Hopefully, you have finished the first blog post I wrote about percentages because this directly follows that one. If you haven’t, it describes how to write percentages in the form of multiplication which is very useful when working with a complicated problem. Here we will discuss the more complicated percentage questions and how to go about solving them. The test likely won’t ask you to solve a simple question like “Decrease Y by X percentage” but is more likely to ask something that involves multiple steps. The two most common are “successive percentages” and “reversing percentages.” Keep reading below to find strategies for solving both of them.
Part 1: Successive Percentages
These questions involve multiple percentages to be taken of the same value to find the answer.
Ex: A book has a retail price P, it is on sale with a 20% discount. Dave uses a super coupon to get an extra 40% off the sale price. What percent of the retail price does Dave pay?
The most common incorrect response I see is P – 20% – 40% = P – 60%, so Dave received a 60% discount. This is wrong because the 40% is a reduction of the sale price, not of the original retail price.Thinking of percentages using the technique in the first blog post will save you here and make it very simple.
P reduced by 20% is P(0.8) and reduced by a further 40% is P(0.8)(0.6) = P(0.48)
So Dave pays 48% of the original retail price.
If you see a problem with a value changed by multiple percentages do not add or subtract the percentages but rewrite them so they can be multiplied!
Part 2: Reversing Percentages
These problems involve receiving the result of a percentage being taken and you need to solve for the original value.
Ex: A population decreased by 30% from 2010 to 2015. The population in 2015 is 150,000, what was the population in 2010?
The most common mistake for this question is simply increasing the population in 2015 by 30%. 150,000*(1.3) = 195,000. This may get you close to the right answer, but it will never be the right answer. Percentages are not reversible in this way. An easy example to think about is below:
100 decreased by 90% is 10. 10 increased by 90% is NOT 100, it’s 19.
Why does it work like this? The simple answer is that 90% of 100 is not equivalent to 90% of 10. The same way 30% of 150,000 is not equal to 30% of the population in 2010.
To solve this properly you should write it as an algebra equation. Let’s call the population in 2010 P. That gives us:
P * (0.7) = 150,000 solving gives us P = 214,285
Rewriting the equations or at least thinking about the algebraically should help a lot when you need to reverse percentages and will save you from making simple mistakes!
Practice: Put the techniques to use and solve these more complicated percentage problems!
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Question 1 of 4
1. Question
A car is on sale for 25% off its original price, but a greedy salesman increased the sale price by 40%! What percentage of the original price is the final price?
Final price is (5) % higher than original price
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Question 2 of 4
2. Question
A termite colony of 12,000 is being treated with pesticide. After the first week, 60% of the termites died, after the second week another 60% of termites died, in the final week 90% of the remaining termites died. How many termites are left?
(192) termites remain.
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Question 3 of 4
3. Question
Bob bought a chair for 30% off what Carl paid. Carl bought the chair on sale for 20% of the retail price. If Bob paid $72, what was the original retail price?
Original retail price was $ (128.57)
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Question 4 of 4
4. Question
In 1970 City A was 22% smaller than City B. City A grew by 46% and is now 18% larger than City B. If City B is 24,000 people today, what was the size of City B in 1970?
City B had (24,868) people.
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Gli obiettivi di ACT e SAT sono gli stessi: misurare quanto un alunno sia pronto per le università statunitensi. I test ACT e SAT sono esami universalmente accettati dai college degli Stati Uniti; ma questo spesso spinge gli studenti a chiedersi: quale test dovrei sostenere?
La risposta a questa domanda sta nel capire perfettamente le differenze tra i due test.
Entrambi gli esami di ammissione al college – ACT e SAT – sono molto popolari. Nel 2018 i dati stimano che 2,1 milioni di studenti hanno sostenuto il SAT, mentre 1,9 milioni hanno svolto invece l’ACT. Non è chiaro quanti studenti abbiano sostenuto entrambi i test, ma gli esperti affermano che è pratica comune, per chi voglia entrare all’università, affrontare entrambi gli esami.
“Sempre più studenti negli ultimi cinque o dieci anni stanno prendendo parte a entrambi”, afferma Joe Korfmacher, ex consigliere di una scuola superiore di New York e attuale direttore della consulenza universitaria presso un ufficio di Collegewise a New York, una società di consulenza per l’ammissione alle università.
