HA2T Semester 1 PRACTICE Final 2

Front

What is the average rate of change of a function f(x) from x = -3 to x = -2?

Back

The average rate of change is calculated as \( \frac{f(-2) - f(-3)}{-2 - (-3)} \). For \( f(x) = 2x^2 + 12x + 16 \), the average rate of change is 2.

Front

Factor the polynomial: x^4 + 27x

Back

The factored form is \( x(x + 3)(x^2 - 3x + 9) \).

Front

Simplify the complex number: (3i)(-5 + i)

Back

The simplified form is \( -3 - 15i \).

Front

Subtract the fractions: \( \frac{5}{x-3} - \frac{1}{x} \)

Back

The result is \( \frac{4x + 3}{x^2 - 3x} \).

Front

What is the logarithmic identity for \( \log\left(\frac{x}{y}\right) \)?

Back

The identity is \( \log x - \log y \).

Front

Define the average rate of change of a function.

Back

The average rate of change of a function over an interval [a, b] is given by \( \frac{f(b) - f(a)}{b - a} \).

Front

What is the factored form of a quadratic equation?

Back

A quadratic equation \( ax^2 + bx + c \) can be factored as \( a(x - r_1)(x - r_2) \), where \( r_1 \) and \( r_2 \) are the roots.

Front

How do you multiply complex numbers?

Back

To multiply complex numbers, use the distributive property and combine like terms. For example, \( (a + bi)(c + di) = ac + adi + bci + bdi^2 \).

Front

What is the formula for subtracting fractions?

Back

To subtract fractions \( \frac{a}{b} - \frac{c}{d} \), find a common denominator: \( \frac{ad - bc}{bd} \).

Front

What is the definition of a logarithm?

Back

A logarithm \( \log_b(a) \) answers the question: 'To what exponent must the base b be raised to produce a?' It is defined as \( b^y = a \).