M1 Math Final Exam

What is the square root of 36?

• 8

• 7

• 6

• 5

Answer explanation

The square root of 36 is the number that, when multiplied by itself, equals 36. Since 6 x 6 = 36, the correct answer is 6.

What is the square root of 81?

• 6

• 7

• 8

• 9

Answer explanation

The square root of 81 is the number that, when multiplied by itself, equals 81. Since 9 x 9 = 81, the correct answer is 9.

• 25

• 5

• 15

• 50

Answer explanation

To solve 5^2, you multiply 5 by itself: 5 x 5 = 25. Therefore, the correct answer is 25.

• 0.1

• 100

• 1

• 10

Answer explanation

To solve 10^2, we calculate 10 raised to the power of 2, which means 10 multiplied by itself: 10 x 10 = 100. Therefore, the correct answer is 100.

Which of the following is an irrational number?

• 9

• 1.25

Answer explanation

The number \(\sqrt{2}\) is irrational because it cannot be expressed as a fraction of two integers. In contrast, 9 is an integer, \(\frac{4}{2}\) equals 2 (a rational number), and 1.25 is also rational.

Which of the following is a rational number?

• 2

• π

• None of the above

Answer explanation

A rational number is any number that can be expressed as a fraction of two integers. The number 2 can be written as 2/1, making it rational. In contrast, π and √3 are irrational numbers.

What type of number is -5?

• Natural number

• Whole number

• Integer

• All of the above

Answer explanation

-5 is an integer because it is a whole number that can be positive, negative, or zero. It is not a natural number (which are positive) or a whole number (which are non-negative). Thus, the correct answer is 'Integer'.

The set of natural numbers includes:

• Negative integers

• Zero and positive numbers (n≥0)

• All integers

• Only positive numbers (n>0)

Answer explanation

The set of natural numbers includes only positive integers (n>0). It does not include negative integers or zero, which are not considered natural numbers in standard definitions.

What categories include: π

• Irrational numbers

• Rational numbers

• Rational numbers & integers

• Rational numbers, integers, & whole numbers

Answer explanation

π is an irrational number because it cannot be expressed as a fraction of two integers. Therefore, the correct category for π is 'Irrational numbers', while the other options include rational numbers, which do not apply.

Which of the following is NOT the name of a triangle?

• Scalene

• Obtuse

• Equilateral

• Parallelogram

Answer explanation

A scalene triangle has all sides of different lengths, an obtuse triangle has one angle greater than 90 degrees, and an equilateral triangle has all sides equal. A parallelogram is a four-sided figure, not a triangle.