cleverpuppy

I have purchased the Online Course. The tests seem a little bit hard for me.

Math:

1. Question 5, Section 2, Online Course Test 4. It has a picture so I cannot type the whole question here
2. Question 20, Section 2, Oline Course Test 4:
If x and y are numbers such that (x+9)(y-9) = 0. What is the smallest value of x^2 + y^2.|
A. 0
B. 9
C. 18
D. 81
E. 162.
Correct Answer: D.
3. Question 12, Section 9, Online Course Test 4.
A set has property X if t^2 0 t is in the set whenever t is in the set. Which of the following sets has property X?
A. (-2,-1,0)
B. (-1,0)
C. (-1,0,1)
D. (0,1)
E. (1,2)
Correct Answer: D.


Writing
1. Question 2, Section 5, OCT 4

First run in 1867 and still taking place every summer, the Belmont Stakes, a horse race for thoroughbred three-year-olds, (was) one of the oldest races in the United States.
B. is
E. has been\
Why not E?

2. Question 5, Section 5
Societies acting through their government make the rules (to state) which acts are illegal, but although war is the most violent of human activities, it has not been declared illegal by any of the world's governments or their agencies.
A. to state
B. stating

Why not A?

PSVicki

Hi,

Math
2: One of the expressions in parenthesis has to equal 0 in order for the equation to be true. In order for this to happen, either x = -9 or y = 9:

(x+9)(y-9) = 0
(0)(y-9) = 0 >> 0 = 0 True
(x+9)(0) = 0 >> 0 = 0 True

Options to make this happen:
1. x = -9: (x+9)(y-9) = 0 >> (-9 + 9)(y-9) = 0 >> (0)(y-9) = 0
2. y = 9: (x+9)(y-9) = 0 >> (x + 9)(9-9) = 0 >> (x+9)(0) = 0

So take the second option, y = 9 (just to avoid the negative number in x = -9. But either option will give you the same result). In order for x^2 + y^2 to be as small as possible, we need x and y to be as small as possible. y = 9. It can't get any smaller. It doesn't matter what x equals. Because we'll always get the same result:

x = 0 >> (0+9)(9-9) = 0
x = 1 >> (1+9)(9-9) = 0
x = 100 >> (100+9)(9-9) = 0 etc.

What's the smallest thing x can be? 0.

x^2 + y^2 = 0^2 + 9^2 = 0 + 81 = 81

PSVicki

I can't understand Math #3. I think something is mistyped.

Writing
1. The present tense "is" is used for general truths that are still true. Plus, the sentence gives the context clue "still being run." It "IS still being run," not "has been still being run." "Has been" would work with "for" or "since" in a sentence like this: "The Belmont Stakes, a horse race for thoroughbred three-year-olds, (has been) run since 1867."

2. This is a hard one but common on the SAT. The purpose of the rules is not TO STATE, as the original sentence indicates. The purpose is likely to govern or to control, but is irrelevant, since the purpose of the rules is not the main idea of the sentence. The use of the infinitive, though, puts the focus on the purpose. By using "stating," the phrase "stating which acts are illegal" becomes an adjective modifying rules.

Consider the difference between these sentences, in which the adjective comes before the noun:
The government makes the controlling rules. (Controlling as an adjective)
The government makes the to control rules. ("To control" makes no sense in front of "rules." If we put it behind rules, the meaning is changed: The government makes the rules to control.")

rspence

Math:

2. We know that x^2 - y^2 = 81. Since squares are always non-negative, (x^2 - y^2) + 2y^2 is greater than or equal to x^2 - y^2, i.e. x^2 + y^2 >= 81. This can occur when x = -9, y = 0.

3. Looks like you typoed somewhere.

cleverpuppy

Sorrrryyyy, I mistyped the question . The correct version is below

3. Question 12, Section 9, Online Course Test 4.
A set has property X if t^2 - t is in the set whenever t is in the set. Which of the following sets has property X?
A. (-2,-1,0)
B. (-1,0)
C. (-1,0,1)
D. (0,1)
E. (1,2)
Correct Answer: D.

btw, thanks a lot! You guys are amazing

RandomHSer

D is right because 0^2-0= 0 which is in the set and 1^1-1=0 which is in the set. The other sets fail for at least one of the members.

cleverpuppy

One more question

y = -2*(x-2)^2 + 3
In the xy plane, line l passes through the point (4,-5) and the vertex of the parabola with the equation above. What is the slope of line l?
A. -4
B. - 1/4
C. 0
D. 1/4
E. 4

Correct Answer: A
Have no idea how to solve this question

piratebay

-2(x-2)^2 + 3
-2(x^2 - 4x + 4) + 3
-2x^2 + 8x - 8 + 3
-2x^2 + 8x - 5

-b/2a = -8/2(-2) = -8/-4 = 2

-2(2)^2 + 8(2) - 5
-2(4) + 16 - 5
-8 + 16 - 5
3

2, 3

y2-y1/x2-x1 = 3+5/2-4 = 8/-2 = -4