Competition · AMC preparation · step 4 of 4

AMC 12 2024B: all 25 problems

Each problem has a solution worked from first principles and the first grade (by CCSS standards) that can solve it.

AMC 12 2024B #1 grade 4+ arithmetic
In a long line of people arranged left to right, the 1013th person from the left is also the 1010th person from the righ…
AMC 12 2024B #2 grade 5+ arithmetic
What is 10! - 7! · 6!
AMC 12 2024B #3 grade 8+ arithmetic
For how many integer values of x is |2x| ≤ 7 π
AMC 12 2024B #4 grade 6+ arithmetic
Balls numbered 1, 2, 3, ... are deposited in 5 bins, labeled A, B, C, D, and E, using the following procedure. Ball 1 is…
AMC 12 2024B #5 grade 6+ algebra
In the following expression, Melanie changed some of the plus signs to minus signs: 1+3+5+7+...+97+99 When the new expre…
AMC 12 2024B #6 grade 8+ number-theory
The national debt of the United States is on track to reach 5×10¹³ dollars by 2033. How many digits does this number of…
AMC 12 2024B #7 grade 8+ geometry-2d
In the figure below WXYZ is a rectangle with WX=4 and WZ=8. Point M lies XY, point A lies on YZ, and ∠ WMA is a right an…
AMC 12 2024B #8 grade 11+ algebra
What value of x satisfies (log₂x · log₃x)/(log₂x+log₃x)=2?
AMC 12 2024B #9 grade 8+ probability
A dartboard is the region B in the coordinate plane consisting of points (x, y) such that |x| + |y| ≤ 8. A target T is t…
AMC 12 2024B #10 grade 6+ arithmetic
A list of 9 real numbers consists of 1, 2.2, 3.2, 5.2, 6.2, and 7, as well as x, y , and z with x ≤ y ≤ z. The range of…
AMC 12 2024B #11 grade 11+ algebra
Let x_n = sin²(n°). What is the mean of x₁,x₂,x₃,…,x₉₀?
AMC 12 2024B #12 grade 12+ algebra, geometry-2d
Suppose z is a complex number with positive imaginary part, with real part greater than 1, and with |z| = 2. In the comp…
AMC 12 2024B #13 grade 9+ algebra
There are real numbers x,y,h and k that satisfy the system of equationsx² + y² - 6x - 8y = hx² + y² - 10x + 4y = kWhat i…
AMC 12 2024B #14 grade 8+ arithmetic
How many different remainders can result when the 100th power of an integer is divided by 125?
AMC 12 2024B #15 grade 11+ geometry-2d, algebra
A triangle in the coordinate plane has vertices A(log₂1,log₂2), B(log₂3,log₂4), and C(log₂7,log₂8). What is the area of…
AMC 12 2024B #16 grade 8+ counting
A group of 16 people will be partitioned into 4 indistinguishable 4-person committees. Each committee will have one chai…
AMC 12 2024B #17 grade 11+ probability, algebra
Integers a and b are randomly chosen without replacement from the set of integers with absolute value not exceeding 10.…
AMC 12 2024B #18 grade 5+ arithmetic
The Fibonacci numbers are defined by F₁ = 1, F₂ = 1, and F_n = F_(n-1) + F_(n-2) for n ≥ 3. What is F₂/F₁ + F₄/F₂ + F₆/F…
AMC 12 2024B #19 grade 11+ geometry-2d
Equilateral △ ABC with side length 14 is rotated about its center by angle θ, where 0 < θ < 60°, to form △ DEF. See the…
AMC 12 2024B #20 grade 10+ geometry-2d
Suppose A, B, and C are points in the plane with AB=40 and AC=42, and let x be the length of the line segment from A to…
AMC 12 2024B #21 grade 11+ geometry-2d, number-theory
The measures of the smallest angles of three different right triangles sum to 90°. All three triangles have side lengths…
AMC 12 2024B #22 grade 10+ geometry-2d, number-theory
Let △ABC be a triangle with integer side lengths and the property that ∠B = 2∠A. What is the least possible perimeter of…
AMC 12 2024B #23 grade 10+ geometry-3d
A right pyramid has regular octagon ABCDEFGH with side length 1 as its base and apex V. Segments AV and DV are perpendic…
AMC 12 2024B #24 grade 10+ geometry-2d, counting
What is the number of ordered triples (a,b,c) of positive integers, with a≤ b≤ c≤ 9, such that there exists a (non-degen…
AMC 12 2024B #25 grade 11+ probability, counting
Pablo will decorate each of 6 identical white balls with either a striped or a dotted pattern, using either red or blue…

A parent dashboard for the family lives at sensimlab.com.