L’idea basica è sempre la stessa: dimostrare quanto sia valido uno studente; obiettivo: l’ingresso in università. Ma nonostante obiettivi simili, i test variano in struttura e tempistica, contenuto e punteggio.
Durata degli esami
Ad esempio, il test SAT richiede tre ore, ma con lo svolgimento del saggio opzionale di 50 minuti, il tempo si somma a quasi quattro ore in totale. L’ACT dura invece due ore e 55 minuti, anche se un test di scrittura opzionale – come nel SAT – di 40 minuti lo allunga a poco più di tre ore e mezza.
Struttura e punteggio dei test
Il SAT presenta 154 domande contro le 215 per l’ACT. Secondo il College Board, che amministra il SAT, chi effettua il test ha più tempo per il SAT – con 1 minuto e 10 secondi per domanda – rispetto ai 49 secondi dell’ACT.
Anche il punteggio per ciascun test differisce. Per il SAT, i punteggi totali vanno da 400-1600; per l’ACT, il punteggio composito va da 1 a 36. Tali intervalli non includono i saggi opzionali, i cui punteggi vengono assegnati separatamente.
I costi
Anche il costo degli esami varia, anche se di poco. Il SAT costa $ 47,50 solo per il test e $ 64,50 se è incluso il saggio opzionale. L’ACT costa $ 50,50 solo per l’esame e $ 67 se è incluso il test di scrittura opzionale. Non sono ovviamente delle differenze enormi, quindi si può dire che il costo sia fondamentalmente il medesimo, ed è vero però che potrebbero essere applicati costi aggiuntivi per altre situazioni, come la registrazione tardiva.
È possibile anche, per alcuni studenti, poter svolgere il SAT o l’ACT gratuitamente, grazie al sostegno statale o alle esenzioni dalle tasse.
Entrambi gli esami sono offerti da organizzazioni no profit. Per il SAT, questa è il College Board, che offre anche corsi di collocamento avanzato e altri servizi per altri eventuali test. L’organizzazione per l’ACT ha invece una portata più limitata, concentrandosi in gran parte sul suo omonimo test.
ACT o SAT: scelta del test da eseguire
Gli studenti che sperano di trovare l’opzione di test più semplice sono sfortunati.
“Questi sono test ad alto rischio, nessuno dei due sarà facile”, afferma Mai Jumamil, direttore dei programmi di preparazione al college presso Kaplan Test Prep, una società con sede a New York.
Korfmacher è della stessa opinione: “Posso sicuramente dire, con certezza, che non esiste un test più semplice”.
Per aiutare gli studenti a prendere una decisione, gli esperti suggeriscono di iniziare con lo svolgere entrambi i test, giusto per fare una prova, e vedere quale esame è più adatto a loro. La tua reale capacità, o quanto riesci a rendere in percentuale è davvero difficile da definire se non sedendosi e affrontando dei test di prove ufficiali sia del SAT che dell’ACT.
Generalmente – afferma Jumamil – gli studenti con delle forti tendenze verso le discipline umanistiche, e con una buona padronanza della lingua inglese possono avere ottimi risultati nell’ACT, che pone maggiore enfasi sulle abilità verbali. Per gli studenti il cui punto forte è invece la matematica, il SAT può offrire risultati migliori.
Suddiviso in diverse sezioni, il SAT ha un test di lettura che richiede 65 minuti, un test di scrittura e lingua di 35 minuti e una sezione matematica di 80 minuti.
L’ACT comprende invece un test di lettura di 35 minuti, un test di inglese di 45 minuti, una sezione di matematica di 60 minuti e un test di scienze di 35 minuti. Il SAT non include una sezione scientifica indipendente ma include domande scientifiche durante l’esame.
In moltissimi concordano che sia meglio per gli studenti sostenere entrambi i test di ammissione al college. In una prospettiva ideale, si dovrebbero eseguire entrambi i test entro l’autunno dell’ultimo anno di scuole superiori e poi scegliere su quale esame puntare definitivamente.
Saggio opzionale, lo faccio o non lo faccio?
Gli esperti hanno opinioni diverse circa la necessità o meno, per uno studente, di svolgere il saggio facoltativo.
