Algebraic Concepts and Problem Solving

Front

What is the formula for the perimeter of a square?

Back

The perimeter (P) of a square is given by the formula P = 4s, where s is the length of one side.

Front

If the area of a square is 81 ft², what is the length of one side?

Back

The length of one side (s) is found by taking the square root of the area: s = √(81) = 9 feet.

Front

What is the relationship between area and perimeter in a square?

Back

The area of a square is related to the perimeter through the side length: Area = s² and Perimeter = 4s.

Front

What is the result of simplifying (−6)² − 4²?

Back

The result is 20, calculated as 36 - 16 = 20.

Front

What is the formula for calculating a percentage increase?

Back

To calculate a percentage increase, use the formula: New Price = Original Price × (1 + Percentage Increase).

Front

If a store marks up a price by 60%, how do you calculate the selling price?

Back

Selling Price = Cost Price × (1 + 0.60). For a cost of $1.50, Selling Price = $1.50 × 1.60 = $2.40.

Front

What is the process for multiplying mixed numbers?

Back

Convert mixed numbers to improper fractions, multiply the fractions, and convert back to a mixed number if necessary.

Front

What is the solution to the equation a² + 2a - 24 = 0?

Back

The solutions are a = -6 and a = 4, found using factoring or the quadratic formula.

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the roots of a quadratic equation: x = (-b ± √(b² - 4ac)) / (2a).

Front

What does it mean to simplify an expression?

Back

Simplifying an expression means to reduce it to its simplest form, combining like terms and performing operations.