Question 1

Can someone help me with this question? It was a grid-in question on the No Calculator section on a practice test and I had no clue how to solve it. It probably doesn't help that I hardly understood anything in my chemistry course that I painfully limped through last year.

How many liters of a 25% saline solution must be added to 3 liters of a 10% solution to obtain a 15% saline solution?

Thanks in advance to anyone who can help!

How many liters of a 25% saline solution must be added to 3 liters of a 10% solution to obtain a 15% saline solution?

Thanks in advance to anyone who can help!

Accepted Answer

This is a problem of weighted average and can be easily done using concept of Alligations

A   -----------  B
25 ----------- 10                        
 -------15-------
5 -------------10

=>  The ratio A:B is 5:10 or 1:2

If quantity of solution B is 3 Litres, the A should be 3/2 = 1.50 Litres

:-)

Question 2

How Did you get 78/5, or 15.6?

Accepted Answer

Oh man - that's a heck of a question!  Okay let's see.

Alright so "Since we're dealing with right triangles, you'll need to use the Pythagorean theorem to figure out the missing side length of the big triangle".  That's easy enough.
5^2 + 12^2 = x^2  
25 + 144 = x^2
169 = x^2
Square Root of both sides (to clear the x^2) makes 13 = x (Because sq rt of 169 = 13)
Also, you could remember that 5-12-13 is a common Pythagorean Triple.
Anyway, that makes the Hypotenuse of the big triangle AE = 13.

"Then, you'll need to recognize that the smaller triangle is similar" to the bigger triangle and "△AED is similar to △CEB"  Okay, not too bad.

"Next, we'll set up proportions to solve for the length of EC."  That means take two corresponding sides of each triangle and set them equal to each other, and one of those sides will be the one we're trying to find, which is EC.

So we'll take sides DE corresponding to BE, because we have the measure of both.  Then we'll use side AE to find CE.

DE/BE = AE/CE
5/1 = 13/x
Cross multiply to get 13 = 5x
Divide both sides by 5 
So x = 13/5
So CE = 13/5

Since we're trying to find AC, we add 13 + 13/5. 
We need a Common Denominator of 5, so we multiply 13/1 (13 as a fraction) by 5:
13(5)/1(5) = 65/5.
Then we add 65/5 + 13/5 = 78/5.
We can divide 78 by 5 to clear the fraction and get the decimal 15.6

Whew!  What a ton of work!  Hope that helps:)

Question 3

So I currently am not taking Algebra II, and I'm in 11th grade. As of right now, I'm taking the below regents level class, College Algebra and Trig. I do not understand any of the trig based questions. I have an SAT to take this weekend. With little to no knowledge on being able to solve those types of questions, should I really study even though theres 99.99% chance I won't understand them?

Accepted Answer

If you have time to spare today, then yes you should. Use Khan academy's videos to help you at least get the basics of sin, cos, and tan. But don't waste your time if you aren't going anywhere. If you spend 1 hr trying to understand, and you still haven't made any progress, focus on your other weak spots that you know you can improve upon. If you do understand the trig, then make sure you familiarize yourself with the calculator's trig functions and do practice prbs. On the test, fill in those questions which you don't understand immediately, and just move on, and only come back to them if you have extra time. Hope this helped. Good luck tomorrow, I'll also be taking it.

Question 4

How many questions will be asked on this part of maths in SAT and on which section ?

Accepted Answer

There will be 25 (with 5 free response questions) questions for the non-calculator section, and 45 (with 7 or 8 free response question) questions for the calculator section.

Question 5

In the example problem with the volume, how would you get the answer? I'm confused what the portion of the vase that is cut out looks like or how to solve it.

Accepted Answer

The vase is basically a box with another box cut out of it (The interior cut out is another rectangular prism). SO = take the volume of the big box and subtract the volume of the small box. Big Box: 2x2x5 = *20*  Small box cut out = 1.5x1.5x4 = *9*    Answer = 20-9 = 11

Question 6

This is one of my hardest subjects in the SAT, partly because I am not familiar with many of the necessary equations for the problems. Are there any really important equations I need to memorize for this?
Thanks in advance!

Accepted Answer

Most of the SAT problems wont ask you to "memorize", but yes there are some topics, like Equation of Circles and Parabolas, which you need to understand and practice thoroughly otherwise, you will have to memorize.

Question 7

Overall, I understand most of the math topics, but the only type that bothers me are the complex numbers like trying to figure out what value is i^26 or i^34 etc. Is there any simple way to solve those types of i values?

Accepted Answer

First you need to be familiar with the powers of i up to i^4. 
i^0 = 1  
i^1 = i
i^2 = -1
i^3 = -i
i^4 = 1.

This allows us to re-examine any i exponent bigger than 4, as any i exponent bigger than 4 can be expressed as a product of i^4 and other i exponents.  But, because i^4 is 1, all that is relevant is the remaining exponents.  For example:

i^26 = i^4*i^4*i^4*i^4*i^4*i^4*i^2 = 1*1*1*1*1*1*i^2 = i^2 = -1
i^9 = i^4*i^4*i^1 = 1*1*i^1 = i^1 = i

For a short cut in finding the results, you can divide the exponent by four and the remainder of the exponent will be the i power that is relevant.  For example:

i^29 = i^1 = i   (29/4 = 7 remainder 1)
i^43 = i^3 = -i  (43/4 = 10 remainder 3)

Question 8

How old do I need to be to write SAT?

Accepted Answer

You can be any age to write the SAT or the ACT. I've had friends who wrote them in grade school.

SAT

Course: SAT > Unit 6

The SAT Math Test: Additional Topics in Math

In this series of articles, we take a closer look at the SAT Math Test.

Math questions on the test fall into different categories called "domains." One of these domains is Additional Topics in Math: questions that ask about geometry and complex numbers.

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