Competition · AMC preparation · step 4 of 4

AMC 10 2007B: all 25 problems

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

AMC 10 2007B #1 grade 4+ geometry-2d
Isabella's house has 3 bedrooms. Each bedroom is 12 feet long, 10 feet wide, and 8 feet high. Isabella must paint the wa…
AMC 10 2007B #2 grade 6+ arithmetic
Define the operation ⋆ by a ⋆ b = (a+b)b. What is (3 ⋆ 5) - (5 ⋆ 3)?
AMC 10 2007B #3 grade 6+ rate-ratio
A college student drove his compact car 120 miles home for the weekend and averaged 30 miles per gallon. On the return t…
AMC 10 2007B #4 grade 8+ geometry-2d
The point O is the center of the circle circumscribed about △ ABC, with ∠ BOC=120° and ∠ AOB=140°, as shown. What is the…
AMC 10 2007B #5 grade 5+ arithmetic
In a certain land, all Arogs are Brafs, all Crups are Brafs, all Dramps are Arogs, and all Crups are Dramps. Which of th…
AMC 10 2007B #6 grade 6+ arithmetic
The 2007 AMC 10 will be scored by awarding 6 points for each correct response, 0 points for each incorrect response, and…
AMC 10 2007B #7 grade 8+ geometry-2d
All sides of the convex pentagon ABCDE are of equal length, and ∠ A= ∠ B = 90°. What is the degree measure of ∠ E?
AMC 10 2007B #8 grade 7+ arithmetic
On the trip home from the meeting where this AMC10 was constructed, the Contest Chair noted that his airport parking rec…
AMC 10 2007B #9 grade 4+ rate-ratio
A cryptographic code is designed as follows. The first time a letter appears in a given message it is replaced by the le…
AMC 10 2007B #10 grade 6+ geometry-2d
Two points B and C are in a plane. Let S be the set of all points A in the plane for which △ ABC has area 1. Which of th…
AMC 10 2007B #11 grade 8+ geometry-2d
A circle passes through the three vertices of an isosceles triangle that has two sides of length 3 and a base of length…
AMC 10 2007B #12 grade 8+ algebra
Tom's age is T years, which is also the sum of the ages of his three children. His age N years ago was twice the sum of…
AMC 10 2007B #13 grade 7+ geometry-2d
Two circles of radius 2 are centered at (2,0) and at (0,2). What is the area of the intersection of the interiors of the…
AMC 10 2007B #14 grade 6+ algebra
Some boys and girls are having a car wash to raise money for a class trip to China. Initially 40% of the group are girls…
AMC 10 2007B #15 grade 8+ geometry-2d
The angles of quadrilateral ABCD satisfy ∠ A=2 ∠ B=3 ∠ C=4 ∠ D. What is the degree measure of ∠ A, rounded to the neares…
AMC 10 2007B #16 grade 6+ arithmetic
A teacher gave a test to a class in which 10% of the students are juniors and 90% are seniors. The average score on the…
AMC 10 2007B #17 grade 8+ geometry-2d
Point P is inside equilateral △ ABC. Points Q, R, and S are the feet of the perpendiculars from P to AB, BC, and CA, res…
AMC 10 2007B #18 grade 8+ geometry-2d
A circle of radius 1 is surrounded by 4 circles of radius r as shown. What is r?
AMC 10 2007B #19 grade 7+ geometry-2d
The wheel shown is spun twice, and the randomly determined numbers opposite the pointer are recorded. The first number i…
AMC 10 2007B #20 grade 7+ geometry-2d
A set of 25 square blocks is arranged into a 5 × 5 square. How many different combinations of 3 blocks can be selected f…
AMC 10 2007B #21 grade 8+ geometry-2d
Right △ ABC has AB=3, BC=4, and AC=5. Square XYZW is inscribed in △ ABC with X and Y on AC, W on AB, and Z on BC. What i…
AMC 10 2007B #22 grade 7+ arithmetic
A player chooses one of the numbers 1 through 4. After the choice has been made, two regular four-sided (tetrahedral) di…
AMC 10 2007B #23 grade 8+ geometry-3d
A pyramid with a square base is cut by a plane that is parallel to its base and 2 units from the base. The surface area…
AMC 10 2007B #24 grade 6+ number-theory
Let n denote the smallest positive integer that is divisible by both 4 and 9, and whose base-10 representation consists…
AMC 10 2007B #25 grade 6+ number-theory
How many pairs of positive integers (a,b) are there such that a and b have no common factors greater than 1 and: a/b + 1…

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