Algebra
f(x) = (2x - 1) / 3
What is f(5)?
f(x) = (2x - 1) / 3
What is f(5)?
3
|x - 5| = 10
What are both solutions?
|x - 5| = 10
What are both solutions?
x = -5, 15
What's the highest possible score on the Math section of the SAT?
What's the highest possible score on the Math section of the SAT?
800
According to a model, the head width, in millimeters, of a worker bumblebee can be estimated by adding 0.6 to four times the body weight of a bee, in grams. According to the model, what would be the head width, in millimeters, of a worker bumblebee that has a body weight of 0.5 grams?
According to a model, the head width, in millimeters, of a worker bumblebee can be estimated by adding 0.6 to four times the body weight of a bee, in grams. According to the model, what would be the head width, in millimeters, of a worker bumblebee that has a body weight of 0.5 grams?
y = 0.6 + 4(0.5) = 2.6
If x2 = a + b and y2 = a + c, which of the following is equal to (x2 - y2)2?
A) a2 - 2ac + c2
B) b2 - 2bc + c2
C) 4a2 - 4abc + c2
D) 4a2 - 2abc + b2c2
If x2 = a + b and y2 = a + c, which of the following is equal to (x2 - y2)2?
A) a2 - 2ac + c2
B) b2 - 2bc + c2
C) 4a2 - 4abc + c2
D) 4a2 - 2abc + b2c2
What score on the SAT Math do you need to score in the top 50% of all test takers?
What score on the SAT Math do you need to score in the top 50% of all test takers?
500-520
A company that provides whale-watching tours takes groups of 21 people at a time. The company's revenue is 80 dollars per adult and 60 dollars per child. If the company's revenue for one group consisting of adults and children was 1,440 dollars, how many people in the group were children?
A company that provides whale-watching tours takes groups of 21 people at a time. The company's revenue is 80 dollars per adult and 60 dollars per child. If the company's revenue for one group consisting of adults and children was 1,440 dollars, how many people in the group were children?
x + y = 21
60x + 80y = 1,440
solving the above system of linear equations gives x = 12
The product of two positive integers is 546. If the first integer is 11 greater than twice the second integer, what is the smaller of the two integers?
The product of two positive integers is 546. If the first integer is 11 greater than twice the second integer, what is the smaller of the two integers?
let x = first integer, y = second integer
x = 2y + 11, xy = 546
(2y + 11)y = 546
2y2 + 11y - 546 = 0
(2y + 39)(y - 14) = 0
y != -39/2 because y is a positive integer; y = 14
xy = 546; x(14) = 546; x = 39
Integers are 14 and 39, so the smaller of the two is 14
What score on the SAT Math do you need to score in the top 5% of all test takers?
What score on the SAT Math do you need to score in the top 5% of all test takers?
740-760
The equation 9x + 5 = a(x + b), where a and b are constants, has no solutions. Which of the following must be true?
I. a = 9
II. b = 5
III. b != 5/9
Choices: None, I only, I and II only, I and III only, II and III only)
The equation 9x + 5 = a(x + b), where a and b are constants, has no solutions. Which of the following must be true?
I. a = 9
II. b = 5
III. b != 5/9
I and III only
In the xy-plane, the graph of the equation y = -x2 + 9x - 100 intersects the line y = c at exactly one point. What is the value of c?
In the xy-plane, the graph of the equation y = -x2 + 9x - 100 intersects the line y = c at exactly one point. What is the value of c?
y = a(x - h)2 + k
y = -(x2 - 2(9/2)x + (9/2)2) + (9/2)2 - 100
y = -(x - 9/2)2 + (-319/4)
y = c = -319/4
An object hangs from a spring. The formula l = 30 + 2w relates the length l, in centimeters, of the spring to the weight w, in newtons, of the object. Which of the following describes the meaning of the 2 in this context?
A) The length, in cm, of the spring with no weight attached.
B) The weight, in newtons, of an object that wills stretch the spring 30 cm.
C) The increase in the weight, in newtons, of the object for each one-cm increase in the length of the spring.
D) The increase in the length, in cm, of the spring for each one-newton increase in the weight of the object.
An object hangs from a spring. The formula l = 30 + 2w relates the length l, in centimeters, of the spring to the weight w, in newtons, of the object. Which of the following describes the meaning of the 2 in this context?
A) The length, in cm, of the spring with no weight attached.
B) The weight, in newtons, of an object that wills stretch the spring 30 cm.
C) The increase in the weight, in newtons, of the object for each one-cm increase in the length of the spring.
D) The increase in the length, in cm, of the spring for each one-newton increase in the weight of the object.
57x2 + (57b + a)x + ab = 0
In the given equation, a and b are constants. The product of the solutions to the given equation is kab, where k is a constant. What is the value of k?
57x2 + (57b + a)x + ab = 0
In the given equation, a and b are constants. The product of the solutions to the given equation is kab, where k is a constant. What is the value of k?
57x(x + b) + a(x + b) = 0
(x + b)(57x + a) = 0; x + b = 0 or 57x + a = 0
x = -b, 57x = -a
x = -b, -a/57, so the product of the solutions = (-b)(-a/57) = (ab)/57
(ab)/57 = kab. ab(1/57) = abk.
k = 1/57
What did SAT originally stand for?
What did SAT originally stand for?
Although it has no meaning as an acryonym today, SAT originally stood for Scholastic Aptitude Test.