1.
What is the sum of angles in a triangle?
Correct Answer
A. 180 degrees
Explanation
The sum of angles in a triangle is always 180 degrees. This is a fundamental property of Euclidean geometry where the internal angles, regardless of the triangle's type (whether it is equilateral, isosceles, or scalene), add up to 180 degrees. This rule arises from the fact that a triangle can be thought of as a portion of a larger shape, specifically a straight line (180 degrees), which is split into three angles when two lines intersect it from different points.
2.
If x + y = 10 and x - y = 2, what is x?
Correct Answer
C. 6
3.
What is the value of Pi (π) rounded to two decimal places?
Correct Answer
A. 3.14
Explanation
The value of Pi (π) rounded to two decimal places is 3.14. Pi is a mathematical constant representing the ratio of a circle's circumference to its diameter. It is an irrational number, meaning its decimal representation goes on indefinitely without repeating. The approximation of 3.14 is commonly used in calculations requiring moderate precision.
4.
How many sides does a hexagon have?
Correct Answer
A. 6
Explanation
A hexagon is a six-sided polygon. This geometric figure is part of the family of n-gons, where 'n' represents the number of sides. A regular hexagon has all sides of equal length and each internal angle will be 120 degrees, but the defining characteristic that identifies any hexagon is simply the count of its sides, which is six.
5.
Which number is considered a prime number?
Correct Answer
C. 29
Explanation
The number 29 is a prime number. Prime numbers are defined as numbers greater than 1 that have no divisors other than 1 and themselves. Testing for primality involves checking for divisibility by any smaller prime numbers; since 29 is not divisible by any prime number less than its square root, it is confirmed as prime.
6.
What is the square root of 144?
Correct Answer
B. 12
Explanation
The square root of 144 is 12. This is calculated by determining what number, when multiplied by itself, equals 144. The operation of finding a square root is the inverse of squaring a number (12^2 = 144). Square roots are fundamental in various fields of mathematics, including geometry and algebra.
7.
What is 15% of 200?
Correct Answer
A. 30
Explanation
To find 15% of 200, convert the percentage to a decimal (15% = 0.15) and multiply it by the number. So, 0.15 x 200 = 30. This calculation is a basic example of finding a percentage of a number, a common operation in arithmetic and essential for understanding proportions and ratios.
8.
What is the next number in the sequence 2, 4, 8, 16?
Correct Answer
C. 32
Explanation
In the sequence 2, 4, 8, 16, each number is doubled to get the next. This pattern is a simple geometric progression where each term is multiplied by a common ratio (2) to get the next term. Following this pattern, doubling 16 results in 32, which is the next number in the sequence.
9.
If the area of a square is 49 sq units, what is the side length?
Correct Answer
B. 7 units
Explanation
If the area of a square is 49 square units, the side length can be found by taking the square root of the area. Since the area of a square is calculated as side length squared (s^2), if s^2 = 49, then s = √49 = 7 units. This relationship between the area and side length of a square is pivotal in understanding properties of squares.
10.
What is the result of 9 cubed (9^3)?
Correct Answer
A. 729
Explanation
The result of 9 cubed (9^3) is 729. Cubing a number is the operation of raising a number to the power of three (9 x 9 x 9). It is used extensively in volume calculations and in algebra for solving cubic equations. The cube of a number can also represent the number of units that make up a cube with sides of that length.