Mathematics & Problem Solving Flashcards

What is the value of 3(x − 2) when x = 4?

Answer: 6

To find the value of 3(x − 2) when x = 4, substitute 4 for x in the expression. First, calculate the value inside the parentheses: 4 - 2 = 2. Then, multiply this result by 3: 3 * 2 = 6. Therefore, the value of the expression is 6.

What is the perimeter of a rectangle with length 8 cm and width 5 cm?

Answer: 26 cm

The perimeter of a rectangle is calculated by adding the lengths of all four sides. The formula is P = 2 * (length + width). For a rectangle with length 8 cm and width 5 cm, the perimeter is 2 * (8 cm + 5 cm) = 2 * 13 cm = 26 cm.

If a triangle has angles of 50° and 60°, what is the measure of the third angle?

Answer: 70°

The sum of the interior angles in any triangle always equals 180 degrees. If two angles are given as 50° and 60°, their sum is 110°. To find the third angle, subtract this sum from 180°: 180° - 110° = 70°.

What is the greatest common factor (GCF) of 18 and 24?

Answer: 6

The greatest common factor (GCF) is the largest number that divides evenly into two or more numbers. The factors of 18 are 1, 2, 3, 6, 9, 18. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. The largest number common to both lists is 6.

Which number is a prime number?

Answer: 17

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Of the given options, 4 is divisible by 2, 9 by 3, and 21 by 3 and 7. Only 17 is solely divisible by 1 and 17, making it a prime number.

If the mean of five numbers is 12, what is their total sum?

Answer: 60

The mean (average) of a set of numbers is calculated by dividing their sum by the count of the numbers. Therefore, if the mean is 12 and there are five numbers, their total sum can be found by multiplying the mean by the count: 12 * 5 = 60.

What is 25% of 80?

Answer: 20

To calculate a percentage of a number, you can convert the percentage to a decimal or a fraction and then multiply. 25% is equivalent to 0.25 or 1/4. Therefore, 25% of 80 is 0.25 * 80 = 20, or (1/4) * 80 = 20.

Which operation is performed first in the expression 6 + 2 × (3 + 1)?

Answer: Parentheses

According to the order of operations (PEMDAS/BODMAS), calculations within parentheses are always performed first. In the expression 6 + 2 × (3 + 1), you must first calculate the sum inside the parentheses, which is (3 + 1) = 4. This step precedes any addition or multiplication outside the parentheses.

Which unit would you use to measure the volume of a liquid?

Answer: Liters

Liters are the standard metric unit for measuring the volume of liquids. While meters measure length, grams measure mass, and degrees measure temperature, liters are specifically used to quantify the space occupied by a liquid. For smaller volumes, milliliters (mL) are commonly used, where 1000 mL equals 1 liter.