College Algebra Practice Exam Guidance

Q1. Subtract and simplify: $(7 - 6i) - (6 + 8i)$

Background

Topic: Complex Numbers

This question tests your ability to perform operations (subtraction) with complex numbers and simplify the result.

Key Terms and Formulas:

• Complex number: $a + bi$, where $a$ is the real part and $b$ is the imaginary part.

• Subtraction: $(a + bi) - (c + di) = (a - c) + (b - d)i$

Step-by-Step Guidance

1. Write both complex numbers: $7 - 6i$ and $6 + 8i$.

2. Subtract the real parts: $7 - 6$.

3. Subtract the imaginary parts: $-6i - 8i$.

4. Combine the results to form a new complex number.

Try solving on your own before revealing the answer!

Final Answer: $1 - 14i$

Subtracting the real and imaginary parts gives $1$for the real part and$-14$ for the imaginary part.

Q2. Multiply: $\sqrt{-16} \cdot \sqrt{-36}$

Background

Topic: Imaginary Numbers and Radical Operations

This question tests your understanding of multiplying square roots of negative numbers, which involves imaginary numbers.

Key Terms and Formulas:

• Imaginary unit: $i$, where $i^2 = -1$

• $\sqrt{-a} = i\sqrt{a}$ for $a > 0$

• Multiplication of radicals: $\sqrt{a} \cdot \sqrt{b} = \sqrt{ab}$

Step-by-Step Guidance

1. Rewrite $\sqrt{-16}$ as $\sqrt{16} \cdot i$ and $\sqrt{-36}$ as $\sqrt{36} \cdot i$.

2. Calculate $\sqrt{16}$ and $\sqrt{36}$ separately.

3. Multiply the results together, including the $i$ terms.

4. Recall that $i \cdot i = i^2 = -1$.

Try solving on your own before revealing the answer!

Final Answer: $-24$

Multiplying the values and using $i^2 = -1$ gives a real number result.

Q3. Use the graphing tool to graph the function.

Background

Topic: Graphing Functions

This question tests your ability to plot a function on a coordinate grid, which is a fundamental skill in college algebra.

Key Terms and Formulas:

• Coordinate axes: $x$ (horizontal), $y$ (vertical)

• Graphing: Plotting points that satisfy the function's equation

Step-by-Step Guidance

1. Identify the function you need to graph (not shown in the image, but typically given in the question).

2. Determine key points (such as intercepts, vertex, or other relevant features).

3. Plot these points on the provided grid.

4. Draw the curve or line that represents the function, connecting the points smoothly.

Try graphing the function on your own before revealing the answer!

Final Answer: Graph of the function (specific function not provided)

The graph should accurately represent the function's behavior based on the points and features you identified.

Q4. Choose the graph of the solution set.

Background

Topic: Solution Sets and Interval Notation

This question tests your ability to interpret and select the correct graph that represents a solution set, often related to inequalities or intervals.

Key Terms and Formulas:

• Solution set: The set of values that satisfy a given equation or inequality

• Interval notation: Describes the range of values included in the solution set

• Graphing solution sets: Visual representation on a number line

Step-by-Step Guidance

1. Read the solution set or inequality (not shown in the image, but typically given in the question).

2. Determine the interval or set of values included in the solution.

3. Match the interval to the correct graph option (A, B, C, or D).

4. Check for open or closed endpoints, arrows, and the range covered.

Try matching the solution set to the correct graph before revealing the answer!

Final Answer: Correct graph option (A, B, C, or D)

The correct graph will visually represent the interval or solution set described in the question.