Step-by-Step Guidance for Mixed Algebra Review

Q1. What is the slope of a line where the graph is: y = -3x + 2?

Background

Topic: Slope-Intercept Form

This question tests your understanding of the slope-intercept form of a linear equation and how to identify the slope.

Key Terms and Formulas:

• Slope-intercept form: $y = mx + b$

• $m$ is the slope, $b$ is the y-intercept

Step-by-Step Guidance

1. Identify the equation: $y = -3x + 2$

2. Compare it to the slope-intercept form $y = mx + b$

3. Determine which part of the equation represents the slope ($m$)

Try solving on your own before revealing the answer!

Q2. Find the equation of the line with slope 2 and passing through the point (3, 6).

Background

Topic: Point-Slope Form

This question tests your ability to write the equation of a line given a slope and a point.

Key Terms and Formulas:

• Point-slope form: $y - y_1 = m(x - x_1)$

• Where $m$ is the slope, $(x_1, y_1)$ is the given point

Step-by-Step Guidance

1. Identify the slope ($m = 2$) and the point ($(x_1, y_1) = (3, 6)$)

2. Substitute these values into the point-slope formula: $y - y_1 = m(x - x_1)$

3. Write the equation with the substituted values

Try solving on your own before revealing the answer!

Q3. Find the equation of the line passing through (2, 6) and perpendicular to the line y = 3x + 5.

Background

Topic: Perpendicular Lines and Point-Slope Form

This question tests your understanding of how to find the equation of a line perpendicular to a given line and passing through a specific point.

Key Terms and Formulas:

• Slope of perpendicular lines: If $m$ is the slope of the original line, the perpendicular slope is $-\frac{1}{m}$

• Point-slope form: $y - y_1 = m(x - x_1)$

Step-by-Step Guidance

1. Identify the slope of the given line ($y = 3x + 5$ has slope $m = 3$)

2. Find the perpendicular slope: $m_{\text{perp}} = -\frac{1}{3}$

3. Use the point-slope form with the point $(2, 6)$ and the perpendicular slope

Try solving on your own before revealing the answer!

Q4. Convert 47,000 to scientific notation.

Background

Topic: Scientific Notation

This question tests your ability to convert a standard number into scientific notation.

Key Terms and Formulas:

• Scientific notation: $a \times 10^n$ where $1 \leq a < 10$ and $n$ is an integer

Step-by-Step Guidance

1. Identify the significant digits in 47,000

2. Count how many places the decimal moves to get a number between 1 and 10

3. Write the number as $a \times 10^n$

Try solving on your own before revealing the answer!

Q5. Convert 0.00042 to scientific notation.

Background

Topic: Scientific Notation

This question tests your ability to convert a small decimal number into scientific notation.

Key Terms and Formulas:

• Scientific notation: $a \times 10^n$

Step-by-Step Guidance

1. Identify the significant digits in 0.00042

2. Count how many places the decimal moves to get a number between 1 and 10

3. Write the number as $a \times 10^n$

Try solving on your own before revealing the answer!

Q6. Expand the following: (3x + 2)(x - 5)

Background

Topic: Expanding Binomials

This question tests your ability to expand two binomials using the distributive property (FOIL method).

Key Terms and Formulas:

• FOIL method: First, Outside, Inside, Last

Step-by-Step Guidance

1. Multiply the first terms: $3x \times x$

2. Multiply the outside terms: $3x \times (-5)$

3. Multiply the inside terms: $2 \times x$

4. Multiply the last terms: $2 \times (-5)$

5. Add all the terms together

Try solving on your own before revealing the answer!

Q7. Expand the following: (2x - 3)(4x + 1)

Background

Topic: Expanding Binomials

This question tests your ability to expand two binomials using the distributive property (FOIL method).

Key Terms and Formulas:

• FOIL method: First, Outside, Inside, Last

Step-by-Step Guidance

1. Multiply the first terms: $2x \times 4x$

2. Multiply the outside terms: $2x \times 1$

3. Multiply the inside terms: $-3 \times 4x$

4. Multiply the last terms: $-3 \times 1$

5. Add all the terms together

Try solving on your own before revealing the answer!

Q8. Simplify the following: x^2 + x^2

Background

Topic: Combining Like Terms

This question tests your ability to combine like terms in an algebraic expression.

Key Terms and Formulas:

• Like terms: Terms with the same variable and exponent

Step-by-Step Guidance

1. Identify the like terms: $x^2$ and $x^2$

2. Add the coefficients of the like terms

Try solving on your own before revealing the answer!

Q9. Simplify the following and write the final answer in standard form: -2m + 12m^2 - 2m

Background

Topic: Combining Like Terms and Standard Form

This question tests your ability to combine like terms and write the answer in standard form (descending order of exponents).

Key Terms and Formulas:

• Standard form: Arrange terms in descending order of exponents

• Like terms: Terms with the same variable and exponent

Step-by-Step Guidance

1. Identify like terms: $-2m$ and $-2m$

2. Combine the coefficients of like terms

3. Write the expression in standard form, with the highest exponent first

Try solving on your own before revealing the answer!