Practice Set 8
- Problem #1: What is the smallest positive integer x such that the value 1+30x is not a prime number?
- Problem #2: Let us use a semisphere to approximate the shape of a brain. The diameter of your brain is 90% of the diameter of my brain. What is the ratio of the volume of your brain to the volume of my brain? Express your answer as a common fraction.
- Problem #3: What is the greatest positive integer less than the square root of 321?
- Problem #4: What integer is closest to √70? Do not use a calculator.
- Problem #5: Baby Einstein is playing Connect-the-Dots...but on a coordinate plane! The point labeled 1 is at (7.5, 10.4). The point labeled 2 is at (12.4, 0.6). What is the slope of the line that Baby Einstein draws connecting points 1 and 2?
- Problem #6: Baby Einstein forms a triangle by connecting the points A(2, 2), B(2, 5), and C(6, 2). What is the perimeter of this triangle?
- Problem #7: The number of diagonals in a convex regular polygon is the same as the number of sides in that polygon. What is the measure of an interior angle of this polygon, in degrees?
- Problem #8: Izzy and Sam are racing their remote-control cars. Izzy's car moves at a speed of 3 meters per second. She agrees to give a 16-meter head start to Sam, whose car moves at 2.5 meters per second. The race ends in a tie. How many meters did Izzy's car drive?
- Problem #9: What is the sum of the greatest and smallest prime factors of 111?
- Problem #10: Each term in a sequence is the sum of the previous two terms. If the sequence contains the terms a, b, c, 20, 33, 53, in that order, what is the value of a?
Solutions
