracted from/less than: switched subtract product of: multiply quotient of/ratio of: divide Vocabulary for Word Problems (contd...) - ANSWER of: multiply per: divide percents: divide by 100 is: equals to what number: variable (e.g. x) Quadratic Formula - ANSWER x=√-b±b2-4ac/2a Solutions of Quadratic Equations - ANSWER f (x+a)(x+b)=0 then x=−a,x=−b Distribution of Negative Sign - ANSWER When you subtract one polynomial from another, distribute the negative sign i.e. change the signs of all the terms of the polynomial that is being subtracted. (x2+xy+2y2)−(3x2−4xy−y2) =x2+xy+2y2−3x2+4xy+y2 =−2x2+5xy+3y2 Finding Value of a Function - ANSWER Substitute (replace) x by what's in the parenthesis without changing anything else. f(x)=x2−3 f(a)=a2−3 f(−2)=(−2)2−3= 1f(a+b)=(a+b)2−3 Imaginary Number - ANSWER i=√-1 i2=−1 Steps of a Scientific Method - ANSWER 1. Question/Problem 2. Hypothesis 3. Experiment 4. Analysis 5. Conclusion Dependent Variable - ANSWER the variable that is measured during the experiment and is affected by the independent variable Constant - ANSWER a variable that remains unchanged during the experiment and is unaffected by other variables Controlled Variable - ANSWER a factor that is kept constant throughout an experiment Rate of Change - ANSWER slope of tangent to the curve at a given point Absolute Zero - ANSWER The lowest possible temperature, about -273 degrees Celsius Alloy - ANSWER a substance composed of two or more metals Atom - ANSWER The smallest part of an element; the fundamental building block of an element. Barometer - ANSWER an instrument that is used to measure atmospheric pressure calorie - ANSWER a unit of heat energy equal to 4.185 joules *remember, it's not the same as Calorie, which is equal to 1 kilocalorie or 1000 calories Carcinogen - ANSWER A cancer causing agent Carnivore - ANSWER Eats only meat Compound - ANSWER A substance made up of two or more chemically bonded elements in a fixed proportion Element - ANSWER A substance consisting of only one type of atoms Concentration - ANSWER Amount of substance dissolved in a given amount of solvent Condensation - ANSWER Change from a gaseous to liquid phase Conductor - ANSWER A material that allows heat and electricity to readily flow through it with minimal resistance Diffusion - ANSWER The flow of liquid or gas from an area of higher concentration to an area of lower concentration Fossil - ANSWER The preserved remains of a very ancient organism Frequency - ANSWER The number of cycles per unit time Infrared Radiation - ANSWER Electromagnetic waves whose wavelength is longer than that of visible light Insulator - ANSWER A material that blocks the flow of heat or electricity Ion - ANSWER An atom or molecule that has become charged by either losing or gaining electrons Kinetic Energy - ANSWER The energy of an object or a system due to its motion Potential Energy - ANSWER The energy of an object or a system due to its position or configuration Ore - ANSWER A piece of raw earth from which a metal can be extracted Osmosis - ANSWER The movement of liquid through a membrane Symbiosis - ANSWER A long-term interaction between two different species in which they both are benefited from the relationship Absolute - ANSWER Viewed or existing independently and not in relation to anything else Accuracy - ANSWER The degree to which the measurement is close to the standard; freedom from mistakes Analogous - ANSWER Different in structure but similar in function Ex. wings of birds and wings of butterflies Homologous - ANSWER Similar in structure, both superficially and anatomically, but different in functions Ex. wings of bats and fins of whales Argument - ANSWER A statement or reasoning for or against something Assumption - ANSWER Something that is accepted to be true, without proof Consistent - ANSWER In agreement with something, not contradicting Contradiction - ANSWER A statement that is opposite to or disagrees with another Correlation - ANSWER A mutual relation between two or more ideas or things that may not have a causal relationship with each other Diminish - ANSWER To become smaller or fade; decrease in size Extrapolation - ANSWER Estimation beyond the observable range Interpolation - ANSWER Creating new data points within the range of existing data points Hypothesis - ANSWER A supposed explanation of a question or a problem that is the starting point for further testing Imply - ANSWER Strongly suggest as opposed to state directly Inference - ANSWER A conclusion reached based on evidence and reasoning Legend - ANSWER Explanation