Algebra
The total cost f(x), in dollars, to lease a car for 36 months from a particular car dealership is given by f(x) = 26x + 1,000, where is the monthly payment, in dollars. What is the total cost to lease a car when the monthly payment is $400?
$15,400
The function g is defined by g(x) = (8x+1)^(1/2). What is the value of g(3)?
g(3) = 5
Each face of a fair 14-sided die is labeled with a number from 1 through 14, with a different number appearing on each face. If the die is rolled one time, what is the probability of rolling a 2?
1/14
In triangle XYZ, the measure of angle X is 24° and the measure of angle Y is 98°. What is the measure of angle Z?
58°
The Pythagorean Theorem
What is a² + b² = c²
In the xy-plane, the graph of the linear function f contains the points (0,3) and (7,31). What equation defines f, where y = f(x)?
f(x) = 4x+3
x^2 = -841
How many distinct real solutions does the given equation have?
Zero
An airplane descends from an altitude of 9,500 feet to 5,000 feet at a constant rate of 400 feet per minute. What type of function best models the relationship between the descending airplane's altitude and time?
A. Decreasing exponential
B. Decreasing linear
C. Increasing exponential
D. Increasing linear
B. Decreasing linear
A right circular cylinder has a volume of 377 cubic centimeters. The area of the base of the cylinder is 13 square centimeters. What is the height, in centimeters, of the cylinder?
29 centimeters
The side lengths of a 30-60-90 right triangle in terms of x
What is x : x√3 : 2x
y=3x
2x+y=12
The solution to the given system of equations is (x,y). What is the value of 5x?
12
f(x) = 2x+3
g(x) = 7x-2
h(x) = 5x+6
The functions f, g, and h are defined as shown. If f(x)*g(x) - h(x) = ax^2 + bx + c, where a, b, and c are constants, what is the value of b?
b = 12
15, 14, 18, 17, x
The mean and the median of the five numbers above are equal. Which of the following is NOT a possible value of x ?
A. 6
B. 11
C. 16
D. 21
A. 6
In right triangle RST, the sum of the measures of angle R and angle S is 90 degrees. The value of sin(R) is 1/2. What is the value of cos(S)?
1/2
The Quadratic Formula
What is x = [-b ± √(b² - 4ac)]/2a
Adam’s school is a 20-minute walk or a 5-minute bus ride away from his house. The bus runs once every 30 minutes, and the number of minutes, w, that Adam waits for the bus varies between 0 and 30. Which of the following inequalities gives the values of w for which it would be faster for Adam to walk to school?
A. W-5 < 20
B. W-5 > 20
C. W+5 < 20
D. W+5 > 20
D. W+5 > 20
The function f is defined by f(x) = a^x + b, where a and b are constants. In the xy-plane, the graph of y = f(x) has an x-intercept at (2,0) and a y-intercept at (0,-323). What is the value of b?
b = -324
The speed of a vehicle is increasing at a rate of 7.3 meters per second squared. What is this rate, in miles per minute squared, rounded to the nearest tenth?
(Use 1 mile = 1,609 meters.)
16.3 miles per minute squared
A circle in the xy-plane has its center at (-4, -6). Line k is tangent to this circle at the point (-7, -7). What is the slope of line k?
-3
Award program for the top scorers on the PSAT.
What is National Merit Scholarship Program
(2/5)x + (7/5)y = 2/7
gx + ky = 5/2
In the given system of equations, g and k are constants. The system has infinitely many solutions. What is the value of g/k
0.2857 or 2/7
-x^2 + bx - 676 = 0
In the given equation, b is a positive integer. The equation has no real solution. What is the greatest possible value of b?
51
The speeds of objects A, B, and C are a meters per second, b meters per second, and c meters per second, respectively. If the speed of object A is 5,900% of the speed of object C and the speed of object C is 0.008% of the speed of object B, which expression represents the value of a + b in terms of c?
A. 1,840c
B. 5,908c
C. 6,025c
D. 12,559c
D. 12,559c
A rectangle is inscribed in a circle, such that each vertex of the rectangle lies on the circumference of the circle. The diagonal of the rectangle is twice the length of the shortest side of the rectangle. The area of the rectangle is 1,089√3 square units. What is the length, in units, of the diameter of the circle?
66
The combined length in time of Math Modules 1 & 2 on the SAT
70 minutes