AMC 10

• 7

• 21

• 49

• 64

• 91

Tags

CCSS.6.EE.A.1

CCSS.6.NS.B.2

• 16

• 17

• 18

• 19

• 20

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.2

CCSS.HSA.REI.B.4

CCSS.HSA.SSE.A.1

What is the maximum number of balls of clay of radius 2 that can completely fit inside a cube of side length 6 assuming the balls can be reshaped but not compressed before they are packed in the cube?

• 3

• 4

• 5

• 6

• 7

Tags

CCSS.HSG.GMD.A.3

Mr. Lopez has a choice of two routes to get to work. Route A is 6 miles long, and his average speed along this route is 30 miles per hour. Route B is 5 miles long, and his average speed along this route is 40 miles per hour, except for a 1/2 mile stretch in a school zone where his average speed is 20 miles per hour. By how many minutes is Route B quicker than Route A?

• 11/4

• 15/4

• 9/2

• 11/2

• 27/4

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.2

CCSS.HSA.REI.B.3

CCSS.HSA.SSE.A.1

The six-digit number 20210A is prime for only one digit What is A?

• 1

• 3

• 5

• 7

• 9

Tags

CCSS.6.EE.A.2

CCSS.6.EE.B.5

CCSS.6.EE.B.6

Elmer the emu takes 44 equal strides to walk between consecutive telephone poles on a rural road. Oscar the ostrich can cover the same distance in 12 equal leaps. The telephone poles are evenly spaced, and the 41st pole along this road is exactly one mile ( 5280 feet) from the first pole. How much longer, in feet, is Oscar's leap than Elmer's stride?

• 6

• 8

• 10

• 11

• 15

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.2

CCSS.HSA.SSE.A.1

CCSS.HSN.Q.A.1

A two-digit positive integer is said to be cuddly if it is equal to the sum of its nonzero tens digit and the square of its units digit. How many two-digit positive integers are cuddly?

• 0

• 1

• 2

• 3

• 4

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

When a certain unfair die is rolled, an even number is 3 times as likely to appear as an odd number. The die is rolled twice. What is the probability that the sum of the numbers rolled is even?

• 3/8

• 4/9

• 5/9

• 9/16

• 5/8

Tags

CCSS.HSS.CP.A.1

CCSS.HSS.CP.A.2

CCSS.HSS.CP.B.7

CCSS.HSS.CP.B.8

CCSS.HSS.MD.A.3

A school has 100 students and 5 teachers. In the first period, each student is taking one class, and each teacher is teaching one class. The enrollments in the classes are 50,20,20,5 and 5 . Let be the average value obtained if a teacher is picked at random and the number of students in their class is noted. Let be the average value obtained if a student was picked at random and the number of students in their class, including the student, is noted. What is t-s ?

• -18.5

• -13.5

• 0

• 13.5

• 18.5

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.MD.A.2

CCSS.HSS.MD.A.3

CCSS.HSS.MD.B.5

Emily sees a ship traveling at a constant speed along a straight section of a river. She walks parallel to the riverbank at a uniform rate faster than the ship. She counts 210 equal steps walking from the back of the ship to the front. Walking in the opposite direction, she counts 42 steps of the same size from the front of the ship to the back. In terms of Emily's equal steps, what is the length of the ship?

• 70

• 84

• 98

• 105

• 126

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.2

CCSS.HSA.REI.B.3

CCSS.HSA.SSE.A.1