When a certain radioactive element decays, the amount at any time t can be calculated using the function
\[E(t) = ae^{t/500}\]
where a is the original amount and t is the elapsed time in years. How many years would it take for an initial amount of 250 milligrams of this element to decay to 100 milligrams?
(A) 125 years (B) 200 years (C) 458 years (D) 496 years (E) 552 years
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The figure above appeared in a problem on an SAT exam. All of the triangles are congruent, the area of the shaded region is 84, and the area of square ABCD is 100. 1. What is the area of one of the triangles? 2. What is the total area of the entire figure? There are some weird analogies on the SSAT, and they usually contain words you know. The problem with the weird analogies is that the words don't have a nice, normal, definitional relationshipat least not in a horizontal sense. Often, weird analogies have vertical relationships. Let's look at an example: Racket is to bat as (A) puck is to hockey (B) rifle is to duck (C) hammer is to nail (D) goalie is to soccer (E) tennis is to baseball You definitely know the words racket and bat. So you try making a sentence. You can't make a definitional sentence with these two words, even though you know them. Your next step is to loo for a vertical relationship: Most weird analogies are verticaland even these are not commonbut there may be one or two analogies that are just plain odd. If you see one, do your best to figure it out quickly and then move on. See if racket is related to any of the words that are in the "C" position. Is racket related to puck? No. Rifle? No. Hammer? No. Goalie? No. Tennis? Maybe. A racket is used to hit the ball in tennis. Does that sentence work for bat and baseball? Sure. Bingo. Practice DrillWeird Analogy Techniques1. Sad is to interested as (A) friendly is to ebullient (B) pleased is to unhappy (C) despair is to obsession (D) angry is to neutral (E) talkative is to anxious 2. Possible is to required as can is to (A) might (B) could (C) reading (D) may (E) must 3. Grape is to tree as (A) water is to pesticide (B) wine is to paper (C) fruit is to vegetable (D) olive is to oil (E) spruce is to pine 4. August it to November as (A) February is to April (B) March is to June (C) July is to May (D) January is to December (E) September is to November What is an Analogy?An analogy, on the SSAT, asks you to: 1. Decide how two words are related. 2. Choose another set of words that has the same relationship. One way to solve analogy problems is the make a sentence. For example: Kitten is to cat as (A) bull is to cow (B) snake is to frog (C) squirrel is to raccoon (D) puppy is to dog (E) spider is to fly You want to be sure you get an easy question like this one right because it's words just as much as a hard one. Here's how to be sure you don't make a careless mistake. Picture what the first two words ("A" and "B") stand for and how those two words are related. Kitten is to cat as (Cross out "is to" and "as". Just picture a kitten and a cat). Kitten ... Cat Make a sentence to describe what you see. A good sentence will do two things: 1. Define one of the words using the other one. 2. Stay short and simple. A kitten ______________________________ cat. Now look at the answer choices and eliminate any that cannot have the same relationship as the one you've gotten in your sentence. (A) bull is to cow (B) snake is to frog (C) squirrel is to raccoon (D) puppy is to dog (E) spider is to fly If your sentence was something like "A kitten is a young cat," you can eliminate all but (D). Stay away from sentences that do not DEFINE the relationship. So, "A kitten is a cat," does not tell you a definition or description of one of the words. Practice DrillsMaking SentencesTry making a sentence for each of these analogies for which you know both words. Ask questions below as a guide.
Question
The graph of the function has a slope of:
(A) 1.29 (B) 0.77 (C) 0.77 (D) 1.29 (E) 2.24 Questions:This tapestry was woven in Peru between 1000 and 1500 A.D. The following questions refer to the rows (numbered in red) of dark brown monkeys. Name the transformation through which the 1. third row appears to be the image of the first row. 2. second row appears to be the image of the first row. 3. fourth row appears to be the image of the third row. 4. sixth row appears to be the image of the second row. QuestionOne prime number divided by another prime number is always A) a fraction between 0 and 1 B) an integer C) a positive noninteger D) a prime number QuestionsDirections: Choose the sentence that contains an error in punctuation, capitalization, or usage. If you find no mistakes, select choice D. 1. A) When crossing the street, walk don't run. B) Most flowers bloom in Spring. C) He is often mistaken for his twin. D) No mistake. 2. A) The fire spread very quickly. B) Etta lost ten pounds while on that diet. C) You should brush your teeth everyday. D) No mistake. 3. A) You'll find my number in the phone book. B) The price increased over last year's price. C) More importantly, the economy is slowing. D) No mistake QuestionCarter was on a diet. When he weighed himself as the start of his diet, he weighed 220 pounds. At the end of 6 months, Carter weighed 180 pounds. What fraction of his original weight did he lose? (A) 1/8 (B) 4/13 (C) 3/16 (D) 2/11 Question
What is the solution set for the above equation?
