Hey guys, I want to start a practice math problem thread here. I know there’s another SAT math thread but that one was from the old SAT, so I thought I would start a new one. I’ll post questions and let you guys try to answer them and then I’ll post the solutions (if you need them). Questions will range from Easy to Difficult.
For i=√(-1), what is the quotient (6-2i)/(2+5i) ?
A) 3 - 2i/5
B) 4 - 3i
C) 1/5 + 2i/3
D) 2/29 - 34i/29
A dietician must include in a diet three foods: A, B, and C. He must include twice as many grams of food A as food C and 5 grams of food B. The three foods must total at most 24 grams. Which of the following inequalities would represent the given problem (Suppose, x is the total grams of food A in grams)?
a. x + 2x + 5 < 24
b. x + 2x + 5 > 24
c. x + 2x + 5 ≤ 24
d. x + 2x + 5 ≥ 24
For your first question D and your second question C
Steps: First question
First multiply by the complex conjugate of which us 2-5i/2-5i then. Once multiplied Simplify the result and you get
2-34i/29
Steps second questions:
I literally says at most total so we know it must be
≤ 24
Hence
x + 2x + 5 ≤ 24
is the answer
The little Einsteins are traveling in their favorite rocket ship. A technical issue arises and the rocket crashes. The path of the rocket can be simulated by the formula 5x² - 6x + 1 = 0. Find the coordinates of the crash site.
I’m sorry I really wasnt sure to make as question… this is too easy
@cerealguy3 when writing exam questions for practice or otherwise, you should be very clear at what your intentions are. I do not understand what x is (is it time? horizontal distance?), or why an equation which can be solved for x is in place of a formula (e.g. position P(t) in terms of time t = …).
@MITer94 Yes. I did forget to do that. I’ll be sure to remember that next time
in this case x specifies distance
@cerealguy3 perfect!
Here’s another one:
Find the perpendicular distance from the point (5, 6) to the line −2x + 3y + 4 = 0
Hint: There is a long way to do it and a short way.
Unless I am missing something, in your diet problem I think you mean for x to refer to grams of food C. If x refers to grams of food A, I get: x + x/2 + 5 <= 24.
@pckeller Yes, you’re right. Good catch.
@ExamMasters if you know the formula for computing distance from a point to a line, it’s just plug and chug.
Yeah I know the formula too, but what is the long way. Just curious. @MITer94 @ExamMasters
@MITer94 @kassh4 Yup, the short way is simply plug into the d = (|Ax + By + C|)/sqrt(A^2 + B^2) formula.
The long method involves getting the equation of the line from the point to the original line. You can do this by first getting the reciprocal slope and using the point given to find the y-intercept of the new line.
Then you have to equate the two linear equations together, which would give you the x value of the point of intersection of the two lines.
You would then need to plug that value into either equation to get the y coordinate. Now, you have 2 points - the original point given and the new point (the x and y value you found).
After this, you have to use the regular distance of a line formula to finally find the distance. You could probably use pythagorean formula too.
It’s way simpler just to use the formula!
@ExamMasters Doesn’t that seem like a bit too much for the SAT?
@kassh4 Well, the SAT has been known to test if students know how to do a question efficiently or not. Plus, the long method really only takes 2 - 3 minutes to do. It’s not that bad. It tests several important concepts from linear algebra.
a. | x – 9 | ≤ 15
b. | x – 9 | ≥ 15
c. | x – 12 | ≥ 3
d. | x – 12 | ≤ 3
a. 2 feet
b. 3 feet
c. 4 feet
d. 8 feet
Here are more questions, from my reddit SAT Practice Problems thread:
11.) An event was held last Saturday, 390 males and females attended the event. The ratio of males to females was 3 to 2. How many females attended the event?
a. 138 females
b. 156 females
c. 234 females
d. 260 females
12.) If an airplane travels 1, 200 miles in 2.5 hours, how far will it travel in 10 hours (given that the speed doesn’t vary)?
a. 4,800 miles
b. 5,300 miles
c. 7,200 miles
d. 12,000 miles
Refer to questions 13 and 14 for the following:
A pig weighing 200 pounds gains 5 pounds per day and costs 45 cents a day to keep. The market price for pigs is 65 cents per pound, but is falling 1 cent per day.
13.) When should the pig be sold to obtain maximum profit?
a. After 7 days
b. After 8 days
c. After 9 days
d. After 10 days
14.) How much is the maximum profit you will earn after selling the pig?
a. $133.20
b. $136.00
c. $138.60
d. $140.00
15.) When purchasing a vehicle priced at $8,800, the sales clerk awards a discount of 7.5%. How much will the final cost of the vehicle be?
a. $8,140.00
b. $8,210.32
c. $8,260.00
d. $8,272.20
For both I set up a mini model in my head.
Number 2 specifically was a bit more complex but the equations is as follows: (x is the width of the strip in feet)
(20 + 2x)(30 + 2x) - 600 = 336
So I tried 3.
(20 + 6)(30 + 6) - 600 = 336
(26)(36) - 600 = 336
936 - 600 = 336
336 = 336
Of course, all of this work does not have to be shown on the exam. This is just the thought process involved in finding the answer.
@ZealousScholar That’s excellent. Try the other ones - questions 13 & 14 are difficult.
Whoa! havent been on in a while…
|x-median| ≤ to the difference from the outer limits and the median
Hence in this case the median is 12 and the distance from the median to both the outer limits is 3
So we get D
Example
We are going to plug in 4 feet
So we …
4*2=8
(2838) - (2030) = 464
We need to get a thinner width so lets try 3
3*2=6
(2636) - (2030) = 336
So we get B
Havent seen that equation… that was helpful… I was doing it the long way
*EDIT * didnt realize there was a second page… this was in response to the last question on the first page