AMC
The instructions on a 350-gram bag of coffee beans say that proper brewing of a large mug of pour-over coffee requires 20 grams of coffee beans. What is the greatest number of properly brewed large mugs of coffee that can be made from the coffee beans in that bag?
A) 16
B) 17
C) 18
D) 19
E) 20
B) 17
x2 - 5x + 5 = 1
Solve for x.
x = 1, 4
A triangle has a base of 18 cm and a height of 15 cm. What is its area?
135 cm2
f(x) = ex + 2x
What is the derivative of f(x) at x = 0
f'(0) = 3
x, y, 22, 14, 10... In this sequence, each term after the first term x is obtained by halving the term that comes before it and then adding 3 to that number. What is the value of x-y?
x=70, y=38
70 - 38 = 32
Jerry wrote down the ones digit of each of the first 2025 positive squares: 1, 4, 9, 6, 5, 6... What is the sum of all the numbers Jerry wrote down?
A) 9025
B) 9070
C) 9090
D) 9115
E) 9160
D) 9115
x = 2y + 5
y = (2x - 3)(x + 9)
How many ordered pairs (x, y) satisfy the system of equations shown above?
2 pairs satisfy the equation
A ladder is leaning against a wall, making a 65° angle with the ground. The foot of the ladder is 8 feet from the house. Find the length of the ladder.
8/cos65 or 19.3 feet
f(x) = 7x5 - x4 + 4x3/2 + (8/(sqrtx)) - 4secx
Find the d2y/dx2 of f(x)
f"(x) = 140x3 - 12x2 + (3/x1/2) + (6/x5/2) - 4tan2(x)sec(x)
if f(x) = 2x and g(x) = x3 + x2 +34x, what is f(g(-3))?
-240
The value of the two-digit number ab in base seven equals the value of the two-digit number ba in base nine. What is a + b?
A) 7
B) 9
C) 10
D) 11
E) 14
A) 7
2y + 3x = 5
6y + k (1/3)x = -5
What value of k would make the lines parallel to each other?
k = -27
In triangle ABC, the measure of ∠B is 90°, BC = 16, and AC = 20. Triangle DEF is similar to triangle ABC, where vertices D, E, and F correspond to vertices A, B, and C, respectively, and each side of triangle DEF is 1/3 the length of the corresponding side of triangle ABC. What is the value of sin F?
3/5 or .6
f(x) = (cos(x) + sin(2x) + 1) / (x2 - π2)
Find limx→π f(x) = ?
1/π
A two-digit number is chosen at random. What is the probability that the chosen number is a multiple of 7?
13/90
In △ABC, AB = 10, AC = 18, and ∠B = 130 degrees. Let O be the center of the circle containing points A, B, and C. What is the degree measure of ∠CAO?
A) 20
B) 30
C) 40
D) 50
E) 60
C) 40
x2 + y2 + 4x - 2y = -1
The equation of a circle in the xy-plane is shown above. What is the radius of the circle?
2
A tangent line to a circle has length 8, and a secant line from the same point has a segment of length 4. What is the length of the remaining segment of the secant?
12
∫0∞(kxe-2x)dx = 1
What is the value of k, if any?
A) 1
B) 2
C) 1/2
D) 4
E) 1/4
F) 2/9
G) k does not exist
D) 4
A rectangular page is to contain 24 square inches to print. The margins at the top and bottom of the page are to be 1.5 inches, and the margins on the left and right are to be 1 inch. What should be the dimensions of the page for the least amount of paper to be used?
9 inch by 6 inch would minimize page area.
Emmy says to Max. "I ordered 36 math club sweatshirts today." Max asks, "How much did each shirt cost?" Emmy responds, "I'll give you a hint. The total cost was $ A B B . B A, where A and B are digits and A ≠ 0." After a pause, Max says, "That was a good price." What is A + B?
A) 7
B) 8
C) 11
D) 14
E) 15
C) 11
Which of the following complex numbers is equivalent to 3-5i/8+2i? (Note: i = sqrt -1)
A) 3/8 - 5i/2
B) 3/8 + 5i/2
C) 7/34 - 23i/34
D) 7/34 + 23i/34
E) All of the above
F) None of the Above
C) 7/34 - 23i/34
In triangle ABC, BD bisects angle ABC, with angle ABD = 60° and angle DBC = 20°. AE bisects angle BAC with angle BAE = 70° and EAC = 10°. What is the measure of angle AED?
80°
The function f has derivatives of all orders at x = 0, and the Maclaurin series for f is
∞
∑ (ln(n))/(3nn3)xn
n = 2
Using the ratio test, determine the interval of convergence of the Maclaurin series for f.
-3 ≤ X ≤ 3
3x+3y+3z = 837
Find x, y, and z.
(6, 4, 3)
(6, 3, 4)
(4, 6, 3)
(4, 3, 6)
(3, 6, 4)
(3, 4, 6)