Problem:
Which of the following is a rational number?
\[\sqrt2\]
\[\sqrt{\pi}\]
\[\sqrt7\]
\[\frac{\sqrt{5}}{\sqrt{25}}\]
\[\frac{\sqrt{64}}{\sqrt{49}}\]
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Problem: Find a relationship between the first two words in each question. To complete the analogy, choose the answer that shows a similar relationship. 1. Remember is to forget as find is to (A) locate (B) keep (C) lose (D) return (E) watch 2. Ship is to anchor as automobile is to (A) brake (B) wheel (C) stop (D) accelerator (E) car 3. End is to abolish as begin is to
(A) establish (B) finish (C) tyranny (D) crusasde (E) monarchy Problem:The first term is 1 in the geometric sequence 1, −3, 9, −27, .... What is the SEVENTH term of the geometric sequence?
A. −243 B. 0−30 C. 081 D. 189 E. 729 What are Domain and Range?
Students are often confused about domain and range of a function. Let's consider the list of points: {(1, 2), (3, 5), (6, 1), (4, 9), (3, 3)}.
The domain is all the xvalues, and the range is all the yvalues. Domain is: {1, 2, 6, 4, 3} Range is: {2, 5, 1, 9, 3} Problem:
An inverse function is quite simple: it is tells you how to get back to the original value. Another way of looking is that an inverse function is just undoing what was done before. For example, if tied your shoes and then untied them, you used an inverse function to untie them! Another example is when a computer reads a number you type in and converts it to binary for internal storage, then prints it out again as a number on the screen for you to see, it's doing an inverse function.
Example: You are traveling at 70 mph and want to know how far you have gone in x hours. You can use a function to represent it. So, f(x) = 60. x
If you want to know the inverse, that is, if you know you have travelled x miles, and you want to know how long you have been traveling for, you use an inverse function.
\[f^{1}(x) = \frac{x}{60}\]
Problems
1. Find the inverse function of f given by f(x) = 2x + 3
2. Find the inverse function of f given by f(x) = ln(x + 2)  3
Problem:
The method of power substitution assumes that you are familiar with the method of ordinary usubstitution and the use of differential notation. Integrate the following using the method of substitution.
\[\int \frac{1}{1 + {\sqrt{x}}} dx \]
Problem:Justine spends $122 to create a lemonade stand. If she sells p cups of lemonade at $2.50 per cup, which of the following expressions represents her profits after expenses?
A. p + 122 B. 2.5  p C. 2.5p  122 D. p  122 Problem: Dividing a CakeFor Acute Alice's birthday, Obtuse Ollie bought a square cake, 9 inches on each side. They wanted to cut into three equal pieces.
Ollie was going to cut the cake as shown at the left below, but Alice said she wouldn't want the piece in the middle. Alice did some figuring and cut the cake as shown at the right above. Find the area of the six triangles formed. Logic QuestionsThe logic portion of the HSPT may appear scary at first. However, one can solve these problems in a straightforward manner. Just translate the abstract relationships in the question into realworld relationships. Try some questions below. 1. Corn flakes cost less than wheat flakes. Oat flakes cost more than wheat flakes. Oat flakes cost less than corn flakes. If the first two statements are true, the third statement is a. true. b. false. c. uncertain. d. repetitive. 2. Gloria is younger than Francesca. Yvonne is older than Gloria. Yvonne is older than Francesca. If the first two statements are true, the third statement is
a. true. b. false. c. uncertain. d. repetitive. 1. If $900 is to be divided equally amongst a group of people, how many persons are in the group? (A) 17 (B) 19 (C) 21 (D) 15 (E) 27 2. Simplify: 6345 (A) 3 (B) 2 (C) 3 (D) 2 (E) 4 3. The Crown Movie Theater collected $705 yesterday. If 54 adults paid $9.50 each and each child paid $3.50 less than each adult, how many children paid admission?
(A) 32 (B) 38 (C) 29 (D) 25 (E) 42
1. John flies 2,880 miles in 9 hours. What is the average speed of his airplane?
a. 285 miles/hour b. 315 miles/hour c. 320 miles/hour d. 340 miles/hour
2. Sarah spent onefifth of her life in school. If she is now 55, how many years did she spend in school?
a. 9 b. 11 c. 13 d. 15
3. Order from least to greatest:
Problem statement: Circle the word or phrase that best describes the meaning of the underlined portion of the word. 1. proactive a. after b. forward c. toward d. behind 2. recession a. against b. see c. under d. back 3. contemporary a. with b. over c. apart d. time 4. etymology a. state of b. prior to c. study of d. quality of 5. vandalize
a. to make happen b. to stop c. to fill d. to continue 1. Which word does NOT belong with the others? a. bed b. curtains c. dresser d. armoire 2. Bird is to hawk as vehicle is to a. truck. b. eagel. c. road. d. tree. 3. Walnuts cost more than peanuts. Walnuts cost less than pistachios. Pistachios cost more than both peanuts and walnuts. If the first two statements are true, the third is a. true. b. false. c. uncertain. d. repetitive. 4. Window is to pan as book is to a. novel. b. glass. c. cover. d. page. 5. Cup is to gallon as centimeter is to
a. yard. b. meter. c. pint. d. inch.
The following problem may require the use of the following basic trigonometry derivatives. Also, the derivative, d/dx, may be represented by D.
\[\frac{d}{dx}sinx = cosx\]
\[\frac{d}{dx}cosx = sinx\]
\[sin^{2}x + cos^{2}x = 1\]
Note the following properties of Natural Logarithms.

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