Partnership for Assessment of Readiness for College and Careers (PARCC) Mathematics: High School Algebra and Functions Syllabus

Mathematics: High School Algebra and Functions syllabus: all 4 chapters

Expand any chapter to see its topics and sub-topics.

1. 1

   Algebra I Core

   3 topics

   • Linear Equations and Inequalities
     • Solving and graphing linear equations
     • Systems of linear equations and inequalities
   • Quadratic Functions and Equations
     • Factoring and the quadratic formula
     • Completing the square
     • Interpreting parabola features
   • Exponential Relationships
     • Growth and decay models
     • Comparing linear and exponential growth
2. 2

   Algebra II Core

   4 topics

   • Polynomial Functions
     • Operations and the Remainder Theorem
     • Zeros and end behavior
   • Rational and Radical Functions
     • Simplifying and solving rational expressions
     • Radical equations and extraneous solutions
   • Exponential and Logarithmic Functions
     • Properties of logarithms
     • Solving exponential and log equations
   • Trigonometric Functions
     • Unit circle and radian measure
     • Modeling periodic phenomena
3. 3

   Functions Across Courses

   3 topics

   • Interpreting Functions
     • Domain, range, and key features
     • Average rate of change
   • Building Functions
     • Combining and transforming functions
     • Inverse functions
   • Function Families and Modeling
     • Selecting appropriate function models
     • Translating between representations
4. 4

   Seeing Structure in Expressions

   3 topics

   • Equivalent Forms of Expressions
     • Rewriting to reveal structure
     • Using structure to solve
   • The Arithmetic of Polynomials and Rational Expressions
     • Closure and operations
     • Partial decomposition concepts
   • Creating Equations to Model Situations
     • Constraints and feasible solutions
     • Rearranging formulas

Partnership for Assessment of Readiness for College and Careers (PARCC) Mathematics: High School Algebra and Functions flashcards — 50 questions with answers

1. What is the slope-intercept form of a linear equation, and what does each variable represent?

   y = mx + b, where m is the slope (rate of change) and b is the y-intercept (the value of y when x = 0).

2. How do you find the slope of a line passing through points (x1, y1) and (x2, y2)?

   m = (y2 - y1) / (x2 - x1), the change in y divided by the change in x.

3. When solving a linear inequality, when must you reverse the inequality sign?

   When you multiply or divide both sides by a negative number.

4. What is the point-slope form of a line through point (x1, y1) with slope m?

   y - y1 = m(x - x1).

5. What is the relationship between the slopes of two perpendicular lines?

   Their slopes are negative reciprocals; the product of the slopes is -1 (m1 * m2 = -1).

6. State the standard form of a quadratic function.

   f(x) = ax^2 + bx + c, where a is not equal to 0.

7. What is the quadratic formula for solving ax^2 + bx + c = 0?

   x = (-b plus or minus the square root of (b^2 - 4ac)) / (2a).

8. What does the discriminant b^2 - 4ac tell you about a quadratic's roots?

   If positive: two distinct real roots; if zero: one repeated real root; if negative: two complex (no real) roots.

9. What is the vertex form of a quadratic, and what is the vertex?

   f(x) = a(x - h)^2 + k, with vertex at (h, k).

10. How do you find the x-coordinate of a quadratic's vertex from standard form?

    x = -b / (2a), which is also the axis of symmetry.

11. What is the general form of an exponential function and the condition on the base?

    f(x) = a * b^x, where a is not 0, b > 0, and b is not equal to 1.

12. In an exponential function f(x) = a*b^x, what does the function represent when b > 1 versus 0 < b < 1?

    b > 1 represents exponential growth; 0 < b < 1 represents exponential decay.

13. What distinguishes a linear function from an exponential function in terms of how values change?

    A linear function changes by a constant difference (equal additions) over equal intervals; an exponential function changes by a constant ratio (equal multiplications) over equal intervals.

14. What is the compound interest formula compounded n times per year?

    A = P(1 + r/n)^(nt), where P is principal, r is annual rate, n is compoundings per year, and t is years.

15. What is the formula for continuous compound (exponential) growth using e?

    A = P * e^(rt), where r is the continuous rate and t is time.

16. What does the degree of a polynomial tell you about its end behavior and maximum number of roots?

    The degree equals the maximum number of real roots and determines end behavior; an nth-degree polynomial has at most n roots and at most n-1 turning points.

17. State the Fundamental Theorem of Algebra.

    Every polynomial of degree n (n >= 1) with complex coefficients has exactly n roots in the complex number system, counting multiplicities.

18. What does the Remainder Theorem state?

    When a polynomial f(x) is divided by (x - c), the remainder equals f(c).

19. What does the Factor Theorem state?

    (x - c) is a factor of polynomial f(x) if and only if f(c) = 0.

20. How does the leading coefficient's sign and the degree's parity affect a polynomial's end behavior?

    Even degree: both ends go the same direction (up if leading coefficient positive, down if negative). Odd degree: ends go opposite directions (up-right/down-left if positive, down-right/up-left if negative).

Partnership for Assessment of Readiness for College and Careers (PARCC) Mathematics: High School Algebra and Functions FAQ