SAT Math questions - explanations?

Question

1. If f(x) = x^2 + 2, which of the following could be a value of f(x)?
a) -2
b) -1
c) 0
d) 1
e) 2

Correct answer is e) 2.

2. A basketball team had a ratio of wins to losses of 3:1. After the team won six games in a row, its ratio of wins to losses became 5:1. How many games had the team won BEFORE winning six games in a row?
a) 3
b) 6
c) 9
d) 15
e) 24

Correct answer is d) 15.

3. A square is inscribed in a circle with radius r. What is the probability that a randomly selected point in the circle will NOT be in the square?
a) (pi - 2) / (pi x r^2)
b) (pi - 2) / pi
c) (pi - 1/2) / pi
d) (1 - r) / pi
e) r / pi

Correct answer: b) (pi - 2) / pi

There are the questions I didn't understand on the practice test, but the book only gives answers and not explanations. Can someone please explain how to do these problems? Thanks!

Answer 1

1. If f(x) = x^2 + 2, which of the following could be a value of f(x)?



f(x) would always be 2 more than a perfect square; it could be 2 more than perfect square 0, which is 2.







2. A basketball team had a ratio of wins to losses of 3:1. After the team won six games in a row, its ratio of wins to losses became 5:1. How many games had the team won BEFORE winning six games in a row?



system of equations:

(using w for number of wins originally, and l for the number of losses which remains constant)

w/l = 3/1 ---> w/l = 3 (before the six wins)

(w+6)/l = 5/1 ---> (w+6)/l = 5 (after the six wins)



w / l = 3

(w + 6)/l = 5



Multiply both equations by l to get rid of the denominator.

w = 3l

w+6 = 5l



You can use the substitution method, using 3l for w in the second equation.

3l + 6 = 5l

2l = 6

l = 3



w = 3l = 3(3) = 9



I get 9 for wins before the winning streak and 15 for wins after.







I don't know how to do the third problem.

Answer 2

1) x^2 can't be a negative number so when you add 2 to it it can;t be A,B,C, or D the only thing it could be is E.



2) Wrong, the correct answer is c) 9 wins. the teams record at first is 9W-3L giving a ratio of 3:1 with six straight wins their record is now 15W-3L with a new ratio of 5:1



3)you need to compare the areas of the two shapes.

area of circle = pi x r^2

area of square = 2r^2

area of space outside square but still in circle =

(pi x r^2) - (2r^2)

now you need the ratio of that last area to the area of the entire circle

[(pi x r^2) - (2r^2)]/[pi x r^2]

the r^2 will all cencel to make (pi - 2)/pi

Answer 3

they provide you with the guideline... you in basic terms could desire to stay with it. #x = -x + a million # (#x) = -(#x) + a million = -(-x + a million) + a million = x - a million + a million = x #(#x) = x (A) think of that it have been #(F) #F = -F + a million yet right here all of us understand that F is comparable to #x it incredibly is comparable to -x + a million so #(#x) = -(#x) + a million = -(-x + a million) + a million = x - a million + a million = x edit: the guy with a sensible call has an outstanding strtegy for distinctive decision questions -- replace letters with numbers, and notice which decision fits as one warning, constantly try each and all the respond possibilities with the form you attempt to make specific there isn't any greater beneficial than one that works. If that occurs, you're able to desire to plug in yet another form to eliminate a decision.

Answer 4

1 x^2+2 positive n >2

since min value of x^2 is 0

so ans is 2