Competition · AMC preparation · step 4 of 4

AMC 12 2003B: 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 2003B #1 grade 6+ arithmetic
Which of the following is the same as (2-4+6-8+10-12+14)/(3-6+9-12+15-18+21)?
AMC 12 2003B #2 grade 5+ arithmetic
Al gets the disease algebritis and must take one green pill and one pink pill each day for two weeks. A green pill costs…
AMC 12 2003B #3 grade 5+ geometry-2d
Rose fills each of the rectangular regions of her rectangular flower bed with a different type of flower. The lengths, i…
AMC 12 2003B #4 grade 6+ rate-ratio
Moe uses a mower to cut his rectangular 90-foot by 150-foot lawn. The swath he cuts is 28 inches wide, but he overlaps e…
AMC 12 2003B #5 grade 8+ rate-ratio
Many television screens are rectangles that are measured by the length of their diagonals. The ratio of the horizontal l…
AMC 12 2003B #6 grade 8+ arithmetic
The second and fourth terms of a geometric sequence are 2 and 6. Which of the following is a possible first term?
AMC 12 2003B #7 grade 8+ algebra
Penniless Pete's piggy bank has no pennies in it, but it has 100 coins, all nickels, dimes, and quarters, whose total va…
AMC 12 2003B #8 grade 2+ arithmetic
Let ♣(x) denote the sum of the digits of the positive integer x. For example, ♣(8)=8 and ♣(123)=1+2+3=6. For how many tw…
AMC 12 2003B #9 grade 8+ algebra
Let f be a linear function for which f(6) - f(2) = 12. What is f(12) - f(2)?
AMC 12 2003B #10 grade 8+ counting
Several figures can be made by attaching two equilateral triangles to the regular pentagon ABCDE in two of the five posi…
AMC 12 2003B #11 grade 6+ rate-ratio
Cassandra sets her watch to the correct time at noon. At the actual time of 1:00 PM, she notices that her watch reads 12…
AMC 12 2003B #12 grade 6+ number-theory
What is the largest integer that is a divisor of (n+1)(n+3)(n+5)(n+7)(n+9) for all positive even integers n?
AMC 12 2003B #13 grade 8+ geometry-3d
An ice cream cone consists of a sphere of vanilla ice cream and a right circular cone that has the same diameter as the…
AMC 12 2003B #14 grade 8+ geometry-2d
In rectangle ABCD, AB=5 and BC=3. Points F and G are on CD so that DF=1 and GC=2. Lines AF and BG intersect at E. Find t…
AMC 12 2003B #15 grade 8+ geometry-2d
A regular octagon ABCDEFGH has an area of one square unit. What is the area of the rectangle ABEF?
AMC 12 2003B #16 grade 8+ geometry-2d
Three semicircles of radius 1 are constructed on diameter AB of a semicircle of radius 2. The centers of the small semic…
AMC 12 2003B #17 grade 11+ algebra
If log (xy³) = 1 and log (x²y) = 1, what is log (xy)?
AMC 12 2003B #18 grade 8+ number-theory
Let x and y be positive integers such that 7x⁵ = 11y¹³. The minimum possible value of x has a prime factorization a^cb^d…
AMC 12 2003B #19 grade 7+ counting
Let S be the set of permutations of the sequence 1,2,3,4,5 for which the first term is not 1. A permutation is chosen ra…
AMC 12 2003B #20 grade 8+ algebra
Part of the graph of f(x) = ax³ + bx² + cx + d is shown. What is b?
AMC 12 2003B #21 grade 11+ geometry-2d
An object moves 8 cm in a straight line from A to B, turns at an angle α, measured in radians and chosen at random from…
AMC 12 2003B #22 grade 10+ geometry-2d
Let ABCD be a rhombus with AC = 16 and BD = 30. Let N be a point on AB, and let P and Q be the feet of the perpendicular…
AMC 12 2003B #23 grade 11+ algebra, counting
The number of x-intercepts on the graph of y=sin(1/x) in the interval (0.0001,0.001) is closest to
AMC 12 2003B #24 grade 9+ algebra
Positive integers a,b, and c are chosen so that a<b<c, and the system of equations 2x + y = 2003 and y = |x-a| + |x-b| +…
AMC 12 2003B #25 grade 10+ geometry-2d
Three points are chosen randomly and independently on a circle. What is the probability that all three pairwise distance…

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