Competition · AMC preparation · step 4 of 4

AMC 8 2000: all 25 problems

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

AMC 8 2000 #1 grade 3+ arithmetic
Aunt Anna is 42 years old. Caitlin is 5 years younger than Brianna, and Brianna is half as old as Aunt Anna. How old is…
AMC 8 2000 #2 grade 6+ arithmetic
Which of these numbers is less than its reciprocal?
AMC 8 2000 #3 grade 6+ arithmetic
How many whole numbers lie in the interval between 5/3 and 2π?
AMC 8 2000 #4 grade 6+ arithmetic
In 1960 only 5% of the working adults in Carlin City worked at home. By 1970 the "at-home" work force had increased to 8…
AMC 8 2000 #5 grade 3+ arithmetic
Each principal of Lincoln High School serves exactly one 3-year term. What is the maximum number of principals this scho…
AMC 8 2000 #6 grade 3+ geometry-2d
Figure ABCD is a square. Inside this square three smaller squares are drawn with the side lengths as labeled. The area o…
AMC 8 2000 #7 grade 7+ arithmetic
What is the minimum possible product of three different numbers of the set {-8,-6,-4,0,3,5,7}?
AMC 8 2000 #8 grade 3+ arithmetic, geometry-3d
Three dice with faces numbered 1 through 6 are stacked as shown. Seven of the eighteen faces are visible, leaving eleven…
AMC 8 2000 #9 grade 6+ arithmetic, number-theory
Three-digit powers of 2 and 5 are used in this "cross-number" puzzle. What is the only possible digit for the outlined s…
AMC 8 2000 #10 grade 6+ arithmetic, rate-ratio
Ara and Shea were once the same height. Since then Shea has grown 20% while Ara has grown half as many inches as Shea. S…
AMC 8 2000 #11 grade 4+ number-theory
The number 64 has the property that it is divisible by its unit digit. How many whole numbers between 10 and 50 have thi…
AMC 8 2000 #12 grade 4+ arithmetic, geometry-2d
A block wall 100 feet long and 7 feet high will be constructed using blocks that are 1 foot high and either 2 feet long…
AMC 8 2000 #13 grade 8+ geometry-2d
In triangle CAT, we have ∠ ACT =∠ ATC and ∠ CAT = 36°. If TR bisects ∠ ATC, then ∠ CRT =
AMC 8 2000 #14 grade 5+ arithmetic, number-theory
What is the units digit of 19¹⁹ + 99⁹⁹?
AMC 8 2000 #15 grade 5+ geometry-2d
Triangles ABC, ADE, and EFG are all equilateral. Points D and G are midpoints of AC and AE, respectively. If AB = 4, wha…
AMC 8 2000 #16 grade 4+ geometry-2d, arithmetic
In order for Mateen to walk a kilometer (1000m) in his rectangular backyard, he must walk the length 25 times or walk it…
AMC 8 2000 #17 grade 6+ arithmetic
The operation otimes is defined for all nonzero numbers by aotimes b =a²/b. Determine [(1otimes 2)otimes 3]-[1otimes (2o…
AMC 8 2000 #18 grade 8+ geometry-2d
Consider these two geoboard quadrilaterals. Which of the following statements is true?
AMC 8 2000 #19 grade 7+ geometry-2d
Three circular arcs of radius 5 units bound the region shown. Arcs AB and AD are quarter-circles, and arc BCD is a semic…
AMC 8 2000 #20 grade 4+ arithmetic, number-theory
You have nine coins: a collection of pennies, nickels, dimes, and quarters having a total value of $1.02, with at least…
AMC 8 2000 #21 grade 7+ probability, counting
Keiko tosses one penny and Ephraim tosses two pennies. The probability that Ephraim gets the same number of heads that K…
AMC 8 2000 #22 grade 7+ geometry-3d
A cube has edge length 2. Suppose that we glue a cube of edge length 1 on top of the big cube so that one of its faces r…
AMC 8 2000 #23 grade 6+ arithmetic
There is a list of seven numbers. The average of the first four numbers is 5, and the average of the last four numbers i…
AMC 8 2000 #24 grade 7+ geometry-2d
If ∠ A = 20° and ∠ AFG =∠ AGF, then ∠ B+∠ D =
AMC 8 2000 #25 grade 6+ geometry-2d
The area of rectangle ABCD is 72 units squared. If point A and the midpoints of BC and CD are joined to form a triangle,…

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