A) {5} B) {20} C) {−5, 20} D) {5, 20} QuestionA car is traveling at x feet per second. The driver sees a red light ahead, and after 1.5 seconds reaction time, the driver applies the brake. After the brake is applied, the car takes x/24 seconds to stop, during which time the average speed of the car is x/2 feet per second. If the car travels 165 feet from the time the driver saw the red light to the time it comes to a complete stop, which of the following equations can be used to find the value of x? A) x^2 + 48x − 3,960 B) x^2 + 48x − 7,920 C) x^2 + 72x − 3,960 D) x^2 + 72x − 7,920 Question
\[ (x^2 + bx  2)(x + 3) = x^3 + 6x^2 + 7x 6 \]
In the equation above, b is a constant. If the equation is true for all values of x, what is the value of b?
A) 2 B) 3 C) 7 D) 9 QuestionMaizah bought a pair of pants and a briefcase at a department store. The sum of the prices before sales tax was $130.00. There was no sales tax on the pants and a 9% sales tax on the briefcase. The total Maizah paid, including the sales tax, was $136.75. What was the price, in dollars, of the pants? Questions:Questions1. Express the ratio 81/36 in decimal form. 2. Express the ratio 36/16 in decimal form. 3. What is the number 36 called with respect to 81 and 36? QuestionsThe questions that follow ask you to find relationships between words. For each question select the answer choice that best completes the meaning of the sentence. 1. Browsing is to shopping as (A) skimming is to reading (B) nodding is to agreeing (C) walking is to running (D) hiking is to climbing (E) seeing is to recognizing 2. Fire is to heat as (A) cold is to snow (B) lamp is to light (C) cool is to breeze (D) wax is to melt (E) music is to listen 3. Stamen is to flower as (A) computer is to monitor (B) lens is to eye (C) socket is to cord (D) spiral is to notebook (E) pillow is to sleep QuestionA department store marks up its clothing 80% over cost. If it sells blue jeans for $14, how much did the store pay for them? (A) $7.78 (B) $17.50 (C) $11.20 (D) $1.12 QuestionThe ratio of teachers to students in a certain school is 1:14. If there are fourteen teachers in the school, how many students are there? (A) 14 (B) 196 (C) 206 (D) 176 Question2y + 6x = 3 y + 3x = 2 How many solutions (x, y) are there to the system of equations above? A) Zero B) One C) Two D) More than two QuestionA voter registration drive was held in Town Y. The number of voters, V, registered T days after the drive began can be estimated by the equation V = 3,450 + 65T. What is the best interpretation of the number 65 in this equation? A) The number of registered voters at the beginning of the registration drive B) The number of registered voters at the end of the registration drive C) The total number of voters registered during the drive D) The number of voters registered each day during the drive QuestionThe stratosphere is the layer of the Earth’s atmosphere that is more than 10 kilometers (km) and less than 50 km above the Earth’s surface. Which of the following inequalities describes all possible heights x, in km, above the Earth’s surface that are in the stratosphere? A) x + 10 < 50 B) x − 10 < 50 C) x + 30 < 20 D) x − 30 < 20 QuestionA sportswriter claims that her football predictions are accurate 60% of the time. During football season, a fan kept records and found that the writer was inaccurate for a total of 16 games, although she did maintain her 60% accuracy. For how many games was the sportswriter accurate? (A) 5 (B) 15 (C) 24 (D) 40 (E) 60 QuestionOn Monday, Gerri ate 1/4 of an apple pie. On Tuesday, she 1/2 of what was left of the pie. What fraction of the entire pie did Gerri eat on both days? (A) 3/8 (B) 1/2 (C) 5/8 (D) 3/4 (E) 7/8 Questions:Complete the following sentences. (ISEE Upper Level.) 1. We seldom fell __________ when we are allowed to speak freely, but any ___________ of our free speech brings anger. A) angry .. defense B) blessed .. restriction C) scholarly .. understanding D) enslaved .. misuse 2. Since movies have become more _________, many people believe television to be ____________. A) helpful .. utilitarian B) expensive .. necessary C) common .. inadequate D) costly .. useless 3. Because of his ________ nature, he often acts purely on impulse. A) stoic B) reflective C) passionate D) wistful 
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