of the symbols used Optimum - ANSWER Most favorable condition, Ex. for growth of specific microbes Precision - ANSWER The quality of being exact Simulation - ANSWER Something represents something else that is similar in nature and function Constant - ANSWER Unchanging in different trials or observations Analyze - ANSWER Examine in detail Apply - ANSWER Make use of in a relevant manner Argument - ANSWER A statement made to convince or persuade Assert - ANSWER To state firmly and positively Characterize - ANSWER Describe the distinctive features of Conclude - ANSWER Arrive to a decision by reasoning Context - ANSWER A set of events or facts pertaining to a particular situation Contrast - ANSWER Differentiate Depict - ANSWER Portray; represent by drawing or other forms of art Determine - ANSWER Conclude after research or a calculation Demonstrate - ANSWER To verify or establish by reasoning and argument Discern - ANSWER To perceive by sight or intellect Distinguish - ANSWER Mark off or recognize as different Establish - ANSWER To show to be valid or true Generalize - ANSWER To make a broad conclusion from a few facts and examples Intent - ANSWER Purpose, intention Implicit - ANSWER Not directly stated but implied and understood Explicit - ANSWER Expressed directly and clearly Omit - ANSWER To leave out or remove Paraphrase - ANSWER To restate in different words Point-of-view - ANSWER How someone sees something; one's opinion or attitude towards something Summarize - ANSWER To give a brief statement of the main points of (something) Visualize - ANSWER To recall or form mental images and pictures Verify - ANSWER To prove something by examination or research FANBOYS - ANSWER Coordinating conjunctions For, And, Nor, But, Or, Yet, So These words are used to combine 2 Independent Clauses into a compound sentence Ex. Anthony planned on going to the park, but the thunderstorm forced him to stay inside. After introductory clauses, use - ANSWER A comma When there is a non-essential-clause - ANSWER Use a comma before and after the clause Between adjectives whose order is reversible - ANSWER Use a comma Ex. intelligent, passionate student passionate, intelligent student Between adjectives whose order is not reversible - ANSWER DO NOT use a comma Ex. beautiful modern art NOT modern beautiful art Between a subject and a verb - ANSWER DO NOT use a comma Between an adjective and a noun - ANSWER DO NOT use a comma Before or after a preposition - ANSWER DO NOT use a comma Comma splice - ANSWER When a comma is mistakenly used between two independent clauses Ex. I plan to attend a liberal arts college, my parents want me to get a well rounded education. (Incorrect) To correct it, replace the comma with a period, a semi-colon or a comma with FANBOYS Possessive form of nouns - ANSWER Use an apostrophe Ex. Mary's horse, river's width etc. Singular and plural possessive - ANSWER Singular: apostrophe before the 's' Ex. boy's (belonging to the boy) Plural: apostrophe after the 's' Ex. boys' (belonging to the boys) Possessive pronouns - ANSWER Have no apostrophe Ex. his, her, their, your, etc. Plural form of letters and numbers - ANSWER Use an apostrophe e.g. 6's, i's etc Before a list - ANSWER Use a colon *Remember you need a full sentence before the colon followed by a list. Before a piece of information that adds to a statement - ANSWER Use a colon its vs. it's - ANSWER its - possessive of "it" - IT owns something it's - contraction of "it is" whose vs. who's - ANSWER whose - possessive of who who's - who is When you see parenthesis in a sentence - ANSWER Apply the same rules you'd use without the parenthesis A dash is used - ANSWER Before and after a non essential clause Before an explanation at the end of a sentence Between a compound subject or a compound object - ANSWER DO NOT use a comma Ex. Tom and Jerry NOT Tom, and Jerry Before an emphatic pronoun - ANSWER DO NOT use a comma Ex. The president himself attended the dinner party. NOT The president, himself ... In an essential clause - ANSWER DO NOT use a comma Ex. Jennifer visited the city where she went to college. NOT Jennifer visited the city, where she went to college. "which" is used . - ANSWER with a non-essential clause with commas (or dashes) before and after the clause "that" is used - ANSWER With an essential clause without commas before or after the clause Subject-Verb Agreement - ANSWER Singular subjects require singular verbs, and plural subjects require plural verbs. Ex. The dogs eat the dog food. (plural) The owner of the dogs feeds the dog