Math 2 - Semester 1 Final Review (2024)

Front

What is the product of the binomials \( (4x-5)(2x-4) \)?

Back

The product is \( 8x^2 - 26x + 20 \).

Front

What is the probability of drawing an eight followed by a two from a standard deck of cards without replacement?

Back

The probability is \( \frac{4}{663} \).

Front

Convert the quadratic equation \( y = x^2 + 16x + 54 \) to vertex form.

Back

The vertex form is \( y = (x + 8)^2 - 10 \).

Front

Solve the quadratic equation \( x^2 + 8x - 25 = 0 \).

Back

The solutions are \( x = -4 \pm \sqrt{41} \).

Front

What is the factored form of the expression \( d^2 + d - 20 \)?

Back

The factored form is \( (d - 4)(d + 5) \).

Front

What is the formula for the quadratic equation?

Back

The quadratic formula is \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \).

Front

What is the vertex of the parabola represented by the equation \( y = ax^2 + bx + c \)?

Back

The vertex is at \( \left(-\frac{b}{2a}, f(-\frac{b}{2a})\right) \).

Front

What is the discriminant of a quadratic equation and what does it indicate?

Back

The discriminant is \( b^2 - 4ac \). It indicates the nature of the roots: if positive, two real roots; if zero, one real root; if negative, no real roots.

Front

How do you find the probability of independent events?

Back

For independent events, multiply the probabilities of each event: \( P(A \text{ and } B) = P(A) \times P(B) \).

Front

What is the standard form of a quadratic equation?

Back

The standard form is \( y = ax^2 + bx + c \), where \( a \neq 0 \).