California High School Proficiency Examination (CHSPE) Mathematics: Algebra and Patterns Syllabus

Mathematics: Algebra and Patterns syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Mathematics: Algebra and Patterns in California High School Proficiency Examination (CHSPE), not a summary of it.

1. 1

   Expressions and Variables

   3 topics

   • Writing Algebraic Expressions
     • Translating words into symbols
     • Identifying terms and coefficients
   • Evaluating Expressions
     • Substituting values for variables
     • Applying order of operations
   • Simplifying Expressions
     • Combining like terms
     • Using the distributive property
2. 2

   Linear Equations and Inequalities

   4 topics

   • Solving One-Step and Two-Step Equations
     • Inverse operations
     • Checking solutions
   • Multi-Step Equations
     • Variables on both sides
     • Equations with fractions
   • Solving and Graphing Inequalities
     • Reversing the sign when needed
     • Representing solutions on a number line
   • Word Problems with Equations
     • Setting up equations from situations
     • Consecutive-integer and age problems
3. 3

   Coordinate Geometry and Functions

   4 topics

   • The Coordinate Plane
     • Plotting ordered pairs
     • Identifying quadrants
   • Graphing Linear Equations
     • Slope and y-intercept
     • Slope-intercept form
   • Interpreting Graphs
     • Reading slope as a rate of change
     • Finding intercepts
   • Function Concepts
     • Input-output relationships
     • Evaluating function rules
4. 4

   Patterns and Sequences

   3 topics

   • Recognizing Numeric Patterns
     • Arithmetic sequences
     • Geometric sequences
   • Extending and Generalizing Patterns
     • Finding the next terms
     • Writing a rule for the nth term
   • Patterns in Tables and Graphs
     • Identifying relationships in data tables
     • Matching patterns to graphs

Mathematics: Algebra and Patterns flashcards for California High School Proficiency Examination (CHSPE)

22 of 50 cards from the Mathematics: Algebra and Patterns deck — real questions with worked answers.

1. In algebra, what does it mean to 'write an algebraic expression'?

   It means to translate a word phrase into a combination of numbers, variables, and operation symbols (with no equals sign), such as turning 'five more than a number' into x + 5.

2. Which keywords in a word phrase signal addition, subtraction, multiplication, and division?

   Addition: sum, plus, more than, increased by. Subtraction: difference, minus, less than, decreased by. Multiplication: product, times, of, twice. Division: quotient, per, divided by, ratio.

3. How do you write 'seven less than a number n' as an algebraic expression?

   n - 7 (the order is reversed: 'less than' subtracts from the number, so it is n - 7, not 7 - n).

4. What is the difference between an expression and an equation?

   An expression is a combination of numbers, variables, and operations with no equals sign (cannot be solved). An equation sets two expressions equal with an = sign and can be solved.

5. What does it mean to 'evaluate' an algebraic expression?

   To substitute given numerical values for the variables and then simplify using the order of operations to get a single numerical result.

6. Evaluate 3x + 5 when x = 4.

   3(4) + 5 = 12 + 5 = 17.

7. What is the order of operations (PEMDAS) used when evaluating expressions?

   Parentheses, Exponents, Multiplication and Division (left to right), then Addition and Subtraction (left to right).

8. Evaluate 2x^2 - y when x = 3 and y = 5.

   2(3)^2 - 5 = 2(9) - 5 = 18 - 5 = 13.

9. What is a 'term' in an algebraic expression?

   A term is a single number, variable, or product of numbers and variables separated from other terms by + or - signs (e.g., in 4x + 3y - 7, the terms are 4x, 3y, and -7).

10. What is a 'coefficient'?

    The numerical factor multiplied by the variable in a term (e.g., in 5x the coefficient is 5; in x it is understood to be 1).

11. What are 'like terms' and why do they matter?

    Like terms have the exact same variable(s) raised to the same power(s) (e.g., 3x and 5x, or 2x^2 and -x^2). Only like terms can be combined by adding or subtracting their coefficients.

12. Simplify 4x + 7 + 2x - 3.

    Combine like terms: (4x + 2x) + (7 - 3) = 6x + 4.

13. State the distributive property and give an example.

    a(b + c) = ab + ac. Example: 3(x + 4) = 3x + 12.

14. Simplify 2(3x - 5) + 4x.

    Distribute: 6x - 10 + 4x, then combine like terms: 10x - 10.

15. What is the goal when solving an equation?

    To isolate the variable on one side of the equation, finding the value that makes the equation true, by performing the same inverse operation on both sides.

16. What are the inverse operations used to solve equations?

    Addition and subtraction are inverses of each other; multiplication and division are inverses of each other. You 'undo' an operation by applying its inverse to both sides.

17. Solve the one-step equation x + 9 = 15.

    Subtract 9 from both sides: x = 6.

18. Solve the one-step equation 4x = 28.

    Divide both sides by 4: x = 7.

19. Solve the two-step equation 2x + 3 = 11.

    Subtract 3: 2x = 8; then divide by 2: x = 4.

20. What is the correct order of steps to solve a two-step equation like ax + b = c?

    First undo addition/subtraction (subtract b from both sides), then undo multiplication/division (divide both sides by a).

21. Solve the two-step equation x/5 - 2 = 3.

    Add 2: x/5 = 5; then multiply both sides by 5: x = 25.

22. What is the general strategy for solving a multi-step equation?

    1) Distribute to remove parentheses, 2) combine like terms on each side, 3) move variable terms to one side and constants to the other, 4) isolate the variable using inverse operations.

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