“In realtà stiamo consigliando ai nostri studenti di non svolgere la sezione di scrittura facoltativa”, afferma di nuovo Korfmacher, spiegando che molti college non lo richiedono più o lo raccomandano solo in via occasionale.
Ma alcuni esperti o direttori di scuole superiori incoraggiano invece i propri studenti a svolgerla, nel caso in cui l’università a cui ci si sta candidando alla fine lo richieda. Altri ancora stimano sia meglio effettuare il saggio semplicemente per fornire più dati di valutazione alle università che accoglieranno la tua domanda, in modo da poter offrire loro anche un’idea circa la tua personalità.
Dati recenti mostrano che, comunque, ad oggi la maggior parte degli studenti completa il saggio facoltativo per ciascun esame.
Come avere successo nell’ ACT e nel SAT
Indipendentemente dal test che gli studenti decidono di sostenere, l’obiettivo è lo stesso: guadagnare un punteggio tale da permetterti di entrare nel college da te prescelto.
Per aiutare voi studenti ad avere successo, noi di Scrambled Eggs Milano siamo da sempre degli esperti per quanto riguarda l’esame SAT. Offriamo suggerimenti strategici per la preparazione del test, che faranno impennare il tuo punteggio fino al massimo possibile! Offriamo dei corsi specifici proprio in preparazione al SAT. Identificheremo e lavoreremo con te per smussare tutti i tuoi punti deboli e per farti avere il miglior risultato!
Scrambled Eggs è una scuola di inglese a Milano. Specializziamo nei corsi di preparazione dell’esame. Offriamo corsi preparazione sat, ielts, toefl, first certificate, e molto di più qua a milano. Il seguente post è per coloro chi studia per l’esame sat a milano e in tutto l’italia.
It’s the day before the SAT! Help! What do I do?
You’ve put in the work, done a number of practice tests, maybe even taken a class. The big day is here sooner than you imagined. What do you do? Do you put in a few more hours of practice? Do you give your brain a break?
First of all, stop with the practice tests. You’re stressing yourself out. If you’re English is not at a native-speaker level, forget about it. You won’t master English in the next 24 hours. Prepare yourself emotionally instead. The last thing you need is those pesky emotions getting in the way of your success. The fact is, even if you’re calm and collected now, they might just get you on test day. Let’s prevent that from happening.
Here’s the key: Don’t try to learn anything new. Instead, organize everything you already know.
The SAT is a big test, and, as with any test, the pressure can really get to you. It happens to the best of us. We’ve taken loads of tests in our lives. It’s agonizing knowing that a few hours may represent who you are (at least on paper) – whether to your country, state, future employer or school. Getting a good score on the SAT can be the difference between getting into the big shot school or having to settle for your fourth choice university. Even years from now, your SAT score may even come up over drinks with friends. The premise of it is terribly absurd. The idea that we put so much focus on this make-it-or-break-it test, a test that is hardly a reflection of someone’s intellect, into planning a student’s future is absolutely cruel. In essence, a test like the SAT is meant to separate us into categories; it’s supposed to be a reflection of who we are, at least academically. Ridiculous – I know! But that’s a topic for another day.
Right now, you have to focus on the positive and for your last-minute prep for that darn test.
Sometimes you put in all necessary work, spend an endless amount of time memorizing words, straining your brain, and then the fateful day arrives. And what happens? You’re blank. Numb. It’s all gone. You can’t remember anything. All that work? – poof! – right into thin air.
For moments like this, make yourself a pre-exam cheat sheet.
Better put, a pre-exam “jitters be gone!” sheet. Take out a sheet of paper, open your already-finished practice tests and notes, and write down the important things. This piece of paper will be your best friend on test day. Trust me. As a super-anxious test taker myself, this trick has helped me ease my anxiety on quite a few occasions.
In fact, it’s a great test trick in general! It helps keep your mind sharp and focused, keeping you from blanking even wandering off into your own la la land. All too often, this sheet has even helped me boost my score. Think of it as a method to push all the important things into the front of your brain and all the trivial things (what time am I meeting Julie for coffee this afternoon?) to the back. Stay focused
Ready to make your cheat sheet? Your goal is to organize all of that cloud of information floating around in your head into one condensed sheet. Take out a sheet of paper and open your already-finished practice tests as well, as any notes you may have taken.
