Q1. Find the equation of the line passing through the points (2, 3) and (4, 7).

Background

Topic: Linear Equations

This question tests your ability to find the equation of a line given two points. This is a fundamental skill in college algebra, involving slope calculation and using the point-slope or slope-intercept form.

Key Terms and Formulas:

• Slope ():

• Point-slope form:

• Slope-intercept form:

Step-by-Step Guidance

1. Identify the coordinates: and .

2. Calculate the slope using .

3. Plug the slope and one point into the point-slope form: .

4. Simplify the equation to get it into slope-intercept form ().

Try solving on your own before revealing the answer!

Q2. Solve the equation for .

Background

Topic: Solving Linear Equations

This question tests your ability to solve a basic linear equation for the variable .

Key Terms and Formulas:

• Linear equation: An equation of the form .

• Solving for : Isolate by performing inverse operations.

Step-by-Step Guidance

1. Add 5 to both sides to isolate the term with .

2. Divide both sides by 2 to solve for .

Try solving on your own before revealing the answer!

Q3. Graph the equation .

Background

Topic: Graphing Linear Equations

This question tests your ability to graph a linear equation using its slope and y-intercept.

Key Terms and Formulas:

• Slope-intercept form:

• Slope (): Indicates the steepness and direction of the line.

• Y-intercept (): The point where the line crosses the y-axis.

Step-by-Step Guidance

1. Identify the slope () and y-intercept ().

2. Plot the y-intercept (0, 4) on the graph.

3. Use the slope to find another point: from (0, 4), move down 2 units and right 1 unit.

4. Draw the line through these points.

Try graphing on your own before revealing the answer!

Q4. Find the coordinates of point H on the graph.

Background

Topic: Coordinate Geometry

This question tests your ability to read and interpret coordinates from a graph.

Key Terms and Formulas:

• Coordinates: values that specify a point's location on the plane.

Step-by-Step Guidance

1. Locate point H on the graph.

2. Read the x-coordinate (horizontal axis) and y-coordinate (vertical axis).

Try identifying the coordinates before revealing the answer!

Q5. Simplify the expression .

Background

Topic: Combining Like Terms

This question tests your ability to simplify algebraic expressions by combining like terms.

Key Terms and Formulas:

• Like terms: Terms with the same variable and exponent.

• Combine like terms by adding their coefficients.

Step-by-Step Guidance

1. Identify like terms: and ; and .

2. Add the coefficients of like terms together.

Try simplifying on your own before revealing the answer!

Q6. Solve the quadratic equation .

Background

Topic: Solving Quadratic Equations

This question tests your ability to solve quadratic equations by factoring.

Key Terms and Formulas:

• Quadratic equation:

• Factoring: Expressing the equation as a product of binomials.

Step-by-Step Guidance

1. Identify , , .

2. Find two numbers that multiply to and add to .

3. Write the equation in factored form.

Try factoring on your own before revealing the answer!

Q7. Find the distance between the points (1, 2) and (4, 6).

Background

Topic: Distance Formula

This question tests your ability to use the distance formula to find the length between two points in the coordinate plane.

Key Terms and Formulas:

• Distance formula:

Step-by-Step Guidance

1. Identify the coordinates: and .

2. Calculate the differences: and .

3. Square the differences and add them together.

4. Take the square root of the sum.

Try calculating the distance before revealing the answer!