Questions:
A Hillview Prep student is currently preparing for her SAT Subject Test in Physics. We started her on a test using the Smart Scoring System. What we found is quite interesting: on easy questions, she was guessing and thus making simple errors. The question on the test is below:
Relate to the following physical principles or topics. (A) pressure (B) energy (C) work (D) force (E) centripetal acceleration Select the quantity that each expression defines.
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Problem: (SAT Subject Test Math Level 2)Three cards are drawn from an ordinary deck of 52 cards. Each card is replaced in the deck before the next card is drawn. What is the probability that at least one of the cards will be a spade?
(A) 3/52 (B) 9/64 (C) 3/8 (D) 37/64 (E) 3/4 Problem:If a square prism is inscribed in a right circular cylinder of radius 3 and height 6, the volume inside the cylinder but outside the prism is:
(A) 2.14 (B) 3.14 (C) 61.6 (D) 115.6 (E) 169.6 Questions:The Great Lakes—Huron, Ontario, Michigan, Erie, and Superior—form the largest freshwater system in the world. Each of the lakes tends to stratify, or form layers of warmer and colder water, depending on the season. This is called seasonal turnover. In winter, for example, the coldest water in the lake lies just below the surface ice. The water gets progressively warmer at deeper levels. In spring, the sun melts the ice, and the surface water warms. Because the surface water is still cooler than the layers below, the water at the surface sinks to the bottom of the lake, forcing the cooler water at the bottom of the lake to the surface. This mixing, known as spring turnover, eliminates the temperature stratification that was established during the winter. In the absence of this thermal layering, wind continues to mix the water to a greater depth, bringing oxygen (O2) to the bottom of the lake and nutrients to the surface. This results in a relatively even distribution of O2 throughout the lake. When summer arrives, the lake again becomes stratified, with warm water at the surface, and cold water at the bottom. A narrow zone of water undergoing rapid temperature changes separates these layers. This zone is called the thermocline. Cool, fall temperatures cause the lake water to mix again, until the surface begins to freeze and the winter stratification is reestablished. The stability of the lake’s stratification depends on several factors: the lake’s depth, shape, and size, as well as the wind and both the inflow and outflow of lake water. Lakes with a lot of water flowing into and out of them do not develop consistent and lasting thermal stratification. Figure 1 shows an example of lake stratification during the summer.
The following problem appeared on the SAT.
A cubic box with edge of length x inches is tied with a string 106 inches long. The string crosses itself at right angles on the top and bottom of the box. If the bow required 10 inches of string, what is the maximum number of inches x could be? 1. Write an equation based on this information. 2. Solve the equation for x. Are we born with the ability to tell which things are close and which are far away? Or, do we learn it? Two psychologists at Cornell University, Eleanor Gibson and Richard Walk, did an interesting experiment to answer this question.
The kitten in the photograph above is sitting on a strip in the middle of a sheet of glass. Behind the kitten is a floor directly underneath the glass; in front of it is another floor several feet below the glass. Even when the kitten is just old enough to move about, it is afraid to move off the "cliff" to the "deep" side. Chicks and baby goats just 1 day old and human infants just old enough to crawl behave exactly the same way. What explains this phenomenon? Surprisingly, it all about inequalities! Question:A certain perfect square has exactly 4 digits (it is an integer between 1,000 and 9,999). The positive square root must have how many digits?
A) 4 B) 3 C) 2 D) 1 E) Cannot be determined from the given information. Randall is scheduling his classes for next term. He has a choice of 3 different science classes, 4 different math classes, and 5 different humanities classes. How many different class schedules can Randall create if he must take 1 science class, 1 math class, and 1 humanities class?
F. 14 G. 23 H. 30 J. 45 K. 60 Moroccan MosaicThe mosaic above was created in the fourteenth century for a wall in Morocco. Write an expression for each of the following parts of it shown in the detail below in terms of a or b or both a and b. Find:1. The perimeter of the square.
2. Its area. 3. The perimeter of the other rectangle. 4. Its area. 5. The perimeter of one of the trapezoids. 6. Its area. SAT Subject Math Test Level 2
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 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. QuestionA prime number is a whole number greater than 1, whose only two whole number factors are 1 and itself. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29.
What’s the big deal about prime numbers? Encryption. Large prime numbers are used for encryption. RSA encryption is based on prime numbers — two prime numbers multiplied together. The original two prime numbers are known as your ‘private key’. When you multiply them together, the product (a number that’s only divisible by one, itself and those two prime numbers) is called the ‘public key’. Question: One 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 QuestionsThe language portion of the HSPT measures you knowledge of English usage and grammar. Directions: 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:The picture on the left is by Belgian artist Peter Raedschelders is titled Turtles Forever.
Each successive row has twice as many turtles as the row above it: 1 2 4 8 16 32 64 128 .... Complete the following proportions: (A) 16/32 = 32/? (B) 2/16 = 16/? (C) 4/64 = 64/? 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? 
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