food. (singular) Subject-Verb Agreement: Singular pronouns - ANSWER If the subject is singular, then the pronouns referring to the subject should be singular as well. Ex. I, he, she, it, every, each, everyone, none, whoever, someone, nobody, either neither, someone etc. Subject-Verb Agreement: Plural Pronouns - ANSWER If the subject is plural, then the pronouns referring to it should be plural as well. Ex. we, you, they, those, few, many, some etc. Subject-Verb Agreement: the clauses after the preposition - ANSWER Do not affect the subject-verb agreement Ex. One of the students is selected. NOT: One of the students are selected. The advantages of this new system are plenty. NOT: The advantages of this new system is plenty. Nominative Pronouns - ANSWER Replace the nouns e.g. I, you, he, she, it, they, we Objective Pronouns - ANSWER Act as direct or indirect objects Ex. me, us, you, him, her, it, them Relative Pronouns - ANSWER Used to identify people, places and objects in general Ex. who, whom, whose, which, what, that, where Simple Past - ANSWER Something that happened in the past and is no longer happening Ex. The guests left yesterday. Present Perfect - ANSWER Something that started in the past and is ongoing has/have + participle form Ex. I have lived in the city for 5 years Past Perfect - ANSWER Something that had happened in the past before another event. had + participle form Sam had worked at a university before he decided to become an actor. Simple Present - ANSWER The action takes place continuously or regularly Ex. My brother comes home late from work. Present, Past, and Participle Forms: swim - ANSWER swim, swam, swum Present, Past, and Participle Forms: run - ANSWER run, ran, run Present, Past, and Participle Forms: come - ANSWER come, came, come Present, Past, and Participle Forms: read - ANSWER read, read, read Present, Past, and Participle Forms: shrink - ANSWER shrink, shrank, shrunk Present, Past, and Participle Forms: fling - ANSWER fling, flung, flung Present, Past, and Participle Forms: bear - ANSWER bear, bore, borne Present, Past, and Participle Forms: bet - ANSWER bet, bet, bet Present, Past, and Participle Forms: cost - ANSWER cost, cost, cost Present, Past, and Participle Forms: lay - ANSWER Present, Past, and Participle Forms: lay Present, Past, and Participle Forms: seek - ANSWER seek, sought, sought Present, Past, and Participle Forms: spin - ANSWER spin, spun, spun Present, Past, and Participle Forms: wake - ANSWER wake, woke, woken Misleading/ambiguous pronoun usage - ANSWER A pronoun should be placed such that it refers to a specific noun, called an antecedent. Parallelism - ANSWER Sentences should group ideas such that the words, phrases, and clauses must share the same grammatical form and parts of speech Ex. Victoria likes swimming and to ride her bike. (incorrect) Victoria likes swimming and riding her bike. (correct) Run-on Sentence - ANSWER Consists of more than one idea and is incorrectly written due to lack of punctuation or conjunctions Ex. Janet is an actress she often appears in major television network shows. (incorrect) Janet is an actress who often appears in major television network shows. (correct) Misplaced Modifiers - ANSWER Modifiers are descriptions that are best placed next to the things they describe. Ex. Cassie had trouble deciding which college to attend at first. (incorrect) At first, Cassie had trouble deciding which college to attend. (correct) Dangling Modifiers - ANSWER Words/phrases that modify a word not clearly stated in a sentence Ex. Crawling on the wall, the cat was startled by a giant spider. (incorrect) Crawling on the wall, a giant spider startled the cat. (correct) "Who" - ANSWER Refers to the person who is the subject of the sentence; always used after the noun He = Who "Whom" - ANSWER Refers to the person who is the object of the sentence; used before a noun or pronoun; used after a preposition Him = Whom Fragments - ANSWER Are incomplete sentences caused by unnecessary words or punctuation Ex. My car is difficult to start in the winter. Because of the cold weather. (incorrect) My car is difficult to start in the winter because of the cold weather. (correct) Prepositional Idioms: abide - ANSWER abide by (obey) abide with (stay) Prepositional Idioms: accustom - ANSWER accustom to Prepositional Idioms: absolve - ANSWER absolve from Prepositional Idioms: coerce - ANSWER coerce into (doing something) Prepositional Idioms: compare - ANSWER compare with (literal) compare to (metaphorical) Prepositional Idioms: comply - ANSWER comply