Online Algebra Lessons for Students

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Algebra, the CAHSEE and You

We at love all math, but we REALLY love algebra so, therefore, letís focus on the two sections that deal with algebra. Itís important that all students and parents understand why these sections are important, how this knowledge will be tested and what tips will help you get that passing score.

First, a quick recap of the test format!

  1. The CAHSEE will test you on SIX sections: five (5) strands of sixth and seventh grade mathematics standards AND algebra 1 standards
  2.  All the questions on the test are worth the same amount of points.
  3. To pass the exam 350/450 (77.8%) is required.
  4. The Algebra and Functions strand and Algebra 1 standards account for 36.25% of the exam. (Just under half of what a student needs to pass!)

Think of it this way Ė even if a student answered all the other questions on the test correctly, you would not pass the CAHSEE. You need to know algebra to pass this test. The good news is that the algebra needed to pass is basic fundamental.

Now that you have a good idea of what is required, letís get to work and look at the algebra and functions strand in greater detail.

Algebra and Functions on the CAHSEE

Seventeen of the 80 CAHSEE multiple choice questions are based on ten selected standards of thirteen grade 7 Algebra and Functions strand. (21.25% of the mathematics portion of the CAHSEE)

What Do Students Need To Know?

  • Generalize numerical and geometric patterns
  • Use a table, graph or symbolic rule to represent the generalizations of a pattern
  • Compare different forms of representations
  • Know the difference between a relations and a function
  • Solve linear equations
  • Important vocabulary: equation, inequality, expression, y-intercept, slope, parallel

Which ten of the thirteen standards will it address?

The CAHSEE will address the following grade 7 algebra and functions standards:

  • AF 1.1 Use variables and appropriate operations to write an expression, an equation, an inequality, or a system of equations or inequalities that represents a verbal description (e.g., three less than a number, half as large as area A).
  • AF 1.2 Use the correct order of operations to evaluate algebraic expressions such as 3(2x + 5)2.
  • AF 1.5 Represent quantitative relationships graphically and interpret the meaning of a specific part of a graph in the situation represented by the graph.
  • AF 2.1 Interpret positive whole-number powers as repeated multiplication and negative whole-number powers as repeated division or multiplication by the multiplicative inverse. Simplify and evaluate expressions that include exponents.
  • AF 2.2 Multiply and divide monomials; extend the process of taking powers and extracting roots to monomials when the latter results in a monomial with an integer exponent. 
  • AF 3.1 Graph functions of the form y = nx2 and y = nx3 and use in solving problems.
  • AF 3.3 Graph linear functions, noting that the vertical change (change in y- value) per unit of horizontal change (change in x- value) is always the same and know that the ratio ("rise over run") is called the slope of a graph.
  • AF 3.4 Plot the values of quantities whose ratios are always the same (e.g., cost to the number of an item, feet to inches, circumference to diameter of a circle). Fit a line to the plot and understand that the slope of the line equals the quantities. 
  •  AF 4.1 Solve two-step linear equations and inequalities in one variable over the rational numbers, interpret the solution or solutions in the context from which they arose, and verify the reasonableness of the results.
  • AF 4.2 Solve multistep problems involving rate, average speed, distance, and time or a direct variation. 

Why Are Algebra and Functions Important?

California is no longer know for itsí agriculture. As we begin the 21st century, our community must prepare our students for 21st century job demands. Presently, many entry-level technical, scientific and health-related jobs require additional training beyond high school. To qualify for additional training for these high-paying jobs, you need to know the basics of algebra in order to effectively and efficiently to remain competitive.

How Will the CAHSEE Test Student Knowledge of Algebra and Functions?

The CAHSEE multiple-choice questions focus mainly on the basic algebra skills necessary to deal with graphs, formulas, linear function and equation solving. When studying for the exam, students should look for examples in texts that address the standards listed above. 

Algebra 1 on the CAHSEE

Twelve of the 80 CASHSEE multiple-choice questions are based on ten of the algebra 1 standards.

What Do Students Need to Know?

  • Recognize equivalent forms of polynomials and other algebraic expressions
  • Understand the meaning of opposite, reciprocal, root and absolute value
  • Identify the graph that matches a particular linear function and find its slope and intercepts
  • Know that lines on a graph are parallel if and only if they have the same slope
    ē Solve linear inequalities
  • Solve problems involving rate, average speed, distance and time
  • Identify the solution to a system of two equations in two unknowns
  • Solve classic algebra rate, work and percent mixture problems
  • Important vocabulary: absolute value, parallel, y-intercept, slope of a line, equation, inequality

Which ten of the 29 standards will it address?