Take it slow. Keep in mind that your goal is to organize it well – “well” meaning in a way that makes perfect sense to YOU. Start with one section, say the Writing. Extract everything you think is important (and could serve as a good reminder pre-test) from the Writing Section, and limit it to one part of your cheat sheet paper.
Look at any test questions you got wrong. Is there a trend? For example, one of the things that the SAT throws at you is “neither…nor” and “either…or”. This is one that’s easy to miss. (In the “Identifying Sentence Errors” sub-section of the writing, you may happen upon “neither…or”, in which case you would have to identify it as a mistake.) Maybe you got a number of these questions wrong. In this case, write something on your sheet along the lines of “neither…nor” so that you remind yourself to keep a careful eye out for it on the test.
If you took a class, look through any notes or any hints your teacher may have given you. If you find any of them might slip your mind, write those on your sheet too. However, be sure to keep it short and clean. Don’t write in full sentences. Make it condensed. No one else will be reading this. Keep in mind that this is for your eyes only, so write for you and only you – it doesn’t have to make sense to anyone else. Is there something you have to remember about the Essay portion? Maybe just make a quick structural outline for yourself.
After you’ve gone through the Writing portion, move on to the Reading. The same idea holds true here. The SAT has a number of questions that they like to use over and over again. Write them down so that you’ll remember what to keep an extra eye out for. For example, a “parallel” sentence structure is fairly huge on the SAT; Anne was driving, talking on the phone, and she drank coffee would be Anne was driving, talking on the phone, and drinking coffee. You will find many questions that test your ability to identify parallelism problems on the test. Do you think that’ll be helpful to remind yourself before the test? Good. Write it down.
Last (but certainly not least), the Math Section. Are there repeated problems you’ve had? Maybe the fractions threw you off a couple times. If you’ve taken a few SAT tests, I’m sure you’ve realized the SAT is highly repetitive in its questions; you essentially encounter the same questions with different numbers. If there’s a question that stumped you a few times, write out an example on your cheat sheet so that you can give it a quick glance beforehand.
Pack all of your SAT test materials the night before. There’s no need to rush in the morning, grabbing everything as you’re running out the door, or even worse – forget something!
As a reminder, here are the materials that you’ll need on SAT test day:
Two sharpened #2 pencils (the SAT test cannot read pens, so leave those at home)
A good eraser
A calculator (Don’t go investing in a brand new top-of-the-line calculator the day before the test. Use the one you’ve been using, the one you’re comfortable with. If you’re not sure whether your calculator is acceptable or not, here is the SAT Calculator policy: https://sat.collegeboard.org/register/calculator-policy)
Extra batteries or backup equipment (You can never be too prepared!)
A watch
A snack or drink (for a quick pick-me-up during your break)
Don’t bring:
Your cellphone
Your laptop or tablet
An MP3 player
A camera
Any recording device
Anything that makes noise
Also, make sure you know what time your test starts and exactly where it is. Keep in mind that you’ll have to arrive before the actual start time to check-in, so plan accordingly. Calculate the exact amount of time it’ll take you to get from your house to the test center (and maybe add on a few minutes, just in case), and set your alarm.
Lastly, be sure to get a good night’s sleep. The last thing you want is to be nodding off at your desk tomorrow.
The morning of the SAT exam, go about your usual routine. If you usually take a shower in the morning, take a shower. If you usually have coffee, have coffee. Don’t chow down on anything that will weigh you down or make your stomach hurt. If anything, avoid super sugary carbs that will give you a temporary boost, only to make you crash a few hours later. Try eating a good, protein-filled breakfast. Eggs are usually a good bet. The last thing you need is something like a pesky stomachache distracting you during your SAT test.
Ready or not, here it goes!
The world is your oyster and you’re gonna crush this test. And if you don’t, it’s all over for you – Kidding! Head out the door with your head held high and your best foot forward!
If you’re in Milan, Italy and feel that you need a quick SAT SOS crash course before your test – or maybe you simply want to talk to somebody and get your head straight – we’re here for you. Scrambled Eggs has your back. Shoot us an email for further information: info@scrambledeggsmilano.it