2006 AMC 10A Problems
Contents
Problem 1
Sandwiches at Joe's Fast Food cost $3 each and sodas cost $2 each. How many dollars will it cost to purchase 5 sandwiches and 8 sodas?
Problem 2
Define . What is ?
Problem 3
The ratio of Mary's age to Alice's age is 3:5. Alice is 30 years old. How many years old is Mary?
Problem 4
A digital watch displays hours and minutes with AM and PM. What is the largest possible sum of the digits in the display?
Problem 5
Doug and Dave shared a pizza with 8 equally-sized slices. Doug wanted a plain pizza, but Dave wanted anchovies on half of the pizza. The cost of a plain pizza was $8, and there was an additional cost of $2 for putting anchovies on one half. Dave at all of the slices of anchovy piaaz and one plain slice. Doug ate the remainder. Each then paid for what he had eaten. How many more dollars did Dave pay than Doug?
Problem 6
What non-zero real value for satisfies ?
Problem 7
Missing diagram
The rectangle is cut into two congruent hexagons, as shown, in such a way that the two hexagons can be repositioned without overlap to form a square. What is ?
Problem 8
A parabola with equation passes through the points (2,3) and (4,3). What is ?
Problem 9
How many sets of two or more consecutive positive integers have a sum of 15?
Problem 10
For how many real values of is an integer?
Problem 11
Which of the following describes the graph of the equation ?
Problem 12
Missing diagram
Rolly wishes to secure his dog with an 8-foot rope to a square shed that is 16 feet on each side. His preliminary drawings are shown.
Which of these arrangements give the dog the greater area to roam, and by how many square feet?