Arithematic sequence
Evaluate: 3 + 6 + 9 + · · · + 33.
198
For all real x, f(3x) = x2 − 3x + 1. Find f(12).
5
Let x be a positive integer. Given that x = 13y and x − y = 564, what is x?
611
Riley is picking 3 people from a soccer team of 11 people to have a role of defender. If the order Riley assigns defenders does not matter, how many ways can Riley assign three defenders?
165
A circle fits inside a 4 × 6 rectangle. Find the largest possible area of the circle in terms of π.
4 π
Find the 11th term in the arithmetic sequence: 9,−3,−15, . . ..
-111
What is the area of the quadrilateral with vertices at (3, 5), (8, 3), (6,−2), and (1, 0)?
29
A train travels 50 miles per hour for the first 40 miles, then slows down to 40 miles per hour for the next 50 miles. What is the average speed of the train in miles per hour? Round your answer to the nearest whole number.
44
If a random integer between 1 and 100, inclusive, is chosen, what is the probability that it is composite? Express your answer as a common fraction.
37/50
Three of the faces of a rectangular prism have areas 20, 24, and 30. What is half of its volume?
60
Find the 101st number in the arithmetic sequence: 275, 371, 467, 563 . . . .
9875
The parabola f(x) = x2 − x − 6 intersects the x-axis and y-axis at three different points. What is the area of the triangle formed by these points?
15
Compute the product of all distinct negative values of x such that (x2 + 7x + 10)(x2 + 2x − 8) + (x2 + 3x − 10) = 0.
-20
Two fair six-sided dice are thrown. What is the probability that at least one of them lands on a 2 or a 5? Express your answer as a common fraction.
5/9
Right triangle ABC with right angle at B has area 9. The lengths of both AB and BC are whole numbers, and the altitude from B to AC has length strictly greater than 2. What is AC2?
45
The 4th term of an arithmetic sequence is 303, the 160th term is 2019, and the nth term is 1678. What is n?
129
Find the distance between the point (0, 0) and the line 5x + 12y = 60. Express your answer as a decimal to the nearest tenth.
4.6
The ratio between two consecutive even integers is 11/12 . Find the product of the integers.
528
A palindrome is a sequence that can be read the same from left to right as from right to left. How many different arrangements of all the letters in RACECAR are palindromes?
6
Find the area of a triangle with side lengths 10, 12, and 14. Express your answer in simplest radical form.
24√6
Connor summed the positive differences between the second perfect square and the first perfect square, the third perfect square and the second perfect square, the fourth perfect square and the third perfect square, and so on through the fifty-first perfect square and the fiftieth perfect square. What was Connor’s result? (The first perfect square is 12 = 1.)
2600
Perpendicular lines intersect at the point (2, 5). The equation of one of these lines is y = x + 3. What is the area of the region in the first quadrant bounded by these two lines, the x-axis, and the y-axis? Express your answer as a common fraction.
41/2
If 2x2 − 25x + 9 = 0, what is the product of the values for x? Express your answer as a common fraction.
9/2
How many ways are there to draw a rectangle from a 9×2 grid of squares if the sides of the rectangle are on the lines of the grid?
135
Carson is designing a spaceship capsule, which is in the shape of a frustum. He designs the capsule by taking a right circular cone with height 24 and base diameter 20, then making a cut parallel to the base such that he can take out a right circular cone with height 12. The remaining piece is Carson’s frustum, and the surface area of the frustum can be written as kπ for some positive whole number k. What is the value of k?
320π