Before we dive into the topics covered in this module, it's important to assess your current knowledge of Algebra 1. Take this benchmarking quiz to see how much you already know and to identify areas where you may need to focus your study.
Once you have completed the quiz, review your results and identify the topics where you scored the lowest. These topics will be important to focus on during the rest of the module. In the Benchmarking Quiz, you will be asked a series of multiple-choice questions that cover a range of topics in Algebra 1. The quiz is designed to help you assess your current knowledge and identify areas where you may need to focus your study. Once you have completed the quiz, you will be able to review your results and see which topics you need to work on. This will help you get the most out of the rest of the module and be better prepared for future studies in Algebra 1.
- What is the value of x in the equation 3x - 7 = 11?
[( )] x = 4 [(X)] x = 6 [( )] x = 8 [( )] x = 10 [[?]] Add 7 to both sides of the equation [[?]] Divide both sides of the equation by 3
- Simplify the expression: 4(2x - 3) + 5
[( )] 8x + 5 [( )] 8x - 7 [(X)] 8x - 12 [( )] 6x - 5 [[?]] Distribute 4 to both terms inside the parentheses [[?]] Add 5 to the result
- Solve the linear equation: 5x - 3 = 2x + 4
[(X)] x = 7/3 [( )] x = 2/3 [( )] x = 3/7 [( )] x = 1 [[?]] Start by subtracting 2x from both sides [[?]] Next, add 3 to both sides and then divide by 3
- Factor the quadratic expression: x^2 - 5x + 6
[(X)] (x - 2)(x - 3) [( )] (x - 1)(x - 4) [( )] (x - 3)(x - 4) [( )] (x - 1)(x - 6) [[?]] Look for two numbers that multiply to 6 and add to -5 [[?]] Write the expression in factored form
- Solve the quadratic equation: x^2 - 4x + 3 = 0
[(X)] x = 1, 3 [( )] x = -1, 3 [( )] x = 1, -3 [( )] x = 0, 4 [[?]] Factor the equation [[?]] Set each factor equal to zero and solve for x
- Simplify the expression: (3x^2 - 4x + 1) - (2x^2 - 3x + 5)
[( )] x^2 + x + 6 [(X)] x^2 - x - 4 [( )] x^2 - 5x - 4 [( )] 5x^2 - x + 6 [[?]] Subtract the corresponding terms of the two expressions [[?]] Combine like terms
- Solve the system of linear equations:
x + 2y = 7 3x - y = 5
[( )] x = 1, y = 3 [(X)] x = 2, y = 2.5 [( )] x = 3, y = 2 [( )] x = 4, y = 1.5 [[?]] Use either the substitution or elimination method [[?]] Solve for one variable and then find the other [[?]] Check your solution by plugging the values back into the original equations
In this module, we will be learning the basics of Algebra 1, which is an important branch of mathematics that deals with variables, equations, and functions. This module is designed for 8th grade students who are new to Algebra 1 or need a refresher on the basics.
In this section, we will learn about variables and how to use them to write expressions. We will also learn how to simplify expressions by combining like terms and using the distributive property.
Select one option question question: Which property of addition do you use to simplify the expression 3x + 2x? [( )] Commutative Property [(X)] Associative Property [( )] Distributive Property [( )] Identity Property
In this section, we will learn how to solve equations with one variable by using inverse operations. We will also learn how to check our solutions to make sure they are valid.
Multiple possible options correct question: Solve for x: 2x + 3 = 7x - 5 [(X)] x = 2 [[ ]] x = 3 [[ ]] x = -3 [[X]] x = 4
In this section, we will learn about linear equations and how to graph them using slope-intercept form. We will also learn how to write equations of lines given two points or a point and a slope.
Linear equations are algebraic equations where the highest power of the variable(s) is 1. These equations are commonly used to model relationships between variables in a variety of contexts.
The slope-intercept form of a linear equation is given by:
y = mx + b
where:
- m is the slope
- b is the y-intercept
- Students may confuse the slope and the y-intercept in the equation.
- Students might not simplify the equation before identifying the slope and the y-intercept.
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What is the slope of the equation
y = 4x - 3?[( )] -4 [(X)] 4 [( )] -3 [( )] 3
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What is the y-intercept of the equation
y = -2x + 5?[[5]]
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Rewrite the following equation in slope-intercept form:
3x - 2y = 6[[-3x/2 + 3]]
The standard form of a linear equation is given by:
Ax + By = C
where:
- A, B, and C are integers
- A is non-negative
- A, B, and C have no common factors other than 1
- Students may not have A, B, and C as integers.
- Students might not ensure that A is non-negative.
- Students may not simplify the equation, leaving common factors in A, B, and C.
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Which of the following equations is in standard form?
[( )] 2x + 3y = 0 [(X)] 4x - 6y = 12 [( )] -3x + 5y = 9 [( )] 1.5x - 2y = 6
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Rewrite the following equation in standard form:
y = 2x - 4[[2x - y = -4]]
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Convert the following standard form equation to slope-intercept form:
6x + 3y = 12[[y = -2x + 4]]
Select one option question question: What is the slope-intercept form of the equation of the line that passes through the points (-2, 3) and (4, 1)? [( )] y = 2x + 1 [( )] y = 2x - 5 [(X)] y = -1/3x + 7/3 [( )] y = -1/3x - 1/3
In this section, we will learn about systems of equations and how to solve them using substitution and elimination. We will also learn how to interpret the solution to a system of equations.
Multiple possible options correct question: Solve the system of equations: -2x + y = 4 4x - 2y = -8 [[X]] x = -1, y = 2 [[ ]] x = 2, y = -4 [[ ]] x = 3, y = -2 [[X]] x = -2, y = 0
In this section, we will learn about quadratic equations and how to graph them using vertex form. We will also learn how to solve quadratic equations using factoring, completing the square, and the quadratic formula.
Select one option question question: What is the quadratic formula? [(X)] x = (-b ± sqrt(b^2 - 4ac)) / 2a [( )] x = -b / 2a [( )] x = -b ± sqrt(b^2 - 4ac) [( )] x = (-b ± sqrt(b^2 + 4ac)) / 2a
Throughout the module, there will be quizzes to test your knowledge on the topics we have covered. These quizzes will help you assess your understanding and identify areas where you may need to review.
During the virtual lecture, we will use active learning strategies to engage with the material and deepen our understanding. These strategies may include group discussions, problem-solving activities, and interactive simulations.
By the end of this module, you should have a strong foundation in Algebra 1 and be able to apply your knowledge to solve real-world problems.