IM2 MIDTERM REVIEW

Front

What is the formula for calculating the future value of an investment compounded monthly?

Back

The future value (FV) can be calculated using the formula: FV = P(1 + r/n)^(nt), where P is the principal amount, r is the annual interest rate (decimal), n is the number of times interest is compounded per year, and t is the number of years.

Front

What is the product of the binomials (a + b)(a - b)?

Back

The product is a^2 - b^2, which is known as the difference of squares.

Front

How do you solve a quadratic equation by factoring?

Back

To solve a quadratic equation by factoring, express the equation in the form ax^2 + bx + c = 0, then factor it into the form (px + q)(rx + s) = 0, and set each factor equal to zero to find the values of x.

Front

What is the factored form of the quadratic expression 3x^2 - 5x - 12?

Back

The factored form is (3x + 4)(x - 3).

Front

What is the product of (3x^2 - 4y)(3x^2 + 4y)?

Back

The product is 9x^4 - 16y^2, which is also a difference of squares.

Front

What is the formula for compound interest?

Back

The formula for compound interest is A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the number of years.

Front

What does it mean to factor a polynomial?

Back

Factoring a polynomial means expressing it as a product of its factors, which are polynomials of lower degrees.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a), used to find the roots of a quadratic equation ax^2 + bx + c = 0.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b^2 - 4ac) determines the nature of the roots of the quadratic equation: if it's positive, there are two distinct real roots; if it's zero, there is one real root; if it's negative, there are two complex roots.

Front

What is the difference between a rational and an irrational number?

Back

A rational number can be expressed as a fraction of two integers, while an irrational number cannot be expressed as a simple fraction.