Mathematical Problem Solving Challenges

The video tutorial covers a series of math problems from the 2018 AMC 8 exam, including topics such as scale models, product value calculation, circle counting games, area calculation of geometric figures, long expression evaluation, travel time calculation, divisibility and remainder problems, mean calculation from a bar graph, tiling a room, and harmonic mean calculation. Each problem is explained step-by-step, demonstrating various mathematical techniques and problem-solving strategies.

What is the height of the replica of the United States Capitol at the amusement park if the original is 289 feet tall and the scale is 1:20?

• 12 feet

• 15 feet

• 13 feet

• 14 feet

What is the final product when simplifying the sequence 2, 3/2, 4/3, 5/4, 6/5, 7/6?

• 1

• 7

• 0

• 2

In a counting game, who is the last person remaining if they leave the circle when the number is a multiple of 7 or contains the digit 7?

• C

• B

• D

• A

What is the area of a 12-sided figure drawn on a one-by-one graph paper?

• 12 cm²

• 15 cm²

• 13 cm²

• 14 cm²

What is the result of the expression 1 - 2 + 3 - 4 + ... + 2017 - 2018 + 2019?

• 1009

• 1011

• 1012

• 1010

How many minutes did the entire trip take if the speed on the highway is three times the speed on the coastal road?

• 70 minutes

• 80 minutes

• 100 minutes

• 90 minutes

What is the remainder when the number 20187 is divided by 8?

• 2

• 4

• 1

• 3

What is the mean number of exercise days reported by students if the total is 109 days over 25 students?

• 4.36

• 4.37

• 4.35

• 4.34

How many tiles in total are needed to tile a 12 by 16 foot room with a border of 1x1 tiles and the rest with 2x2 tiles?

• 86

• 88

• 85

• 87

What is the harmonic mean of the numbers 1, 2, and 4?

• 12/7

• 6/7

• 7/12

• 7/6