with (rule or law) Prepositional Idioms: contemporary - ANSWER contemporary of (a person) contemporary with (an event) Prepositional Idioms: depend - ANSWER depend on (not upon) Prepositional Idioms: differ - ANSWER differ from (a thing) differ with (a person over something) Commonly Misused Words: accept/except - ANSWER accept: to agree to or receive except: "other than" or "but" Commonly Misused Words: affect/effect - ANSWER affect: is a verb meaning "to influence" effect: is a noun meaning "a change that is the result of an action or other cause" Commonly Misused Words: among/between - ANSWER Among is used to discuss multiple objects that are not distinct. It indicates the subject is in the vicinity of objects or people, but does not give the subject's exact location. Example: She was forced to choose among a myriad of science classes. Example: Fear spread among the students as the pop quiz was announced. Between is used to describe a set of distinct (countable), separately named objects. It also gives the precise location of the subject - the subject is between specific objects. It comes down to the number of objects being discussed, and how distinct those objects are. Example: The race between Amy and Emeril was very close. Example: She needed to choose between physics, chemistry, and biology. Commonly Misused Words: Assure/Ensure/Insure - ANSWER Assure: To convince Ensure: To make certain of Insure: To guard against loss Commonly Misused Words: complement/compliment - ANSWER complement: something that completes or adds to something else compliment: praise Commonly Misused Words: fewer/less - ANSWER fewer: is used with countable items such as hours, bills, sticks etc. less: is used with uncountable items such as time, money, wood etc. Commonly Misused Words: too many/too much - ANSWER too many: is used with countable items such as gallons, grains, sheets etc. too much: is used with uncountable items such as milk, sand, paper etc. Commonly Misused Words: lay/lie - ANSWER lay: to put or place lie: to rest or stay Commonly Misused Words: principal/principle - ANSWER principal: head or first principle: a basic truth or law Commonly Misused Words: their/there/they're - ANSWER their: possessive form of they there: an adverb specifying location they're: they are Commonly Misused Words: your/you're - ANSWER your: possessive form of you you're: you are Words/phrases that suggest continuation - ANSWER furthermore, moreover, in addition, in fact, indeed etc Words/phrases that suggest contradiction - ANSWER however, despite, but, whereas, while, although, though, in contrast etc. Words/phrases that suggest comparison - ANSWER likewise, similarly, just as, like etc. Words/phrases that suggest conclusion - ANSWER therefore, thus, in other words etc. Words/phrases that suggest causation - ANSWER because, since, as a result, due to etc. Prepositional Idioms: point - ANSWER point to Prepositional Idioms: indifferent - ANSWER indifferent to/toward Prepositional Idioms: efficient - ANSWER efficient at Prepositional Idioms: in awe - ANSWER in awe of Prepositional Idioms: familiar - ANSWER familiar with Prepositional Idioms: have confidence - ANSWER have confidence in Prepositional Idioms: adept - ANSWER adept in/at Prepositional Idioms: in contrast - ANSWER in contrast to *contrast with Prepositional Idioms: compensate - ANSWER compensate for Prepositional Idioms: capable - ANSWER capable of Prepositional Idioms: sympathize - ANSWER sympathize with Prepositional Idioms: puzzled/confused/perplexed - ANSWER puzzled/confused/perplexed by i to the nth power - ANSWER 1, -1, i or -i Matrix Addition - ANSWER Add the corresponding elements together Ex. [153−7] + [−24−317] = [−19010] Matrix (Scalar) Multiplication - ANSWER Multiply the scalar to each element of the matrix −2[−25−30]=[4−1060] Solving linear equations - ANSWER Isolate the variable by inverse (opposite) operations. Solving simultaneous equations by Substitution - ANSWER Express one variable in terms of the other and substitute. Solving simultaneous equations by elimination - ANSWER Cancel one of the variables by addition. Conjugate of a complex number - ANSWER Change the sign of the imaginary number, the sign of the real number stays the same Ex. a+bi and a-bi 4-6i and 4+6i Slope-intercept form - ANSWER Y=mx+b Quadrants - ANSWER Generally, one part of a larger object that has been divided into four parts Each of the 4 regions the co-ordinate axes divide the plane into Sum of interior angles of polygons - ANSWER 180×(n-2) n →# of sides Mid-point formula - ANSWER (x1 + x2/2 ,y1 + y2/2) Distance Formula - ANSWER d=√(x2−x1)2+(y2−y1)2 Parallel lines - ANSWER Two lines in the same plane that never intersect have equal slope m1=m2 Perpendicular lines - ANSWER Lines that intersect to form right (90°) angles have opposite reciprocal slopes m1=−1/m2 Line of symmetry - ANSWER A line that divides a figure into two halves that are mirror images of each other. Sum of exterior angles of a polygon - ANSWER 360° Point-Slope form - ANSWER y−y1=m(x−x1) Perpendicular Bisector - ANSWER A line that cuts a line segment into two equal halves and forms right angles (90°) with that segment Number of diagonals in a polygon - ANSWER n(n−3)/2 Where n is the number of sides Equation of a circle - ANSWER (x−h)2+(y−k)2=r2 (h,k)→center r→radius Vertical Line - ANSWER x = a(constant) (has an undefined slope) Horizontal Line - ANSWER y = b (Constant) (has a zero slope) Equation of a Parabola - ANSWER y=a(x−h)2+k (h,k)→vertex Angles on a straight line - ANSWER Have a sum of (add up to) 180° Vertical angles - ANSWER Are congruent (have equal measures) Sector - ANSWER The region bounded by two radii of a circle and their intercepted arc Corresponding angles formed by parallel lines - ANSWER One outside and one inside the parallel lines, both on the same side of the transversal and have congruent (equal) measures Alternate interior angles formed by parallel lines - ANSWER Both inside the parallel lines; on either side of the transversal; non adjacent; are congruent (equal) Arc - ANSWER Part of the circumference of a circle SOHCAHTOA - ANSWER Mnemonic for the values of sin, cos, and tan sin θ - ANSWER opposite/hypotenuse cosθ - ANSWER adjacent/hypotenuse Same-Side Interior Angles - ANSWER Interior angles on the same side of the transversal; have a sum of (add to) 180° tanθ - ANSWER opposite/adjacent cosecθ - ANSWER 1/sinθ secθ - ANSWER 1/cosθ Area of a sector - ANSWER central angle */ area360° cotθ - ANSWER 1/tanθ Interior angles of a triangle - ANSWER Have a sum of (add to) 180° Exterior angle of a triangle - ANSWER Is equal to the sum of the remote interior angles sin2θ+cos2θ - ANSWER 1 Scalene triangle - ANSWER A triangle with no equal sides Isosceles triangle - ANSWER A triangle with 2 equal sides (called legs) The base angles (angles opposite the legs) are consequently congruent Length of an arc - ANSWER central angle * circumference/360° or central angle/360° × circumference Equilateral triangle - ANSWER A triangle with all sides equal (consequently all the angles are equal to 60°) Triangle sides inequality - ANSWER a+b c a-b c area of a triangle - ANSWER A=12(base×height) Pythagorean Theorem - ANSWER Within a right triangle: a2+b2=c2 Where a and b are the legs (sides that make up the right angle) and c is the hypotenuse (side that is opposite the right angle) Special triangle 45°−45°−90° - ANSWER Sides are in a ratio of 1:1:√2 Tangent line - ANSWER A line in the plane of a circle that intersects the circle at exactly one point Special triangle 30°−60°−90° - ANSWER Sides are in a ratio of 1:√3:2 Central angle - ANSWER An angle whose vertex is the center of the circle Volume of a rectangular solid - ANSWER v=l×w×h Pythagorean Triples - ANSWER Sets of integers that satisfy the Pythagorean Theorem Examples include: (3, 4, 5), (5, 12, 13), (6, 8, 10), (7, 24, 25) surface area of a rectangular solid - ANSWER A=2(lw+lh+wh) Sum of interior angles of a quadrilateral - ANSWER 360° Area of a parallelogram - ANSWER A = base × height Volume of a cube - ANSWER V=S3 Parallelogram properties - ANSWER Opposite sides are equal and parallel; opposite angles are equal Area of a rectangle - ANSWER A = length × width Surface area of a cube - ANSWER S=6s2 Perimeter of a rectangle - ANSWER p = 2(l+w) Properties of a rectangle - ANSWER All the properties of a parallelogram; each angle 90°; diagonals are equal and bisect each other Volume of a cylinder - ANSWER V=πr2h Area of a square - ANSWER A = (Side)2 Perimeter of a square - ANSWER 4 × side Properties of a square - ANSWER All the properties of a rectangle; diagonals meet at 90°; all sides congruent (equal) Surface area of a cylinder - ANSWER Closed cylinder: 2πrh+2πr2 Open (at both bases): 2πrh Diagonal of a box - ANSWER d=√a2+b2+c2 Area of a trapezoid - ANSWER A=12×h×(b1+b2) h is the height of the trapezoid b1 and b2 are the bases (parallel sides) Volume of a sphere - ANSWER V=4/3πr3 Properties of a trapezoid - ANSWER Only one pair of opposite sides are parallel Surface area of a sphere - ANSWER A = 4πr2 log(ab) - ANSWER log a + log b log (a/b) - ANSWER log a - log b log a b - ANSWER b log a log b a - ANSWER log a/log b Properties of a rhombus - ANSWER All the properties of a parallelogram; all sides congruent (equal) Regular Polygon - ANSWER A polygon that is both equilateral (all sides are the same length) and equiangular (all angles have the same measure) Regular Hexagon - ANSWER A six-sided figure with congruent sides and angles. Each interior angle has a measure of 120°. Regular Pentagon - ANSWER A five-sided figure with congruent sides and angles. Each interior angle has a measure of 108°. Regular Octagon - ANSWER An eight-sided figure with congruent sides and angles. Each interior angle has a measure of 135°. Regular Decagon - ANSWER A ten-sided figure with congruent sides and angles. Each interior angle has a measure of 144°. Point-Slope Form - ANSWER y−y1=m(x−x1) Where m is the slope and (x1, y1) is a point on the line Reciprocal - ANSWER Switching the numerator and denominator of a number. For an integer, it is 1 divided by that number. Ex. the reciprocal of 4 is 1/4 Ex. the reciprocal of 5/3is3/5 Opposite (Negative) Reciprocal - ANSWER Taking the reciprocal of the number and changing the sign of the number. For an integer, the opposite reciprocal is dividing that integer by 1 and changing the sign. Ex. The opposite reciprocal of −4 is 14 For a fraction, the opposite reciprocal is switching the numerator and denominator and changing the sign Ex. The opposite reciprocal of 53 is −35 The slopes of perpendicular lines are opposite reciprocals of each other Associative Property (of Addition) - ANSWER Changing the grouping of addition will not change the outcome Ex. (a + b) + c = a + (b + c) (3 + 4) + 5 = 12 and 3 + (4 + 5) = 12 Associative Property of Multiplication - ANSWER Changing the grouping of multiplication will not change the outcome Ex. (a × b) × c = a × (b × c) (3 × 4) × 5 = 60 and 3 × (4 × 5) = 60 Commutative Property (of Addition) - ANSWER When adding two numbers, the order in which the numbers are added does not matter Ex. 2 + 5 = 7 and 5 + 2 = 7 Note: This does not hold true for subtraction Ex. 5 − 2 = 3 and 2 − 5 = -3 Commutative Property (of Multiplication) - ANSWER When multiplying two (or more) numbers, the order in which the numbers are multiplied does not matter Ex. 2 × 5 = 10 and 5 × 2 = 10 Note: This does not hold true for division Ex. 5 ÷ 2 = 5/2 or 2.5 and 2 ÷ 5 = 2/5 or 0.4 Transitive Property (of Equality) - ANSWER If a = b and b = c then a = c Reflexive Property - ANSWER Any number is equal to itself Ex. a = a or 2 = 2 Symmetric Property - ANSWER If x = y, then y = x The symmetric property allows any equation to be written in two ways Ex. y = 2x + 5 is the same as 2x + 5 = y Substitution Property - ANSWER If x = y, then x may be replaced by y in any equation or expression Distributive Property (of Multiplication) - ANSWER When multiplying a sum, you can multiply each individual term separately and then add the products Ex. a × (b + c) = (a × b) + (a × c) Identity (or Zero) Property of Addition - ANSWER When zero is added to any number, the sum is that number Ex. a + 0 = a 2 + 0 = 2 Identity (or One) Property of Multiplication - ANSWER When one is multiplied by any number, the product is that number Ex. a × 1 = a 2 × 1 = 2 Zero Property of Multiplication - ANSWER When zero is multiplied by any number, the product is zero Ex. a × 0 = 0 3 × 0 = 0 Addition (Additive) Property of Equality - ANSWER Any quantity can be added to both sides of an equation and the equation will maintain its equality. Ex. If a = c then a + b = c + b Multiplication (Multiplicative) Property of Equality - ANSWER Any quantity can be multiplied to both sides of an equation and the equation will maintain its equality. Ex. If a = c then a × b = c × b Subtraction Property of Equality - ANSWER Any quantity can be subtracted from both sides of an equation and the equation will maintain its equality. Ex. If a = c then a − b = c − b Division Property of Equality - ANSWER Any quantity (except zero) can divide both sides of an equation and the equation will maintain its equality. Ex. If a = c (and b is not equal to zero), then a/b = c/b active voice - ANSWER The subject of the sentence performs the action (the verb). Example: The boy rode the horse. passive voice - ANSWER The action of the sentence (the verb) is performed ON the subject of the sentence. In many cases of the passive voice, the noun performing the action is either A) not mentioned in the sentence or B) in a (prepositional phrase). Example: The horse was ridden (by the boy).