Geometry
Algebra
Mental Math (NO PAPER)
Counting & Probability
Number Theory
100
Carl has 5 cubes each having side length 1, and Kate has 5 cubes each having side length 2.
The total volume of these 10 cubes
What is 45?
100
The simplified form of
What is -1?
100
The value of 1 - (-2) - 3 - (-4) - 5 - (-6)
What is 5?
100
Portia's high school has 3 times as many students as Lara's high school. The two high schools have a total of 2600 students.
The number of students in Portia's high school
What is 1950?
100
The hundreds digit of 20! - 15!
What is 0?
200
Jackson's paintbrush makes a narrow strip with a width of 6.5 millimeters. Jackson has enough paint to make a strip 25 meters long.
The number of square centimeters of paper Jackson could paint
What is 1625?
200
The ratio of w to x is 4 : 3, the ratio of y to z is 3 : 2, and the ratio of z to x is 1 : 6.
The ratio of w to y
What is 16 : 3?
200
A = 3 + 4 + 5 - 7
B = 3 x 4 x 5 x 7
C = -1 - (-2)(-3)
The value A + B / C
What is -55?
200
In an after-school program for juniors and seniors, there is a debate team with an equal number of students from each class on the team. Among the 28 students in the program, 25% of the juniors and 10% of the seniors are on the debate team.
The number of juniors in the program
What is 8?
200
The sum of two natural numbers is 1111. One of the two numbers is divisible by 10. If the units digit of that number is erased, the other number is obtained.
The difference of these two numbers
What is 909?
300
A 3 - 4 - 5 right triangle is inscribed in circle A, and a 5 - 12 - 13 right triangle is inscribed in circle B.
The ratio of the area of circle A to the area of circle B
What is 25 / 169?
300
The sum of all real numbers x for which |x2 - 12x + 34| = 2
What is 18?
300
M = 4
A = (4 x 5 x 6 x 7) / (1 x 3 x 5 x 7)
T = -2 + 7 - 5 + 8 - 1 - 3 + 2
H = The units digit of 46
The product MATH divided by 2
What is 576?
300
At a math contest, 57 students are wearing blue shirts, and another 75 students are wearing yellow shirts. The 132 students are assigned into 66 pairs. In exactly 23 of these pairs, both students are wearing blue shirts.
The number of pairs where both students are wearing yellow shirts
What is 32?
300
The units digit of 20222023 + 20232022
What is 7?
400
Two lines with slopes 1/2 and 2 intersect at (2, 2).
The area of the triangle enclosed by these two lines and the line x + y = 10
What is 6?
400
Ana and Bonita are born on the same date in different years, n years apart. Last year Ana was 5 times as old as Bonita. This year Ana's age is the square of Bonita's age.
The value of n
What is 12?
400
A = The value 23 + 34
B = The value 3 x 4 + 5 x 6
C = The value 5! / 4!
D = The largest value x for which x3 < 4000
E = The value 4/2 x 3/2 x 5/2 x 2/3
The value A + B + C, all multiplied by D / E
What is 408?
400
The number of 4-digit positive integers (between 1000 and 9999) divisible by 5 having only even digits
What is 100?
400
Let a1 = 1, a2 = 3, and an+2 = an+1 + an for all positive n.
The number of even values in a1, a2, a3, ..., a15
What is 5?
500
In a plane, four circles with radii 1, 3, 5, 7 are tangent to line L at the same point A, but they may be on either side of L. Region S consists of all the points that lie inside exactly one of the four circles.
The maximum possible area of region S
What is 65pi?
500
Maureen is keeping track of the mean of her quiz scores this semester. If Maureen scores an 11 on the next quiz, her mean will increase by 1. If she scores an 11 on each of the next three quizzes, her mean will increase by 2.
The mean of her quiz scores currently
What is 7?
500
S = The smallest positive integer
I = The largest prime under 100
G = The value 3 x 6 + 4 x 6 + 8 x 7
M = The probability of rolling a six then a seven on a seven-sided dice
A = The value -1 - 3 - 5 - 7 - 9 - 11 - 13 - 15 - 17 - 19
W = 201 / 3 + 6 + 7 x 3
The product SIGMA plus the quantity W
What is -19306?
500
A box contains 28 red balls, 20 green balls, 19 yellow balls, 13 blue balls, 11 white balls, and 9 black balls.
The minimum number of balls that must be drawn from the box without replacement to guarantee that at least 15 balls of a single color will be drawn
What is 76?
500
the sum of all integer bases b > 9 for which 17b is a factor of 97b
What is 070?