1.
What is the result of 15 divided by 3 times 2 plus 5?
Correct Answer
C. 15
Explanation
To solve the expression 15 ÷ 3 x 2 + 5, we must follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). In this case, we first perform the division: 15 ÷ 3 = 5. Next, we proceed with the multiplication: 5 x 2 = 10. Finally, we add 5 to get the result: 10 + 5 = 15.
2.
Which term describes a polygon with all sides and angles equal?
Correct Answer
A. Regular
Explanation
In geometry, a polygon with all sides and all angles equal is specifically termed a "regular polygon." It's important to differentiate this from "equilateral," which refers only to the equality of sides. A square, for example, is a regular polygon because it has both equal sides and equal angles, while a rhombus, with equal sides but potentially unequal angles, is not.
3.
Simplify: (-3)^2
Correct Answer
C. 9
Explanation
When a negative number is squared, the result is always positive. This is because squaring a number involves multiplying it by itself. In the case of (-3)², we have (-3) x (-3). The multiplication of two negative numbers always yields a positive product, hence (-3)² = 9.
4.
What is the prime factorization of 60?
Correct Answer
A. 2^2 x 3 x 5
Explanation
Prime factorization is the process of expressing a number as the product of its prime factors. To find the prime factorization of 60, we start by dividing it by the smallest prime number, 2. This gives us 30. We can divide by 2 again to get 15. 15 is divisible by 3, resulting in 5, which is a prime number. Therefore, the prime factorization of 60 is 2 x 2 x 3 x 5, which can be written more compactly as 2² x 3 x 5.
5.
Calculate the area of a triangle with a base of 10 cm and a height of 14 cm.
Correct Answer
B. 70 cm squared
Explanation
Calculating the area of a triangle involves utilizing the formula: (1/2) x base x height. In this specific scenario, the triangle's base measures 10 cm and its height is 14 cm. Substituting these values into the formula, we obtain (1/2) x 10 cm x 14 cm. Simplifying this expression, we arrive at 5 cm x 14 cm, which ultimately yields 70 cm² as the area of the triangle.
6.
Solve for x if 4x + 5 = 21.
Correct Answer
A. 4
Explanation
To determine the value of 'x' in the equation 4x + 5 = 21, we must isolate 'x' by employing inverse operations. Initially, we subtract 5 from both sides of the equation, resulting in 4x = 16. To fully isolate 'x', we divide both sides of the equation by 4, which ultimately yields x = 4.
7.
What is the volume of a cube with side length 3 cm?
Correct Answer
C. 27 cm cubed
Explanation
Calculating the volume of a cube entails cubing the length of one of its sides, which is mathematically represented as side x side x side. In this instance, the cube possesses a side length of 3 cm. Therefore, its volume is computed as 3 cm x 3 cm x 3 cm, resulting in a volume of 27 cm³.
8.
If the circumference of a circle is 31.4 cm, what is its diameter? (Use pi approximately equal to 3.14)
Correct Answer
A. 10 cm
Explanation
The relationship between a circle's circumference (C) and its diameter (d) is given by the formula C = πd, where π (pi) is a mathematical constant approximately equal to 3.14. To determine the diameter when the circumference is known, we rearrange the formula to d = C/π. Substituting the given circumference of 31.4 cm, we get d = 31.4 cm / 3.14 = 10 cm.
9.
Convert 1500 milliliters to liters.
Correct Answer
A. 1.5 liters
Explanation
Within the metric system, units are interrelated by powers of 10. Specifically, 1 liter (L) is composed of 1000 milliliters (ml). Consequently, converting a quantity from milliliters to liters necessitates dividing the number of milliliters by 1000. In this case, 1500 ml ÷ 1000 yields 1.5 L.
10.
What is the probability of rolling an even number on a standard six-sided die?
Correct Answer
A. 1/2
Explanation
The concept of probability is defined as the ratio of favorable outcomes to the total number of possible outcomes. A standard six-sided die features three faces displaying even numbers (2, 4, and 6) out of a total of six faces. Therefore, the probability of obtaining an even number upon rolling the die is 3/6, which can be simplified to 1/2.