The CAHSEE will address the following algebra 1 standards:

  1. Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root and raising to a fractional power. They understand and use the rules of exponents.
  2. Students solve equations and inequalities involving absolute values.
  3. Students simplify expressions before solving linear equations and inequalities in one variable, such as 3(2x-5) + 4(x-2) = 12.
  4. Students solve multi-step problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step.
  5. Students graph a linear equation and compute the x- and y- intercepts (e.g., graph 2x + 6y = 4). They are also able to sketch the region defined by linear inequality (e.g., they sketch the region defined by 2x + 6y < 4).
  6. Students verify that a point lies on a line, given an equation on the line. Students are able to derive linear equations by using the point-slope formula.
  7. Students understand the concepts of parallel lines and perpendicular lines and how those slopes are related. Students are able to find the equation of a line perpendicular to a given line that passes through a given point.
  8. Students solve a system of two linear equations in two variables algebraically and are able to interpret the answer graphically. Students are able to solve a system of two linear inequalities in two variables and to sketch the solution sets.
  9. Students add, subtract, multiply, and divide monomials and polynomials. Students solve multi-step problems, including word problems, by using these techniques.
  10. Students apply algebraic techniques to solve rate problems, work problems, and percent mixture problems.

Why is Algebra Important?

Although it may not seem apparent, algebra is used in everyday life all day long. Simply working on an excel worksheet, a very common program, requires knowledge of how numbers will affect one another. (i.e. If I multiply a number will my answer be larger or smaller than the original number? It depends on what you are multiplying by. How much money do I need to save each month for my kids to go to college? Is my electric bill correct and what should I expect to spend on the summer month judging by past experience and the increase in rates?)

Besides just everyday use, algebra has become the subject that ďweeds outĒ candidates for jobs in fields that donít require much algebra on the job. Knowing the fundamentals of algebra keeps your options open for your future.

How Will the CAHSEE Test Student Knowledge of Algebra 1?

The twelve multiple-choice questions of the algebra 1 portion of the CAHSEE will test student general understanding of algebraic concepts. Basically, do students understand the symbols, the vocabulary, the mathematical structure of the equations, the visual representation of functions and relations and the ďbig ideaĒ behind these concepts.

Now that you knowÖ.now what? Take the Test!

The best way to prepare for the exam is to know what will actually be on the exam. We hope that this guideline will allow students to focus their efforts so they have the best chance possible to pass. Besides knowing what is on the exam, good test taking practices increase studentsí chances of doing well too. Follow these test-taking tips to increase your chances of passing the CAHSEE right away!

Test-Taking Tips for the CAHSEE

  1. Prepare, prepare, prepare. Donít leave something this important to the last minute. Determine what you know and what you donít know so you can find someone to help you. By law, schools must students that donít pass the exam. Ask what your local school offers.
  2. Know your daily habits. Don't forget to eat breakfast, take any medication or drink your daily coffee, if that is your routine. It's always best to eat a good breakfast. However, if you know eating breakfast won't agree with your stomach, skip it. You don't want to rush through the test because you don't feel well. Know your own personal daily rhythms.
  3. Answer the easy questions first. Get those out of the way while you are fresh. Donít forget to go back and take good guesses at the harder questions. 
  4. Eliminate wrong answers right away, and guess. The CAHSEE does NOT penalize students for wrong answers so donít leave any answers blank.
  5. Check your work. Everyone makes silly mistakes with math so check everything. The CAHSEE is NOT a timed test so students have all the time they need.
  6. Be precise with your pencil. The CAHSEE is a fill in the bubble test. Donít make any stray marks on your scantron. Double check that you donít skip bubbles or mark a question with two bubbles.
  7. Write in your booklet. Cross out answers. Draw stars next to questions you skipped initially. Draw out your problems to give you clues to the right answer. (REMEMBER Ė keep your scantron neat!)
  8. Think about the big concept. The test is designed to test vocabulary and very general concepts. If you are doing a lot of calculations on a problem, you probably read it wrong. 
  9. Reason backwards from the answers. If you canít find the answer, plug in the choices.
  10. Do your best every time! Donít blow off an opportunity because you donít feel well or you had a bad weekend. Push yourself to do your best work.


Source: California. California Department of Education. Preparing for the California High School Exit Exam. Sacramento: CDE Press, 2004.


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