SAMPLE College Math

‭Written‬‭sentences‬‭can‬‭be‬‭converted‬‭into‬‭mathematical‬‭expressions‬‭so‬‭that‬‭they‬‭can‬‭be‬‭solved‬‭to‬‭arrive‬ ‭at‬ ‭meaningful‬ ‭solutions.‬ ‭For‬ ‭instance,‬ ‭“a‬ ‭number‬ ‭is‬ ‭multiplied‬ ‭by‬ ‭10‬ ‭and‬ ‭then‬ ‭added‬ ‭to‬ ‭8‬‭to‬‭get‬‭48”.‬ ‭Assume the number is‬ ‭and the mathematical equation becomes:‬ ‭ ‬ ‭10‬‭ ‬ + ‭8‬ = ‭48‬ ‭It‬ ‭should‬‭be‬‭noted‬‭that‬‭the‬‭two‬‭sides‬‭of‬‭the‬‭equation‬‭should‬‭balance‬‭each‬‭other‬‭using‬‭the‬‭equal‬‭to‬‭(=)‬ ‭sign. Let us solve a few more examples to get a better understanding.‬

‭Word Problem‬

‭Algebraic Translation‬

( ‭2 ‬‭ ‬‭ ‭2‬+‬ ‭1 0 ‬) = ‭35‬ ‭2 ‭ ‬ ‬ ‭ ‬‭– ‬‭ ‬‭6 ‬‭ ‬‭– ‬‭ ‬‭5 ‬‭ ‬ = ‭ ‬‭3 ‬

‭Kathy‬‭asks‬‭her‬‭mother‬‭how‬‭old‬‭she‬‭is.‬‭Her‬‭mother‬‭replies,‬‭“If‬‭you‬ ‭double my age and add 10 to it, then divide by 2, you get 35.”‬

‭Marlin‬‭gets‬‭his‬‭monthly‬‭pocket‬‭money.‬‭He‬‭saves‬‭half‬‭of‬‭it,‬‭and‬‭then‬ ‭makes‬ ‭two‬ ‭purchases‬ ‭worth‬ ‭$6‬ ‭and‬ ‭$5.‬ ‭Finally‬ ‭when‬‭he‬‭reaches‬ ‭home, he is left with $3.‬

‭A‬ ‭bus‬ ‭starts‬ ‭leaves‬ ‭the‬ ‭station‬ ‭filled‬‭to‬‭capacity.‬‭At‬‭the‬‭first‬‭stop,‬ ‭half‬‭the‬‭passengers‬‭get‬‭off‬‭and‬‭10‬‭get‬‭on‬‭board.‬‭At‬‭the‬‭next‬‭station,‬ ‭12‬‭get‬‭off‬‭while‬‭15‬‭get‬‭on‬‭board.‬‭Now,‬‭the‬‭number‬‭of‬‭passengers‬‭in‬ ‭the bus is 28.‬

‭ ‬− ‭2 ‭ ‬ ‬ + ‭10‬ − ‭12‬ + ‭15‬ = ‭28‬

‭D. Mathematical Translations of Inequalities from Words‬ ‭Inequalities‬ ‭can‬ ‭also‬ ‭be‬ ‭translated‬ ‭from‬ ‭words‬‭into‬‭mathematical‬‭equations.‬‭For‬‭instance,‬‭we‬‭need‬‭to‬ ‭translate‬ ‭the‬ ‭sentence,‬ ‭“a‬ ‭number‬ ‭minus‬ ‭6‬ ‭is‬ ‭less‬ ‭than‬ ‭2”‬ ‭into‬ ‭an‬ ‭inequality.‬ ‭“A‬ ‭number”‬ ‭states‬ ‭the‬ ‭presence‬ ‭of‬ ‭an‬ ‭unknown‬ ‭variable.‬ ‭Let‬ ‭us‬ ‭denote‬ ‭that‬ ‭by‬ ‭.‬ ‭After‬‭subtracting‬‭6‬‭from‬ ‭,‬‭this‬‭expression‬ ‭ ‬ ‭ ‬ ‭should be less than (denoted by inequality sign <) 2. Now the expression becomes:‬ ‭ ‬‭–6‬ < ‭2‬ ‭Similarly,‬ ‭mathematical‬ ‭expressions‬ ‭can‬ ‭be‬ ‭formed‬ ‭using‬ ‭different‬‭inequality‬‭notations‬‭like‬‭more‬‭than‬ ‭(>), less than (<), at most (≤), at least (≥), etc., as shown below.‬

‭ ‬ + ‭5‬ < ‭15‬ ‭5‬‭ ‬‭≤25‬ ‭ ‬ − ‭5≥17‬ ‭ ‬> ‭65‬

‭The sum of 5 more than the number is no more than 15‬

‭Five boxes of cereal costs at most 25 dollars‬

‭The difference between a number and 5 is at least 17‬

‭Jenny’s height is greater than 65 inches‬

‭E. Solving Equations‬ ‭In‬‭order‬‭to‬‭solve‬‭the‬‭equations,‬‭it‬‭is‬‭important‬‭to‬‭move‬‭all‬‭variables‬‭to‬‭one‬‭side‬‭using‬‭inverse‬‭operations‬ ‭(addition ‬ ‭subtraction‬ ‭&‬ ‭multiplication division).‬ ‭It‬ ‭should‬ ‭be‬ ‭noted‬ ‭that‬ ‭applying‬ ‭inverse‬ ‭operations‬ ‭on‬ ‭both‬ ‭sides‬ ‭of‬‭an‬‭equation‬‭keeps‬‭the‬‭balance.‬‭For‬‭instance,‬‭the‬‭equation‬ ‭can‬‭be‬ ‭ ‬‭–3‬ = ‭7‬

‭© 2023 ACHIEVE ULTIMATE CREDIT-BY-EXAM GUIDE‬‭|‬‭COLLEGE MATH‬

‭5‬

Made with FlippingBook - Online Brochure Maker