M1 Core Midterm Review

What is the square root of 49?

• 5

• 6

• 7

• 8

Answer explanation

The square root of 49 is the number that, when multiplied by itself, equals 49. Since 7 x 7 = 49, the correct answer is 7.

What is the square root of 64?

• 6

• 7

• 8

• 9

Answer explanation

The square root of 64 is the number that, when multiplied by itself, equals 64. Since 8 x 8 = 64, the correct answer is 8.

Which of the following is an irrational number?

• √10

• √16

• 4

• 1.25

Answer explanation

√10 is an irrational number because it cannot be expressed as a fraction of two integers. In contrast, √16 equals 4 (a whole number), and 1.25 is a rational number (can be expressed as 5/4).

Which of the following is a rational number?

• √2

• 1/4

• None of the above

Answer explanation

A rational number is any number that can be expressed as a fraction of two integers. 1/4 is a fraction (1 divided by 4), making it a rational number. In contrast, √2 and π are irrational numbers.

What type of number is −3?

• Natural number

• Whole number

• Integer

• All of the above

Answer explanation

−3 is not a natural number or a whole number, as both are non-negative. However, it is an integer, which includes negative numbers. Therefore, the correct answer is 'Integer'.

The set of whole numbers includes:

• Negative integers

• Zero and positive numbers (n≥0)

• All integers

• Only positive numbers (n>0)

Answer explanation

The set of whole numbers includes zero and all positive numbers (n≥0). It does not include negative integers or only positive numbers, making 'Zero and positive numbers (n≥0)' the correct choice.

• Irrational numbers

• Rational numbers

• Rational numbers & integers

• Rational numbers, integers, & whole numbers

Answer explanation

The correct choice is 'Irrational numbers' because π (pi) cannot be expressed as a fraction of two integers, making it irrational. The other categories include only numbers that can be expressed as fractions.

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

• Isosceles

• Right

• Acute

• Parallelogram

Answer explanation

The correct answer is 'Parallelogram' because it is a type of quadrilateral, not a triangle. The other options—Isosceles, Right, and Acute—are all classifications of triangles based on their sides and angles.

Which of the following names a triangle based on its angles?

• Isosceles

• Equilateral

• Scalene

• Obtuse

Answer explanation

The term 'Obtuse' describes a triangle with one angle greater than 90 degrees, categorizing it based on angles. In contrast, Isosceles, Equilateral, and Scalene refer to side lengths, not angles.

Which of the following names a triangle by its sides?

• Obtuse

• Right

• Acute

• Scalene

Answer explanation

A triangle can be classified by its sides as scalene, isosceles, or equilateral. The term 'scalene' specifically refers to a triangle with all sides of different lengths, making it the correct choice here.