Competition · AMC preparation · step 4 of 4

AMC 8 2002: 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 2002 #1 grade 7+ geometry-2d, counting
A circle and two distinct lines are drawn on a sheet of paper. What is the largest possible number of points of intersec…
AMC 8 2002 #2 grade 4+ number-theory, counting
How many different combinations of $5 bills and $2 bills can be used to make a total of $17? Order does not matter in th…
AMC 8 2002 #3 grade 6+ arithmetic
What is the smallest possible average of four distinct positive even integers?
AMC 8 2002 #4 grade 4+ number-theory
The year 2002 is a palindrome (a number that reads the same from left to right as it does from right to left). What is t…
AMC 8 2002 #5 grade 4+ number-theory
Carlos Montado was born on Saturday, November 9, 2002. On what day of the week will Carlos be 706 days old?
AMC 8 2002 #6 grade 6+ rate-ratio
A birdbath is designed to overflow so that it will be self-cleaning. Water flows in at the rate of 20 milliliters per mi…
AMC 8 2002 #7 grade 6+ rate-ratio
The students in Mrs. Sawyer's class were asked to do a taste test of five kinds of candy. Each student chose one kind of…
AMC 8 2002 #8 grade 2+ arithmetic
Problems 8,9 and 10 use the data found in the accompanying paragraph and table: Juan organizes the stamps in his collect…
AMC 8 2002 #9 grade 4+ arithmetic
Problems 8,9 and 10 use the data found in the accompanying paragraph and table: Juan organizes the stamps in his collect…
AMC 8 2002 #10 grade 6+ arithmetic
Problems 8,9 and 10 use the data found in the accompanying paragraph and table: Juan organizes the stamps in his collect…
AMC 8 2002 #11 grade 4+ geometry-2d, counting
A sequence of squares is made of identical square tiles. The edge of each square is one tile length longer than the edge…
AMC 8 2002 #12 grade 7+ probability
A board game spinner is divided into three regions labeled A, B and C. The probability of the arrow stopping on region A…
AMC 8 2002 #13 grade 6+ geometry-3d
For his birthday, Bert gets a box that holds 125 jellybeans when filled to capacity. A few weeks later, Carrie gets a la…
AMC 8 2002 #14 grade 7+ rate-ratio
A merchant offers a large group of items at 30% off. Later, the merchant takes 20% off these sale prices. The total disc…
AMC 8 2002 #15 grade 6+ geometry-2d
Which of the following polygons has the largest area?
AMC 8 2002 #16 grade 8+ geometry-2d
Right isosceles triangles are constructed on the sides of a 3-4-5 right triangle, as shown. A capital letter represents…
AMC 8 2002 #17 grade 4+ arithmetic, algebra
In a mathematics contest with ten problems, a student gains 5 points for a correct answer and loses 2 points for an inco…
AMC 8 2002 #18 grade 6+ rate-ratio, algebra
Gage skated 1 hr 15 min each day for 5 days and 1 hr 30 min each day for 3 days. How long would he have to skate the nin…
AMC 8 2002 #19 grade 4+ counting, number-theory
How many whole numbers between 99 and 999 contain exactly one 0?
AMC 8 2002 #20 grade 7+ geometry-2d
The area of triangle XYZ is 8 square inches. Points A and B are midpoints of congruent segments XY and XZ. Altitude XC b…
AMC 8 2002 #21 grade 7+ probability, counting
Harold tosses a coin four times. The probability that he gets at least as many heads as tails is
AMC 8 2002 #22 grade 6+ geometry-3d
Six cubes, each an inch on an edge, are fastened together, as shown. Find the total surface area in square inches. Inclu…
AMC 8 2002 #23 grade 4+ geometry-2d, counting
A corner of a tiled floor is shown. If the entire floor is tiled in this way and each of the four corners looks like thi…
AMC 8 2002 #24 grade 6+ rate-ratio
Miki has a dozen oranges of the same size and a dozen pears of the same size. Miki uses her juicer to extract 8 ounces o…
AMC 8 2002 #25 grade 6+ rate-ratio, algebra
Loki, Moe, Nick and Ott are good friends. Ott had no money, but the others did. Moe gave Ott one-fifth of his money, Lok…

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