Geometry and Trigonometry
The area of a square is 64 square inches. What is the side length, in inches, of this square?
8
The function f is defined as f(x) = 8x. For what value of x does f(x) equal 72?
9
x = 49; y = x+9. The graphs of the given equations intersect at the point (x, y) in the xy-plane. What is the value of y?
58
Factor this expression: x2 + 9x + 20
(x + 4)(x + 5)
There are 55 students in Spanish club. A sample of the Spanish club students was selected at random and asked whether they intend to enroll in a new study program. Of those surveyed, 20% responded that they intend to enroll in the study program. Based on this survey, which of the following is the best estimate of the total number of Spanish club students who intend to enroll in the study program?
11
Triangle ABC and triangle DEF are similar triangles where AB and DE are corresponding sides. If DE = 2AB and the perimeter of triangle ABC is 20, what is the perimeter of triangle DEF?
40
5x = 15
-4x + y = -2
The solution to the given system of equations is (x, y). What is the value of x + y?
13
v = - w/150x. The given equation relates the distinct positive numbers v, w, and x. Write an equation that correctly expresses w in terms of v and x?
w = -150vx
Factor this expression: x2 - 11x + 28
(x - 7)(x - 4)
At a certain time and day, the Washington Monument in Washington, DC, casts a shadow that is 300 feet long. At the same time, a nearby cherry tree casts a shadow that is 16 feet long. Given that the Washington Monument is approximately 555 feet tall, what is the height in feet of the cherry tree?
29.6
Square X has a side length of 12 centimeters. The perimeter of square Y is 2 times the perimeter of square X. What is the length, in centimeters, of one side of square Y?
24
The function h is defined as h(x) = 4x + 28. The graph of y = h(x) in the xy-plane has an x-intercept at (a, 0) and a y-intercept at (0, b), where a and b are constants. What is the value of a + b?
21
(2x - 2)/(x+5) = 1 - (1/(x+5))
What is the solution to the equation?
6
Factor this expression: 3x2 - 6x - 4x + 8
(x - 2)(3x - 4)
After 20% of the original number of marbles in a group were removed from the group, 360 marbles remained in the group. How many marbles were removed from the group?
90
In the xy-plane, a circle with radius 5 has center (-8,6). Find the equation of the circle.
(x + 8)2 + (y - 6)2 = 25
y = 2x + 10
y = 2x - 1
At how many points do the graphs of the given equations intersect in the xy-plane?
Zero
The function g is defined as g(x) = (x + 14)(t - x), where t is a constant. In the xy-plane, the graph of y = g(x) passes through the point (24, 0). What is the value of g(0)?
336
Factor this expression: 6x2 + 37x + 6
(x + 6)(6x + 1)
A cargo helicopter delivers only 100-pound packages and 120-pound packages. For each delivery trip, the helicopter must carry at least 10 packages, and the total weight of the packages can be at most 1,100 pounds. What is the maximum number of 120-pound packages that the helicopter can carry per trip?
5
Parallelogram ABCD is similar to parallelogram PQRS. The length of each side of parallelogram PQRS is 2 times the length of its corresponding side of parallelogram ABCD. The area of parallelogram ABCD is 5 square centimeters. What is the area, in square centimeters, of parallelogram PQRS?
20
The functions f and g are defined as f(x) = 1/4x - 9 and g(x) = 3/4x + 21. If the function h is defined as h(x) = f(x) + g(x), what is the x-coordinate of the x-intercept of the graph y = h(x) in the xy-plane?
-12
In the expression 3(2x2 + px + 8) - 16x (p + 4), p is a constant. This expression is equivalent to the expression 6x2 - 155x + 24. What is the value of p?
7
Factor this expression: 6x2 - 5x - 4
(2x + 1)(3x - 4)
Data set A consists of the heights of 75 buildings and has a mean of 32 meters. Data set B consists of the heights of 50 buildings and has a mean of 62 meters. Data set C consists of the heights of the 125 buildings from data sets A and B. What is the mean, in meters, of data set C?
44